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

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

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

2012-11-15

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

Terrestrial water storage changes over Xinjiang extracted by combining Gaussian filter and multichannel singular spectrum analysis from GRACE

NASA Astrophysics Data System (ADS)

Guo, Jinyun; Li, Wudong; Chang, Xiaotao; Zhu, Guangbin; Liu, Xin; Guo, Bin

2018-04-01

Water resource management is crucial for the economic and social development of Xinjiang, an arid area located in the Northwest China. In this paper, the time variations of gravity recovery and climate experiment (GRACE)-derived monthly gravity field models from 2003 January to 2013 December are analysed to study the terrestrial water storage (TWS) changes in Xinjiang using the multichannel singular spectrum analysis (MSSA) with a Gaussian smoothing radius of 400 km. As an extended singular spectrum analysis (SSA), MSSA is more flexible to deal with multivariate time-series in terms of estimating periodic components and trend, reducing noise and identifying patterns of similar spatiotemporal behaviour thanks to the data-adaptive nature of the base functions. Combining MSSA and Gaussian filter can not only obviously remove the north-south striping errors in the GRACE solutions but also reduce the leakage errors, which can increase the signal-to-noise ratio by comparing with the traditional procedure, that is, empirical decorrelation method followed with the Gaussian filtering. The spatiotemporal characteristics of TWS changes in Xinjiang were validated against the Global Land Dynamics Assimilation System, the Climate Prediction Center and in-situ precipitation data. The water storage in Xinjiang shows the relatively large fluctuation from 2003 January to 2013 December, with a drop from 2006 January to 2008 December due to the drought event and an obvious rise from 2009 January to 2010 December because of the high precipitation. Spatially, the TWS has been increasing in the south Xinjiang, but decreasing in the north Xinjiang. The minimum rate of water storage change is -4.4 mm yr-1 occurring in the central Tianshan Mountain.

A Novel approach for predicting monthly water demand by combining singular spectrum analysis with neural networks

NASA Astrophysics Data System (ADS)

Zubaidi, Salah L.; Dooley, Jayne; Alkhaddar, Rafid M.; Abdellatif, Mawada; Al-Bugharbee, Hussein; Ortega-Martorell, Sandra

2018-06-01

Valid and dependable water demand prediction is a major element of the effective and sustainable expansion of municipal water infrastructures. This study provides a novel approach to quantifying water demand through the assessment of climatic factors, using a combination of a pretreatment signal technique, a hybrid particle swarm optimisation algorithm and an artificial neural network (PSO-ANN). The Singular Spectrum Analysis (SSA) technique was adopted to decompose and reconstruct water consumption in relation to six weather variables, to create a seasonal and stochastic time series. The results revealed that SSA is a powerful technique, capable of decomposing the original time series into many independent components including trend, oscillatory behaviours and noise. In addition, the PSO-ANN algorithm was shown to be a reliable prediction model, outperforming the hybrid Backtracking Search Algorithm BSA-ANN in terms of fitness function (RMSE). The findings of this study also support the view that water demand is driven by climatological variables.

The principles of quantification applied to in vivo proton MR spectroscopy.

PubMed

Helms, Gunther

2008-08-01

Following the identification of metabolite signals in the in vivo MR spectrum, quantification is the procedure to estimate numerical values of their concentrations. The two essential steps are discussed in detail: analysis by fitting a model of prior knowledge, that is, the decomposition of the spectrum into the signals of singular metabolites; then, normalization of these signals to yield concentration estimates. Special attention is given to using the in vivo water signal as internal reference.

Quantum walks with an anisotropic coin I: spectral theory

NASA Astrophysics Data System (ADS)

Richard, S.; Suzuki, A.; Tiedra de Aldecoa, R.

2018-02-01

We perform the spectral analysis of the evolution operator U of quantum walks with an anisotropic coin, which include one-defect models, two-phase quantum walks, and topological phase quantum walks as special cases. In particular, we determine the essential spectrum of U, we show the existence of locally U-smooth operators, we prove the discreteness of the eigenvalues of U outside the thresholds, and we prove the absence of singular continuous spectrum for U. Our analysis is based on new commutator methods for unitary operators in a two-Hilbert spaces setting, which are of independent interest.

Multifractal spectrum of physiological signals: a mechanism-related approach

NASA Astrophysics Data System (ADS)

Pavlov, Alexey N.; Pavlova, Olga N.; Abdurashitov, Arkady S.; Arinushkin, Pavel A.; Runnova, Anastasiya E.; Semyachkina-Glushkovskaya, Oxana V.

2017-04-01

In this paper we discuss an approach for mechanism-related analysis of physiological signals performed with the wavelet-based multifractal formalism. This approach assumes estimation of the singularity spectrum for the band-pass filtered processes at different physiological conditions in order to provide explanation of the occurred changes in the Hölder exponents and the multi-fractality degree. We illustrate the considered approach using two examples, namely, the dynamics of the cerebral blood flow (CBF) and the electrical activity of the brain.

Naked singularities in higher dimensional Vaidya space-times

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

Ghosh, S. G.; Dadhich, Naresh

We investigate the end state of the gravitational collapse of a null fluid in higher-dimensional space-times. Both naked singularities and black holes are shown to be developing as the final outcome of the collapse. The naked singularity spectrum in a collapsing Vaidya region (4D) gets covered with the increase in dimensions and hence higher dimensions favor a black hole in comparison to a naked singularity. The cosmic censorship conjecture will be fully respected for a space of infinite dimension.

The performance of one belt and one road exchange rate: Based on improved singular spectrum analysis

NASA Astrophysics Data System (ADS)

Lai, Lin; Guo, Kun

2017-10-01

;One Belt and One Road; strategy in China is on push of foreign trade openness at northwest, southwest and northeast, absorption of the excess capacity and new support for economic increase. However, the fluctuation in RMB exchange rate with the countries along the road is unstable so related Chinese enterprises will face high risk of exchange rate. Precise explanation or prediction for exchange rate has been the challengeable hop point in the international finance. This paper decomposed the One Belt One Road Exchange Rate Index (OBORR) and the RMB Effective Exchange Rate Index (CNYX) into trend term, market fluctuation term and noise term using improved singular spectrum analysis (SSA). It turns out that the increasing velocity of OBORR is greater than that of CNYX in the long term, and there is dynamic lead-lag structure in the medium term. In the short term, the fluctuation range and frequency of OBORR are greater than those of CNYX, which means there will be more exchange rate risks in One Belt and One Road countries.

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.

3D seismic data de-noising and reconstruction using Multichannel Time Slice Singular Spectrum Analysis

NASA Astrophysics Data System (ADS)

Rekapalli, Rajesh; Tiwari, R. K.; Sen, Mrinal K.; Vedanti, Nimisha

2017-05-01

Noises and data gaps complicate the seismic data processing and subsequently cause difficulties in the geological interpretation. We discuss a recent development and application of the Multi-channel Time Slice Singular Spectrum Analysis (MTSSSA) for 3D seismic data de-noising in time domain. In addition, L1 norm based simultaneous data gap filling of 3D seismic data using MTSSSA also discussed. We discriminated the noises from single individual time slices of 3D volumes by analyzing Eigen triplets of the trajectory matrix. We first tested the efficacy of the method on 3D synthetic seismic data contaminated with noise and then applied to the post stack seismic reflection data acquired from the Sleipner CO2 storage site (pre and post CO2 injection) from Norway. Our analysis suggests that the MTSSSA algorithm is efficient to enhance the S/N for better identification of amplitude anomalies along with simultaneous data gap filling. The bright spots identified in the de-noised data indicate upward migration of CO2 towards the top of the Utsira formation. The reflections identified applying MTSSSA to pre and post injection data correlate well with the geology of the Southern Viking Graben (SVG).

Simultaneous and independent optical impairments monitoring using singular spectrum analysis of asynchronously sampled signal amplitudes

NASA Astrophysics Data System (ADS)

Guesmi, Latifa; Menif, Mourad

2015-09-01

Optical performance monitoring (OPM) becomes an inviting topic in high speed optical communication networks. In this paper, a novel technique of OPM based on a new elaborated computation approach of singular spectrum analysis (SSA) for time series prediction is presented. Indeed, various optical impairments among chromatic dispersion (CD), polarization mode dispersion (PMD) and amplified spontaneous emission (ASE) noise are a major factors limiting quality of transmission data in the systems with data rates lager than 40 Gbit/s. This technique proposed an independent and simultaneous multi-impairments monitoring, where we used SSA of time series analysis and forecasting. It has proven their usefulness in the temporal analysis of short and noisy time series in several fields, that it is based on the singular value decomposition (SVD). Also, advanced optical modulation formats (100 Gbit/s non-return-to zero dual-polarization quadrature phase shift keying (NRZ-DP-QPSK) and 160 Gbit/s DP-16 quadrature amplitude modulation (DP-16QAM)) offering high spectral efficiencies have been successfully employed by analyzing their asynchronously sampled amplitude. The simulated results proved that our method is efficient on CD, first-order PMD, Q-factor and OSNR monitoring, which enabled large monitoring ranges, the CD in the range of 170-1700 ps/nm.Km and 170-1110 ps/nm.Km for 100 Gbit/s NRZ-DP-QPSK and 160 Gbit/s DP-16QAM respectively, and also the DGD up to 20 ps is monitored. We could accurately monitor the OSNR in the range of 10-40 dB with monitoring error remains less than 1 dB in the presence of large accumulated CD.

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.

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.

Multifractal analysis of heartbeat dynamics during meditation training

NASA Astrophysics Data System (ADS)

Song, Renliang; Bian, Chunhua; Ma, Qianli D. Y.

2013-04-01

We investigate the multifractality of heartbeat dynamics during Chinese CHI meditation in healthy young adults. The results show that the range of multifractal singularity spectrum of heartbeat interval time series during meditation is significantly narrower than those in the pre-meditation state of the same subject, which indicates that during meditation the heartbeat becomes regular and the degree of multifractality decreases.

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

PubMed

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

2016-01-01

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

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

PubMed Central

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

2016-01-01

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

Daily rainfall forecasting for one year in a single run using Singular Spectrum Analysis

NASA Astrophysics Data System (ADS)

Unnikrishnan, Poornima; Jothiprakash, V.

2018-06-01

Effective modelling and prediction of smaller time step rainfall is reported to be very difficult owing to its highly erratic nature. Accurate forecast of daily rainfall for longer duration (multi time step) may be exceptionally helpful in the efficient planning and management of water resources systems. Identification of inherent patterns in a rainfall time series is also important for an effective water resources planning and management system. In the present study, Singular Spectrum Analysis (SSA) is utilized to forecast the daily rainfall time series pertaining to Koyna watershed in Maharashtra, India, for 365 days after extracting various components of the rainfall time series such as trend, periodic component, noise and cyclic component. In order to forecast the time series for longer time step (365 days-one window length), the signal and noise components of the time series are forecasted separately and then added together. The results of the study show that the method of SSA could extract the various components of the time series effectively and could also forecast the daily rainfall time series for longer duration such as one year in a single run with reasonable accuracy.

Dispersive optical solitons and modulation instability analysis of Schrödinger-Hirota equation with spatio-temporal dispersion and Kerr law nonlinearity

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru

2018-01-01

This paper obtains the dark, bright, dark-bright or combined optical and singular solitons to the perturbed nonlinear Schrödinger-Hirota equation (SHE) with spatio-temporal dispersion (STD) and Kerr law nonlinearity in optical fibers. The integration algorithm is the Sine-Gordon equation method (SGEM). Furthermore, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis and the MI gain spectrum is got.

Multifractality as a Measure of Complexity in Solar Flare Activity

NASA Astrophysics Data System (ADS)

Sen, Asok K.

2007-03-01

In this paper we use the notion of multifractality to describe the complexity in H α flare activity during the solar cycles 21, 22, and 23. Both northern and southern hemisphere flare indices are analyzed. Multifractal behavior of the flare activity is characterized by calculating the singularity spectrum of the daily flare index time series in terms of the Hölder exponent. The broadness of the singularity spectrum gives a measure of the degree of multifractality or complexity in the flare index data. The broader the spectrum, the richer and more complex is the structure with a higher degree of multifractality. Using this broadness measure, complexity in the flare index data is compared between the northern and southern hemispheres in each of the three cycles, and among the three cycles in each of the two hemispheres. Other parameters of the singularity spectrum can also provide information about the fractal properties of the flare index data. For instance, an asymmetry to the left or right in the singularity spectrum indicates a dominance of high or low fractal exponents, respectively, reflecting a relative abundance of large or small fluctuations in the total energy emitted by the flares. Our results reveal that in the even (22nd) cycle the singularity spectra are very similar for the northern and southern hemispheres, whereas in the odd cycles (21st and 23rd) they differ significantly. In particular, we find that in cycle 21, the northern hemisphere flare index data have higher complexity than its southern counterpart, with an opposite pattern prevailing in cycle 23. Furthermore, small-scale fluctuations in the flare index time series are predominant in the northern hemisphere in the 21st cycle and are predominant in the southern hemisphere in the 23rd cycle. Based on these findings one might suggest that, from cycle to cycle, there exists a smooth switching between the northern and southern hemispheres in the multifractality of the flaring process. This new observational result may bring an insight into the mechanisms of the solar dynamo operation and may also be useful for forecasting solar cycles.

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus and their use in data fitting.

PubMed

Field, Timothy R; Bain, Alex D

2014-01-01

Even for large quadrupolar interactions, the powder spectrum of the central transition for a half-integral spin is relatively narrow, because it is unperturbed to first order. However, the second-order perturbation is still orientation dependent, so it generates a characteristic lineshape. This lineshape has both finite step discontinuities and singularities where the spectrum is infinite, in theory. The relative positions of these features are well-known and they play an important role in fitting experimental data. However, there has been relatively little discussion of how high the steps are, so we present explicit formulae for these heights. This gives a full characterization of the features in this lineshape which can lead to an analysis of the spectrum without the usual laborious powder average. The transition frequency, as a function of the orientation angles, shows critical points: maxima, minima and saddle points. The maxima and minima correspond to the step discontinuities and the saddle points generate the singularities. Near a maximum, the contours are ellipses, whose dimensions are determined by the second derivatives of the frequency with respect to the polar and azimuthal angles. The density of points is smooth as the contour levels move up and down, but then drops to zero when a maximum is passed, giving a step. The height of the step is determined by the Hessian matrix-the matrix of all partial second derivatives. The points near the poles and the saddle points require a more detailed analysis, but this can still be done analytically. The resulting formulae are then compared to numerical simulations of the lineshape. We expand this calculation to include a relatively simple case where there is chemical shielding anisotropy and use this to fit experimental (139)La spectra of La2O3. Copyright © 2014 Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

Baydaroğlu, Özlem; Koçak, Kasım; Duran, Kemal

2018-06-01

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

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.

Bound states of spin-half particles in a static gravitational field close to the black hole field

NASA Astrophysics Data System (ADS)

Spencer-Smith, A. F.; Gossel, G. H.; Berengut, J. C.; Flambaum, V. V.

2013-03-01

We consider the bound-state energy levels of a spin-1/2 fermion in the gravitational field of a near-black hole object. In the limit that the metric of the body becomes singular, all binding energies tend to the rest-mass energy (i.e. total energy approaches zero). We present calculations of the ground state energy for three specific interior metrics (Florides, Soffel and Schwarzschild) for which the spectrum collapses and becomes quasi-continuous in the singular metric limit. The lack of zero or negative energy states prior to this limit being reached prevents particle pair production occurring. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides and Soffel metrics the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the centre. The behaviour of the energy level spectrum is discussed in the context of the semi-classical approximation and using general properties of the metric.

Financial Markets during Highly Anxious Time: Multifractal Fluctuations in Asset Returns

NASA Astrophysics Data System (ADS)

Siokis, Fotios M.

Building on the notion that systems and in particular complex systems such as stock exchange markets reveal their structure better when they are under stress, we analyze the multifractal character and nonlinear properties of four major stock market indices during financial meltdowns by means of the multifractal detrended fluctuation analysis (MF-DFA). The three distinct financial crises under investigation are the Black Monday, the Dot-Com and the Great Recession. Scaling and Hurst exponents are derived as well as the singularity spectra. The results show that all indices exhibit strong multifractal properties. The complexity of the markets is higher under the Black Monday event revealed by the width of the singularity spectrum and the higher α0 parameter.

Multifractal and wavelet analysis of epileptic seizures

NASA Astrophysics Data System (ADS)

Dick, Olga E.; Mochovikova, Irina A.

The aim of the study is to develop quantitative parameters of human electroencephalographic (EEG) recordings with epileptic seizures. We used long-lasting recordings from subjects with epilepsy obtained as part of their clinical investigation. The continuous wavelet transform of the EEG segments and the wavelet-transform modulus maxima method enable us to evaluate the energy spectra of the segments, to fin lines of local maximums, to gain the scaling exponents and to construct the singularity spectra. We have shown that the significant increase of the global energy with respect to background and the redistribution of the energy over the frequency range are observed in the patterns involving the epileptic activity. The singularity spectra expand so that the degree of inhomogenety and multifractality of the patterns enhances. Comparing the results gained for the patterns during different functional probes such as open and closed eyes or hyperventilation we demonstrate the high sensitivity of the analyzed parameters (the maximal global energy, the width and asymmetry of the singularity spectrum) for detecting the epileptic patterns.

Purely Singular Continuous Spectrum for CMV Operators Generated by Subshifts

NASA Astrophysics Data System (ADS)

Ong, Darren C.

2014-03-01

We prove uniform absence of point spectrum for CMV operators corresponding to the period doubling subshift. We also prove almost sure absence of point spectrum for CMV operators corresponding to a class of Sturmian subshifts. Lastly, we prove almost sure absence of point spectrum for CMV operators corresponding to some subshifts generated by a coding of a rotation.

Multifractal properties of solar filaments and sunspots numbers

NASA Astrophysics Data System (ADS)

Wu, Nan; Li, Qi-Xiu; Zou, Peng

2015-07-01

We analyze multifractal properties of low (LLSFNs; < 50 °), high (HLSFNs; ⩾ 50 °), full-disk (FDSFNs; 0 ° ˜ 90 °) solar filament numbers (SFNs) and international sunspot numbers (ISNs) by estimating characteristic parameters (α0, Δα , spectrum skewness) of f (α) singularity spectrum. We find that the SFNs and ISNs have multifractal nature. The obtained α0 and Δα indicate that long-term behaviour of the solar filaments is more complex than that of the sunspots and the high-latitude filaments is the most complex in long-term behaviour. The spectrum skewnesses manifest that the ISNs display well symmetrical distribution in singularity strengths, whereas the SFNs are dominated by low singularity strengths, which means that the long-term behaviour of sunspots has homogenous structures and the filaments display averagely small fluctuations in amplitude. To detect the origin of their multifractality, we decompose the raw data of ISNs and SFNs: smoothed data represent ˜11-year cyclic activities and detrended data represent accidental activities. We also calculate their f (α) spectra, respectively. We find that the ˜11-year cyclic activities of filaments and sunspots tend to be a monofractal and display a bit predominance of low singularity strengths. Their accidental activities have the most complex behaviour than the raw and smoothed data. The accidental activities are dominated by high singularity strengths showing averagely large fluctuations in amplitude. Furthermore, multifractal properties from α0 and Δα of the accidental activities have the same features as that of raw data. We think that the ˜11-year periodic activity determines global fluctuations, while the accidental activities rule local complexity.

Particle creation by naked singularities in higher dimensions

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

Miyamoto, Umpei; Nemoto, Hiroya; Shimano, Masahiro

Recently, the possibility was pointed out by one of the present authors and his collaborators that an effective naked singularity referred to as ''a visible border of spacetime'' is generated by high-energy particle collision in the context of large extra dimensions or TeV-scale gravity. In this paper, we investigate the particle creation by a naked singularity in general dimensions, while adopting a model in which a marginally naked singularity forms in the collapse of a homothetic lightlike pressureless fluid. We find that the spectrum deviates from that of Hawking radiation due to scattering near the singularity but can be recastmore » in quasithermal form. The temperature is always higher than that of Hawking radiation of a same-mass black hole, and can be arbitrarily high depending on a parameter in the model. This implies that, in principle, the naked singularity may be distinguished from a black hole in collider experiments.« less

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

NASA Astrophysics Data System (ADS)

Du, Kongchang; Zhao, Ying; Lei, Jiaqiang

2017-09-01

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

Multifractal Turbulence in the Heliosphere

NASA Astrophysics Data System (ADS)

Macek, Wieslaw M.; Wawrzaszek, Anna

2010-05-01

We consider a solar wind plasma with frozen-in interplanetary magnetic fields, which is a complex nonlinear system that may exhibit chaos and intermittency, resulting in a multifractal scaling of plasma characteristics. We analyze time series of plasma velocity and interplanetary magnetic field strengths measured during space missions onboard various spacecraft, such as Helios, Advanced Composition Explorer, Ulysses, and Voyager, exploring different regions of the heliosphere during solar minimum and maximum. To quantify the multifractality of solar wind turbulence, we use a generalized two-scale weighted Cantor set with two different rescaling parameters [1]. We investigate the resulting spectrum of generalized dimensions and the corresponding multifractal singularity spectrum depending on the parameters of this new cascade model [2]. We show that using the model with two different scaling parameters one can explain the multifractal singularity spectrum, which is often asymmetric. In particular, the multifractal scaling of magnetic fields is asymmetric in the outer heliosphere, in contrast to the symmetric spectrum observed in the heliosheath as described by the standard one-scale model [3]. We hope that the generalized multifractal model will be a useful tool for analysis of intermittent turbulence in the heliospheric plasma. We thus believe that multifractal analysis of various complex environments can shed light on the nature of turbulence. [1] W. M. Macek and A. Szczepaniak, Generalized two-scale weighted Cantor set model for solar wind turbulence, Geophys. Res. Lett., 35, L02108 (2008), doi:10.1029/2007GL032263. [2] W. M. Macek and A. Wawrzaszek, Evolution of asymmetric multifractal scaling of solar wind turbulence in the outer heliosphere, J. Geophys. Res., A013795 (2009), doi:10.1029/2008JA013795. [3] W. M. Macek and A. Wawrzaszek, Multifractal turbulence at the termination shock, in Solar Wind Twelve, edited by M. Maximovic et al., American Institute of Physics, 2010.

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.

On the curious spectrum of duality invariant higher-derivative gravity

NASA Astrophysics Data System (ADS)

Hohm, Olaf; Naseer, Usman; Zwiebach, Barton

2016-08-01

We analyze the spectrum of the exactly duality and gauge invariant higher-derivative double field theory. While this theory is based on a chiral CFT and does not correspond to a standard string theory, our analysis illuminates a number of issues central in string theory. The full quadratic action is rewritten as a two-derivative theory with additional fields. This allows for a simple analysis of the spectrum, which contains two massive spin-2 ghosts and massive scalars, in addition to the massless fields. Moreover, in this formulation, the massless or tensionless limit α ' → ∞ is non-singular and leads to an enhanced gauge symmetry. We show that the massive modes can be integrated out exactly at the quadratic level, leading to an infinite series of higher-derivative corrections. Finally, we present a ghost-free massive extension of linearized double field theory, which employs a novel mass term for the dilaton and metric.

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.

Fetal heart rate deceleration detection using a discrete cosine transform implementation of singular spectrum analysis.

PubMed

Warrick, P A; Precup, D; Hamilton, E F; Kearney, R E

2007-01-01

To develop a singular-spectrum analysis (SSA) based change-point detection algorithm applicable to fetal heart rate (FHR) monitoring to improve the detection of deceleration events. We present a method for decomposing a signal into near-orthogonal components via the discrete cosine transform (DCT) and apply this in a novel online manner to change-point detection based on SSA. The SSA technique forms models of the underlying signal that can be compared over time; models that are sufficiently different indicate signal change points. To adapt the algorithm to deceleration detection where many successive similar change events can occur, we modify the standard SSA algorithm to hold the reference model constant under such conditions, an approach that we term "base-hold SSA". The algorithm is applied to a database of 15 FHR tracings that have been preprocessed to locate candidate decelerations and is compared to the markings of an expert obstetrician. Of the 528 true and 1285 false decelerations presented to the algorithm, the base-hold approach improved on standard SSA, reducing the number of missed decelerations from 64 to 49 (21.9%) while maintaining the same reduction in false-positives (278). The standard SSA assumption that changes are infrequent does not apply to FHR analysis where decelerations can occur successively and in close proximity; our base-hold SSA modification improves detection of these types of event series.

An adaptive singular spectrum analysis method for extracting brain rhythms of electroencephalography

PubMed Central

Hu, Hai; Guo, Shengxin; Liu, Ran

2017-01-01

Artifacts removal and rhythms extraction from electroencephalography (EEG) signals are important for portable and wearable EEG recording devices. Incorporating a novel grouping rule, we proposed an adaptive singular spectrum analysis (SSA) method for artifacts removal and rhythms extraction. Based on the EEG signal amplitude, the grouping rule determines adaptively the first one or two SSA reconstructed components as artifacts and removes them. The remaining reconstructed components are then grouped based on their peak frequencies in the Fourier transform to extract the desired rhythms. The grouping rule thus enables SSA to be adaptive to EEG signals containing different levels of artifacts and rhythms. The simulated EEG data based on the Markov Process Amplitude (MPA) EEG model and the experimental EEG data in the eyes-open and eyes-closed states were used to verify the adaptive SSA method. Results showed a better performance in artifacts removal and rhythms extraction, compared with the wavelet decomposition (WDec) and another two recently reported SSA methods. Features of the extracted alpha rhythms using adaptive SSA were calculated to distinguish between the eyes-open and eyes-closed states. Results showed a higher accuracy (95.8%) than those of the WDec method (79.2%) and the infinite impulse response (IIR) filtering method (83.3%). PMID:28674650

Detecting weak position fluctuations from encoder signal using singular spectrum analysis.

PubMed

Xu, Xiaoqiang; Zhao, Ming; Lin, Jing

2017-11-01

Mechanical fault or defect will cause some weak fluctuations to the position signal. Detection of such fluctuations via encoders can help determine the health condition and performance of the machine, and offer a promising alternative to the vibration-based monitoring scheme. However, besides the interested fluctuations, encoder signal also contains a large trend and some measurement noise. In applications, the trend is normally several orders larger than the concerned fluctuations in magnitude, which makes it difficult to detect the weak fluctuations without signal distortion. In addition, the fluctuations can be complicated and amplitude modulated under non-stationary working condition. To overcome this issue, singular spectrum analysis (SSA) is proposed for detecting weak position fluctuations from encoder signal in this paper. It enables complicated encode signal to be reduced into several interpretable components including a trend, a set of periodic fluctuations and noise. A numerical simulation is given to demonstrate the performance of the method, it shows that SSA outperforms empirical mode decomposition (EMD) in terms of capability and accuracy. Moreover, linear encoder signals from a CNC machine tool are analyzed to determine the magnitudes and sources of fluctuations during feed motion. The proposed method is proven to be feasible and reliable for machinery condition monitoring. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Holographic curvature perturbations in a cosmology with a space-like singularity

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

Ferreira, Elisa G.M.; Brandenberger, Robert; Institute for Theoretical Studies, ETH Zürich,Clausiusstr. 47, Zürich, CH-8092

2016-07-19

We study the evolution of cosmological perturbations in an anti-de-Sitter (AdS) bulk through a cosmological singularity by mapping the dynamics onto the boundary conformal fields theory by means of the AdS/CFT correspondence. We consider a deformed AdS space-time obtained by considering a time-dependent dilaton which induces a curvature singularity in the bulk at a time which we call t=0, and which asymptotically approaches AdS both for large positive and negative times. The boundary field theory becomes free when the bulk curvature goes to infinity. Hence, the evolution of the fluctuations is under better controle on the boundary than in themore » bulk. To avoid unbounded particle production across the bounce it is necessary to smooth out the curvature singularity at very high curvatures. We show how the bulk cosmological perturbations can be mapped onto boundary gauge field fluctuations. We evolve the latter and compare the spectrum of fluctuations on the infrared scales relevant for cosmological observations before and after the bounce point. We find that the index of the power spectrum of fluctuations is the same before and after the bounce.« less

Big bounce with finite-time singularity: The F(R) gravity description

NASA Astrophysics Data System (ADS)

Odintsov, S. D.; Oikonomou, V. K.

An alternative to the Big Bang cosmologies is obtained by the Big Bounce cosmologies. In this paper, we study a bounce cosmology with a Type IV singularity occurring at the bouncing point in the context of F(R) modified gravity. We investigate the evolution of the Hubble radius and we examine the issue of primordial cosmological perturbations in detail. As we demonstrate, for the singular bounce, the primordial perturbations originating from the cosmological era near the bounce do not produce a scale-invariant spectrum and also the short wavelength modes after these exit the horizon, do not freeze, but grow linearly with time. After presenting the cosmological perturbations study, we discuss the viability of the singular bounce model, and our results indicate that the singular bounce must be combined with another cosmological scenario, or should be modified appropriately, in order that it leads to a viable cosmology. The study of the slow-roll parameters leads to the same result indicating that the singular bounce theory is unstable at the singularity point for certain values of the parameters. We also conformally transform the Jordan frame singular bounce, and as we demonstrate, the Einstein frame metric leads to a Big Rip singularity. Therefore, the Type IV singularity in the Jordan frame becomes a Big Rip singularity in the Einstein frame. Finally, we briefly study a generalized singular cosmological model, which contains two Type IV singularities, with quite appealing features.

Multifractal detrended cross-correlation analysis in the MENA area

NASA Astrophysics Data System (ADS)

El Alaoui, Marwane; Benbachir, Saâd

2013-12-01

In this paper, we investigated multifractal cross-correlations qualitatively and quantitatively using a cross-correlation test and the Multifractal detrended cross-correlation analysis method (MF-DCCA) for markets in the MENA area. We used cross-correlation coefficients to measure the level of this correlation. The analysis concerns four stock market indices of Morocco, Tunisia, Egypt and Jordan. The countries chosen are signatory of the Agadir agreement concerning the establishment of a free trade area comprising Arab Mediterranean countries. We computed the bivariate generalized Hurst exponent, Rényi exponent and spectrum of singularity for each pair of indices to measure quantitatively the cross-correlations. By analyzing the results, we found the existence of multifractal cross-correlations between all of these markets. We compared the spectrum width of these indices; we also found which pair of indices has a strong multifractal cross-correlation.

Energy levels of a scalar particle in a static gravitational field close to the black hole limit

NASA Astrophysics Data System (ADS)

Gossel, G. H.; Berengut, J. C.; Flambaum, V. V.

2011-10-01

The bound-state energy levels of a scalar particle in the gravitational field of finite-sized objects with interiors described by the Florides and Schwarzschild metrics are found. For these metrics, bound states with zero energy (where the binding energy is equal to the rest mass of the scalar particle) only exist when a singularity occurs in the metric. Therefore, in contrast to the Coulomb case, no pairs are produced in the non-singular static metric. For the Florides metric the singularity occurs in the black hole limit, while for the Schwarzschild interior metric it corresponds to infinite pressure at the center. Moreover, the energy spectrum is shown to become quasi-continuous as the metric becomes singular.

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.

Four-parameter potential box with inverse square singular boundaries

NASA Astrophysics Data System (ADS)

Alhaidari, A. D.; Taiwo, T. J.

2018-03-01

Using the Tridiagonal Representation Approach (TRA), we obtain solutions (energy spectrum and corresponding wavefunctions) for a four-parameter potential box with inverse square singularity at the boundaries. It could be utilized in physical applications to replace the widely used one-parameter infinite square potential well (ISPW). The four parameters of the potential provide an added flexibility over the one-parameter ISPW to control the physical features of the system. The two potential parameters that give the singularity strength at the boundaries are naturally constrained to avoid the inherent quantum anomalies associated with the inverse square potential.

Non-parametric characterization of long-term rainfall time series

NASA Astrophysics Data System (ADS)

Tiwari, Harinarayan; Pandey, Brij Kishor

2018-03-01

The statistical study of rainfall time series is one of the approaches for efficient hydrological system design. Identifying, and characterizing long-term rainfall time series could aid in improving hydrological systems forecasting. In the present study, eventual statistics was applied for the long-term (1851-2006) rainfall time series under seven meteorological regions of India. Linear trend analysis was carried out using Mann-Kendall test for the observed rainfall series. The observed trend using the above-mentioned approach has been ascertained using the innovative trend analysis method. Innovative trend analysis has been found to be a strong tool to detect the general trend of rainfall time series. Sequential Mann-Kendall test has also been carried out to examine nonlinear trends of the series. The partial sum of cumulative deviation test is also found to be suitable to detect the nonlinear trend. Innovative trend analysis, sequential Mann-Kendall test and partial cumulative deviation test have potential to detect the general as well as nonlinear trend for the rainfall time series. Annual rainfall analysis suggests that the maximum changes in mean rainfall is 11.53% for West Peninsular India, whereas the maximum fall in mean rainfall is 7.8% for the North Mountainous Indian region. The innovative trend analysis method is also capable of finding the number of change point available in the time series. Additionally, we have performed von Neumann ratio test and cumulative deviation test to estimate the departure from homogeneity. Singular spectrum analysis has been applied in this study to evaluate the order of departure from homogeneity in the rainfall time series. Monsoon season (JS) of North Mountainous India and West Peninsular India zones has higher departure from homogeneity and singular spectrum analysis shows the results to be in coherence with the same.

Accuracy evaluation of Fourier series analysis and singular spectrum analysis for predicting the volume of motorcycle sales in Indonesia

NASA Astrophysics Data System (ADS)

Sasmita, Yoga; Darmawan, Gumgum

2017-08-01

This research aims to evaluate the performance of forecasting by Fourier Series Analysis (FSA) and Singular Spectrum Analysis (SSA) which are more explorative and not requiring parametric assumption. Those methods are applied to predicting the volume of motorcycle sales in Indonesia from January 2005 to December 2016 (monthly). Both models are suitable for seasonal and trend component data. Technically, FSA defines time domain as the result of trend and seasonal component in different frequencies which is difficult to identify in the time domain analysis. With the hidden period is 2,918 ≈ 3 and significant model order is 3, FSA model is used to predict testing data. Meanwhile, SSA has two main processes, decomposition and reconstruction. SSA decomposes the time series data into different components. The reconstruction process starts with grouping the decomposition result based on similarity period of each component in trajectory matrix. With the optimum of window length (L = 53) and grouping effect (r = 4), SSA predicting testing data. Forecasting accuracy evaluation is done based on Mean Absolute Percentage Error (MAPE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE). The result shows that in the next 12 month, SSA has MAPE = 13.54 percent, MAE = 61,168.43 and RMSE = 75,244.92 and FSA has MAPE = 28.19 percent, MAE = 119,718.43 and RMSE = 142,511.17. Therefore, to predict volume of motorcycle sales in the next period should use SSA method which has better performance based on its accuracy.

An operational modal analysis method in frequency and spatial domain

NASA Astrophysics Data System (ADS)

Wang, Tong; Zhang, Lingmi; Tamura, Yukio

2005-12-01

A frequency and spatial domain decomposition method (FSDD) for operational modal analysis (OMA) is presented in this paper, which is an extension of the complex mode indicator function (CMIF) method for experimental modal analysis (EMA). The theoretical background of the FSDD method is clarified. Singular value decomposition is adopted to separate the signal space from the noise space. Finally, an enhanced power spectrum density (PSD) is proposed to obtain more accurate modal parameters by curve fitting in the frequency domain. Moreover, a simulation case and an application case are used to validate this method.

Entanglement Entropy across the Superfluid-Insulator Transition: A Signature of Bosonic Criticality.

PubMed

Frérot, Irénée; Roscilde, Tommaso

2016-05-13

We study the entanglement entropy and entanglement spectrum of the paradigmatic Bose-Hubbard model, describing strongly correlated bosons on a lattice. The use of a controlled approximation-the slave-boson approach-allows us to study entanglement in all regimes of the model (and, most importantly, across its superfluid-Mott-insulator transition) at a minimal cost. We find that the area-law scaling of entanglement-verified in all the phases-exhibits a sharp singularity at the transition. The singularity is greatly enhanced when the transition is crossed at fixed, integer filling, due to a richer entanglement spectrum containing an additional gapless mode, which descends from the amplitude (Higgs) mode of the global excitation spectrum-while this mode remains gapped at the generic (commensurate-incommensurate) transition with variable filling. Hence, the entanglement properties contain a unique signature of the two different forms of bosonic criticality exhibited by the Bose-Hubbard model.

Multichannel Singular Spectrum Analysis in the Estimates of Common Environmental Effects Affecting GPS Observations

NASA Astrophysics Data System (ADS)

Gruszczynska, Marta; Rosat, Severine; Klos, Anna; Gruszczynski, Maciej; Bogusz, Janusz

2018-03-01

We described a spatio-temporal analysis of environmental loading models: atmospheric, continental hydrology, and non-tidal ocean changes, based on multichannel singular spectrum analysis (MSSA). We extracted the common annual signal for 16 different sections related to climate zones: equatorial, arid, warm, snow, polar and continents. We used the loading models estimated for a set of 229 ITRF2014 (International Terrestrial Reference Frame) International GNSS Service (IGS) stations and discussed the amount of variance explained by individual modes, proving that the common annual signal accounts for 16, 24 and 68% of the total variance of non-tidal ocean, atmospheric and hydrological loading models, respectively. Having removed the common environmental MSSA seasonal curve from the corresponding GPS position time series, we found that the residual station-specific annual curve modelled with the least-squares estimation has the amplitude of maximum 2 mm. This means that the environmental loading models underestimate the seasonalities observed by the GPS system. The remaining signal present in the seasonal frequency band arises from the systematic errors which are not of common environmental or geophysical origin. Using common mode error (CME) estimates, we showed that the direct removal of environmental loading models from the GPS series causes an artificial loss in the CME power spectra between 10 and 80 cycles per year. When environmental effect is removed from GPS series with MSSA curves, no influence on the character of spectra of CME estimates was noticed.

Multichannel Singular Spectrum Analysis in the Estimates of Common Environmental Effects Affecting GPS Observations

NASA Astrophysics Data System (ADS)

Gruszczynska, Marta; Rosat, Severine; Klos, Anna; Gruszczynski, Maciej; Bogusz, Janusz

2018-05-01

We described a spatio-temporal analysis of environmental loading models: atmospheric, continental hydrology, and non-tidal ocean changes, based on multichannel singular spectrum analysis (MSSA). We extracted the common annual signal for 16 different sections related to climate zones: equatorial, arid, warm, snow, polar and continents. We used the loading models estimated for a set of 229 ITRF2014 (International Terrestrial Reference Frame) International GNSS Service (IGS) stations and discussed the amount of variance explained by individual modes, proving that the common annual signal accounts for 16, 24 and 68% of the total variance of non-tidal ocean, atmospheric and hydrological loading models, respectively. Having removed the common environmental MSSA seasonal curve from the corresponding GPS position time series, we found that the residual station-specific annual curve modelled with the least-squares estimation has the amplitude of maximum 2 mm. This means that the environmental loading models underestimate the seasonalities observed by the GPS system. The remaining signal present in the seasonal frequency band arises from the systematic errors which are not of common environmental or geophysical origin. Using common mode error (CME) estimates, we showed that the direct removal of environmental loading models from the GPS series causes an artificial loss in the CME power spectra between 10 and 80 cycles per year. When environmental effect is removed from GPS series with MSSA curves, no influence on the character of spectra of CME estimates was noticed.

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.

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.

On the curious spectrum of duality invariant higher-derivative gravity

DOE PAGES

Hohm, Olaf; Naseer, Usman; Zwiebach, Barton

2016-08-31

Here, we analyze the spectrum of the exactly duality and gauge invariant higher-derivative double field theory. While this theory is based on a chiral CFT and does not correspond to a standard string theory, our analysis illuminates a number of issues central in string theory. The full quadratic action is rewritten as a two-derivative theory with additional fields. This allows for a simple analysis of the spectrum, which contains two massive spin-2 ghosts and massive scalars, in addition to the massless fields. Moreover, in this formulation, the massless or tensionless limit α' → ∞ is non-singular and leads to anmore » enhanced gauge symmetry. We show that the massive modes can be integrated out exactly at the quadratic level, leading to an infinite series of higher-derivative corrections. Lastly, we present a ghost-free massive extension of linearized double field theory, which employs a novel mass term for the dilaton and metric.« less

Adaptive fault feature extraction from wayside acoustic signals from train bearings

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

Complete particle-pair annihilation as a dynamical signature of the spectral singularity

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

Li, G.R.; Zhang, X.Z.; Song, Z., E-mail: nkquantum@gmail.com

2014-10-15

Motivated by the physical relevance of a spectral singularity of interacting many-particle system, we explore the dynamics of two bosons as well as fermions in one-dimensional system with imaginary delta interaction strength. Based on the exact solution, it shows that the two-particle collision leads to amplitude-reduction of the wave function. For fermion pair, the amplitude-reduction depends on the spin configuration of two particles. In both cases, the residual amplitude can vanish when the relative group velocity of two single-particle Gaussian wave packets with equal width reaches the magnitude of the interaction strength, exhibiting complete particle-pair annihilation at the spectral singularity.more » - Highlights: • We investigate the physical relevance of a spectral singularity. • The two-particle collision leads to amplitude-reduction of the wave function. • There is a singularity spectrum which leads to complete particle-pair annihilation. • Complete particle-pair annihilation can only occur for two distinguishable bosons and singlet fermions. • Pair annihilation provides a detection method of the spectral singularity in the experiment.« less

Optical solitons, explicit solutions and modulation instability analysis with second-order spatio-temporal dispersion

NASA Astrophysics Data System (ADS)

Inc, Mustafa; Isa Aliyu, Aliyu; Yusuf, Abdullahi; Baleanu, Dumitru

2017-12-01

This paper obtains the dark, bright, dark-bright or combined optical and singular solitons to the nonlinear Schrödinger equation (NLSE) with group velocity dispersion coefficient and second-order spatio-temporal dispersion coefficient, which arises in photonics and waveguide optics and in optical fibers. The integration algorithm is the sine-Gordon equation method (SGEM). Furthermore, the explicit solutions of the equation are derived by considering the power series solutions (PSS) theory and the convergence of the solutions is guaranteed. Lastly, the modulation instability analysis (MI) is studied based on the standard linear-stability analysis and the MI gain spectrum is obtained.

Subspace techniques to remove artifacts from EEG: a quantitative analysis.

PubMed

Teixeira, A R; Tome, A M; Lang, E W; Martins da Silva, A

2008-01-01

In this work we discuss and apply projective subspace techniques to both multichannel as well as single channel recordings. The single-channel approach is based on singular spectrum analysis(SSA) and the multichannel approach uses the extended infomax algorithm which is implemented in the opensource toolbox EEGLAB. Both approaches will be evaluated using artificial mixtures of a set of selected EEG signals. The latter were selected visually to contain as the dominant activity one of the characteristic bands of an electroencephalogram (EEG). The evaluation is performed both in the time and frequency domain by using correlation coefficients and coherence function, respectively.

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.

X-ray edge singularity in resonant inelastic x-ray scattering (RIXS)

NASA Astrophysics Data System (ADS)

Markiewicz, Robert; Rehr, John; Bansil, Arun

2013-03-01

We develop a lattice model based on the theory of Mahan, Noziéres, and de Dominicis for x-ray absorption to explore the effect of the core hole on the RIXS cross section. The dominant part of the spectrum can be described in terms of the dynamic structure function S (q , ω) dressed by matrix element effects, but there is also a weak background associated with multi-electron-hole pair excitations. The model reproduces the decomposition of the RIXS spectrum into well- and poorly-screened components. An edge singularity arises at the threshold of both components. Fairly large lattice sizes are required to describe the continuum limit. Supported by DOE Grant DE-FG02-07ER46352 and facilitated by the DOE CMCSN, under grant number DE-SC0007091.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

Diffraction analysis of customized illumination technique

NASA Astrophysics Data System (ADS)

Lim, Chang-Moon; Kim, Seo-Min; Eom, Tae-Seung; Moon, Seung Chan; Shin, Ki S.

2004-05-01

Various enhancement techniques such as alternating PSM, chrome-less phase lithography, double exposure, etc. have been considered as driving forces to lead the production k1 factor towards below 0.35. Among them, a layer specific optimization of illumination mode, so-called customized illumination technique receives deep attentions from lithographers recently. A new approach for illumination customization based on diffraction spectrum analysis is suggested in this paper. Illumination pupil is divided into various diffraction domains by comparing the similarity of the confined diffraction spectrum. Singular imaging property of individual diffraction domain makes it easier to build and understand the customized illumination shape. By comparing the goodness of image in each domain, it was possible to achieve the customized shape of illumination. With the help from this technique, it was found that the layout change would not gives the change in the shape of customized illumination mode.

Spectral Characteristics of the Unitary Critical Almost-Mathieu Operator

NASA Astrophysics Data System (ADS)

Fillman, Jake; Ong, Darren C.; Zhang, Zhenghe

2017-04-01

We discuss spectral characteristics of a one-dimensional quantum walk whose coins are distributed quasi-periodically. The unitary update rule of this quantum walk shares many spectral characteristics with the critical Almost-Mathieu Operator; however, it possesses a feature not present in the Almost-Mathieu Operator, namely singularity of the associated cocycles (this feature is, however, present in the so-called Extended Harper's Model). We show that this operator has empty absolutely continuous spectrum and that the Lyapunov exponent vanishes on the spectrum; hence, this model exhibits Cantor spectrum of zero Lebesgue measure for all irrational frequencies and arbitrary phase, which in physics is known as Hofstadter's butterfly. In fact, we will show something stronger, namely, that all spectral parameters in the spectrum are of critical type, in the language of Avila's global theory of analytic quasiperiodic cocycles. We further prove that it has empty point spectrum for each irrational frequency and away from a frequency-dependent set of phases having Lebesgue measure zero. The key ingredients in our proofs are an adaptation of Avila's Global Theory to the present setting, self-duality via the Fourier transform, and a Johnson-type theorem for singular dynamically defined CMV matrices which characterizes their spectra as the set of spectral parameters at which the associated cocycles fail to admit a dominated splitting.

Long Term Precipitation Pattern Identification and Derivation of Non Linear Precipitation Trend in a Catchment using Singular Spectrum Analysis

NASA Astrophysics Data System (ADS)

Unnikrishnan, Poornima; Jothiprakash, Vinayakam

2017-04-01

Precipitation is the major component in the hydrologic cycle. Awareness of not only the total amount of rainfall pertaining to a catchment, but also the pattern of its spatial and temporal distribution are equally important in the management of water resources systems in an efficient way. Trend is the long term direction of a time series; it determines the overall pattern of a time series. Singular Spectrum Analysis (SSA) is a time series analysis technique that decomposes the time series into small components (eigen triples). This property of the method of SSA has been utilized to extract the trend component of the rainfall time series. In order to derive trend from the rainfall time series, we need to select components corresponding to trend from the eigen triples. For this purpose, periodogram analysis of the eigen triples have been proposed to be coupled with SSA, in the present study. In the study, seasonal data of England and Wales Precipitation (EWP) for a time period of 1766-2013 have been analyzed and non linear trend have been derived out of the precipitation data. In order to compare the performance of SSA in deriving trend component, Mann Kendall (MK) test is also used to detect trends in EWP seasonal series and the results have been compared. The result showed that the MK test could detect the presence of positive or negative trend for a significance level, whereas the proposed methodology of SSA could extract the non-linear trend present in the rainfall series along with its shape. We will discuss further the comparison of both the methodologies along with the results in the presentation.

Optical Manifestations of the Electron-Electron Interaction

NASA Astrophysics Data System (ADS)

Portengen, Taco

1995-01-01

In this thesis, two optical manifestations of the electron-electron interaction are studied: the Fermi -edge singularity in doped quantum wells and quantum wires, and second-harmonic generation in mixed-valent compounds. First, we construct a theory of the Fermi-edge singularity that can systematically account for the finite mass of a hole created in the valence subband of a quantum well or quantum wire. The dynamical response for finite hole mass depends crucially on the dimensionality of the Fermi sea. Whereas in three dimensions the infrared divergence is suppressed, in two dimensions a one-over-square-root singularity survives, while in one dimension the spectrum is even more singular with recoil than without recoil. This explains the large optical singularities observed in quantum wires. Correlations change the prefactor, but not the exponent of the threshold behaviour in two and in three dimensions, while in one dimension, they affect neither the prefactor nor the exponent. Second, we apply our theory to the Frohlich polaron, a manifestation of the electron-phonon rather than the electron-electron interaction. The new method of calculating the Green's function removes unphysical features of the conventional cumulant expansion that had remained unnoticed in the literature up to now. Third, in an effort to investigate the impact of coherence on optical properties, we calculate the linear and nonlinear optical characteristics of mixed-valent compounds. Second -harmonic generation can only occur for solutions of the theoretical Falicov-Kimball model that have a built-in coherence between the itinerant d-electrons and localized f-holes. By contrast, second-harmonic generation cannot occur for solutions with f-site occupation as a good quantum number. The interaction between optically created quasiparticles leads to a threshold singularity in the absorption spectrum, and greatly enhances the second-harmonic conversion efficiency at half the gap frequency. As an experimental test of coherence we propose the measurement of the second-harmonic susceptibility of SmB_6..

Fermi-Edge Singularity of Spin-Polarized Electrons

NASA Astrophysics Data System (ADS)

Plochocka-Polack, P.; Groshaus, J. G.; Rappaport, M.; Umansky, V.; Gallais, Y.; Pinczuk, A.; Bar-Joseph, I.

2007-05-01

We study the absorption spectrum of a two-dimensional electron gas (2DEG) in a magnetic field. We find that at low temperatures, when the 2DEG is spin polarized, the absorption spectra, which correspond to the creation of spin up or spin down electrons, differ in magnitude, linewidth, and filling factor dependence. We show that these differences can be explained as resulting from the creation of a Mahan exciton in one case, and of a power law Fermi-edge singularity in the other.

A spectral approach for the stability analysis of turbulent open-channel flows over granular beds

NASA Astrophysics Data System (ADS)

Camporeale, C.; Canuto, C.; Ridolfi, L.

2012-01-01

A novel Orr-Sommerfeld-like equation for gravity-driven turbulent open-channel flows over a granular erodible bed is here derived, and the linear stability analysis is developed. The whole spectrum of eigenvalues and eigenvectors of the complete generalized eigenvalue problem is computed and analyzed. The fourth-order eigenvalue problem presents singular non-polynomial coefficients with non-homogenous Robin-type boundary conditions that involve first and second derivatives. Furthermore, the Exner condition is imposed at an internal point. We propose a numerical discretization of spectral type based on a single-domain Galerkin scheme. In order to manage the presence of singular coefficients, some properties of Jacobi polynomials have been carefully blended with numerical integration of Gauss-Legendre type. The results show a positive agreement with the classical experimental data and allow one to relate the different types of instability to such parameters as the Froude number, wavenumber, and the roughness scale. The eigenfunctions allow two types of boundary layers to be distinguished, scaling, respectively, with the roughness height and the saltation layer for the bedload sediment transport.

FAST TRACK COMMUNICATION: SUSY transformations with complex factorization constants: application to spectral singularities

NASA Astrophysics Data System (ADS)

Samsonov, Boris F.

2010-10-01

Supersymmetric (SUSY) transformation operators with complex factorization constants are analyzed as operators acting in the Hilbert space of functions square integrable on the positive semiaxis. The obtained results are applied to Hamiltonians possessing spectral singularities which are non-Hermitian SUSY partners of self-adjoint operators. A new regularization procedure for the resolution of the identity operator in terms of a continuous biorthonormal set of the non-Hermitian Hamiltonian eigenfunctions is proposed. It is also argued that if the binorm of continuous spectrum eigenfunctions is interpreted in the same way as the norm of similar functions in the usual Hermitian case, then one can state that the function corresponding to a spectral singularity has zero binorm.

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 privileged spectrum of cnoidal ion holes and its extension by imperfect ion trapping

NASA Astrophysics Data System (ADS)

Schamel, Hans; Das, Nilakshi; Borah, Prathana

2018-01-01

The fundamental properties of nonlinear ion hole modes propagating in current-driven collisionless plasmas are derived. Making use of Schamel's alternative method their spatial structure ϕ (x) and phase velocities u0 are analyzed and found to depend crucially on the used trapped ion distribution fit. A regular fit represents a continuous spectrum, which is called privileged or perfect since it yields a definite u0 and appears most realistic. A singular fit, on the other hand, involving jumps and moderate slope singularities at the separatrix, does reveal further classes of hole equilibria at the cost, however, of a well-defined u0. This explains why Bernstein, Greene, Kruskal (BGK)-solutions of the Vlasov-Poisson system, exhibiting a strong slope singularity of their derived trapped particle distribution, can principally not provide definite u0 s. The nonlinear dispersion relation (or u0) of privileged ion holes, on the other hand, is equivalent with that of cnoidal electron holes, i.e. in addition to the ordinary ion acoustic branch there exists a correspondence to the "Langmuir" branch and to the multiple "slow electron acoustic" branches, reflecting different trapping scenarios.

Single-hole spectral function and spin-charge separation in the t-J model

NASA Astrophysics Data System (ADS)

Mishchenko, A. S.; Prokof'ev, N. V.; Svistunov, B. V.

2001-07-01

Worm algorithm Monte Carlo simulations of the hole Green function with subsequent spectral analysis were performed for 0.1<=J/t<=0.4 on lattices with up to L×L=32×32 sites at a temperature as low as T=J/40, and present, apparently, the hole spectral function in the thermodynamic limit. Spectral analysis reveals a δ-function-sharp quasiparticle peak at the lower edge of the spectrum that is incompatible with the power-law singularity and thus rules out the possibility of spin-charge separation in this parameter range. Spectral continuum features two peaks separated by a gap ~4÷5 t.

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

ERIC Educational Resources Information Center

Yanai, Haruo; Mukherjee, Bishwa Nath

1987-01-01

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

The singular nature of auditory and visual scene analysis in autism

PubMed Central

Lin, I.-Fan; Shirama, Aya; Kato, Nobumasa

2017-01-01

Individuals with autism spectrum disorder often have difficulty acquiring relevant auditory and visual information in daily environments, despite not being diagnosed as hearing impaired or having low vision. Resent psychophysical and neurophysiological studies have shown that autistic individuals have highly specific individual differences at various levels of information processing, including feature extraction, automatic grouping and top-down modulation in auditory and visual scene analysis. Comparison of the characteristics of scene analysis between auditory and visual modalities reveals some essential commonalities, which could provide clues about the underlying neural mechanisms. Further progress in this line of research may suggest effective methods for diagnosing and supporting autistic individuals. This article is part of the themed issue ‘Auditory and visual scene analysis'. PMID:28044025

Nonlinear stratospheric variability: multifractal de-trended fluctuation analysis and singularity spectra

PubMed Central

Domeisen, Daniela I. V.

2016-01-01

Characterizing the stratosphere as a turbulent system, temporal fluctuations often show different correlations for different time scales as well as intermittent behaviour that cannot be captured by a single scaling exponent. In this study, the different scaling laws in the long-term stratospheric variability are studied using multifractal de-trended fluctuation analysis (MF-DFA). The analysis is performed comparing four re-analysis products and different realizations of an idealized numerical model, isolating the role of topographic forcing and seasonal variability, as well as the absence of climate teleconnections and small-scale forcing. The Northern Hemisphere (NH) shows a transition of scaling exponents for time scales shorter than about 1 year, for which the variability is multifractal and scales in time with a power law corresponding to a red spectrum, to longer time scales, for which the variability is monofractal and scales in time with a power law corresponding to white noise. Southern Hemisphere (SH) variability also shows a transition at annual scales. The SH also shows a narrower dynamical range in multifractality than the NH, as seen in the generalized Hurst exponent and in the singularity spectra. The numerical integrations show that the models are able to reproduce the low-frequency variability but are not able to fully capture the shorter term variability of the stratosphere. PMID:27493560

Singularities in the lineshape of a second-order perturbed quadrupolar nucleus. The magic-angle spinning case.

PubMed

Field, Timothy R; Bain, Alex D

2014-01-01

For a nucleus with a half-integral spin and a strong quadrupole coupling, the central transition (from magnetic quantum number -1/2 to +1/2) in the spectrum shows a characteristic lineshape. By strong coupling, we mean an interaction strong enough so that second-order perturbation theory is needed, yet still sufficient. The spectrum of a static sample is well-known and the magic-angle-spinning (MAS spectrum) is different, but still can be calculated. The important features of both these spectra are singularities and steps in the lineshape, since these are the main tools in fitting the calculated spectrum to experimental data. A useful tool in this investigation is a plot of the frequency as a function of orientation over the surface of the unit sphere. These plots have maxima, minima and saddle points, and these correspond to the features of the spectrum. We used these plots to define both the positions and derive new formulae for the heights of the features and we now extend this to the magic-angle spinning case. For the first time, we identify the orientations corresponding to the features of the MAS spectra and derive formulae for the heights. We then compare the static and MAS cases and show the relationships between the features in the two spectra. Copyright © 2014 Elsevier Inc. All rights reserved.

Treatment of singularities in a middle-crack tension specimen

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Singularities in Optimal Structural Design

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Singularities in optimal structural design

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

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

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

Study on common seasonal signals in GPS time series and environmental loadings using Multichannel Singular Spectrum Analysis

NASA Astrophysics Data System (ADS)

Gruszczynska, Marta; Rosat, Severine; Klos, Anna; Bogusz, Janusz

2017-04-01

Seasonal oscillations in the GPS position time series can arise from real geophysical effects and numerical artefacts. According to Dong et al. (2002) environmental loading effects can account for approximately 40% of the total variance of the annual signals in GPS time series, however using generally acknowledged methods (e.g. Least Squares Estimation, Wavelet Decomposition, Singular Spectrum Analysis) to model seasonal signals we are not able to separate real from spurious signals (effects of mismodelling aliased into annual period as well as draconitic). Therefore, we propose to use Multichannel Singular Spectrum Analysis (MSSA) to determine seasonal oscillations (with annual and semi-annual periods) from GPS position time series and environmental loading displacement models. The MSSA approach is an extension of the classical Karhunen-Loève method and it is a special case of SSA for multivariate time series. The main advantage of MSSA is the possibility to extract common seasonal signals for stations from selected area and to investigate the causality between a set of time series as well. In this research, we explored the ability of MSSA application to separate real geophysical effects from spurious effects in GPS time series. For this purpose, we used GPS position changes and environmental loading models. We analysed the topocentric time series from 250 selected stations located worldwide, delivered from Network Solution obtained by the International GNSS Service (IGS) as a contribution to the latest realization of the International Terrestrial Reference System (namely ITRF2014, Rebishung et al., 2016). We also researched atmospheric, hydrological and non-tidal oceanic loading models provided by the EOST/IPGS Loading Service in the Centre-of-Figure (CF) reference frame. The analysed displacements were estimated from ERA-Interim (surface pressure), MERRA-land (soil moisture and snow) as well as ECCO2 ocean bottom pressure. We used Multichannel Singular Spectrum Analysis to determine common seasonal signals in two case studies with adopted a 3-years lag-window as the optimal window size. We also inferred the statistical significance of oscillations through the Monte Carlo MSSA method (Allen and Robertson, 1996). In the first case study, we investigated the common spatio-temporal seasonal signals for all stations. For this purpose, we divided selected stations with respect to the continents. For instance, for stations located in Europe, seasonal oscillations accounts for approximately 45% of the GPS-derived data variance. Much higher variance of seasonal signals is explained by hydrological loadings of about 92%, while the non-tidal oceanic loading accounted for 31% of total variance. In the second case study, we analysed the capability of the MSSA method to establish a causality between several time series. Each of estimated Principal Component represents pattern of the common signal for all analysed data. For ZIMM station (Zimmerwald, Switzerland), the 1st, 2nd and 9th, 10th Principal Components, which accounts for 35% of the variance, corresponds to the annual and semi-annual signals. In this part, we applied the non-parametric MSSA approach to extract the common seasonal signals for GPS time series and environmental loadings for each of the 250 stations with clear statement, that some part of seasonal signal reflects the real geophysical effects. REFERENCES: 1. Allen, M. and Robertson, A.: 1996, Distinguishing modulated oscillations from coloured noise in multivariate datasets. Climate Dynamics, 12, No. 11, 775-784. DOI: 10.1007/s003820050142. 2. Dong, D., Fang, P., Bock, Y., Cheng, M.K. and Miyazaki, S.: 2002, Anatomy of apparent seasonal variations from GPS-derived site position time series. Journal of Geophysical Research, 107, No. B4, 2075. DOI: 10.1029/2001JB000573. 3. Rebischung, P., Altamimi, Z., Ray, J. and Garayt, B.: 2016, The IGS contribution to ITRF2014. Journal of Geodesy, 90, No. 7, 611-630. DOI:10.1007/s00190-016-0897-6.

A data base and analysis program for shuttle main engine dynamic pressure measurements

NASA Technical Reports Server (NTRS)

Coffin, T.

1986-01-01

A dynamic pressure data base management system is described for measurements obtained from space shuttle main engine (SSME) hot firing tests. The data were provided in terms of engine power level and rms pressure time histories, and power spectra of the dynamic pressure measurements at selected times during each test. Test measurements and engine locations are defined along with a discussion of data acquisition and reduction procedures. A description of the data base management analysis system is provided and subroutines developed for obtaining selected measurement means, variances, ranges and other statistics of interest are discussed. A summary of pressure spectra obtained at SSME rated power level is provided for reference. Application of the singular value decomposition technique to spectrum interpolation is discussed and isoplots of interpolated spectra are presented to indicate measurement trends with engine power level. Program listings of the data base management and spectrum interpolation software are given. Appendices are included to document all data base measurements.

On the Ice Nucleation Spectrum

NASA Technical Reports Server (NTRS)

Barahona, D.

2012-01-01

This work presents a novel formulation of the ice nucleation spectrum, i.e. the function relating the ice crystal concentration to cloud formation conditions and aerosol properties. The new formulation is physically-based and explicitly accounts for the dependency of the ice crystal concentration on temperature, supersaturation, cooling rate, and particle size, surface area and composition. This is achieved by introducing the concepts of ice nucleation coefficient (the number of ice germs present in a particle) and nucleation probability dispersion function (the distribution of ice nucleation coefficients within the aerosol population). The new formulation is used to generate ice nucleation parameterizations for the homogeneous freezing of cloud droplets and the heterogeneous deposition ice nucleation on dust and soot ice nuclei. For homogeneous freezing, it was found that by increasing the dispersion in the droplet volume distribution the fraction of supercooled droplets in the population increases. For heterogeneous ice nucleation the new formulation consistently describes singular and stochastic behavior within a single framework. Using a fundamentally stochastic approach, both cooling rate independence and constancy of the ice nucleation fraction over time, features typically associated with singular behavior, were reproduced. Analysis of the temporal dependency of the ice nucleation spectrum suggested that experimental methods that measure the ice nucleation fraction over few seconds would tend to underestimate the ice nuclei concentration. It is shown that inferring the aerosol heterogeneous ice nucleation properties from measurements of the onset supersaturation and temperature may carry significant error as the variability in ice nucleation properties within the aerosol population is not accounted for. This work provides a simple and rigorous ice nucleation framework where theoretical predictions, laboratory measurements and field campaign data can be reconciled, and that is suitable for application in atmospheric modeling studies.

Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism

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

Ramos, J. J.; White, R. L.

The classic problem of the dynamic evolution and Landau damping of linear Langmuir electron waves in a collisionless plasma with Maxwellian background is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies. The corresponding complete basis of singular normal modes is obtained, along with their orthogonality relation. This yields easily the general expression of the time-reversal-invariant solution for any initial-value problem. Examples are then given for specific initial conditions that illustrate different behaviors of the Landau-damped macroscopic moments of the perturbations.

Strange non-chaotic attractors in a state controlled-cellular neural network-based quasiperiodically forced MLC circuit

NASA Astrophysics Data System (ADS)

Ezhilarasu, P. Megavarna; Inbavalli, M.; Murali, K.; Thamilmaran, K.

2018-07-01

In this paper, we report the dynamical transitions to strange non-chaotic attractors in a quasiperiodically forced state controlled-cellular neural network (SC-CNN)-based MLC circuit via two different mechanisms, namely the Heagy-Hammel route and the gradual fractalisation route. These transitions were observed through numerical simulations and hardware experiments and confirmed using statistical tools, such as maximal Lyapunov exponent spectrum and its variance and singular continuous spectral analysis. We find that there is a remarkable agreement of the results from both numerical simulations as well as from hardware experiments.

Normal-mode-based analysis of electron plasma waves with second-order Hermitian formalism

DOE PAGES

Ramos, J. J.; White, R. L.

2018-03-01

The classic problem of the dynamic evolution and Landau damping of linear Langmuir electron waves in a collisionless plasma with Maxwellian background is cast as a second-order, self-adjoint problem with a continuum spectrum of real and positive squared frequencies. The corresponding complete basis of singular normal modes is obtained, along with their orthogonality relation. This yields easily the general expression of the time-reversal-invariant solution for any initial-value problem. Examples are then given for specific initial conditions that illustrate different behaviors of the Landau-damped macroscopic moments of the perturbations.

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

NASA Astrophysics Data System (ADS)

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

2013-07-01

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

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

PubMed

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

2008-09-01

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

Cosmic censorship in Lovelock theory

NASA Astrophysics Data System (ADS)

Camanho, Xián O.; Edelstein, José D.

2013-11-01

In analyzing maximally symmetric Lovelock black holes with non-planar horizon topologies, many novel features have been observed. The existence of finite radius singularities, a mass gap in the black hole spectrum and solutions displaying multiple horizons are noteworthy examples. Naively, in all these cases, the appearance of naked singularities seems unavoidable, leading to the question of whether these theories are consistent gravity theories. We address this question and show that whenever the cosmic censorship conjecture is threaten, an instability generically shows up driving the system to a new configuration with presumably no naked singularities. Also, the same kind of instability shows up in the process of spherical black holes evaporation in these theories, suggesting a new phase for their decay. We find circumstantial evidence indicating that, contrary to many claims in the literature, the cosmic censorship hypothesis holds in Lovelock theory.

Unitary Quantum Lattice Algorithms for Turbulence

DTIC Science & Technology

2016-05-23

BECs one finds singular quantized vortices with zero density at the cores. This is what is seen experimentally, in Fig. 1. In an early simulation ...constant density in a healing length) there should be some differences. In a simulation on 57603-grid, we found the total kinetic energy spectrum has a...from these simulations : (a) the incompressible energy spectrum Einc k( ) <<Ecomp k( ), Equ k( ) for k < 200 , (b) for nearly the complete

Role of reservoirs in sustained seismicity of Koyna-Warna region—a statistical analysis

NASA Astrophysics Data System (ADS)

Yadav, Amrita; Gahalaut, Kalpna; Purnachandra Rao, N.

2018-03-01

Koyna-Warna region in western India is a globally recognized site of reservoir-triggered seismicity near the Koyna and Warna reservoirs. The region has been reported with several M > 5 earthquakes in the last five decades including M6.3 Koyna earthquake which is considered as the largest triggered earthquake worldwide. In the present study, a detailed statistical analysis has been done for long period earthquake catalogues during 1968-2004 of MERI and 2005-2012 of CSIR-NGRI to find out the spatio-temporal influence of the Koyna and Warna reservoirs impoundment on the seismicity of the region. Depending upon the earthquake clusters, we divided the region into three different zones and performed power spectrum and singular spectrum analysis (SSA) on them. For the time period 1983-1995, the earthquake zone near the Warna reservoir; for 1996-2004, the earthquake zone near the Koyna reservoir; and for 2005-2012, the earthquake zone near the Warna reservoir found to be influenced by the annual water level variations in the reservoirs that confirm the continuous role of both the reservoirs in the seismicity of the Koyna-Warna region.

Chaos, ergodic convergence, and fractal instability for a thermostated canonical harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.; Isbister, Dennis J.

2001-02-01

The authors thermostat a qp harmonic oscillator using the two additional control variables ζ and ξ to simulate Gibbs' canonical distribution. In contrast to the motion of purely Hamiltonian systems, the thermostated oscillator motion is completely ergodic, covering the full four-dimensional \\{q,p,ζ,ξ\\} phase space. The local Lyapunov spectrum (instantaneous growth rates of a comoving corotating phase-space hypersphere) exhibits singularities like those found earlier for Hamiltonian chaos, reinforcing the notion that chaos requires kinetic-as opposed to statistical-study, both at and away from equilibrium. The exponent singularities appear to have a fractal character.

Singularity analysis: theory and further developments

NASA Astrophysics Data System (ADS)

Cheng, Qiuming

2015-04-01

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

How universal is the entanglement spectrum?

NASA Astrophysics Data System (ADS)

Chandran, Anushya; Khemani, Vedika; Sondhi, Shivaji

2014-03-01

It is now commonly believed that the ground state entanglement spectrum (ES) exhibits universal features characteristic of a given phase. In this letter, we show that this belief is false in general. Most significantly, we show that the entanglement Hamiltonian can undergo quantum phase transitions in which its ground state and low energy spectrum exhibit singular changes, even when the physical system remains in the same phase. For broken symmetry problems, this implies that the ES and the Renyi entropies can mislead entirely, while for quantum Hall systems the ES has much less universal content than assumed to date.

How Universal Is the Entanglement Spectrum?

NASA Astrophysics Data System (ADS)

Chandran, Anushya; Khemani, Vedika; Sondhi, S. L.

2014-08-01

It is now commonly believed that the ground state entanglement spectrum (ES) exhibits universal features characteristic of a given phase. In this Letter, we show that this belief is false in general. Most significantly, we show that the entanglement Hamiltonian can undergo quantum phase transitions in which its ground state and low-energy spectrum exhibit singular changes, even when the physical system remains in the same phase. For broken symmetry problems, this implies that the low-energy ES and the Rényi entropies can mislead entirely, while for quantum Hall systems, the ES has much less universal content than assumed to date.

Investigation of the complexity of streamflow fluctuations in a large heterogeneous lake catchment in China

NASA Astrophysics Data System (ADS)

Ye, Xuchun; Xu, Chong-Yu; Li, Xianghu; Zhang, Qi

2018-05-01

The occurrence of flood and drought frequency is highly correlated with the temporal fluctuations of streamflow series; understanding of these fluctuations is essential for the improved modeling and statistical prediction of extreme changes in river basins. In this study, the complexity of daily streamflow fluctuations was investigated by using multifractal detrended fluctuation analysis (MF-DFA) in a large heterogeneous lake basin, the Poyang Lake basin in China, and the potential impacts of human activities were also explored. Major results indicate that the multifractality of streamflow fluctuations shows significant regional characteristics. In the study catchment, all the daily streamflow series present a strong long-range correlation with Hurst exponents bigger than 0.8. The q-order Hurst exponent h( q) of all the hydrostations can be characterized well by only two parameters: a (0.354 ≤ a ≤ 0.384) and b (0.627 ≤ b ≤ 0.677), with no pronounced differences. Singularity spectrum analysis pointed out that small fluctuations play a dominant role in all daily streamflow series. Our research also revealed that both the correlation properties and the broad probability density function (PDF) of hydrological series can be responsible for the multifractality of streamflow series that depends on watershed areas. In addition, we emphasized the relationship between watershed area and the estimated multifractal parameters, such as the Hurst exponent and fitted parameters a and b from the q-order Hurst exponent h( q). However, the relationship between the width of the singularity spectrum (Δ α) and watershed area is not clear. Further investigation revealed that increasing forest coverage and reservoir storage can effectively enhance the persistence of daily streamflow, decrease the hydrological complexity of large fluctuations, and increase the small fluctuations.

A miniaturized near infrared spectrometer for non-invasive sensing of bio-markers as a wearable healthcare solution

NASA Astrophysics Data System (ADS)

Bae, Jungmok; Druzhin, Vladislav V.; Anikanov, Alexey G.; Afanasyev, Sergey V.; Shchekin, Alexey; Medvedev, Anton S.; Morozov, Alexander V.; Kim, Dongho; Kim, Sang Kyu; Moon, Hyunseok; Jang, Hyeongseok; Shim, Jaewook; Park, Jongae

2017-02-01

A novel miniaturized near-infrared spectrometer readily mountable to wearable devices for continuous monitoring of individual's key bio-markers was proposed. Spectrum is measured by sequential illuminations with LED's, having independent spectrum profiles and a continuous detection of light radiations from the skin tissue with a single cell PD. Based on Tikhonov regularization with singular value decomposition, a spectrum resolution less than 10nm was reconstructed based on experimentally measured LED profiles. A prototype covering first overtone band (1500-1800nm) where bio-markers have pronounced absorption peaks was fabricated and verified of its performance. Reconstructed spectrum shows that the novel concept of miniaturized spectrometer is valid.

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).

A laboratory analogue of the event horizon using slow light in an atomic medium.

PubMed

Leonhardt, Ulf

2002-01-24

Singularities underlie many optical phenomena. The rainbow, for example, involves a particular type of singularity-a ray catastrophe-in which light rays become infinitely intense. In practice, the wave nature of light resolves these infinities, producing interference patterns. At the event horizon of a black hole, time stands still and waves oscillate with infinitely small wavelengths. However, the quantum nature of light results in evasion of the catastrophe and the emission of Hawking radiation. Here I report a theoretical laboratory analogue of an event horizon: a parabolic profile of the group velocity of light brought to a standstill in an atomic medium can cause a wave singularity similar to that associated with black holes. In turn, the quantum vacuum is forced to create photon pairs with a characteristic spectrum, a phenomenon related to Hawking radiation. The idea may initiate a theory of 'quantum' catastrophes, extending classical catastrophe theory.

Multivariate singular spectrum analysis and the road to phase synchronization

NASA Astrophysics Data System (ADS)

Groth, Andreas; Ghil, Michael

2010-05-01

Singular spectrum analysis (SSA) and multivariate SSA (M-SSA) are based on the classical work of Kosambi (1943), Loeve (1945) and Karhunen (1946) and are closely related to principal component analysis. They have been introduced into information theory by Bertero, Pike and co-workers (1982, 1984) and into dynamical systems analysis by Broomhead and King (1986a,b). Ghil, Vautard and associates have applied SSA and M-SSA to the temporal and spatio-temporal analysis of short and noisy time series in climate dynamics and other fields in the geosciences since the late 1980s. M-SSA provides insight into the unknown or partially known dynamics of the underlying system by decomposing the delay-coordinate phase space of a given multivariate time series into a set of data-adaptive orthonormal components. These components can be classified essentially into trends, oscillatory patterns and noise, and allow one to reconstruct a robust "skeleton" of the dynamical system's structure. For an overview we refer to Ghil et al. (Rev. Geophys., 2002). In this talk, we present M-SSA in the context of synchronization analysis and illustrate its ability to unveil information about the mechanisms behind the adjustment of rhythms in coupled dynamical systems. The focus of the talk is on the special case of phase synchronization between coupled chaotic oscillators (Rosenblum et al., PRL, 1996). Several ways of measuring phase synchronization are in use, and the robust definition of a reasonable phase for each oscillator is critical in each of them. We illustrate here the advantages of M-SSA in the automatic identification of oscillatory modes and in drawing conclusions about the transition to phase synchronization. Without using any a priori definition of a suitable phase, we show that M-SSA is able to detect phase synchronization in a chain of coupled chaotic oscillators (Osipov et al., PRE, 1996). Recently, Muller et al. (PRE, 2005) and Allefeld et al. (Intl. J. Bif. Chaos, 2007) have demonstrated the usefulness of principal component analysis in detecting phase synchronization from multivariate time series. The present talk provides a generalization of this idea and presents a robust implementation thereof via M-SSA.

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

NASA Technical Reports Server (NTRS)

Burken, John J.

1992-01-01

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

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

NASA Technical Reports Server (NTRS)

Burken, John J.

1992-01-01

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

Removing non-stationary noise in spectrum sensing using matrix factorization

NASA Astrophysics Data System (ADS)

van Bloem, Jan-Willem; Schiphorst, Roel; Slump, Cornelis H.

2013-12-01

Spectrum sensing is key to many applications like dynamic spectrum access (DSA) systems or telecom regulators who need to measure utilization of frequency bands. The International Telecommunication Union (ITU) recommends a 10 dB threshold above the noise to decide whether a channel is occupied or not. However, radio frequency (RF) receiver front-ends are non-ideal. This means that the obtained data is distorted with noise and imperfections from the analog front-end. As part of the front-end the automatic gain control (AGC) circuitry mainly affects the sensing performance as strong adjacent signals lift the noise level. To enhance the performance of spectrum sensing significantly we focus in this article on techniques to remove the noise caused by the AGC from the sensing data. In order to do this we have applied matrix factorization techniques, i.e., SVD (singular value decomposition) and NMF (non-negative matrix factorization), which enables signal space analysis. In addition, we use live measurement results to verify the performance and to remove the effects of the AGC from the sensing data using above mentioned techniques, i.e., applied on block-wise available spectrum data. In this article it is shown that the occupancy in the industrial, scientific and medical (ISM) band, obtained by using energy detection (ITU recommended threshold), can be an overestimation of spectrum usage by 60%.

Seismic noise attenuation using an online subspace tracking algorithm

NASA Astrophysics Data System (ADS)

Zhou, Yatong; Li, Shuhua; Zhang, Dong; Chen, Yangkang

2018-02-01

We propose a new low-rank based noise attenuation method using an efficient algorithm for tracking subspaces from highly corrupted seismic observations. The subspace tracking algorithm requires only basic linear algebraic manipulations. The algorithm is derived by analysing incremental gradient descent on the Grassmannian manifold of subspaces. When the multidimensional seismic data are mapped to a low-rank space, the subspace tracking algorithm can be directly applied to the input low-rank matrix to estimate the useful signals. Since the subspace tracking algorithm is an online algorithm, it is more robust to random noise than traditional truncated singular value decomposition (TSVD) based subspace tracking algorithm. Compared with the state-of-the-art algorithms, the proposed denoising method can obtain better performance. More specifically, the proposed method outperforms the TSVD-based singular spectrum analysis method in causing less residual noise and also in saving half of the computational cost. Several synthetic and field data examples with different levels of complexities demonstrate the effectiveness and robustness of the presented algorithm in rejecting different types of noise including random noise, spiky noise, blending noise, and coherent noise.

Quantum square-well with logarithmic central spike

NASA Astrophysics Data System (ADS)

Znojil, Miloslav; Semorádová, Iveta

2018-01-01

Singular repulsive barrier V (x) = -gln(|x|) inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction ℒeff(x) = -gln[ψ∗(x)ψ(x)] in nonlinear Schrödinger equation. In the linearized case, Rayleigh-Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small g or after an amendment of the unperturbed Hamiltonian. At any spike strength g, the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables x = expy which interchanges the roles of the asymptotic and central boundary conditions.

Spectra of random operators with absolutely continuous integrated density of states

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

Rio, Rafael del, E-mail: delrio@iimas.unam.mx, E-mail: delriomagia@gmail.com

2014-04-15

The structure of the spectrum of random operators is studied. It is shown that if the density of states measure of some subsets of the spectrum is zero, then these subsets are empty. In particular follows that absolute continuity of the integrated density of states implies singular spectra of ergodic operators is either empty or of positive measure. Our results apply to Anderson and alloy type models, perturbed Landau Hamiltonians, almost periodic potentials, and models which are not ergodic.

Using metabolic flux data to further constrain the metabolic solution space and predict internal flux patterns: the Escherichia coli spectrum.

PubMed

Wiback, Sharon J; Mahadevan, Radhakrishnan; Palsson, Bernhard Ø

2004-05-05

Constraint-based metabolic modeling has been used to capture the genome-scale, systems properties of an organism's metabolism. The first generation of these models has been built on annotated gene sequence. To further this field, we now need to develop methods to incorporate additional "omic" data types including transcriptomics, metabolomics, and fluxomics to further facilitate the construction, validation, and predictive capabilities of these models. The work herein combines metabolic flux data with an in silico model of central metabolism of Escherichia coli for model centric integration of the flux data. The extreme pathways for this network, which define the allowable solution space for all possible flux distributions, are analyzed using the alpha-spectrum. The alpha-spectrum determines which extreme pathways can and cannot contribute to the metabolic flux distribution for a given condition and gives the allowable range of weightings on each extreme pathway that can contribute. Since many extreme pathways cannot be used under certain conditions, the result is a "condition-specific" solution space that is a subset of the original solution space. The alpha-spectrum results are used to create a "condition-specific" extreme pathway matrix that can be analyzed using singular value decomposition (SVD). The first mode of the SVD analysis characterizes the solution space for a given condition. We show that SVD analysis of the alpha-spectrum extreme pathway matrix that incorporates measured uptake and byproduct secretion rates, can predict internal flux trends for different experimental conditions. These predicted internal flux trends are, in general, consistent with the flux trends measured using experimental metabolic flux analysis techniques. Copyright 2004 Wiley Periodicals, Inc.

Providing long-term trend and gravimetric factor at Chandler period from superconducting gravimeter records by using Singular Spectrum Analysis along with its multivariate extension

NASA Astrophysics Data System (ADS)

Gruszczynska, M.; Rosat, S.; Klos, A.; Bogusz, J.

2017-12-01

In this study, Singular Spectrum Analysis (SSA) along with its multivariate extension MSSA (Multichannel SSA) were used to estimate long-term trend and gravimetric factor at the Chandler wobble frequency from superconducting gravimeter (SG) records. We have used data from seven stations located worldwide and contributing to the International Geodynamics and Earth Tides Service (IGETS). The timespan ranged from 15 to 19 years. Before applying SSA and MSSA, we had removed local tides, atmospheric (ECMWF data), hydrological (MERRA2 products) loadings and non-tidal ocean loading (ECCO2 products) effects. In the first part of analysis, we used the SSA approach in order to estimate the long-term trends from SG observations. We use the technique based on the classical Karhunen-Loève spectral decomposition of time series into long-term trend, oscillations and noise. In the second part, we present the determination of common time-varying pole tide (annual and Chandler wobble) to estimate gravimetric factor from SG time series using the MSSA approach. The presented method takes advantage over traditional methods like Least Squares Estimation by determining common modes of variability which reflect common geophysical field. We adopted a 6-year lag-window as the optimal length to extract common seasonal signals and the Chandler components of the Earth polar motion. The signals characterized by annual and Chandler wobble account for approximately 62% of the total variance of residual SG data. Then, we estimated the amplitude factors and phase lags of Chandler wobble with respect to the IERS (International Earth Rotation and Reference Systems Service) polar motion observations. The resulting gravimetric factors at the Chandler Wobble period are finally compared with previously estimates. A robust estimate of the gravimetric Earth response to the Chandlerian component of the polar motion is required to better constrain the mantle anelasticity at this frequency and hence the attenuation models of the Earth interior.

2-COLOR Pupil Imaging Method to Detect Stellar Oscillations

NASA Astrophysics Data System (ADS)

Costantino, Sigismondi; Alessandro, Cacciani; Mauro, Dolci; Stuart, Jeffries; Eric, Fossat; Ludovico, Cesario; Paolo, Rapex; Luca, Bertello; Ferenc, Varadi; Wolfgang, Finsterle

Stellar intensity oscillations from the ground are strongly affected by atmospheric noise. For solar-type stars even Antarctic scintillation noise is still overwhelming. We proposed and tested a differential method that images on the same CCD detector two-color pupils of the telescope in order to compensate for intensity sky fluctuations guiding and saturation problems. SOHO data reveal that our method has an efficiency of 70% respect to the absolute amplitude variations. Using two instruments at Dome C and South Pole we can further minimize atmospheric color noise with cross-spectrum methods. This way we also decrease the likelihood of gaps in the data string due to bad weather. Observationally while waiting for the South Pole/Dome-C sites we are carrying on tests from available telescopes and Big Bear Mt. Wilson Teramo Milano. On the data analysis side we use the Random Lag Singular Cross-Spectrum Analysis which eliminates noise from the observed signal better than traditional Fourier transform. This method is also well-suited for extracting common oscillatory components from two or more observations including their relative phases as we are planning to do

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

NASA Technical Reports Server (NTRS)

Williams, Robert L., III

1992-01-01

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

Multifractal detrended cross-correlation analysis on air pollutants of University of Hyderabad Campus, India

NASA Astrophysics Data System (ADS)

Manimaran, P.; Narayana, A. C.

2018-07-01

In this paper, we study the multifractal characteristics and cross-correlation behaviour of Air Pollution Index (API) time series data through multifractal detrended cross-correlation analysis method. We analyse the daily API records of nine air pollutants of the university of Hyderabad campus for a period of three years (2013-2016). The cross-correlation behaviour has been measured from the Hurst scaling exponents and the singularity spectrum quantitatively. From the results, it is found that the cross-correlation analysis shows anti-correlation behaviour for all possible 36 bivariate time series. We also observe the existence of multifractal nature in all the bivariate time series in which many of them show strong multifractal behaviour. In particular, the hazardous particulate matter PM2.5 and inhalable particulate matter PM10 shows anti-correlated behaviour with all air pollutants.

Price-volume multifractal analysis of the Moroccan stock market

NASA Astrophysics Data System (ADS)

El Alaoui, Marwane

2017-11-01

In this paper, we analyzed price-volume multifractal cross-correlations of Moroccan Stock Exchange. We chose the period from January 1st 2000 to January 20th 2017 to investigate the multifractal behavior of price change and volume change series. Then, we used multifractal detrended cross-correlations analysis method (MF-DCCA) and multifractal detrended fluctuation analysis (MF-DFA) to analyze the series. We computed bivariate generalized Hurst exponent, Rényi exponent and spectrum of singularity for each pair of indices to measure quantitatively cross-correlations. Furthermore, we used detrended cross-correlations coefficient (DCCA) and cross-correlation test (Q(m)) to analyze cross-correlation quantitatively and qualitatively. By analyzing results, we found existence of price-volume multifractal cross-correlations. The spectrum width has a strong multifractal cross-correlation. We remarked that volume change series is anti-persistent when we analyzed the generalized Hurst exponent for all moments q. The cross-correlation test showed the presence of a significant cross-correlation. However, DCCA coefficient had a small positive value, which means that the level of correlation is not very significant. Finally, we analyzed sources of multifractality and their degree of contribution in the series.

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

NASA Astrophysics Data System (ADS)

Ghosh, Somnath

2018-05-01

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

[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.

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

NASA Astrophysics Data System (ADS)

Workman, Eli Joseph

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

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

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.

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.

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.

Gauss-Bonnet cosmology unifying late and early-time acceleration eras with intermediate eras

NASA Astrophysics Data System (ADS)

Oikonomou, V. K.

2016-07-01

In this paper we demonstrate that with vacuum F(G) gravity it is possible to describe the unification of late and early-time acceleration eras with the radiation and matter domination era. The Hubble rate of the unified evolution contains two mild singularities, so called Type IV singularities, and the evolution itself has some appealing features, such as the existence of a deceleration-acceleration transition at late times. We also address quantitatively a fundamental question related to modified gravity models description of cosmological evolution: Is it possible for all modified gravity descriptions of our Universe evolution, to produce a nearly scale invariant spectrum of primordial curvature perturbations? As we demonstrate, the answer for the F(G) description is no, since the resulting power spectrum is not scale invariant, in contrast to the F(R) description studied in the literature. Therefore, although the cosmological evolution can be realized in the context of vacuum F(G) gravity, the evolution is not compatible with the observational data, in contrast to the F(R) gravity description of the same cosmological evolution.

The origins of cosmic rays and quantum effects on gravity

NASA Technical Reports Server (NTRS)

Tomozawa, Y.

1985-01-01

The energy spectrum of primary cosmic rays is explained by particles emitted during a thermal expansion of explosive objects inside and near the galaxy, remnants of which may be supernova and/or active talaxies, or even stars or galaxies that disappeared from our sight after the explosion. A power law energy spectrum for cosmic rays, E to the (-alpha -1, is obtained from an expansion rate T is proportional to R to the alpha. Using the solution of the Einstein equation, we obtain a spectrum which agrees very well with experimental data. The implication of an inflationary early universe on the cosmic ray spectrum is also discussed. It is also suggested that the conflict between this model and the singularity theorem in classical general relativity may be eliminated by quantum effects.

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

PubMed

Ghosh, Somnath

2018-05-10

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

Quantum probe of Hořava-Lifshitz gravity

NASA Astrophysics Data System (ADS)

Gurtug, O.; Mangut, M.

2018-04-01

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

Interlaminar stress singularities at a straight free edge in composite laminates

NASA Technical Reports Server (NTRS)

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

1981-01-01

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

Submicron scale tissue multifractal anisotropy in polarized laser light scattering

NASA Astrophysics Data System (ADS)

Das, Nandan Kumar; Dey, Rajib; Chakraborty, Semanti; Panigrahi, Prasanta K.; Meglinski, Igor; Ghosh, Nirmalya

2018-03-01

The spatial fluctuations of the refractive index within biological tissues exhibit multifractal anisotropy, leaving its signature as a spectral linear diattenuation of scattered polarized light. The multifractal anisotropy has been quantitatively assessed by the processing of relevant Mueller matrix elements in the Fourier domain, utilizing the Born approximation and subsequent multifractal analysis. The differential scaling exponent and width of the singularity spectrum appear to be highly sensitive to the structural multifractal anisotropy at the micron/sub-micron length scales. An immediate practical use of these multifractal anisotropy parameters was explored for non-invasive screening of cervical precancerous alterations ex vivo, with the indication of a strong potential for clinical diagnostic purposes.

A New Trend-Following Indicator: Using SSA to Design Trading Rules

NASA Astrophysics Data System (ADS)

Leles, Michel Carlo Rodrigues; Mozelli, Leonardo Amaral; Guimarães, Homero Nogueira

Singular Spectrum Analysis (SSA) is a non-parametric approach that can be used to decompose a time-series as trends, oscillations and noise. Trend-following strategies rely on the principle that financial markets move in trends for an extended period of time. Moving Averages (MAs) are the standard indicator to design such strategies. In this study, SSA is used as an alternative method to enhance trend resolution in comparison with the traditional MA. New trading rules using SSA as indicator are proposed. This paper shows that for the Down Jones Industrial Average (DJIA) and Shangai Securities Composite Index (SSCI) time-series the SSA trading rules provided, in general, better results in comparison to MA trading rules.

Analysis and design of nonlinear resonances via singularity theory

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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.

Detecting Multifractal Properties in Asset Returns:

NASA Astrophysics Data System (ADS)

Lux, Thomas

It has become popular recently to apply the multifractal formalism of statistical physics (scaling analysis of structure functions and f(α) singularity spectrum analysis) to financial data. The outcome of such studies is a nonlinear shape of the structure function and a nontrivial behavior of the spectrum. Eventually, this literature has moved from basic data analysis to estimation of particular variants of multifractal models for asset returns via fitting of the empirical τ(q) and f(α) functions. Here, we reinvestigate earlier claims of multifractality using four long time series of important financial markets. Taking the recently proposed multifractal models of asset returns as our starting point, we show that the typical "scaling estimators" used in the physics literature are unable to distinguish between spurious and "true" multiscaling of financial data. Designing explicit tests for multiscaling, we can in no case reject the null hypothesis that the apparent curvature of both the scaling function and the Hölder spectrum are spuriously generated by the particular fat-tailed distribution of financial data. Given the well-known overwhelming evidence in favor of different degrees of long-term dependence in the powers of returns, we interpret this inability to reject the null hypothesis of multiscaling as a lack of discriminatory power of the standard approach rather than as a true rejection of multiscaling. However, the complete "failure" of the multifractal apparatus in this setting also raises the question whether results in other areas (like geophysics) suffer from similar shortcomings of the traditional methodology.

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

ERIC Educational Resources Information Center

Hofmann, Richard J.

1978-01-01

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

An analysis of the vertical structure equation for arbitrary thermal profiles

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1989-01-01

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

An analysis of the vertical structure equation for arbitrary thermal profiles

NASA Technical Reports Server (NTRS)

Cohn, Stephen E.; Dee, Dick P.

1987-01-01

The vertical structure equation is a singular Sturm-Liouville problem whose eigenfunctions describe the vertical dependence of the normal modes of the primitive equations linearized about a given thermal profile. The eigenvalues give the equivalent depths of the modes. The spectrum of the vertical structure equation and the appropriateness of various upper boundary conditions, both for arbitrary thermal profiles were studied. The results depend critically upon whether or not the thermal profile is such that the basic state atmosphere is bounded. In the case of a bounded atmosphere it is shown that the spectrum is always totally discrete, regardless of details of the thermal profile. For the barotropic equivalent depth, which corresponds to the lowest eigen value, upper and lower bounds which depend only on the surface temperature and the atmosphere height were obtained. All eigenfunctions are bounded, but always have unbounded first derivatives. It was proved that the commonly invoked upper boundary condition that vertical velocity must vanish as pressure tends to zero, as well as a number of alternative conditions, is well posed. It was concluded that the vertical structure equation always has a totally discrete spectrum under the assumptions implicit in the primitive equations.

Joint multifractal analysis based on the partition function approach: analytical analysis, numerical simulation and empirical application

NASA Astrophysics Data System (ADS)

Xie, Wen-Jie; Jiang, Zhi-Qiang; Gu, Gao-Feng; Xiong, Xiong; Zhou, Wei-Xing

2015-10-01

Many complex systems generate multifractal time series which are long-range cross-correlated. Numerous methods have been proposed to characterize the multifractal nature of these long-range cross correlations. However, several important issues about these methods are not well understood and most methods consider only one moment order. We study the joint multifractal analysis based on partition function with two moment orders, which was initially invented to investigate fluid fields, and derive analytically several important properties. We apply the method numerically to binomial measures with multifractal cross correlations and bivariate fractional Brownian motions without multifractal cross correlations. For binomial multifractal measures, the explicit expressions of mass function, singularity strength and multifractal spectrum of the cross correlations are derived, which agree excellently with the numerical results. We also apply the method to stock market indexes and unveil intriguing multifractality in the cross correlations of index volatilities.

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.

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

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

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

NASA Astrophysics Data System (ADS)

Dun, Xiaohong

2018-05-01

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

Assessment of 48 Stock markets using adaptive multifractal approach

NASA Astrophysics Data System (ADS)

Ferreira, Paulo; Dionísio, Andreia; Movahed, S. M. S.

2017-11-01

In this paper, Stock market comovements are examined using cointegration, Granger causality tests and nonlinear approaches in context of mutual information and correlations. Since underlying data sets are affected by non-stationarities and trends, we also apply Adaptive Multifractal Detrended Fluctuation Analysis (AMF-DFA) and Adaptive Multifractal Detrended Cross-Correlation Analysis (AMF-DXA). We find only 170 pair of Stock markets cointegrated, and according to the Granger causality and mutual information, we realize that the strongest relations lies between emerging markets, and between emerging and frontier markets. According to scaling exponent given by AMF-DFA, h(q = 2) > 1, we find that all underlying data sets belong to non-stationary process. According to Efficient Market Hypothesis (EMH), only 8 markets are classified in uncorrelated processes at 2 σ confidence interval. 6 Stock markets belong to anti-correlated class and dominant part of markets has memory in corresponding daily index prices during January 1995 to February 2014. New-Zealand with H = 0 . 457 ± 0 . 004 and Jordan with H = 0 . 602 ± 0 . 006 are far from EMH. The nature of cross-correlation exponents based on AMF-DXA is almost multifractal for all pair of Stock markets. The empirical relation, Hxy ≤ [Hxx +Hyy ] / 2, is confirmed. Mentioned relation for q > 0 is also satisfied while for q < 0 there is a deviation from this relation confirming behavior of markets for small fluctuations is affected by contribution of major pair. For larger fluctuations, the cross-correlation contains information from both local (internal) and global (external) conditions. Width of singularity spectrum for auto-correlation and cross-correlation are Δαxx ∈ [ 0 . 304 , 0 . 905 ] and Δαxy ∈ [ 0 . 246 , 1 . 178 ] , respectively. The wide range of singularity spectrum for cross-correlation confirms that the bilateral relation between Stock markets is more complex. The value of σDCCA indicates that all pairs of stock market studied in this time interval belong to cross-correlated processes.

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

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

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

Absorption spectrum analysis based on singular value decomposition for photoisomerization and photodegradation in organic dyes

NASA Astrophysics Data System (ADS)

Kawabe, Yutaka; Yoshikawa, Toshio; Chida, Toshifumi; Tada, Kazuhiro; Kawamoto, Masuki; Fujihara, Takashi; Sassa, Takafumi; Tsutsumi, Naoto

2015-10-01

In order to analyze the spectra of inseparable chemical mixtures, many mathematical methods have been developed to decompose them into the components relevant to species from series of spectral data obtained under different conditions. We formulated a method based on singular value decomposition (SVD) of linear algebra, and applied it to two example systems of organic dyes, being successful in reproducing absorption spectra assignable to cis/trans azocarbazole dyes from the spectral data after photoisomerization and to monomer/dimer of cyanine dyes from those during photodegaradation process. For the example of photoisomerization, polymer films containing the azocarbazole dyes were prepared, which have showed updatable holographic stereogram for real images with high performance. We made continuous monitoring of absorption spectrum after optical excitation and found that their spectral shapes varied slightly after the excitation and during recovery process, of which fact suggested the contribution from a generated photoisomer. Application of the method was successful to identify two spectral components due to trans and cis forms of azocarbazoles. Temporal evolution of their weight factors suggested important roles of long lifetimed cis states in azocarbazole derivatives. We also applied the method to the photodegradation of cyanine dyes doped in DNA-lipid complexes which have shown efficient and durable optical amplification and/or lasing under optical pumping. The same SVD method was successful in the extraction of two spectral components presumably due to monomer and H-type dimer. During the photodegradation process, absorption magnitude gradually decreased due to decomposition of molecules and their decaying rates strongly depended on the spectral components, suggesting that the long persistency of the dyes in DNA-complex related to weak tendency of aggregate formation.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-09-01

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

Interlaminar stress singularities at a straight free edge in composite laminates

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

The feature extraction of "cat-eye" targets based on bi-spectrum

NASA Astrophysics Data System (ADS)

Zhang, Tinghua; Fan, Guihua; Sun, Huayan

2016-10-01

In order to resolve the difficult problem of detection and identification of optical targets in complex background or in long-distance transmission, this paper mainly study the range profiles of "cat-eye" targets using bi-spectrum. For the problems of laser echo signal attenuation serious and low Signal-Noise Ratio (SNR), the multi-pulse laser signal echo signal detection algorithm which is based on high-order cumulant, filter processing and the accumulation of multi-pulse is proposed. This could improve the detection range effectively. In order to extract the stable characteristics of the one-dimensional range profile coming from the cat-eye targets, a method is proposed which extracts the bi-spectrum feature, and uses the singular value decomposition to simplify the calculation. Then, by extracting data samples of different distance, type and incidence angle, verify the stability of the eigenvector and effectiveness extracted by bi-spectrum.

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.

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.

Separability of spatiotemporal spectra of image sequences. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Eckert, Michael P.; Buchsbaum, Gershon; Watson, Andrew B.

1992-01-01

The spatiotemporal power spectrum was calculated of 14 image sequences in order to determine the degree to which the spectra are separable in space and time, and to assess the validity of the commonly used exponential correlation model found in the literature. The spectrum was expanded by a Singular Value Decomposition into a sum of separable terms and an index was defined of spatiotemporal separability as the fraction of the signal energy that can be represented by the first (largest) separable term. All spectra were found to be highly separable with an index of separability above 0.98. The power spectra of the sequences were well fit by a separable model. The power spectrum model corresponds to a product of exponential autocorrelation functions separable in space and time.

Effect of radiance-to-reflectance transformation and atmosphere removal on maximum likelihood classification accuracy of high-dimensional remote sensing data

NASA Technical Reports Server (NTRS)

Hoffbeck, Joseph P.; Landgrebe, David A.

1994-01-01

Many analysis algorithms for high-dimensional remote sensing data require that the remotely sensed radiance spectra be transformed to approximate reflectance to allow comparison with a library of laboratory reflectance spectra. In maximum likelihood classification, however, the remotely sensed spectra are compared to training samples, thus a transformation to reflectance may or may not be helpful. The effect of several radiance-to-reflectance transformations on maximum likelihood classification accuracy is investigated in this paper. We show that the empirical line approach, LOWTRAN7, flat-field correction, single spectrum method, and internal average reflectance are all non-singular affine transformations, and that non-singular affine transformations have no effect on discriminant analysis feature extraction and maximum likelihood classification accuracy. (An affine transformation is a linear transformation with an optional offset.) Since the Atmosphere Removal Program (ATREM) and the log residue method are not affine transformations, experiments with Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data were conducted to determine the effect of these transformations on maximum likelihood classification accuracy. The average classification accuracy of the data transformed by ATREM and the log residue method was slightly less than the accuracy of the original radiance data. Since the radiance-to-reflectance transformations allow direct comparison of remotely sensed spectra with laboratory reflectance spectra, they can be quite useful in labeling the training samples required by maximum likelihood classification, but these transformations have only a slight effect or no effect at all on discriminant analysis and maximum likelihood classification accuracy.

Adaptive filtering and maximum entropy spectra with application to changes in atmospheric angular momentum

NASA Technical Reports Server (NTRS)

Penland, Cecile; Ghil, Michael; Weickmann, Klaus M.

1991-01-01

The spectral resolution and statistical significance of a harmonic analysis obtained by low-order MEM can be improved by subjecting the data to an adaptive filter. This adaptive filter consists of projecting the data onto the leading temporal empirical orthogonal functions obtained from singular spectrum analysis (SSA). The combined SSA-MEM method is applied both to a synthetic time series and a time series of AAM data. The procedure is very effective when the background noise is white and less so when the background noise is red. The latter case obtains in the AAM data. Nevertheless, reliable evidence for intraseasonal and interannual oscillations in AAM is detected. The interannual periods include a quasi-biennial one and an LF one, of 5 years, both related to the El Nino/Southern Oscillation. In the intraseasonal band, separate oscillations of about 48.5 and 51 days are ascertained.

The El Nino/Southern Oscillation and Future Soybean Prices

NASA Technical Reports Server (NTRS)

Keppenne, C.

1993-01-01

Recently, it was shown that the application of a method combining singular spectrum analysis (SSA) and the maximum entropy method to univariate indicators of the coupled ocean-atmosphere El Nino/Southern Oscillation (ENSO) phenomenon can be helpful in determining whether an El Nino (EN) or La Nina (LN) event will occur. SSA - a variant of principal component analysis applied in the time domain - filters out variability unrelated to ENSO and separates the quasi-biennial (QB), two-to-three year variability, from a lower-frequency (LF) four-to-six year EN-LN cycle; the total variance associated with ENSO combines the QB and LF modes. ENSO has been known to affect weather conditions over much of the globe. For example, EN events have been connected with unusually rainy weather over the Central and Western US, while the opposite phases of the oscillation (LN) have been plausibly associated with extreme dry conditions over much of the same geographical area...

Towards a systematic construction of realistic D-brane models on a del Pezzo singularity

NASA Astrophysics Data System (ADS)

Dolan, Matthew J.; Krippendorf, Sven; Quevedo, Fernando

2011-10-01

A systematic approach is followed in order to identify realistic D-brane models at toric del Pezzo singularities. Requiring quark and lepton spectrum and Yukawas from D3 branes and massless hypercharge, we are led to Pati-Salam extensions of the Standard Model. Hierarchies of masses, flavour mixings and control of couplings select higher order del Pezzo singularities, minimising the Higgs sector prefers toric del Pezzos with dP 3 providing the most successful compromise. Then a supersymmetric local string model is presented with the following properties at low energies: (i) the MSSM spectrum plus a local B - L gauge field or additional Higgs fields depending on the breaking pattern, (ii) a realistic hierarchy of quark and lepton masses and (iii) realistic flavour mixing between quark and lepton families with computable CKM and PMNS matrices, and CP violation consistent with observations. In this construction, kinetic terms are diagonal and under calculational control suppressing standard FCNC contributions. Proton decay operators of dimension 4, 5, 6 are suppressed, and gauge couplings can unify depending on the breaking scales from string scales at energies in the range 1012-1016 GeV, consistent with TeV soft-masses from moduli mediated supersymmetry breaking. The GUT scale model corresponds to D3 branes at dP 3 with two copies of the Pati-Salam gauge symmetry SU(4) × SU(2) R × SU(2) L . D-brane instantons generate a non-vanishing μ-term. Right handed sneutrinos can break the B - L symmetry and induce a see-saw mechanism of neutrino masses and R-parity violating operators with observable low-energy implications.

Online Detection of Broken Rotor Bar Fault in Induction Motors by Combining Estimation of Signal Parameters via Min-norm Algorithm and Least Square Method

NASA Astrophysics Data System (ADS)

Wang, Pan-Pan; Yu, Qiang; Hu, Yong-Jun; Miao, Chang-Xin

2017-11-01

Current research in broken rotor bar (BRB) fault detection in induction motors is primarily focused on a high-frequency resolution analysis of the stator current. Compared with a discrete Fourier transformation, the parametric spectrum estimation technique has a higher frequency accuracy and resolution. However, the existing detection methods based on parametric spectrum estimation cannot realize online detection, owing to the large computational cost. To improve the efficiency of BRB fault detection, a new detection method based on the min-norm algorithm and least square estimation is proposed in this paper. First, the stator current is filtered using a band-pass filter and divided into short overlapped data windows. The min-norm algorithm is then applied to determine the frequencies of the fundamental and fault characteristic components with each overlapped data window. Next, based on the frequency values obtained, a model of the fault current signal is constructed. Subsequently, a linear least squares problem solved through singular value decomposition is designed to estimate the amplitudes and phases of the related components. Finally, the proposed method is applied to a simulated current and an actual motor, the results of which indicate that, not only parametric spectrum estimation technique.

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

PubMed

Ye, Jieping; Li, Qi

2005-06-01

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

Exotic singularities and spatially curved loop quantum cosmology

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

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

2011-03-15

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

Redundant single gimbal control moment gyroscope singularity analysis

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Boundary Approximation Methods for Sloving Elliptic Problems on Unbounded Domains

NASA Astrophysics Data System (ADS)

Li, Zi-Cai; Mathon, Rudolf

1990-08-01

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

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

New classification methods on singularity of mechanism

NASA Astrophysics Data System (ADS)

Luo, Jianguo; Han, Jianyou

2010-07-01

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

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

NASA Technical Reports Server (NTRS)

Bedrossian, Nazareth Sarkis

1987-01-01

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

Treatment of singularities in cracked bodies

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Treatment of singularities in cracked bodies

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

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

PubMed

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

2017-01-01

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

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

PubMed Central

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

2017-01-01

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

Synchronization of world economic activity

NASA Astrophysics Data System (ADS)

Groth, Andreas; Ghil, Michael

2017-12-01

Common dynamical properties of business cycle fluctuations are studied in a sample of more than 100 countries that represent economic regions from all around the world. We apply the methodology of multivariate singular spectrum analysis (M-SSA) to identify oscillatory modes and to detect whether these modes are shared by clusters of phase- and frequency-locked oscillators. An extension of the M-SSA approach is introduced to help analyze structural changes in the cluster configuration of synchronization. With this novel technique, we are able to identify a common mode of business cycle activity across our sample, and thus point to the existence of a world business cycle. Superimposed on this mode, we further identify several major events that have markedly influenced the landscape of world economic activity in the postwar era.

Synchronization of world economic activity.

PubMed

Groth, Andreas; Ghil, Michael

2017-12-01

Common dynamical properties of business cycle fluctuations are studied in a sample of more than 100 countries that represent economic regions from all around the world. We apply the methodology of multivariate singular spectrum analysis (M-SSA) to identify oscillatory modes and to detect whether these modes are shared by clusters of phase- and frequency-locked oscillators. An extension of the M-SSA approach is introduced to help analyze structural changes in the cluster configuration of synchronization. With this novel technique, we are able to identify a common mode of business cycle activity across our sample, and thus point to the existence of a world business cycle. Superimposed on this mode, we further identify several major events that have markedly influenced the landscape of world economic activity in the postwar era.

Sensitivity analysis of automatic flight control systems using singular value concepts

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

Singularity perturbed zero dynamics of nonlinear systems

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Variational approach to stability boundary for the Taylor-Goldstein equation

NASA Astrophysics Data System (ADS)

Hirota, Makoto; Morrison, Philip J.

2015-11-01

Linear stability of inviscid stratified shear flow is studied by developing an efficient method for finding neutral (i.e., marginally stable) solutions of the Taylor-Goldstein equation. The classical Miles-Howard criterion states that stratified shear flow is stable if the local Richardson number JR is greater than 1/4 everywhere. In this work, the case of JR > 0 everywhere is considered by assuming strictly monotonic and smooth profiles of the ambient shear flow and density. It is shown that singular neutral modes that are embedded in the continuous spectrum can be found by solving one-parameter families of self-adjoint eigenvalue problems. The unstable ranges of wavenumber are searched for accurately and efficiently by adopting this method in a numerical algorithm. Because the problems are self-adjoint, the variational method can be applied to ascertain the existence of singular neutral modes. For certain shear flow and density profiles, linear stability can be proven by showing the non-existence of a singular neutral mode. New sufficient conditions, extensions of the Rayleigh-Fjortoft stability criterion for unstratified shear flows, are derived in this manner. This work was supported by JSPS Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation # 55053270.

Continuations of the nonlinear Schrödinger equation beyond the singularity

NASA Astrophysics Data System (ADS)

Fibich, G.; Klein, M.

2011-07-01

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

Polymer quantization of the Einstein-Rosen wormhole throat

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

Kunstatter, Gabor; Peltola, Ari; Louko, Jorma

2010-01-15

We present a polymer quantization of spherically symmetric Einstein gravity in which the polymerized variable is the area of the Einstein-Rosen wormhole throat. In the classical polymer theory, the singularity is replaced by a bounce at a radius that depends on the polymerization scale. In the polymer quantum theory, we show numerically that the area spectrum is evenly spaced and in agreement with a Bohr-Sommerfeld semiclassical estimate, and this spectrum is not qualitatively sensitive to issues of factor ordering or boundary conditions except in the lowest few eigenvalues. In the limit of small polymerization scale we recover, within the numericalmore » accuracy, the area spectrum obtained from a Schroedinger quantization of the wormhole throat dynamics. The prospects of recovering from the polymer throat theory a full quantum-corrected spacetime are discussed.« less

Singularity and Nonnormality in the Classification of Compositional Data

USGS Publications Warehouse

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

1998-01-01

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

Integrable mappings and the notion of anticonfinement

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

On the initial singularity problem in rainbow cosmology

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

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

2015-08-01

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

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

NASA Astrophysics Data System (ADS)

Fuchssteiner, Benno; Carillo, Sandra

1989-01-01

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

Singularity-free interpretation of the thermodynamics of supercooled water

NASA Astrophysics Data System (ADS)

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

1996-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-10-01

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

Excitation Spectra in Crystal Plasticity

NASA Astrophysics Data System (ADS)

Ovaska, Markus; Lehtinen, Arttu; Alava, Mikko J.; Laurson, Lasse; Zapperi, Stefano

2017-12-01

Plastically deforming crystals exhibit scale-free fluctuations that are similar to those observed in driven disordered elastic systems close to depinning, but the nature of the yielding critical point is still debated. Here, we study the marginal stability of ensembles of dislocations and compute their excitation spectrum in two and three dimensions. Our results show the presence of a singularity in the distribution of excitation stresses, i.e., the stress needed to make a localized region unstable, that is remarkably similar to the one measured in amorphous plasticity and spin glasses. These results allow us to understand recent observations of extended criticality in bursty crystal plasticity and explain how they originate from the presence of a pseudogap in the excitation spectrum.

Coulomb gap: how a metal film becomes an insulator

PubMed

Butko; DiTusa; Adams

2000-02-14

Electron tunneling measurements of the density of states (DOS) in ultrathin Be films reveal that a correlation gap mediates their insulating behavior. In films with sheet resistance R<5000 Omega the correlation singularity appears as the usual perturbative ln(V) zero bias anomaly (ZBA) in the DOS. As R is increased further, however, the ZBA grows and begins to dominate the DOS spectrum. This evolution continues until a nonperturbative |V| Efros-Shklovskii Coulomb gap spectrum finally emerges in the highest R films. Transport measurements of films which display this gap are well described by a universal variable range hopping law R(T) = (h/2e(2))exp(T0/T)(1/2).

Distinguishing Majorana bound states and Andreev bound states with microwave spectra

NASA Astrophysics Data System (ADS)

Zhang, Zhen-Tao

2018-04-01

Majorana fermions are a fascinating and not yet confirmed quasiparticles in condensed matter physics. Here we propose using microwave spectra to distinguish Majorana bound states (MBSs) from topological trivial Andreev bound states. By numerically calculating the transmission and Zeeman field dependence of the many-body excitation spectrum of a 1D Josephson junction, we find that the two kinds of bound states have distinct responses to variations in the related parameters. Furthermore, the singular behaviors of the MBSs spectrum could be attributed to the robust fractional Josephson coupling and nonlocality of MBSs. Our results provide a feasible method to verify the existence of MBSs and could accelerate its application to topological quantum computation.

Modeling the relationship between photosynthetically active radiation and global horizontal irradiance using singular spectrum analysis

NASA Astrophysics Data System (ADS)

Zempila, Melina-Maria; Taylor, Michael; Bais, Alkiviadis; Kazadzis, Stelios

2016-10-01

We report on the construction of generic models to calculate photosynthetically active radiation (PAR) from global horizontal irradiance (GHI), and vice versa. Our study took place at stations of the Greek UV network (UVNET) and the Hellenic solar energy network (HNSE) with measurements from NILU-UV multi-filter radiometers and CM pyranometers, chosen due to their long (≈1 M record/site) high temporal resolution (≈1 min) record that captures a broad range of atmospheric environments and cloudiness conditions. The uncertainty of the PAR measurements is quantified to be ±6.5% while the uncertainty involved in GHI measurements is up to ≈±7% according to the manufacturer. We show how multi-linear regression and nonlinear neural network (NN) models, trained at a calibration site (Thessaloniki) can be made generic provided that the input-output time series are processed with multi-channel singular spectrum analysis (M-SSA). Without M-SSA, both linear and nonlinear models perform well only locally. M-SSA with 50 time-lags is found to be sufficient for identification of trend, periodic and noise components in aerosol, cloud parameters and irradiance, and to construct regularized noise models of PAR from GHI irradiances. Reconstructed PAR and GHI time series capture ≈95% of the variance of the cross-validated target measurements and have median absolute percentage errors <2%. The intra-site median absolute error of M-SSA processed models were ≈8.2±1.7 W/m2 for PAR and ≈9.2±4.2 W/m2 for GHI. When applying the models trained at Thessaloniki to other stations, the average absolute mean bias between the model estimates and measured values was found to be ≈1.2 W/m2 for PAR and ≈0.8 W/m2 for GHI. For the models, percentage errors are well within the uncertainty of the measurements at all sites. Generic NN models were found to perform marginally better than their linear counterparts.

Pseudorandom binary injection of levitons for electron quantum optics

NASA Astrophysics Data System (ADS)

Glattli, D. C.; Roulleau, P.

2018-03-01

The recent realization of single-electron sources lets us envision performing electron quantum optics experiments, where electrons can be viewed as flying qubits propagating in a ballistic conductor. To date, all electron sources operate in a periodic electron injection mode, leading to energy spectrum singularities in various physical observables which sometimes hide the bare nature of physical effects. To go beyond this, we propose a spread-spectrum approach where electron flying qubits are injected in a nonperiodic manner following a pseudorandom binary bit pattern. Extending the Floquet scattering theory approach from periodic to spread-spectrum drive, the shot noise of pseudorandom binary sequences of single-electron injection can be calculated for leviton and nonleviton sources. Our new approach allows us to disentangle the physics of the manipulated excitations from that of the injection protocol. In particular, the spread-spectrum approach is shown to provide better knowledge of electronic Hong-Ou-Mandel correlations and to clarify the nature of the pulse train coherence and the role of the dynamical orthogonality catastrophe for noninteger charge injection.

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

NASA Astrophysics Data System (ADS)

Suramlishvili, Nugzar; Eggers, Jens; Fontelos, Marco

2014-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-08-01

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

Fully developed turbulence and complex time singularities

NASA Astrophysics Data System (ADS)

Dombre, T.; Gagne, Y.; Hopfinger, E.

The hypothesis of Frisch and Morf (1981), relating intermittent bursts observed in high-pass-filtered turbulent-flow data to complex time singularities in the solution of the Navier-Stokes equations, is tested experimentally. Velocity signals filtered at high-pass frequency 1 kHz and low-pass frequency 6 kHz are recorded for 7 min at sampling frequency 20 kHz in a flow of mean velocity 6.1 m/s, with mesh length d = 7.5 cm, observation point x/d = 40, R sub lambda = 67, dissipation length eta = 0.5 mm, and Kolmogorov frequency fK = about 2 kHz. The results are presented in graphs, and it is shown that the exponential behavior of the energy spectrum settles well before fK, the spectra of individual bursts having exponential behavior and delta(asterisk) values consistent with the Frisch-Morf hypothesis, at least for high-amplitude events.

Evolution of coherence singularities of Schell-model beams.

PubMed

Rodrigo, José A; Alieva, Tatiana

2015-08-01

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

Stochastic subspace identification for operational modal analysis of an arch bridge

NASA Astrophysics Data System (ADS)

Loh, Chin-Hsiung; Chen, Ming-Che; Chao, Shu-Hsien

2012-04-01

In this paer the application of output-only system identification technique, known as Stochastic Subspace Identification (SSI) algorithms, for civil infrastructures is carried out. The ability of covariance driven stochastic subspace identification (SSI-COV) was proved through the analysis of the ambient data of an arch bridge under operational condition. A newly developed signal processing technique, Singular Spectrum analysis (SSA), capable to smooth noisy signals, is adopted for pre-processing the recorded data before the SSI. The conjunction of SSA and SSICOV provides a useful criterion for the system order determination. With the aim of estimating accurate modal parameters of the structure in off-line analysis, a stabilization diagram is constructed by plotting the identified poles of the system with increasing the size of data Hankel matrix. Identification task of a real structure, Guandu Bridge, is carried out to identify the system natural frequencies and mode shapes. The uncertainty of the identified model parameters from output-only measurement of the bridge under operation condition, such as temperature and traffic loading conditions, is discussed.

Drivers and variability of the Chl fluorescence emission spectrum from the leaf through the canopy

NASA Astrophysics Data System (ADS)

Magney, T. S.; Frankenberg, C.; Grossman, K.; Koehler, P.; North, G.; Porcar-Castell, A.; Stutz, J.; Fisher, J.

2017-12-01

Recent advances in the retrieval of solar induced chlorophyll fluorescence (SIF) from remote sensing platforms provide a significant step towards mapping instantaneous plant photosynthesis across space and time. However, our current understanding of the variability and controls on the shape of the chlorophyll fluorescence (ChlF) spectrum is limited. To address these uncertainties, we have developed instrumentation to make highly resolved spectral measurements of SIF from both leaf and canopy scales. At the leaf scale, we simultaneously collected active (PAM) and passive (675-850 nm) fluorescence with photosynthesis across a range of species and conditions; and at the canopy scale, diurnal and seasonal Fraunhofer-based SIF retrievals across the red and far-red spectrum are made at four different flux tower sites (Costa Rica, Iowa (2), and Colorado). From both of these scales we are able to determine (1) the variability in steady-state spectra across species and individuals; and (2) the environmental, functional, and structural controls on SIF. Here we report on the sensitivity of SIF spectra from a singular value decomposition analysis; and present on the mechanisms - pigment concentration, species, non-photochemical and photochemical quenching, and environmental conditions - controlling SIF variability. Further, we will discuss how an improved understanding of leaf-level variability can inform canopy level SIF, and ultimately how such information may enable proper interpretation of satellite retrievals.

Nonnormal operators in physics, a singular-vectors approach: illustration in polarization optics.

PubMed

Tudor, Tiberiu

2016-04-20

The singular-vectors analysis of a general nonnormal operator defined on a finite-dimensional complex vector space is given in the frame of a pure operatorial ("nonmatrix," "coordinate-free") approach, performed in a Dirac language. The general results are applied in the field of polarization optics, where the nonnormal operators are widespread as operators of various polarization devices. Two nonnormal polarization devices representative for the class of nonnormal and even pathological operators-the standard two-layer elliptical ideal polarizer (singular operator) and the three-layer ambidextrous ideal polarizer (singular and defective operator)-are analyzed in detail. It is pointed out that the unitary polar component of the operator exists and preserves, in such pathological case too, its role of converting the input singular basis of the operator in its output singular basis. It is shown that for any nonnormal ideal polarizer a complementary one exists, so that the tandem of their operators uniquely determines their (common) unitary polar component.

Reconstruction of a nonminimal coupling theory with scale-invariant power spectrum

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

Qiu, Taotao, E-mail: qiutt@ntu.edu.tw

2012-06-01

A nonminimal coupling single scalar field theory, when transformed from Jordan frame to Einstein frame, can act like a minimal coupling one. Making use of this property, we investigate how a nonminimal coupling theory with scale-invariant power spectrum could be reconstructed from its minimal coupling counterpart, which can be applied in the early universe. Thanks to the coupling to gravity, the equation of state of our universe for a scale-invariant power spectrum can be relaxed, and the relation between the parameters in the action can be obtained. This approach also provides a means to address the Big-Bang puzzles and anisotropymore » problem in the nonminimal coupling model within Jordan frame. Due to the equivalence between the two frames, one may be able to find models that are free of the horizon, flatness, singularity as well as anisotropy problems.« 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.

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.

Infrared spectroscopic ellipsometry of micrometer-sized SiO2 line gratings

NASA Astrophysics Data System (ADS)

Walder, Cordula; Zellmeier, Matthias; Rappich, Jörg; Ketelsen, Helge; Hinrichs, Karsten

2017-09-01

For the design and process control of periodic nano-structured surfaces spectroscopic ellipsometry is already established in the UV-VIS spectral regime. The objective of this work is to show the feasibility of spectroscopic ellipsometry in the infrared, exemplarily, on micrometer-sized SiO2 line gratings grown on silicon wafers. The grating period ranges from 10 to about 34 μm. The IR-ellipsometric spectra of the gratings exhibit complex changes with structure variations. Especially in the spectral range of the oxide stretching modes, the presence of a Rayleigh singularity can lead to pronounced changes of the spectrum with the sample geometry. The IR-ellipsometric spectra of the gratings are well reproducible by calculations with the RCWA method (Rigorous Coupled Wave Analysis). Therefore, infrared spectroscopic ellipsometry allows the quantitative characterization and process control of micrometer-sized structures.

What is the right formalism to search for resonances?

NASA Astrophysics Data System (ADS)

Mikhasenko, M.; Pilloni, A.; Nys, J.; Albaladejo, M.; Fernández-Ramírez, C.; Jackura, A.; Mathieu, V.; Sherrill, N.; Skwarnicki, T.; Szczepaniak, A. P.

2018-03-01

Hadron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. Hereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B→ ψ π K and B→ \\bar{D}π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.

Singular F(R) cosmology unifying early- and late-time acceleration with matter and radiation domination era

NASA Astrophysics Data System (ADS)

Odintsov, S. D.; Oikonomou, V. K.

2016-06-01

We present some cosmological models which unify the late- and early-time acceleration eras with the radiation and the matter domination era, and we realize the cosmological models by using the theoretical framework of F(R) gravity. Particularly, the first model unifies the late- and early-time acceleration with the matter domination era, and the second model unifies all the evolution eras of our Universe. The two models are described in the same way at early and late times, and only the intermediate stages of the evolution have some differences. Each cosmological model contains two Type IV singularities which are chosen to occur one at the end of the inflationary era and one at the end of the matter domination era. The cosmological models at early times are approximately identical to the R 2 inflation model, so these describe a slow-roll inflationary era which ends when the slow-roll parameters become of order one. The inflationary era is followed by the radiation era and after that the matter domination era follows, which lasts until the second Type IV singularity, and then the late-time acceleration era follows. The models have two appealing features: firstly they produce a nearly scale invariant power spectrum of primordial curvature perturbations and a scalar-to-tensor ratio which are compatible with the most recent observational data and secondly, it seems that the deceleration-acceleration transition is crucially affected by the presence of the second Type IV singularity which occurs at the end of the matter domination era. As we demonstrate, the Hubble horizon at early times shrinks, as expected for an initially accelerating Universe, then during the matter domination era, it expands and finally after the Type IV singularity, the Hubble horizon starts to shrink again, during the late-time acceleration era. Intriguingly enough, the deceleration-acceleration transition, occurs after the second Type IV singularity. In addition, we investigate which F(R) gravity can successfully realize each of the four cosmological epochs.

Modern CACSD using the Robust-Control Toolbox

NASA Technical Reports Server (NTRS)

Chiang, Richard Y.; Safonov, Michael G.

1989-01-01

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

Development of a sensitivity analysis technique for multiloop flight control systems

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

Autonomous strange nonchaotic oscillations in a system of mechanical rotators

NASA Astrophysics Data System (ADS)

Jalnine, Alexey Yu.; Kuznetsov, Sergey P.

2017-05-01

We investigate strange nonchaotic self-oscillations in a dissipative system consisting of three mechanical rotators driven by a constant torque applied to one of them. The external driving is nonoscillatory; the incommensurable frequency ratio in vibrational-rotational dynamics arises due to an irrational ratio of diameters of the rotating elements involved. It is shown that, when losing stable equilibrium, the system can demonstrate two- or three-frequency quasi-periodic, chaotic and strange nonchaotic self-oscillations. The conclusions of the work are confirmed by numerical calculations of Lyapunov exponents, fractal dimensions, spectral analysis, and by special methods of detection of a strange nonchaotic attractor (SNA): phase sensitivity and analysis using rational approximation for the frequency ratio. In particular, SNA possesses a zero value of the largest Lyapunov exponent (and negative values of the other exponents), a capacitive dimension close to 2 and a singular continuous power spectrum. In general, the results of this work shed a new light on the occurrence of strange nonchaotic dynamics.

Chandler wobble: two more large phase jumps revealed

NASA Astrophysics Data System (ADS)

Malkin, Zinovy; Miller, Natalia

2010-12-01

Investigations of the anomalies in the Earth rotation, in particular, the polar motion components, play an important role in our understanding of the processes that drive changes in the Earth's surface, interior, atmosphere, and ocean. This paper is primarily aimed at investigation of the Chandler wobble (CW) at the whole available 163-year interval to search for the major CW amplitude and phase variations. First, the CW signal was extracted from the IERS (International Earth Rotation and Reference Systems Service) Pole coordinates time series using two digital filters: the singular spectrum analysis and Fourier transform. The CW amplitude and phase variations were examined by means of the wavelet transform and Hilbert transform. Results of our analysis have shown that, besides the well-known CW phase jump in the 1920s, two other large phase jumps have been found in the 1850s and 2000s. As in the 1920s, these phase jumps occurred contemporarily with a sharp decrease in the CW amplitude.

Multifractal detrended cross-correlation analysis on gold, crude oil and foreign exchange rate time series

NASA Astrophysics Data System (ADS)

Pal, Mayukha; Madhusudana Rao, P.; Manimaran, P.

2014-12-01

We apply the recently developed multifractal detrended cross-correlation analysis method to investigate the cross-correlation behavior and fractal nature between two non-stationary time series. We analyze the daily return price of gold, West Texas Intermediate and Brent crude oil, foreign exchange rate data, over a period of 18 years. The cross correlation has been measured from the Hurst scaling exponents and the singularity spectrum quantitatively. From the results, the existence of multifractal cross-correlation between all of these time series is found. We also found that the cross correlation between gold and oil prices possess uncorrelated behavior and the remaining bivariate time series possess persistent behavior. It was observed for five bivariate series that the cross-correlation exponents are less than the calculated average generalized Hurst exponents (GHE) for q<0 and greater than GHE when q>0 and for one bivariate series the cross-correlation exponent is greater than GHE for all q values.

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.

Optical study of Dirac fermions and related phonon anomalies in the antiferromagnetic compound CaFeAsF

NASA Astrophysics Data System (ADS)

Xu, B.; Xiao, H.; Gao, B.; Ma, Y. H.; Mu, G.; Marsik, P.; Sheveleva, E.; Lyzwa, F.; Dai, Y. M.; Lobo, R. P. S. M.; Bernhard, C.

2018-05-01

We performed optical studies on CaFeAsF single crystals, a parent compound of the 1111-type iron-based superconductors that undergoes a structural phase transition from tetragonal to orthorhombic at Ts=121 K and a magnetic one to a spin density wave (SDW) state at TN=110 K. In the low-temperature optical conductivity spectrum, after the subtraction of a narrow Drude peak, we observe a pronounced singularity around 300 cm-1 that separates two regions of quasilinear conductivity. We outline that these characteristic absorption features are signatures of Dirac fermions, similar to what was previously reported for the BaFe2As2 system [Z.-G. Chen et al., Phys. Rev. Lett. 119, 096401 (2017), 10.1103/PhysRevLett.119.096401]. In support of this interpretation, we show that for the latter system this singular feature disappears rapidly upon electron and hole doping, as expected if it arises from a van Hove singularity in between two Dirac cones. Finally, we show that one of the infrared-active phonon modes (the Fe-As mode at 250 cm-1) develops a strongly asymmetric line shape in the SDW state and note that this behavior can be explained in terms of a strong coupling with the Dirac fermions.

Hard sphere perturbation theory of dense fluids with singular perturbation

NASA Astrophysics Data System (ADS)

Mon, K. K.

2000-02-01

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

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

NASA Technical Reports Server (NTRS)

Woodward, F. A.

1981-01-01

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

The foreign exchange market: return distributions, multifractality, anomalous multifractality and the Epps effect

NASA Astrophysics Data System (ADS)

Drożdż, Stanisław; Kwapień, Jarosław; Oświȩcimka, Paweł; Rak, Rafał

2010-10-01

We present a systematic study of various statistical characteristics of high-frequency returns from the foreign exchange market. This study is based on six exchange rates forming two triangles: EUR-GBP-USD and GBP-CHF-JPY. It is shown that the exchange rate return fluctuations for all of the pairs considered are well described by the non-extensive statistics in terms of q-Gaussians. There exist some small quantitative variations in the non-extensivity q-parameter values for different exchange rates (which depend also on the time scales studied), and this can be related to the importance of a given exchange rate in the world's currency trade. Temporal correlations organize the series of returns such that they develop the multifractal characteristics for all of the exchange rates, with a varying degree of symmetry of the singularity spectrum f(α), however. The most symmetric spectrum is identified for the GBP/USD. We also form time series of triangular residual returns and find that the distributions of their fluctuations develop disproportionately heavier tails as compared to small fluctuations, which excludes description in terms of q-Gaussians. The multifractal characteristics of these residual returns reveal such anomalous properties as negative singularity exponents and even negative singularity spectra. Such anomalous multifractal measures have so far been considered in the literature in connection with diffusion-limited aggregation and with turbulence. Studying the cross-correlations among different exchange rates, we found that market inefficiency on short time scales leads to the occurrence of the Epps effect on much longer time scales, but comparable to the ones for the stock market. Although the currency market is much more liquid than the stock markets and has a much greater transaction frequency, the building up of correlations takes up to several hours—a duration that does not differ much from what is observed in the stock markets. This may suggest that non-synchronicity of transactions is not the unique source of the observed effect.

Three-dimensional vibrations of cylindrical elastic solids with V-notches and sharp radial cracks

NASA Astrophysics Data System (ADS)

McGee, O. G.; Kim, J. W.

2010-02-01

This paper provides free vibration data for cylindrical elastic solids, specifically thick circular plates and cylinders with V-notches and sharp radial cracks, for which no extensive previously published database is known to exist. Bending moment and shear force singularities are known to exist at the sharp reentrant corner of a thick V-notched plate under transverse vibratory motion, and three-dimensional (3-D) normal and transverse shear stresses are known to exist at the sharp reentrant terminus edge of a V-notched cylindrical elastic solid under 3-D free vibration. A theoretical analysis is done in this work utilizing a variational Ritz procedure including these essential singularity effects. The procedure incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of " edge functions" that explicitly model the 3-D stress singularities which exist along a reentrant terminus edge (i.e., α>180°) of the V-notch. The first set of polynomials guarantees convergence to exact frequencies, as sufficient terms are retained. The second set of edge functions—in addition to representing the corner stress singularities—substantially accelerates the convergence of frequency solutions. This is demonstrated through extensive convergence studies that have been carried out by the investigators. Numerical analysis has been carried out and the results have been given for cylindrical elastic solids with various V-notch angles and depths. The relative depth of the V-notch is defined as (1- c/ a), and the notch angle is defined as (360°- α). For a very small notch angle (1° or less), the notch may be regarded as a "sharp radial crack." Accurate (four significant figure) frequencies are presented for a wide spectrum of notch angles (360°- α), depths (1- c/ a), and thickness ratios ( a/ h for plates and h/ a for cylinders). An extended database of frequencies for completely free thick sectorial, semi-circular, and segmented plates and cylinders are also reported herein as interesting special cases. A generalization of the elasticity-based Ritz analysis and findings applicable here is an arbitrarily shaped V-notched cylindrical solid, being a surface traced out by a family of generatrix, which pass through the circumference of an arbitrarily shaped V-notched directrix curve, r( θ), several of which are described for future investigations and close extensions of this work.

Resonances in Coupled π K - η K Scattering from Quantum Chromodynamics

DOE PAGES

Dudek, Jozef J.; Edwards, Robert G.; Thomas, Christopher E.; ...

2014-10-01

Using first-principles calculation within Quantum Chromodynamics, we are able to reproduce the pattern of experimental strange resonances which appear as complex singularities within coupled πK, ηK scattering amplitudes. We make use of numerical computation within the lattice discretized approach to QCD, extracting the energy dependence of scattering amplitudes through their relation- ship to the discrete spectrum of the theory in a finite-volume, which we map out in unprecedented detail.

Spectral Estimation: An Overdetermined Rational Model Equation Approach.

DTIC Science & Technology

1982-09-15

A-A123 122 SPECTRAL ESTIMATION: AN OVERDETERMINEO RATIONAL MODEL 1/2 EQUATION APPROACH..(U) ARIZONA STATE UNIV TEMPE DEPT OF ELECTRICAL AND COMPUTER...2 0 447,_______ 4. TITLE (mAd Sabile) S. TYPE or REPORT a PEP40D COVERED Spectral Estimation; An Overdeteruined Rational Final Report 9/3 D/8 to...andmmd&t, by uwek 7a5 4 Rational Spectral Estimation, ARMA mo~Ie1, AR model, NMA Mdle, Spectrum, Singular Value Decomposition. Adaptivb Implementatlan

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

PubMed

Herlin, Antoine; Jacquemet, Vincent

2012-05-01

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

A novel finite element analysis of three-dimensional circular crack

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

$$ \\mathcal{N} $$ = 4 superconformal bootstrap of the K 3 CFT

DOE PAGES

Lin, Ying-Hsuan; Shao, Shu-Heng; Simmons-Duffin, David; ...

2017-05-23

We study two-dimensional (4; 4) superconformal eld theories of central charge c = 6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the BPS N = 4 superconformal blocks with c = 6 and bosonic Virasoro conformal blocks with c = 28, and an exact result on the moduli dependence of a certain integrated BPS 4-point function. Nontrivial bounds on the non-BPS spectrum in the K3 CFT are obtained as functions of the CFT moduli, that interpolate between the free orbifold points and singular CFT points. Wemore » observe directly from the CFT perspective the signature of a continuous spectrum above a gap at the singular moduli, and fi nd numerically an upper bound on this gap that is saturated by the A1 N = 4 cigar CFT. We also derive an analytic upper bound on the fi rst nonzero eigenvalue of the scalar Laplacian on K3 in the large volume regime, that depends on the K3 moduli data. As two byproducts, we find an exact equivalence between a class of BPS N = 2 superconformal blocks and Virasoro conformal blocks in two dimensions, and an upper bound on the four-point functions of operators of sufficiently low scaling dimension in three and four dimensional CFTs.« less

$$ \\mathcal{N} $$ = 4 superconformal bootstrap of the K 3 CFT

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

Lin, Ying-Hsuan; Shao, Shu-Heng; Simmons-Duffin, David

We study two-dimensional (4; 4) superconformal eld theories of central charge c = 6, corresponding to nonlinear sigma models on K3 surfaces, using the superconformal bootstrap. This is made possible through a surprising relation between the BPS N = 4 superconformal blocks with c = 6 and bosonic Virasoro conformal blocks with c = 28, and an exact result on the moduli dependence of a certain integrated BPS 4-point function. Nontrivial bounds on the non-BPS spectrum in the K3 CFT are obtained as functions of the CFT moduli, that interpolate between the free orbifold points and singular CFT points. Wemore » observe directly from the CFT perspective the signature of a continuous spectrum above a gap at the singular moduli, and fi nd numerically an upper bound on this gap that is saturated by the A1 N = 4 cigar CFT. We also derive an analytic upper bound on the fi rst nonzero eigenvalue of the scalar Laplacian on K3 in the large volume regime, that depends on the K3 moduli data. As two byproducts, we find an exact equivalence between a class of BPS N = 2 superconformal blocks and Virasoro conformal blocks in two dimensions, and an upper bound on the four-point functions of operators of sufficiently low scaling dimension in three and four dimensional CFTs.« less

Linear, multivariable robust control with a mu perspective

NASA Technical Reports Server (NTRS)

Packard, Andy; Doyle, John; Balas, Gary

1993-01-01

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

Multifractality and Network Analysis of Phase Transition

PubMed Central

Li, Wei; Yang, Chunbin; Han, Jihui; Su, Zhu; Zou, Yijiang

2017-01-01

Many models and real complex systems possess critical thresholds at which the systems shift dramatically from one sate to another. The discovery of early-warnings in the vicinity of critical points are of great importance to estimate how far the systems are away from the critical states. Multifractal Detrended Fluctuation analysis (MF-DFA) and visibility graph method have been employed to investigate the multifractal and geometrical properties of the magnetization time series of the two-dimensional Ising model. Multifractality of the time series near the critical point has been uncovered from the generalized Hurst exponents and singularity spectrum. Both long-term correlation and broad probability density function are identified to be the sources of multifractality. Heterogeneous nature of the networks constructed from magnetization time series have validated the fractal properties. Evolution of the topological quantities of the visibility graph, along with the variation of multifractality, serve as new early-warnings of phase transition. Those methods and results may provide new insights about the analysis of phase transition problems and can be used as early-warnings for a variety of complex systems. PMID:28107414

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

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

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

2013-02-15

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

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

NASA Technical Reports Server (NTRS)

Paduano, James D.; Downing, David R.

1987-01-01

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

New Developments in the Theory of HTSC [High Temperature Superconductors

DOE R&D Accomplishments Database

Abrikosov, A.A.

1994-09-01

The superconductor is supposed to consist of alternating layers of two kinds: (1) layers with an attractive electron interaction and an effective mass of usual magnitude, (2) layers without interaction and with a large effective mass. The overlap between the layers is assumed to be small, its energy, t, being much less than {Delta}. It is shown, that such a model explains the most peculiar property found in experiments on electronic Raman light scattering in BSCCO 2212: different threshold values for the Raman satellite measured at two different polarizations of the incident and scattered light. The tunneling conductance G(V)= dJ/dV is analyzed for the same model. In order to fit the qualitative features of experimental data, it is assumed that the tunneling probability to the normal layers is much less, than to the superconducting layers. The conductance is calculated for the case t{much_lt}{Delta}. A brief analysis is given for the case t{approximately}{Delta}, which proves that such an assumption definitely contradicts the experimental data for BSCCO. The possible nature of the electronic states in the normal layers is discussed. In connection with the experimental discovery (angle resolved photoemission spectroscopy, ARPES) of the extended saddle point singularities in the electron spectrum of a variety of HTSC consequences are derived for T{sub c} and {Delta} in a simple model. A large enhancement of superconductivity is possible if the singularity has a sufficient extension and is located close to the Fermi energy. In order to explain the anisotropy of the energy gap, observed in ARPES experiments, on the basis of the "extended saddle point singularities" an assumption is done that the Coulomb interactions are weakly screened, i.e. the Debye screening radius is much larger than the lattice period; this makes the electron interaction long ranged (E-L model).

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

NASA Astrophysics Data System (ADS)

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

1999-07-01

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

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

NASA Astrophysics Data System (ADS)

Paolino, Armando; Pizzi, Marco

2008-01-01

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

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

NASA Astrophysics Data System (ADS)

Yamada, Katsuhiko; Jikuya, Ichiro

2014-09-01

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

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

PubMed Central

2011-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-02-01

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

Singularly Perturbed Lie Bracket Approximation

DOE PAGES

Durr, Hans-Bernd; Krstic, Miroslav; Scheinker, Alexander; ...

2015-03-27

Here, we consider the interconnection of two dynamical systems where one has an input-affine vector field. We show that by employing a singular perturbation analysis and the Lie bracket approximation technique, the stability of the overall system can be analyzed by regarding the stability properties of two reduced, uncoupled systems.

Higher order supersymmetric truncated oscillators

NASA Astrophysics Data System (ADS)

Fernández C., David J.; Morales-Salgado, Vicente Said

2018-01-01

We study the supersymmetric partners of the harmonic oscillator with an infinite potential barrier at the origin and obtain the conditions under which it is possible to add levels to the energy spectrum of these systems. It is found that instead of the usual rule for non-singular potentials, where the order of the transformation corresponds to the maximum number of levels which can be added, now it is the integer part of half the order of the transformation which gives the maximum number of levels to be created.

What is the right formalism to search for resonances?

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

Mikhasenko, M.; Pilloni, A.; Nys, J.

Hmore » adron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. ereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B → ψ π K and B → D ¯ π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.« less

What is the right formalism to search for resonances?

DOE PAGES

Mikhasenko, M.; Pilloni, A.; Nys, J.; ...

2018-03-17

Hmore » adron decay chains constitute one of the main sources of information on the QCD spectrum. We discuss the differences between several partial wave analysis formalisms used in the literature to build the amplitudes. We match the helicity amplitudes to the covariant tensor basis. ereby, we pay attention to the analytical properties of the amplitudes and separate singularities of kinematical and dynamical nature. We study the analytical properties of the spin-orbit (LS) formalism, and some of the covariant tensor approaches. In particular, we explicitly build the amplitudes for the B → ψ π K and B → D ¯ π π decays, and show that the energy dependence of the covariant approach is model dependent. We also show that the usual recursive construction of covariant tensors explicitly violates crossing symmetry, which would lead to different resonance parameters extracted from scattering and decay processes.« less

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

NASA Astrophysics Data System (ADS)

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

2006-10-01

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

Computational singular perturbation analysis of stochastic chemical systems with stiffness

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Nonlinear zero-sum differential game analysis by singular perturbation methods

NASA Technical Reports Server (NTRS)

Sinar, J.; Farber, N.

1982-01-01

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

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.

Generalization of helicoidal beams for short pulses.

PubMed

Thomas, Jean-Louis; Brunet, Thomas; Coulouvrat, François

2010-01-01

A generalization to the transient regime is developed for waves with a phase singularity of the screw type. These singular waves are commonly called vortices for all kind of waves as, for instance, optical vortex or acoustical vortex. We generalize the definition of vortices to get an azimuthal velocity invariant for all the frequency components contained in the broad spectrum of a short pulse. This generalization leads to a modification of the orbital angular momentum definition. Another generalization is introduced by considering helicoidal waves with a finite number of turns. We demonstrate that, in this last case, the topological charge is no longer an integer. This provides a physical interpretation to vortices of fractional charge that are involved here to take into account the diffraction occurring at both tips of the now finite helical wave front. We show that shortening the pulse implies an angular localization of the wave energy and, as a consequence, a spreading of the angular momentum amplitude due to the uncertainty principle.

Gravitational radiation from a cylindrical naked singularity

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

Nakao, Ken-ichi; Morisawa, Yoshiyuki

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

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.

Recurrence quantity analysis based on singular value decomposition

NASA Astrophysics Data System (ADS)

Bian, Songhan; Shang, Pengjian

2017-05-01

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

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.

Oscillatory singular integrals and harmonic analysis on nilpotent groups

PubMed Central

Ricci, F.; Stein, E. M.

1986-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2002-05-01

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

Strong core hole in resonant inelastic x-ray scattering (RIXS)

NASA Astrophysics Data System (ADS)

Markiewicz, Robert; Rehr, John; Bansil, Arun

2014-03-01

We apply a lattice version of Mahan, Nozières, and de Dominicis theory1 to RIXS calculations to understand the role of the core hole. The model reproduces the decomposition of the RIXS spectrum into well- and poorly-screened components. While the calculation can reproduce the full multiband spectrum, single pair excitations contribute the dominant part to the RIXS spectrum, and they can be described as the dynamic structure function S(q , ω) dressed by matrix element effects. We find evidence for an edge singularity at the RIXS threshold, similar to that found in x-ray absorption. We will discuss comparisons with long core hole lifetime calculations, and extensions to a system with antiferromagnetic order. 1. G.D. Mahan, Phys. Rev. 163, 612 (1967); P. Nozières and C.T. De Dominicis, ibid. 178, 1097 (1969). Supported by DOE Grants DE-FG02-07ER46352 and DE-FG03-97ER45623 and facilitated by the DOE CMCSN, under grant number DE-SC0007091.

A rapid local singularity analysis algorithm with applications

NASA Astrophysics Data System (ADS)

Chen, Zhijun; Cheng, Qiuming; Agterberg, Frits

2015-04-01

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

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

NASA Astrophysics Data System (ADS)

Liu, Rong; Chen, Xue; Ding, Zijing

2018-01-01

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

Caustic Singularities Of High-Gain, Dual-Shaped Reflectors

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

The Zeldovich & Adhesion approximations and applications to the local universe

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Singularity detection in FOG-based pavement data by wavelet transform

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

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

NASA Astrophysics Data System (ADS)

Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya

2016-12-01

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

Theoretical aspects of fracture mechanics

NASA Astrophysics Data System (ADS)

Atkinson, C.; Craster, R. V.

1995-03-01

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

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).

Nonlinear multivariate and time series analysis by neural network methods

NASA Astrophysics Data System (ADS)

Hsieh, William W.

2004-03-01

Methods in multivariate statistical analysis are essential for working with large amounts of geophysical data, data from observational arrays, from satellites, or from numerical model output. In classical multivariate statistical analysis, there is a hierarchy of methods, starting with linear regression at the base, followed by principal component analysis (PCA) and finally canonical correlation analysis (CCA). A multivariate time series method, the singular spectrum analysis (SSA), has been a fruitful extension of the PCA technique. The common drawback of these classical methods is that only linear structures can be correctly extracted from the data. Since the late 1980s, neural network methods have become popular for performing nonlinear regression and classification. More recently, neural network methods have been extended to perform nonlinear PCA (NLPCA), nonlinear CCA (NLCCA), and nonlinear SSA (NLSSA). This paper presents a unified view of the NLPCA, NLCCA, and NLSSA techniques and their applications to various data sets of the atmosphere and the ocean (especially for the El Niño-Southern Oscillation and the stratospheric quasi-biennial oscillation). These data sets reveal that the linear methods are often too simplistic to describe real-world systems, with a tendency to scatter a single oscillatory phenomenon into numerous unphysical modes or higher harmonics, which can be largely alleviated in the new nonlinear paradigm.

Genetic aspects of autism spectrum disorders: insights from animal models

PubMed Central

Banerjee, Swati; Riordan, Maeveen; Bhat, Manzoor A.

2014-01-01

Autism spectrum disorders (ASDs) are a complex neurodevelopmental disorder that display a triad of core behavioral deficits including restricted interests, often accompanied by repetitive behavior, deficits in language and communication, and an inability to engage in reciprocal social interactions. ASD is among the most heritable disorders but is not a simple disorder with a singular pathology and has a rather complex etiology. It is interesting to note that perturbations in synaptic growth, development, and stability underlie a variety of neuropsychiatric disorders, including ASD, schizophrenia, epilepsy, and intellectual disability. Biological characterization of an increasing repertoire of synaptic mutants in various model organisms indicates synaptic dysfunction as causal in the pathophysiology of ASD. Our understanding of the genes and genetic pathways that contribute toward the formation, stabilization, and maintenance of functional synapses coupled with an in-depth phenotypic analysis of the cellular and behavioral characteristics is therefore essential to unraveling the pathogenesis of these disorders. In this review, we discuss the genetic aspects of ASD emphasizing on the well conserved set of genes and genetic pathways implicated in this disorder, many of which contribute to synapse assembly and maintenance across species. We also review how fundamental research using animal models is providing key insights into the various facets of human ASD. PMID:24605088

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

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

A tool to automatically analyze electromagnetic tracking data from high dose rate brachytherapy of breast cancer patients.

PubMed

Götz, Th I; Lahmer, G; Strnad, V; Bert, Ch; Hensel, B; Tomé, A M; Lang, E W

2017-01-01

During High Dose Rate Brachytherapy (HDR-BT) the spatial position of the radiation source inside catheters implanted into a female breast is determined via electromagnetic tracking (EMT). Dwell positions and dwell times of the radiation source are established, relative to the patient's anatomy, from an initial X-ray-CT-image. During the irradiation treatment, catheter displacements can occur due to patient movements. The current study develops an automatic analysis tool of EMT data sets recorded with a solenoid sensor to assure concordance of the source movement with the treatment plan. The tool combines machine learning techniques such as multi-dimensional scaling (MDS), ensemble empirical mode decomposition (EEMD), singular spectrum analysis (SSA) and particle filter (PF) to precisely detect and quantify any mismatch between the treatment plan and actual EMT measurements. We demonstrate that movement artifacts as well as technical signal distortions can be removed automatically and reliably, resulting in artifact-free reconstructed signals. This is a prerequisite for a highly accurate determination of any deviations of dwell positions from the treatment plan.

A tool to automatically analyze electromagnetic tracking data from high dose rate brachytherapy of breast cancer patients

PubMed Central

Lahmer, G.; Strnad, V.; Bert, Ch.; Hensel, B.; Tomé, A. M.; Lang, E. W.

2017-01-01

During High Dose Rate Brachytherapy (HDR-BT) the spatial position of the radiation source inside catheters implanted into a female breast is determined via electromagnetic tracking (EMT). Dwell positions and dwell times of the radiation source are established, relative to the patient’s anatomy, from an initial X-ray-CT-image. During the irradiation treatment, catheter displacements can occur due to patient movements. The current study develops an automatic analysis tool of EMT data sets recorded with a solenoid sensor to assure concordance of the source movement with the treatment plan. The tool combines machine learning techniques such as multi-dimensional scaling (MDS), ensemble empirical mode decomposition (EEMD), singular spectrum analysis (SSA) and particle filter (PF) to precisely detect and quantify any mismatch between the treatment plan and actual EMT measurements. We demonstrate that movement artifacts as well as technical signal distortions can be removed automatically and reliably, resulting in artifact-free reconstructed signals. This is a prerequisite for a highly accurate determination of any deviations of dwell positions from the treatment plan. PMID:28934238

Computational singular perturbation analysis of stochastic chemical systems with stiffness

DOE PAGES

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

2017-01-25

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

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

PubMed

Kisdi, Éva

2015-04-01

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

Singularities in Dromo formulation. Analysis of deep flybys

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

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

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

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

PubMed Central

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

2010-01-01

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

Collapsing vortex filaments and the spectrum of quantum turbulence

NASA Astrophysics Data System (ADS)

Andryushchenko, V. A.; Nemirovskii, S. K.

2017-01-01

The method of correlation functions and the method of quantum vortex configurations are used to calculate the energy spectrum of a three-dimensional velocity field that is induced by collapsing (immediately before reconnection) vortex filaments. The formulation of this problem is motivated by the idea of modeling classical turbulence by a set of chaotic quantized vortex filaments. Among the various arguments that support the idea of quasi-classical behavior for quantum turbulence, the most persuasive is probably the resulting Kolmogorov energy spectrum resembling E ( k ) ∝ k - 5 / 3 that was obtained in a number of numerical studies. Another goal is associated with an important and intensely studied theme that relates to the role of hydrodynamic collapse in the formation of turbulence spectra. Calculations have demonstrated that vortex filaments create a velocity field at the moment of contact, which has a singularity. This configuration of vortex filaments generates the spectrum E(k), which bears the resemblance to the Kolmogorov law. A possible cause for this observation is discussed, as well as the likely reasons behind any deviations. The obtained results are discussed from the perspective of both classical and quantum turbulence.

Finite-temperature spin dynamics in a perturbed quantum critical Ising chain with an E₈ symmetry.

PubMed

Wu, Jianda; Kormos, Márton; Si, Qimiao

2014-12-12

A spectrum exhibiting E₈ symmetry is expected to arise when a small longitudinal field is introduced in the transverse-field Ising chain at its quantum critical point. Evidence for this spectrum has recently come from neutron scattering measurements in cobalt niobate, a quasi-one-dimensional Ising ferromagnet. Unlike its zero-temperature counterpart, the finite-temperature dynamics of the model has not yet been determined. We study the dynamical spin structure factor of the model at low frequencies and nonzero temperatures, using the form factor method. Its frequency dependence is singular, but differs from the diffusion form. The temperature dependence of the nuclear magnetic resonance (NMR) relaxation rate has an activated form, whose prefactor we also determine. We propose NMR experiments as a means to further test the applicability of the E₈ description for CoNb₂O₆.

Interplay of Collective Excitations in Quantum Well Intersubband Resonances

NASA Technical Reports Server (NTRS)

Li, Jian-Zhong; Ning, C. Z.

2003-01-01

Intersubband resonances in a semiconductor quantum well (QW) display some of the most fascinating features involving various collective excitations such as Fermi-edge singularity (FES) and intersubband plasmon (ISP). Using a density matrix approach, we treated many-body effects such as depolarization, vertex correction, and self-energy consistently for a two-subband system. We found a systematic change in resonance spectra from FES-dominated to ISP-dominated features, as QW- width or electron density is varied. Such an interplay between FES and ISP significantly changes both line shape and peak position of the absorption spectrum. In particular, we found that a cancellation of FES and ISP undresses the resonant responses and recovers the single-particle features of absorption for semiconductors with a strong nonparabolicity such as InAs, leading to a dramatic broadening of the absorption spectrum.

Mass quantization of the Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Vaz, Cenalo; Witten, Louis

1999-07-01

We examine the Wheeler-DeWitt equation for a static, eternal Schwarzschild black hole in Kuchař-Brown variables and obtain its energy eigenstates. Consistent solutions vanish in the exterior of the Kruskal manifold and are nonvanishing only in the interior. The system is reminiscent of a particle in a box. States of definite parity avoid the singular geometry by vanishing at the origin. These definite parity states admit a discrete energy spectrum, depending on one quantum number which determines the Arnowitt-Deser-Misner mass of the black hole according to a relation conjectured long ago by Bekenstein M~nMp. If attention is restricted only to these quantized energy states, a black hole is described not only by its mass but also by its parity. States of indefinite parity do not admit a quantized mass spectrum.

Anomalous symmetry breaking in classical two-dimensional diffusion of coherent atoms

NASA Astrophysics Data System (ADS)

Pugatch, Rami; Bhattacharyya, Dipankar; Amir, Ariel; Sagi, Yoav; Davidson, Nir

2014-03-01

The electromagnetically induced transparency (EIT) spectrum of atoms diffusing in and out of a narrow beam is measured and shown to manifest the two-dimensional δ-function anomaly in a classical setting. In the limit of small-area beams, the EIT line shape is independent of power, and equal to the renormalized local density of states of a free particle Hamiltonian. The measured spectra for different powers and beam sizes collapses to a single universal curve with a characteristic logarithmic Van Hove singularity close to resonance.

Massive gravity and the suppression of anisotropies and gravitational waves in a matter-dominated contracting universe

NASA Astrophysics Data System (ADS)

Lin, Chunshan; Quintin, Jerome; Brandenberger, Robert H.

2018-01-01

We consider a modified gravity model with a massive graviton, but which nevertheless only propagates two gravitational degrees of freedom and which is free of ghosts. We show that non-singular bouncing cosmological background solutions can be generated. In addition, the mass term for the graviton prevents anisotropies from blowing up in the contracting phase and also suppresses the spectrum of gravitational waves compared to that of the scalar cosmological perturbations. This addresses two of the main problems of the matter bounce scenario.

Analysis of the Fisher solution

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Shoom, Andrey A.

2010-01-01

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

Analysis of the Fisher solution

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

Abdolrahimi, Shohreh; Shoom, Andrey A.

2010-01-15

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

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.

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

PubMed Central

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

2013-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Inelastic losses in X-ray absorption theory

NASA Astrophysics Data System (ADS)

Campbell, Luke Whalin

There is a surprising lack of many body effects observed in XAS (X-ray Absorption Spectroscopy) experiments. While collective excitations and other satellite effects account for between 20% and 40% of the spectral weight of the core hole and photoelectron excitation spectrum, the only commonly observed many body effect is a relatively structureless amplitude reduction to the fine structure, typically no more than a 10% effect. As a result, many particle effects are typically neglected in the XAS codes used to predict and interpret modern experiments. To compensate, the amplitude reduction factor is simply fitted to experimental data. In this work, a quasi-boson model is developed to treat the case of XAS, when the system has both a photoelectron and a core hole. We find that there is a strong interference between the extrinsic and intrinsic losses. The interference reduces the excitation amplitudes at low energies where the core hole and photo electron induced excitations tend to cancel. At high energies, the interference vanishes, and the theory reduces to the sudden approximation. The x-ray absorption spectrum including many-body excitations is represented by a convolution of the one-electron absorption spectrum with an energy dependent spectral function. The latter has an asymmetric quasiparticle peak and broad satellite structure. The net result is a phasor sum, which yields the many body amplitude reduction and phase shift of the fine structure oscillations (EXAFS), and possibly additional satellite structure. Calculations for several cases of interest are found to be in reasonable agreement with experiment. Edge singularity effects and deviations from the final state rule arising from this theory are also discussed. The ab initio XAS code FEFF has been extended for calculations of the many body amplitude reduction and phase shift in x-ray spectroscopies. A new broadened plasmon pole self energy is added. The dipole matrix elements are modified to include a projection operator to calculate deviations from the final state rule and edge singularities.

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

NASA Technical Reports Server (NTRS)

Adams, Richard J.

1993-01-01

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

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

NASA Astrophysics Data System (ADS)

Ng, C. S.; Bhattacharjee, A.

1996-08-01

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

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

PubMed

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

2015-06-01

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

Structure and propagation of supersonic singularities from helicoidal sources

NASA Technical Reports Server (NTRS)

Myers, M. K.; Farassat, F.

1987-01-01

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

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

NASA Astrophysics Data System (ADS)

Ivanov, Victor; Osetrov, Evgenii

2018-02-01

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

Renormalized asymptotic enumeration of Feynman diagrams

NASA Astrophysics Data System (ADS)

Borinsky, Michael

2017-10-01

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

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

Ghatak, Ananya, E-mail: gananya04@gmail.com; Mandal, Raka Dona Ray, E-mail: rakad.ray@gmail.com; Mandal, Bhabani Prasad, E-mail: bhabani.mandal@gmail.com

We complexify a 1-d potential V(x)=V{sub 0}cosh{sup 2}μ(tanh[(x−μd)/d]+tanh(μ)){sup 2} which exhibits bound, reflecting and free states to study various properties of a non-Hermitian system. This potential turns out a PT-symmetric non-Hermitian potential when one of the parameters (μ,d) becomes imaginary. For the case of μ→iμ, we have an entire real bound state spectrum. Explicit scattering states are constructed to show reciprocity at certain discrete values of energy even though the potential is not parity symmetric. Coexistence of deep energy minima of transmissivity with the multiple spectral singularities (MSS) is observed. We further show that this potential becomes invisible from themore » left (or right) at certain discrete energies. The penetrating states in the other case (d→id) are always reciprocal even though it is PT-invariant and no spectral singularity (SS) is present in this case. The presence of MSS and reflectionlessness is also discussed for the free states in the later case. -- Highlights: •Existence of multiple spectral singularities (MSS) in PT-symmetric non-Hermitian system is shown. •Reciprocity is restored at discrete positive energies even for parity non-invariant complex system. •Co-existence of MSS with deep energy minima of transitivity is obtained. •Possibilities of both unidirectional and bidirectional invisibility are explored for a non-Hermitian system. •Penetrating states are shown to be reciprocal for all energies for PT-symmetric system.« less

[Study on Application of NIR Spectral Information Screening in Identification of Maca Origin].

PubMed

Wang, Yuan-zhong; Zhao, Yan-li; Zhang, Ji; Jin, Hang

2016-02-01

Medicinal and edible plant Maca is rich in various nutrients and owns great medicinal value. Based on near infrared diffuse reflectance spectra, 139 Maca samples collected from Peru and Yunnan were used to identify their geographical origins. Multiplication signal correction (MSC) coupled with second derivative (SD) and Norris derivative filter (ND) was employed in spectral pretreatment. Spectrum range (7,500-4,061 cm⁻¹) was chosen by spectrum standard deviation. Combined with principal component analysis-mahalanobis distance (PCA-MD), the appropriate number of principal components was selected as 5. Based on the spectrum range and the number of principal components selected, two abnormal samples were eliminated by modular group iterative singular sample diagnosis method. Then, four methods were used to filter spectral variable information, competitive adaptive reweighted sampling (CARS), monte carlo-uninformative variable elimination (MC-UVE), genetic algorithm (GA) and subwindow permutation analysis (SPA). The spectral variable information filtered was evaluated by model population analysis (MPA). The results showed that RMSECV(SPA) > RMSECV(CARS) > RMSECV(MC-UVE) > RMSECV(GA), were 2. 14, 2. 05, 2. 02, and 1. 98, and the spectral variables were 250, 240, 250 and 70, respectively. According to the spectral variable filtered, partial least squares discriminant analysis (PLS-DA) was used to build the model, with random selection of 97 samples as training set, and the other 40 samples as validation set. The results showed that, R²: GA > MC-UVE > CARS > SPA, RMSEC and RMSEP: GA < MC-UVE < CARS

A problem with inverse time for a singularly perturbed integro-differential equation with diagonal degeneration of the kernel of high order

NASA Astrophysics Data System (ADS)

Bobodzhanov, A. A.; Safonov, V. F.

2016-04-01

We consider an algorithm for constructing asymptotic solutions regularized in the sense of Lomov (see [1], [2]). We show that such problems can be reduced to integro-differential equations with inverse time. But in contrast to known papers devoted to this topic (see, for example, [3]), in this paper we study a fundamentally new case, which is characterized by the absence, in the differential part, of a linear operator that isolates, in the asymptotics of the solution, constituents described by boundary functions and by the fact that the integral operator has kernel with diagonal degeneration of high order. Furthermore, the spectrum of the regularization operator A(t) (see below) may contain purely imaginary eigenvalues, which causes difficulties in the application of the methods of construction of asymptotic solutions proposed in the monograph [3]. Based on an analysis of the principal term of the asymptotics, we isolate a class of inhomogeneities and initial data for which the exact solution of the original problem tends to the limit solution (as \\varepsilon\\to+0) on the entire time interval under consideration, also including a boundary-layer zone (that is, we solve the so-called initialization problem). The paper is of a theoretical nature and is designed to lead to a greater understanding of the problems in the theory of singular perturbations. There may be applications in various applied areas where models described by integro-differential equations are used (for example, in elasticity theory, the theory of electrical circuits, and so on).

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

PubMed

Halburd, R G

2017-05-01

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

A new family of N dimensional superintegrable double singular oscillators and quadratic algebra Q(3) ⨁ so(n) ⨁ so(N-n)

NASA Astrophysics Data System (ADS)

Fazlul Hoque, Md; Marquette, Ian; Zhang, Yao-Zhong

2015-11-01

We introduce a new family of N dimensional quantum superintegrable models consisting of double singular oscillators of type (n, N-n). The special cases (2,2) and (4,4) have previously been identified as the duals of 3- and 5-dimensional deformed Kepler-Coulomb systems with u(1) and su(2) monopoles, respectively. The models are multiseparable and their wave functions are obtained in (n, N-n) double-hyperspherical coordinates. We obtain the integrals of motion and construct the finitely generated polynomial algebra that is the direct sum of a quadratic algebra Q(3) involving three generators, so(n), so(N-n) (i.e. Q(3) ⨁ so(n) ⨁ so(N-n)). The structure constants of the quadratic algebra itself involve the Casimir operators of the two Lie algebras so(n) and so(N-n). Moreover, we obtain the finite dimensional unitary representations (unirreps) of the quadratic algebra and present an algebraic derivation of the degenerate energy spectrum of the superintegrable model.

An improved pulse sequence and inversion algorithm of T2 spectrum

NASA Astrophysics Data System (ADS)

Ge, Xinmin; Chen, Hua; Fan, Yiren; Liu, Juntao; Cai, Jianchao; Liu, Jianyu

2017-03-01

The nuclear magnetic resonance transversal relaxation time is widely applied in geological prospecting, both in laboratory and downhole environments. However, current methods used for data acquisition and inversion should be reformed to characterize geological samples with complicated relaxation components and pore size distributions, such as samples of tight oil, gas shale, and carbonate. We present an improved pulse sequence to collect transversal relaxation signals based on the CPMG (Carr, Purcell, Meiboom, and Gill) pulse sequence. The echo spacing is not constant but varies in different windows, depending on prior knowledge or customer requirements. We use the entropy based truncated singular value decomposition (TSVD) to compress the ill-posed matrix and discard small singular values which cause the inversion instability. A hybrid algorithm combining the iterative TSVD and a simultaneous iterative reconstruction technique is implemented to reach the global convergence and stability of the inversion. Numerical simulations indicate that the improved pulse sequence leads to the same result as CPMG, but with lower echo numbers and computational time. The proposed method is a promising technique for geophysical prospecting and other related fields in future.

High doping effect on the thermoelectric properties of p-type lead telluride

NASA Astrophysics Data System (ADS)

Dmitriev, A. V.

2018-04-01

We study theoretically the effect of heavy doping on the thermoelectric properties of p-type PbTe in the acceptor doping interval of 5 × 1019 to 4 × 1020 cm-3 and in the temperature range of 300 to 900 K. In our calculations, a three-band model of the PbTe electron energy spectrum is used that takes into account not only the light electron and hole bands but also the heavy-hole band. This so-called Σ-band plays an important role in the emergence of the figure-of-merit increase in this material at heavy acceptor doping. The calculated thermoelectric characteristics appear to be sensitive to the doping level. An increase in the figure-of-merit up to ZT ≈ 1.3 at 900 K was found at the doping level of 2 × 1020 cm-3. The maximum of ZT on the temperature axis is situated close to the temperature at which the light hole and heavy hole band edges coincide and hence, a prominent density-of-states singularity appears in the valence band, and the Fermi level lies near this singularity.

Eigenvector dynamics: General theory and some applications

NASA Astrophysics Data System (ADS)

Allez, Romain; Bouchaud, Jean-Philippe

2012-10-01

We propose a general framework to study the stability of the subspace spanned by P consecutive eigenvectors of a generic symmetric matrix H0 when a small perturbation is added. This problem is relevant in various contexts, including quantum dissipation (H0 is then the Hamiltonian) and financial risk control (in which case H0 is the assets' return covariance matrix). We argue that the problem can be formulated in terms of the singular values of an overlap matrix, which allows one to define an overlap distance. We specialize our results for the case of a Gaussian orthogonal H0, for which the full spectrum of singular values can be explicitly computed. We also consider the case when H0 is a covariance matrix and illustrate the usefulness of our results using financial data. The special case where the top eigenvalue is much larger than all the other ones can be investigated in full detail. In particular, the dynamics of the angle made by the top eigenvector and its true direction defines an interesting class of random processes.

Polynomials for crystal frameworks and the rigid unit mode spectrum

PubMed Central

Power, S. C.

2014-01-01

To each discrete translationally periodic bar-joint framework in , we associate a matrix-valued function defined on the d-torus. The rigid unit mode (RUM) spectrum of is defined in terms of the multi-phases of phase-periodic infinitesimal flexes and is shown to correspond to the singular points of the function and also to the set of wavevectors of harmonic excitations which have vanishing energy in the long wavelength limit. To a crystal framework in Maxwell counting equilibrium, which corresponds to being square, the determinant of gives rise to a unique multi-variable polynomial . For ideal zeolites, the algebraic variety of zeros of on the d-torus coincides with the RUM spectrum. The matrix function is related to other aspects of idealized framework rigidity and flexibility, and in particular leads to an explicit formula for the number of supercell-periodic floppy modes. In the case of certain zeolite frameworks in dimensions two and three, direct proofs are given to show the maximal floppy mode property (order N). In particular, this is the case for the cubic symmetry sodalite framework and some other idealized zeolites. PMID:24379422

Analysis of Drude model using fractional derivatives without singular kernels

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Beyond singular values and loop shapes

NASA Technical Reports Server (NTRS)

Stein, G.

1985-01-01

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

Singular instantons in Eddington-inspired-Born-Infeld gravity

DOE PAGES

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

2017-03-23

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

Singularity-free dynamic equations of spacecraft-manipulator systems

NASA Astrophysics Data System (ADS)

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

2011-12-01

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

Spectral dimension controlling the decay of the quantum first-detection probability

NASA Astrophysics Data System (ADS)

Thiel, Felix; Kessler, David A.; Barkai, Eli

2018-06-01

We consider a quantum system that is initially localized at xin and that is repeatedly projectively probed with a fixed period τ at position xd. We ask for the probability Fn that the system is detected at xd for the very first time, where n is the number of detection attempts. We relate the asymptotic decay and oscillations of Fn with the system's energy spectrum, which is assumed to be absolutely continuous. In particular, Fn is determined by the Hamiltonian's measurement spectral density of states (MSDOS) f (E ) that is closely related to the density of energy states (DOS). We find that Fn decays like a power law whose exponent is determined by the power-law exponent dS of f (E ) around its singularities E*. Our findings are analogous to the classical first passage theory of random walks. In contrast to the classical case, the decay of Fn is accompanied by oscillations with frequencies that are determined by the singularities E*. This gives rise to critical detection periods τc at which the oscillations disappear. In the ordinary case dS can be identified with the spectral dimension associated with the DOS. Furthermore, the singularities E* are the van Hove singularities of the DOS in this case. We find that the asymptotic statistics of Fn depend crucially on the initial and detection state and can be wildly different for out-of-the-ordinary states, which is in sharp contrast to the classical theory. The properties of the first-detection probabilities can alternatively be derived from the transition amplitudes. All our results are confirmed by numerical simulations of the tight-binding model, and of a free particle in continuous space both with a normal and with an anomalous dispersion relation. We provide explicit asymptotic formulas for the first-detection probability in these models.

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.

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles

DOE PAGES

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.

2017-04-18

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicitymore » $L$. This gives the relation between the finite-volume spectrum and the infinite-volume $$\\textbf 2 \\to \\textbf 2$$, $$\\textbf 2 \\to \\textbf 3$$ and $$\\textbf 3 \\to \\textbf 3$$ scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass $m$, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K-matrix has no singularities below the three-particle threshold. Finally, the quantization condition is exact up to corrections of the order $$\\mathcal{O}(e^{-mL})$$ and holds for any choice of total momenta satisfying the boundary conditions.« less

Relating the finite-volume spectrum and the two-and-three-particle S matrix for relativistic systems of identical scalar particles

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

Briceño, Raúl A.; Hansen, Maxwell T.; Sharpe, Stephen R.

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicitymore » $L$. This gives the relation between the finite-volume spectrum and the infinite-volume $$\\textbf 2 \\to \\textbf 2$$, $$\\textbf 2 \\to \\textbf 3$$ and $$\\textbf 3 \\to \\textbf 3$$ scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass $m$, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K-matrix has no singularities below the three-particle threshold. Finally, the quantization condition is exact up to corrections of the order $$\\mathcal{O}(e^{-mL})$$ and holds for any choice of total momenta satisfying the boundary conditions.« less

Evidence of Deterministic Components in the Apparent Randomness of GRBs: Clues of a Chaotic Dynamic

PubMed Central

Greco, G.; Rosa, R.; Beskin, G.; Karpov, S.; Romano, L.; Guarnieri, A.; Bartolini, C.; Bedogni, R.

2011-01-01

Prompt γ-ray emissions from gamma-ray bursts (GRBs) exhibit a vast range of extremely complex temporal structures with a typical variability time-scale significantly short – as fast as milliseconds. This work aims to investigate the apparent randomness of the GRB time profiles making extensive use of nonlinear techniques combining the advanced spectral method of the Singular Spectrum Analysis (SSA) with the classical tools provided by the Chaos Theory. Despite their morphological complexity, we detect evidence of a non stochastic short-term variability during the overall burst duration – seemingly consistent with a chaotic behavior. The phase space portrait of such variability shows the existence of a well-defined strange attractor underlying the erratic prompt emission structures. This scenario can shed new light on the ultra-relativistic processes believed to take place in GRB explosions and usually associated with the birth of a fast-spinning magnetar or accretion of matter onto a newly formed black hole. PMID:22355609

Evidence of deterministic components in the apparent randomness of GRBs: clues of a chaotic dynamic.

PubMed

Greco, G; Rosa, R; Beskin, G; Karpov, S; Romano, L; Guarnieri, A; Bartolini, C; Bedogni, R

2011-01-01

Prompt γ-ray emissions from gamma-ray bursts (GRBs) exhibit a vast range of extremely complex temporal structures with a typical variability time-scale significantly short - as fast as milliseconds. This work aims to investigate the apparent randomness of the GRB time profiles making extensive use of nonlinear techniques combining the advanced spectral method of the Singular Spectrum Analysis (SSA) with the classical tools provided by the Chaos Theory. Despite their morphological complexity, we detect evidence of a non stochastic short-term variability during the overall burst duration - seemingly consistent with a chaotic behavior. The phase space portrait of such variability shows the existence of a well-defined strange attractor underlying the erratic prompt emission structures. This scenario can shed new light on the ultra-relativistic processes believed to take place in GRB explosions and usually associated with the birth of a fast-spinning magnetar or accretion of matter onto a newly formed black hole.

Magnetic evaluation of hydrogen pressures changes on MHD fluctuations in IR-T1 tokamak plasma

NASA Astrophysics Data System (ADS)

Alipour, Ramin; Ghanbari, Mohamad R.

2018-04-01

Identification of tokamak plasma parameters and investigation on the effects of each parameter on the plasma characteristics is important for the better understanding of magnetohydrodynamic (MHD) activities in the tokamak plasma. The effect of different hydrogen pressures of 1.9, 2.5 and 2.9 Torr on MHD fluctuations of the IR-T1 tokamak plasma was investigated by using of 12 Mirnov coils, singular value decomposition and wavelet analysis. The parameters such as plasma current, loop voltage, power spectrum density, energy percent of poloidal modes, dominant spatial structures and temporal structures of poloidal modes at different plasma pressures are plotted. The results indicate that the MHD activities at the pressure of 2.5 Torr are less than them at other pressures. It also has been shown that in the stable area of plasma and at the pressure of 2.5 Torr, the magnetic force and the force of plasma pressure are in balance with each other and the MHD activities are at their lowest level.

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

NASA Astrophysics Data System (ADS)

Chen, Guoxiong; Cheng, Qiuming

2016-02-01

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

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

NASA Astrophysics Data System (ADS)

Szybisz, Martín A.; Szybisz, Leszek

2009-08-01

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

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

PubMed

Takacs, T; Jüttler, B

2012-11-01

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

SVD/MCMC Data Analysis Pipeline for Global Redshifted 21-cm Spectrum Observations of the Cosmic Dawn and Dark Ages

NASA Astrophysics Data System (ADS)

Burns, Jack O.; Tauscher, Keith; Rapetti, David; Mirocha, Jordan; Switzer, Eric

2018-01-01

We have designed a complete data analysis pipeline for constraining Cosmic Dawn physics using sky-averaged spectra in the VHF range (40-200 MHz) obtained either from the ground (e.g., the Experiment to Detect Global Epoch of Reionization Signal, EDGES; and the Cosmic Twilight Polarimeter, CTP) or from orbit above the lunar farside (e.g., the Dark Ages Radio Explorer, DARE). In the case of DARE, we avoid Earth-based RFI, ionospheric effects, and radio solar emissions (when observing at night). To extract the 21-cm spectrum, we parametrize the cosmological signal and systematics with two separate sets of modes defined through Singular Value Decomposition (SVD) of training set curves. The training set for the 21-cm spin-flip brightness temperatures is composed of theoretical models of the first stars, galaxies and black holes created by varying physical parameters within the ares code. The systematics training set is created using sky and beam data to model the beam-weighted foregrounds (which are about four orders of magnitude larger than the signal) as well as expected lab data to model receiver systematics. To constrain physical parameters determining the 21-cm spectrum, we apply to the extracted signal a series of consecutive fitting techniques including two usages of a Markov Chain Monte Carlo (MCMC) algorithm. Importantly, our pipeline efficiently utilizes the significant differences between the foreground and the 21-cm signal in spatial and spectral variations. In addition, it incorporates for the first time polarization data, dramatically improving the constraining power. We are currently validating this end-to-end pipeline using detailed simulations of the signal, foregrounds and instruments. This work was directly supported by the NASA Solar System Exploration Research Virtual Institute cooperative agreement number 80ARC017M0006 and funding from the NASA Ames Research Center cooperative agreement NNX16AF59G.

Spectral Characteristics of Wake Vortex Sound During Roll-Up

NASA Technical Reports Server (NTRS)

Booth, Earl R., Jr. (Technical Monitor); Zhang, Yan; Wang, Frank Y.; Hardin, Jay C.

2003-01-01

This report presents an analysis of the sound spectra generated by a trailing aircraft vortex during its rolling-up process. The study demonstrates that a rolling-up vortex could produce low frequency (less than 100 Hz) sound with very high intensity (60 dB above threshold of human hearing) at a distance of 200 ft from the vortex core. The spectrum then drops o rapidly thereafter. A rigorous analytical approach has been adopted in this report to derive the spectrum of vortex sound. First, the sound pressure was solved from an alternative treatment of the Lighthill s acoustic analogy approach [1]. After the application of Green s function for free space, a tensor analysis was applied to permit the removal of the source term singularity of the wave equation in the far field. Consequently, the sound pressure is expressed in terms of the retarded time that indicates the time history and spacial distribution of the sound source. The Fourier transformation is then applied to the sound pressure to compute its spectrum. As a result, the Fourier transformation greatly simplifies the expression of the vortex sound pressure involving the retarded time, so that the numerical computation is applicable with ease for axisymmetric line vortices during the rolling-up process. The vortex model assumes that the vortex circulation is proportional to the time and the core radius is a constant. In addition, the velocity profile is assumed to be self-similar along the aircraft flight path, so that a benchmark vortex velocity profile can be devised to obtain a closed form solution, which is then used to validate the numerical calculations for other more realistic vortex profiles for which no closed form solutions are available. The study suggests that acoustic sensors operating at low frequency band could be profitably deployed for detecting the vortex sound during the rolling-up process.

Temporal multiscaling characteristics of particulate matter PM 10 and ground-level ozone O3 concentrations in Caribbean region

NASA Astrophysics Data System (ADS)

Plocoste, Thomas; Calif, Rudy; Jacoby-Koaly, Sandra

2017-11-01

A good knowledge of the intermittency of atmospheric pollutants is crucial for air pollution management. We consider here particulate matter PM 10 and ground-level ozone O3 time series in Guadeloupe archipelago which experiments a tropical and humid climate in the Caribbean zone. The aim of this paper is to study their scaling statistics in the framework of fully developed turbulence and Kolmogorov's theory. Firstly, we estimate their Fourier power spectra and consider their scaling properties in the physical space. The power spectra computed follows a power law behavior for both considered pollutants. Thereafter we study the scaling behavior of PM 10 and O3 time series. Contrary to numerous studies where the multifractal detrended fluctuation analysis is frequently applied, here, the classical structure function analysis is used to extract the scaling exponent or multifractal spectrum ζ(q) ; this function provides a full characterization of a process at all intensities and all scales. The obtained results show that PM 10 and O3 possess intermittent and multifractal properties. The singularity spectrum MS(α) also confirms both pollutants multifractal features. The originality of this work comes from a statistical modeling performed on ζ(q) and MS(α) by a lognormal model to compute the intermittency parameter μ. By contrast with PM 10 which mainly depends on puffs of Saharan dust (synoptic-scale), O3 is more intermittent due to variability of its local precursors. The results presented in this paper can help to better understand the mechanisms governing the dynamics of PM 10 and O3 in Caribbean islands context.

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

NASA Technical Reports Server (NTRS)

Bristow, D. R.

1979-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1997-01-01

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

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

PubMed

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

2015-08-21

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

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

NASA Astrophysics Data System (ADS)

You, J. H.; Bolt, H.

2001-10-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Aerodynamic influence coefficient method using singularity splines

NASA Technical Reports Server (NTRS)

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

1974-01-01

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

Transverse cracking and stiffness reduction in composite laminates

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

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

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

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

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

Probing strong correlations with light scattering: Example of the quantum Ising model

DOE PAGES

Babujian, H. M.; Karowski, M.; Tsvelik, A. M.

2016-10-01

In this article we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap m. The Raman cross section has a strong singularity when the energy of the outgoing photon is at the spectral gap ω f ≈ m and a square root threshold when the frequency difference between the incident and outgoing photons ω i₋ω f≈2m. Finally, the latter feature reflects the fermionic nature of the Ising model excitations.

Probing strong correlations with light scattering: Example of the quantum Ising model

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

Babujian, H. M.; Karowski, M.; Tsvelik, A. M.

In this article we calculate the nonlinear susceptibility and the resonant Raman cross section for the paramagnetic phase of the ferromagnetic quantum Ising model in one dimension. In this region the spectrum of the Ising model has a gap m. The Raman cross section has a strong singularity when the energy of the outgoing photon is at the spectral gap ω f ≈ m and a square root threshold when the frequency difference between the incident and outgoing photons ω i₋ω f≈2m. Finally, the latter feature reflects the fermionic nature of the Ising model excitations.

Effective equations and the inverse cascade theory for Kolmogorov flows

NASA Technical Reports Server (NTRS)

Weinan, E.; Shu, Chi-Wang

1992-01-01

We study the two dimensional Kolmogorov flows in the limit as the forcing frequency goes to infinity. Direct numerical simulation indicates that the low frequency energy spectrum evolves to a universal kappa (exp -4) decay law. We derive effective equations governing the behavior of the large scale flow quantities. We then present numerical evidence that with smooth initial data, the solution to the effective equation develops a kappa (exp -4) type singularity at a finite time. This gives a convenient explanation for the kappa (exp -4) decay law exhibited by the original Kolmogorov flows.

Theory of High-T{sub c} Superconducting Cuprates Based on Experimental Evidence

DOE R&D Accomplishments Database

Abrikosov, A. A.

1999-12-10

A model of superconductivity in layered high-temperature superconducting cuprates is proposed, based on the extended saddle point singularities in the electron spectrum, weak screening of the Coulomb interaction and phonon-mediated interaction between electrons plus a small short-range repulsion of Hund's, or spin-fluctuation, origin. This permits to explain the large values of T{sub c}, features of the isotope effect on oxygen and copper, the existence of two types of the order parameter, the peak in the inelastic neutron scattering, the positive curvature of the upper critical field, as function of temperature etc.

Maximum Entropy Methods as the Bridge Between Microscopic and Macroscopic Theory

NASA Astrophysics Data System (ADS)

Taylor, Jamie M.

2016-09-01

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

Statistical Analysis of the Ionosphere based on Singular Value Decomposition

NASA Astrophysics Data System (ADS)

Demir, Uygar; Arikan, Feza; Necat Deviren, M.; Toker, Cenk

2016-07-01

Ionosphere is made up of a spatio-temporally varying trend structure and secondary variations due to solar, geomagnetic, gravitational and seismic activities. Hence, it is important to monitor the ionosphere and acquire up-to-date information about its state in order both to better understand the physical phenomena that cause the variability and also to predict the effect of the ionosphere on HF and satellite communications, and satellite-based positioning systems. To charaterise the behaviour of the ionosphere, we propose to apply Singular Value Decomposition (SVD) to Total Electron Content (TEC) maps obtained from the TNPGN-Active (Turkish National Permanent GPS Network) CORS network. TNPGN-Active network consists of 146 GNSS receivers spread over Turkey. IONOLAB-TEC values estimated from each station are spatio-temporally interpolated using a Universal Kriging based algorithm with linear trend, namely IONOLAB-MAP, with very high spatial resolution. It is observed that the dominant singular value of TEC maps is an indicator of the trend structure of the ionosphere. The diurnal, seasonal and annual variability of the most dominant value is the representation of solar effect on ionosphere in midlatitude range. Secondary and smaller singular values are indicators of secondary variation which can have significance especially during geomagnetic storms or seismic disturbances. The dominant singular values are related to the physical basis vectors where ionosphere can be fully reconstructed using these vectors. Therefore, the proposed method can be used both for the monitoring of the current state of a region and also for the prediction and tracking of future states of ionosphere using singular values and singular basis vectors. This study is supported by by TUBITAK 115E915 and Joint TUBITAK 114E092 and AS CR14/001 projects.

Fusion information entropy method of rolling bearing fault diagnosis based on n-dimensional characteristic parameter distance

NASA Astrophysics Data System (ADS)

Ai, Yan-Ting; Guan, Jiao-Yue; Fei, Cheng-Wei; Tian, Jing; Zhang, Feng-Ling

2017-05-01

To monitor rolling bearing operating status with casings in real time efficiently and accurately, a fusion method based on n-dimensional characteristic parameters distance (n-DCPD) was proposed for rolling bearing fault diagnosis with two types of signals including vibration signal and acoustic emission signals. The n-DCPD was investigated based on four information entropies (singular spectrum entropy in time domain, power spectrum entropy in frequency domain, wavelet space characteristic spectrum entropy and wavelet energy spectrum entropy in time-frequency domain) and the basic thought of fusion information entropy fault diagnosis method with n-DCPD was given. Through rotor simulation test rig, the vibration and acoustic emission signals of six rolling bearing faults (ball fault, inner race fault, outer race fault, inner-ball faults, inner-outer faults and normal) are collected under different operation conditions with the emphasis on the rotation speed from 800 rpm to 2000 rpm. In the light of the proposed fusion information entropy method with n-DCPD, the diagnosis of rolling bearing faults was completed. The fault diagnosis results show that the fusion entropy method holds high precision in the recognition of rolling bearing faults. The efforts of this study provide a novel and useful methodology for the fault diagnosis of an aeroengine rolling bearing.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

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.

Singularity detection by wavelet approach: application to electrocardiogram signal

NASA Astrophysics Data System (ADS)

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

2010-01-01

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

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

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Kathiresan, K.

1976-01-01

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

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

PubMed

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

2017-02-06

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

Resistive MHD Stability Analysis in Near Real-time

NASA Astrophysics Data System (ADS)

Glasser, Alexander; Kolemen, Egemen

2017-10-01

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

Multiscale Analysis in the Compressible Rotating and Heat Conducting Fluids

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

On the Convergence of Stresses in Fretting Fatigue

PubMed Central

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

2016-01-01

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

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.

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).

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

Detrending moving average algorithm for multifractals

NASA Astrophysics Data System (ADS)

Gu, Gao-Feng; Zhou, Wei-Xing

2010-07-01

The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter θ determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measures and higher-dimensional multifractals, which is a generalization of the DMA method. The performance of the one-dimensional and two-dimensional MFDMA methods is investigated using synthetic multifractal measures with analytical solutions for backward (θ=0) , centered (θ=0.5) , and forward (θ=1) detrending windows. We find that the estimated multifractal scaling exponent τ(q) and the singularity spectrum f(α) are in good agreement with the theoretical values. In addition, the backward MFDMA method has the best performance, which provides the most accurate estimates of the scaling exponents with lowest error bars, while the centered MFDMA method has the worse performance. It is found that the backward MFDMA algorithm also outperforms the multifractal detrended fluctuation analysis. The one-dimensional backward MFDMA method is applied to analyzing the time series of Shanghai Stock Exchange Composite Index and its multifractal nature is confirmed.

Observability and synchronization of neuron models.

PubMed

Aguirre, Luis A; Portes, Leonardo L; Letellier, Christophe

2017-10-01

Observability is the property that enables recovering the state of a dynamical system from a reduced number of measured variables. In high-dimensional systems, it is therefore important to make sure that the variable recorded to perform the analysis conveys good observability of the system dynamics. The observability of a network of neuron models depends nontrivially on the observability of the node dynamics and on the topology of the network. The aim of this paper is twofold. First, to perform a study of observability using four well-known neuron models by computing three different observability coefficients. This not only clarifies observability properties of the models but also shows the limitations of applicability of each type of coefficients in the context of such models. Second, to study the emergence of phase synchronization in networks composed of neuron models. This is done performing multivariate singular spectrum analysis which, to the best of the authors' knowledge, has not been used in the context of networks of neuron models. It is shown that it is possible to detect phase synchronization: (i) without having to measure all the state variables, but only one (that provides greatest observability) from each node and (ii) without having to estimate the phase.

Dynamic bifurcation and strange nonchaos in a two-frequency parametrically driven nonlinear oscillator

NASA Astrophysics Data System (ADS)

Premraj, D.; Suresh, K.; Palanivel, J.; Thamilmaran, K.

2017-09-01

A periodically forced series LCR circuit with Chua's diode as a nonlinear element exhibits slow passage through Hopf bifurcation. This slow passage leads to a delay in the Hopf bifurcation. The delay in this bifurcation is a unique quantity and it can be predicted using various numerical analysis. We find that when an additional periodic force is added to the system, the delay in bifurcation becomes chaotic which leads to an unpredictability in bifurcation delay. Further, we study the bifurcation of the periodic delay to chaotic delay in the slow passage effect through strange nonchaotic delay. We also report the occurrence of strange nonchaotic dynamics while varying the parameter of the additional force included in the system. We observe that the system exhibits a hitherto unknown dynamical transition to a strange nonchaotic attractor. With the help of Lyapunov exponent, we explain the new transition to strange nonchaotic attractor and its mechanism is studied by making use of rational approximation theory. The birth of SNA has also been confirmed numerically, using Poincaré maps, phase sensitivity exponent, the distribution of finite-time Lyapunov exponents and singular continuous spectrum analysis.

Oscillatory modes of extended Nile River records (A.D. 622-1922)

NASA Astrophysics Data System (ADS)

Kondrashov, D.; Feliks, Y.; Ghil, M.

2005-05-01

The historical records of the low- and high-water levels of the Nile River are among the longest climatic records that have near-annual resolution. There are few gaps in the first part of the records (A.D. 622-1470) and larger gaps later (A.D. 1471-1922). We apply advanced spectral methods, Singular-Spectrum Analysis (SSA) and the Multi-Taper Method (MTM), to fill the gaps and to locate interannual and interdecadal periodicities. The gap filling uses a novel, iterative version of SSA. Our analysis reveals several statistically significant features of the records: a nonlinear, data-adaptive trend that includes a 256-year cycle, a quasi-quadriennial (4.2-year) and a quasi-biennial (2.2-year) mode, as well as additional periodicities of 64, 19, 12, and, most strikingly, 7 years. The quasi-quadriennial and quasi-biennial modes support the long-established connection between the Nile River discharge and the El-Niño/Southern Oscillation (ENSO) phenomenon in the Indo-Pacific Ocean. The longest periods might be of astronomical origin. The 7-year periodicity, possibly related to the biblical cycle of lean and fat years, seems to be due to North Atlantic influences.

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

NASA Astrophysics Data System (ADS)

Emge, Darren K.; Adalı, Tülay

2014-06-01

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

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

PubMed

Szybisz, Martín A; Szybisz, Leszek

2009-08-01

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

Seasonal and Interannual Variations of Heat Fluxes in the Barents Sea Region

NASA Astrophysics Data System (ADS)

Bashmachnikov, I. L.; Yurova, A. Yu.; Bobylev, L. P.; Vesman, A. V.

2018-03-01

Seasonal and interannual variations in adjective heat fluxes in the ocean ( dQ oc) and the convergence of advective heat fluxes in the atmosphere ( dQ atm) in the Barents Sea region have been investigated over the period of 1993-2012 using the results of the MIT regional eddy-permitting model and ERA-Interim atmospheric reanalysis. Wavelet analysis and singular spectrum analysis are used to reveal concealed periodicities. Seasonal 2- to 4- and 5- to 8-year cycles are revealed in the dQ oc and dQ atm data. It is also found that seasonal variations in dQ oc are primarily determined by the integrated volume fluxes through the western boundary of the Barents Sea, whereas the 20-year trend is determined by the temperature variation of the transported water. A cross-wavelet analysis of dQ oc and dQ atm in the Barents Sea region shows that the seasonal variations in dQ oc and dQ atm are nearly in-phase, while their interannual variations are out-of-phase. It is concluded that the basin of the Barents Sea plays an important role in maintaining the feedback mechanism (the Bjerknes compensation) of the ocean-atmosphere system in the Arctic region.

Model validity and frequency band selection in operational modal analysis

NASA Astrophysics Data System (ADS)

Au, Siu-Kui

2016-12-01

Experimental modal analysis aims at identifying the modal properties (e.g., natural frequencies, damping ratios, mode shapes) of a structure using vibration measurements. Two basic questions are encountered when operating in the frequency domain: Is there a mode near a particular frequency? If so, how much spectral data near the frequency can be included for modal identification without incurring significant modeling error? For data with high signal-to-noise (s/n) ratios these questions can be addressed using empirical tools such as singular value spectrum. Otherwise they are generally open and can be challenging, e.g., for modes with low s/n ratios or close modes. In this work these questions are addressed using a Bayesian approach. The focus is on operational modal analysis, i.e., with 'output-only' ambient data, where identification uncertainty and modeling error can be significant and their control is most demanding. The approach leads to 'evidence ratios' quantifying the relative plausibility of competing sets of modeling assumptions. The latter involves modeling the 'what-if-not' situation, which is non-trivial but is resolved by systematic consideration of alternative models and using maximum entropy principle. Synthetic and field data are considered to investigate the behavior of evidence ratios and how they should be interpreted in practical applications.

The Semantics of Plurals: A Defense of Singularism

ERIC Educational Resources Information Center

Florio, Salvatore

2010-01-01

In this dissertation, I defend "semantic singularism", which is the view that syntactically plural terms, such as "they" or "Russell and Whitehead", are semantically singular. A semantically singular term is a term that denotes a single entity. Semantic singularism is to be distinguished from "syntactic singularism", according to which…

Sample-to-sample fluctuations of power spectrum of a random motion in a periodic Sinai model.

PubMed

Dean, David S; Iorio, Antonio; Marinari, Enzo; Oshanin, Gleb

2016-09-01

The Sinai model of a tracer diffusing in a quenched Brownian potential is a much-studied problem exhibiting a logarithmically slow anomalous diffusion due to the growth of energy barriers with the system size. However, if the potential is random but periodic, the regime of anomalous diffusion crosses over to one of normal diffusion once a tracer has diffused over a few periods of the system. Here we consider a system in which the potential is given by a Brownian bridge on a finite interval (0,L) and then periodically repeated over the whole real line and study the power spectrum S(f) of the diffusive process x(t) in such a potential. We show that for most of realizations of x(t) in a given realization of the potential, the low-frequency behavior is S(f)∼A/f^{2}, i.e., the same as for standard Brownian motion, and the amplitude A is a disorder-dependent random variable with a finite support. Focusing on the statistical properties of this random variable, we determine the moments of A of arbitrary, negative, or positive order k and demonstrate that they exhibit a multifractal dependence on k and a rather unusual dependence on the temperature and on the periodicity L, which are supported by atypical realizations of the periodic disorder. We finally show that the distribution of A has a log-normal left tail and exhibits an essential singularity close to the right edge of the support, which is related to the Lifshitz singularity. Our findings are based both on analytic results and on extensive numerical simulations of the process x(t).

Formation of turbulence around flow singularities

NASA Technical Reports Server (NTRS)

Zak, M.

1983-01-01

The formation of turbulence around singular points of a flow such as stagnation points, tangential jumps of velocity, are analyzed. It is proved that turbulence is inevitably generated by the rear stagnation point, but cannot be generated by the nose stagnation point of a streamlined body. Special attention is paid to an evolution of turbulence induced by a tangential jump of velocity. A qualitative analysis of a turbulent flow between two rotating concentric cylinders and around a streamlined cylinder is given.

Black holes in loop quantum gravity: the complete space-time.

PubMed

Gambini, Rodolfo; Pullin, Jorge

2008-10-17

We consider the quantization of the complete extension of the Schwarzschild space-time using spherically symmetric loop quantum gravity. We find an exact solution corresponding to the semiclassical theory. The singularity is eliminated but the space-time still contains a horizon. Although the solution is known partially numerically and therefore a proper global analysis is not possible, a global structure akin to a singularity-free Reissner-Nordström space-time including a Cauchy horizon is suggested.

Robustness analysis of multirate and periodically time varying systems

NASA Technical Reports Server (NTRS)

Berg, Martin C.; Mason, Gregory S.

1991-01-01

A new method for analyzing the stability and robustness of multirate and periodically time varying systems is presented. It is shown that a multirate or periodically time varying system can be transformed into an equivalent time invariant system. For a SISO system, traditional gain and phase margins can be found by direct application of the Nyquist criterion to this equivalent time invariant system. For a MIMO system, structured and unstructured singular values can be used to determine the system's robustness. The limitations and implications of utilizing this equivalent time invariant system for calculating gain and phase margins, and for estimating robustness via singular value analysis are discussed.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

Complex eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method

NASA Technical Reports Server (NTRS)

Newman, M.; Mann, F. I.

1977-01-01

An extension of the Tridiagonal Reduction (FEER) method to complex eigenvalue analysis in NASTRAN is described. As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum are extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order is much lower than that of the full size problem. The reduction process is effected automatically, and thus avoids the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admits mass, damping and stiffness matrices which are unrestricted in character, i.e., they may be real, complex, symmetric or unsymmetric, singular or non-singular.

Recent developments in rotary-wing aerodynamic theory

NASA Technical Reports Server (NTRS)

Johnson, W.

1986-01-01

Current progress in the computational analysis of rotary-wing flowfields is surveyed, and some typical results are presented in graphs. Topics examined include potential theory, rotating coordinate systems, lifting-surface theory (moving singularity, fixed wing, and rotary wing), panel methods (surface singularity representations, integral equations, and compressible flows), transonic theory (the small-disturbance equation), wake analysis (hovering rotor-wake models and transonic blade-vortex interaction), limitations on computational aerodynamics, and viscous-flow methods (dynamic-stall theories and lifting-line theory). It is suggested that the present algorithms and advanced computers make it possible to begin working toward the ultimate goal of turbulent Navier-Stokes calculations for an entire rotorcraft.

Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

NASA Technical Reports Server (NTRS)

Atluri, S. N.; Nakagaki, M.; Kathiresan, K.

1980-01-01

In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.

Emerging spectra of singular correlation matrices under small power-map deformations

NASA Astrophysics Data System (ADS)

Vinayak; Schäfer, Rudi; Seligman, Thomas H.

2013-09-01

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used, this implies an analysis of highly singular correlation matrices. We attack this problem by using the so-called power map, which was introduced to reduce noise. Its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so-emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

Emerging spectra of singular correlation matrices under small power-map deformations.

PubMed

Vinayak; Schäfer, Rudi; Seligman, Thomas H

2013-09-01

Correlation matrices are a standard tool in the analysis of the time evolution of complex systems in general and financial markets in particular. Yet most analysis assume stationarity of the underlying time series. This tends to be an assumption of varying and often dubious validity. The validity of the assumption improves as shorter time series are used. If many time series are used, this implies an analysis of highly singular correlation matrices. We attack this problem by using the so-called power map, which was introduced to reduce noise. Its nonlinearity breaks the degeneracy of the zero eigenvalues and we analyze the sensitivity of the so-emerging spectra to correlations. This sensitivity will be demonstrated for uncorrelated and correlated Wishart ensembles.

Differential Kinematics Of Contemporary Industrial Robots

NASA Astrophysics Data System (ADS)

Szkodny, T.

2014-08-01

The paper presents a simple method of avoiding singular configurations of contemporary industrial robot manipulators of such renowned companies as ABB, Fanuc, Mitsubishi, Adept, Kawasaki, COMAU and KUKA. To determine the singular configurations of these manipulators a global form of description of the end-effector kinematics was prepared, relative to the other links. On the basis of this description , the formula for the Jacobian was defined in the end-effector coordinates. Next, a closed form of the determinant of the Jacobian was derived. From the formula, singular configurations, where the determinant's value equals zero, were determined. Additionally, geometric interpretations of these configurations were given and they were illustrated. For the exemplary manipulator, small corrections of joint variables preventing the reduction of the Jacobian order were suggested. An analysis of positional errors, caused by these corrections, was presented

Integrated tools for control-system analysis

NASA Technical Reports Server (NTRS)

Ostroff, Aaron J.; Proffitt, Melissa S.; Clark, David R.

1989-01-01

The basic functions embedded within a user friendly software package (MATRIXx) are used to provide a high level systems approach to the analysis of linear control systems. Various control system analysis configurations are assembled automatically to minimize the amount of work by the user. Interactive decision making is incorporated via menu options and at selected points, such as in the plotting section, by inputting data. There are five evaluations such as the singular value robustness test, singular value loop transfer frequency response, Bode frequency response, steady-state covariance analysis, and closed-loop eigenvalues. Another section describes time response simulations. A time response for random white noise disturbance is available. The configurations and key equations used for each type of analysis, the restrictions that apply, the type of data required, and an example problem are described. One approach for integrating the design and analysis tools is also presented.

Naked singularity resolution in cylindrical collapse

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

Kurita, Yasunari; Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502; Nakao, Ken-ichi

In this paper, we study the gravitational collapse of null dust in cylindrically symmetric spacetime. The naked singularity necessarily forms at the symmetry axis. We consider the situation in which null dust is emitted again from the naked singularity formed by the collapsed null dust and investigate the backreaction by this emission for the naked singularity. We show a very peculiar but physically important case in which the same amount of null dust as that of the collapsed one is emitted from the naked singularity as soon as the ingoing null dust hits the symmetry axis and forms the nakedmore » singularity. In this case, although this naked singularity satisfies the strong curvature condition by Krolak (limiting focusing condition), geodesics which hit the singularity can be extended uniquely across the singularity. Therefore, we may say that the collapsing null dust passes through the singularity formed by itself and then leaves for infinity. Finally, the singularity completely disappears and the flat spacetime remains.« less

Spectral simplicity of apparent complexity. I. The nondiagonalizable metadynamics of prediction

NASA Astrophysics Data System (ADS)

Riechers, Paul M.; Crutchfield, James P.

2018-03-01

Virtually all questions that one can ask about the behavioral and structural complexity of a stochastic process reduce to a linear algebraic framing of a time evolution governed by an appropriate hidden-Markov process generator. Each type of question—correlation, predictability, predictive cost, observer synchronization, and the like—induces a distinct generator class. Answers are then functions of the class-appropriate transition dynamic. Unfortunately, these dynamics are generically nonnormal, nondiagonalizable, singular, and so on. Tractably analyzing these dynamics relies on adapting the recently introduced meromorphic functional calculus, which specifies the spectral decomposition of functions of nondiagonalizable linear operators, even when the function poles and zeros coincide with the operator's spectrum. Along the way, we establish special properties of the spectral projection operators that demonstrate how they capture the organization of subprocesses within a complex system. Circumventing the spurious infinities of alternative calculi, this leads in the sequel, Part II [P. M. Riechers and J. P. Crutchfield, Chaos 28, 033116 (2018)], to the first closed-form expressions for complexity measures, couched either in terms of the Drazin inverse (negative-one power of a singular operator) or the eigenvalues and projection operators of the appropriate transition dynamic.

Sufficient Condition for Finite-Time Singularity in a High-Symmetry Euler Flow

NASA Astrophysics Data System (ADS)

Bhattacharjee, A.; Ng, C. S.

1997-11-01

The possibility of a finite-time singularity (FTS) with a smooth initial condition is considered in a high-symmetry Euler flow (the Kida flow). It has been shown recently [C. S. Ng and A. Bhattacharjee, Phys. Rev. E 54 1530, 1996] that there must be a FTS if the fourth order pressure derivative (p_xxxx) is always positive within a finite range X on the x-axis around the origin. This sufficient condition is now extended to the case when the range X is itself time-dependent. It is shown that a FTS must still exist even when X arrow 0 if the p_xxxx value at the origin is growing faster than X-2. It is tested statistically that p_xxxx at the origin is most probably positive for a Kida flow with random Fourier amplitudes and that it is generally growing as energy cascades to Fourier modes with higher wavenumbers k. The condition that p_xxxx grows faster than X-2 is found to be satisfied when the spectral index ν of the energy spectrum E(k) ∝ k^-ν of the random flow is less than 3.

Sufficient condition for finite-time singularity and tendency towards self-similarity in a high-symmetry flow

NASA Astrophysics Data System (ADS)

Ng, C. S.; Bhattacharjee, A.

A highly symmetric Euler flow, first proposed by Kida (1985), and recently simulated by Boratav and Pelz (1994) is considered. It is found that the fourth order spatial derivative of the pressure (pxxxx) at the origin is most probably positive. It is demonstrated that if pxxxx grows fast enough, there must be a finite-time singularity (FTS). For a random energy spectrum E(k) ∞ k-v, a FTS can occur if the spectral index v<3. Furthermore, a positive pxxxx has the dynamical consequence of reducing the third derivative of the velocity uxxx at the origin. Since the expectation value of uxxx is zero for a random distribution of energy, an ever decreasing uxxx means that the Kida flow has an intrinsic tendency to deviate from a random state. By assuming that uxxx reaches the minimum value for a given spectral profile, the velocity and pressure are found to have locally self-similar forms similar in shape to what are found in numerical simulations. Such a quasi self-similar solution relaxes the requirement for FTS to v<6. A special self-similar solution that satisfies Kelvin's circulation theorem and exhibits a FTS is found for v=2.

Intangible pointlike tracers for liquid-crystal-based microsensors

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

Brasselet, Etienne; Juodkazis, Saulius

2010-12-15

We propose an optical detection technique for liquid-crystal-based sensors that is based on polarization-resolved tracking of optical singularities and does not rely on standard observation of light-intensity changes caused by modifications of the liquid crystal orientational ordering. It uses a natural two-dimensional network of polarization singularities embedded in the transverse cross section of a probe beam that passes through a liquid crystal sample, in our case, a nematic droplet held in laser tweezers. The identification and spatial evolution of such a topological fingerprint is retrieved from subwavelength polarization-resolved imaging, and the mechanical constraint exerted on the molecular ordering by themore » trapping beam itself is chosen as the control parameter. By restricting our analysis to one type of point singularity, C points, which correspond to location in space where the polarization azimuth is undefined, we show that polarization singularities appear as intangible pointlike tracers for liquid-crystal-based three-dimensional microsensors. The method has a superresolution potential and can be used to visualize changes at the nanoscale.« less

Optimal control of dissipative nonlinear dynamical systems with triggers of coupled singularities

NASA Astrophysics Data System (ADS)

Stevanović Hedrih, K.

2008-02-01

This paper analyses the controllability of motion of nonconservative nonlinear dynamical systems in which triggers of coupled singularities exist or appear. It is shown that the phase plane method is useful for the analysis of nonlinear dynamics of nonconservative systems with one degree of freedom of control strategies and also shows the way it can be used for controlling the relative motion in rheonomic systems having equivalent scleronomic conservative or nonconservative system For the system with one generalized coordinate described by nonlinear differential equation of nonlinear dynamics with trigger of coupled singularities, the functions of system potential energy and conservative force must satisfy some conditions defined by a Theorem on the existence of a trigger of coupled singularities and the separatrix in the form of "an open a spiral form" of number eight. Task of the defined dynamical nonconservative system optimal control is: by using controlling force acting to the system, transfer initial state of the nonlinear dynamics of the system into the final state of the nonlinear dynamics in the minimal time for that optimal control task

Primordial non-Gaussianity and power asymmetry with quantum gravitational effects in loop quantum cosmology

NASA Astrophysics Data System (ADS)

Zhu, Tao; Wang, Anzhong; Kirsten, Klaus; Cleaver, Gerald; Sheng, Qin

2018-02-01

Loop quantum cosmology provides a resolution of the classical big bang singularity in the deep Planck era. The evolution, prior to the usual slow-roll inflation, naturally generates excited states at the onset of the slow-roll inflation. It is expected that these quantum gravitational effects could leave its fingerprints on the primordial perturbation spectrum and non-Gaussianity, and lead to some observational evidences in the cosmic microwave background. While the impact of the quantum effects on the primordial perturbation spectrum has been already studied and constrained by current data, in this paper we continue to study such effects but now on the non-Gaussianity of the primordial curvature perturbations. We present detailed and analytical calculations of the non-Gaussianity and show explicitly that the corrections due to the quantum effects are at the same magnitude of the slow-roll parameters in the observable scales and thus are well within current observational constraints. Despite this, we show that the non-Gaussianity in the squeezed limit can be enhanced at superhorizon scales and it is these effects that can yield a large statistical anisotropy on the power spectrum through the Erickcek-Kamionkowski-Carroll mechanism.

Canonical coordinates and meson spectra for scalar deformed Script N = 4 SYM from the AdS/CFT correspondence

NASA Astrophysics Data System (ADS)

Shock, Jonathan P.

2006-10-01

Two points on the Coulomb branch of Script N = 4 super Yang Mills are investigated using their supergravity duals. By switching on condensates for the scalars in the Script N = 4 multiplet with a form which preserves a subgroup of the original R-symmetry, disk and sphere configurations of D3-branes are formed in the dual supergravity background. The analytic, canonical metric for these geometries is formulated and the singularity structure is studied. Quarks are introduced into the corresponding field theories using D7-brane probes and the meson spectrum is calculated. For one of the condensate configurations, a mass gap is found and shown analytically to be present in the massless limit. It is also found that there is a stepped spectrum with eigenstate degeneracy in the limit of small quark masses and this result is shown analytically. In the second, similar deformation it is necessary to understand the full D3-D7 brane interaction to study the limit of small quark masses. For quark masses larger than the condensate scale the spectrum is calculated and shown to be discrete as expected.

Stacked sparse autoencoder in hyperspectral data classification using spectral-spatial, higher order statistics and multifractal spectrum features

NASA Astrophysics Data System (ADS)

Wan, Xiaoqing; Zhao, Chunhui; Wang, Yanchun; Liu, Wu

2017-11-01

This paper proposes a novel classification paradigm for hyperspectral image (HSI) using feature-level fusion and deep learning-based methodologies. Operation is carried out in three main steps. First, during a pre-processing stage, wave atoms are introduced into bilateral filter to smooth HSI, and this strategy can effectively attenuate noise and restore texture information. Meanwhile, high quality spectral-spatial features can be extracted from HSI by taking geometric closeness and photometric similarity among pixels into consideration simultaneously. Second, higher order statistics techniques are firstly introduced into hyperspectral data classification to characterize the phase correlations of spectral curves. Third, multifractal spectrum features are extracted to characterize the singularities and self-similarities of spectra shapes. To this end, a feature-level fusion is applied to the extracted spectral-spatial features along with higher order statistics and multifractal spectrum features. Finally, stacked sparse autoencoder is utilized to learn more abstract and invariant high-level features from the multiple feature sets, and then random forest classifier is employed to perform supervised fine-tuning and classification. Experimental results on two real hyperspectral data sets demonstrate that the proposed method outperforms some traditional alternatives.

Cycle of phase, coherence and polarization singularities in Young's three-pinhole experiment.

PubMed

Pang, Xiaoyan; Gbur, Greg; Visser, Taco D

2015-12-28

It is now well-established that a variety of singularities can be characterized and observed in optical wavefields. It is also known that these phase singularities, polarization singularities and coherence singularities are physically related, but the exact nature of their relationship is still somewhat unclear. We show how a Young-type three-pinhole interference experiment can be used to create a continuous cycle of transformations between classes of singularities, often accompanied by topological reactions in which different singularities are created and annihilated. This arrangement serves to clarify the relationships between the different singularity types, and provides a simple tool for further exploration.

Vibrations of Bladed Disk Assemblies

DTIC Science & Technology

1991-03-29

34, Contract Report to Gas Trubines, General Motors Corp., Indianapolis (31 pages). 3 Afolabi, D., 1982, "Some Vibration Characteristics of an Aeroengine ...10. SOUACIOFPUNOiNG NO. Bolling Air Force Base PROGRAM 0mo.0aC-r TASK "o mW Washington, D.C. 20332-6448 1 LFAANT NO. No. N. O Vibrations of Bladed Disk...identfy by loC* n u r) 011LO . 0.ou* sum G. Blade vibrations , singularity theory, singular perturbation analysis, mode localization iS. AST.OACT

Spectral analysis of a family of binary inflation rules

NASA Astrophysics Data System (ADS)

Baake, Michael; Grimm, Uwe; Mañibo, Neil

2018-01-01

The family of primitive binary substitutions defined by 1 \\mapsto 0 \\mapsto 0 1^m with m\\in N is investigated. The spectral type of the corresponding diffraction measure is analysed for its geometric realisation with prototiles (intervals) of natural length. Apart from the well-known Fibonacci inflation (m=1 ), the inflation rules either have integer inflation factors, but non-constant length, or are of non-Pisot type. We show that all of them have singular diffraction, either of pure point type or essentially singular continuous.

Application of reiteration of Hankel singular value decomposition in quality control

NASA Astrophysics Data System (ADS)

Staniszewski, Michał; Skorupa, Agnieszka; Boguszewicz, Łukasz; Michalczuk, Agnieszka; Wereszczyński, Kamil; Wicher, Magdalena; Konopka, Marek; Sokół, Maria; Polański, Andrzej

2017-07-01

Medical centres are obliged to store past medical records, including the results of quality assurance (QA) tests of the medical equipment, which is especially useful in checking reproducibility of medical devices and procedures. Analysis of multivariate time series is an important part of quality control of NMR data. In this work we proposean anomaly detection tool based on Reiteration of Hankel Singular Value Decomposition method. The presented method was compared with external software and authors obtained comparable results.

Symmetry and singularity properties of second-order ordinary differential equations of Lie's type III

NASA Astrophysics Data System (ADS)

Andriopoulos, K.; Leach, P. G. L.

2007-04-01

We extend the work of Abraham-Shrauner [B. Abraham-Shrauner, Hidden symmetries and linearization of the modified Painleve-Ince equation, J. Math. Phys. 34 (1993) 4809-4816] on the linearization of the modified Painleve-Ince equation to a wider class of nonlinear second-order ordinary differential equations invariant under the symmetries of time translation and self-similarity. In the process we demonstrate a remarkable connection with the parameters obtained in the singularity analysis of this class of equations.

Workshop on Condition Based Maintenance Held in Atlantic Beach, North Carolina on November 15 - 17, 1993

DTIC Science & Technology

1993-11-17

pounds of Torque Over Three Minutes Continuous Operation IYMCO1A 14 DMAE Corporation C-130 Engine Gearbox January 19925 Stress Wave Analysis - I in’. I...FaUi.O The CBM needs associated with surface initiated failure mechanisms can be divided into I singular defects and low (h/a) operation. Singular defec-t...These include nicks, scratches, corrosion pits and dents caused by third’ body particles (hard or soft). These defects cause local stress risers

On important precursor of singular optics (tutorial)

NASA Astrophysics Data System (ADS)

Polyanskii, Peter V.; Felde, Christina V.; Bogatyryova, Halina V.; Konovchuk, Alexey V.

2018-01-01

The rise of singular optics is usually associated with the seminal paper by J. F. Nye and M. V. Berry [Proc. R. Soc. Lond. A, 336, 165-189 (1974)]. Intense development of this area of modern photonics has started since the early eighties of the XX century due to invention of the interfrence technique for detection and diagnostics of phase singularities, such as optical vortices in complex speckle-structured light fields. The next powerful incentive for formation of singular optics into separate area of the science on light was connectected with discovering of very practical technique for creation of singular optical beams of various kinds on the base of computer-generated holograms. In the eghties and ninetieth of the XX century, singular optics evolved, almost entirely, under the approximation of complete coherency of light field. Only at the threshold of the XXI century, it has been comprehended that the singular-optics approaches can be fruitfully expanded onto partially spatially coherent, partially polarized and polychromatic light fields supporting singularities of new kinds, that has been resulted in establishing of correlation singular optics. Here we show that correlation singular optics has much deeper roots, ascending to "pre-singular" and even pre-laser epoch and associated with the concept of partial coherence and polarization. It is remarcable that correlation singular optics in its present interpretation has forestalled the standard coherent singular optics. This paper is timed to the sixtieth anniversary of the most profound precursor of modern correlation singular optics [J. Opt. Soc. Am., 47, 895-902 (1957)].

Geonic black holes and remnants in Eddington-inspired Born-Infeld gravity.

PubMed

Olmo, Gonzalo J; Rubiera-Garcia, D; Sanchis-Alepuz, Helios

We show that electrically charged solutions within the Eddington-inspired Born-Infeld theory of gravity replace the central singularity by a wormhole supported by the electric field. As a result, the total energy associated with the electric field is finite and similar to that found in the Born-Infeld electromagnetic theory. When a certain charge-to-mass ratio is satisfied, in the lowest part of the mass and charge spectrum the event horizon disappears, yielding stable remnants. We argue that quantum effects in the matter sector can lower the mass of these remnants from the Planck scale down to the TeV scale.

Engineered circuit QED with dense resonant modes

NASA Astrophysics Data System (ADS)

Wilhelm, Frank; Egger, Daniel

2013-03-01

In circuit quantum electrodynamics even in the ultrastrong coupling regime, strong quasi-resonant interaction typically involves only one mode of the resonator as the mode spacing is comparable to the frequency of the mode. We are going to present an engineered hybrid transmission line consisting of a left-handed and a right-handed portion that has a low-frequency van-Hove singularity hence showing a dense mode spectrum at an experimentally accessible point. This gives rise to strong multi-mode coupling and can be utilized in multiple ways to create strongly correlated microwave photons. Supported by DARPA through the QuEST program and by NSERC Discovery grants

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

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

Meek, Garrett A.; Levine, Benjamin G., E-mail: levine@chemistry.msu.edu

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplingsmore » at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.« less

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-05-01

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Wave function continuity and the diagonal Born-Oppenheimer correction at conical intersections.

PubMed

Meek, Garrett A; Levine, Benjamin G

2016-05-14

We demonstrate that though exact in principle, the expansion of the total molecular wave function as a sum over adiabatic Born-Oppenheimer (BO) vibronic states makes inclusion of the second-derivative nonadiabatic energy term near conical intersections practically problematic. In order to construct a well-behaved molecular wave function that has density at a conical intersection, the individual BO vibronic states in the summation must be discontinuous. When the second-derivative nonadiabatic terms are added to the Hamiltonian, singularities in the diagonal BO corrections (DBOCs) of the individual BO states arise from these discontinuities. In contrast to the well-known singularities in the first-derivative couplings at conical intersections, these singularities are non-integrable, resulting in undefined DBOC matrix elements. Though these singularities suggest that the exact molecular wave function may not have density at the conical intersection point, there is no physical basis for this constraint. Instead, the singularities are artifacts of the chosen basis of discontinuous functions. We also demonstrate that continuity of the total molecular wave function does not require continuity of the individual adiabatic nuclear wave functions. We classify nonadiabatic molecular dynamics methods according to the constraints placed on wave function continuity and analyze their formal properties. Based on our analysis, it is recommended that the DBOC be neglected when employing mixed quantum-classical methods and certain approximate quantum dynamical methods in the adiabatic representation.

Local performance optimization for a class of redundant eight-degree-of-freedom manipulators

NASA Technical Reports Server (NTRS)

Williams, Robert L., II

1994-01-01

Local performance optimization for joint limit avoidance and manipulability maximization (singularity avoidance) is obtained by using the Jacobian matrix pseudoinverse and by projecting the gradient of an objective function into the Jacobian null space. Real-time redundancy optimization control is achieved for an eight-joint redundant manipulator having a three-axis spherical shoulder, a single elbow joint, and a four-axis spherical wrist. Symbolic solutions are used for both full-Jacobian and wrist-partitioned pseudoinverses, partitioned null-space projection matrices, and all objective function gradients. A kinematic limitation of this class of manipulators and the limitation's effect on redundancy resolution are discussed. Results obtained with graphical simulation are presented to demonstrate the effectiveness of local redundant manipulator performance optimization. Actual hardware experiments performed to verify the simulated results are also discussed. A major result is that the partitioned solution is desirable because of low computation requirements. The partitioned solution is suboptimal compared with the full solution because translational and rotational terms are optimized separately; however, the results show that the difference is not significant. Singularity analysis reveals that no algorithmic singularities exist for the partitioned solution. The partitioned and full solutions share the same physical manipulator singular conditions. When compared with the full solution, the partitioned solution is shown to be ill-conditioned in smaller neighborhoods of the shared singularities.

Evolution of singularities in a partially coherent vortex beam.

PubMed

van Dijk, Thomas; Visser, Taco D

2009-04-01

We study the evolution of phase singularities and coherence singularities in a Laguerre-Gauss beam that is rendered partially coherent by letting it pass through a spatial light modulator. The original beam has an on-axis minumum of intensity--a phase singularity--that transforms into a maximum of the far-field intensity. In contrast, although the original beam has no coherence singularities, such singularities are found to develop as the beam propagates. This disappearance of one kind of singularity and the gradual appearance of another is illustrated with numerical examples.

The relationship between two fast/slow analysis techniques for bursting oscillations

PubMed Central

Teka, Wondimu; Tabak, Joël; Bertram, Richard

2012-01-01

Bursting oscillations in excitable systems reflect multi-timescale dynamics. These oscillations have often been studied in mathematical models by splitting the equations into fast and slow subsystems. Typically, one treats the slow variables as parameters of the fast subsystem and studies the bifurcation structure of this subsystem. This has key features such as a z-curve (stationary branch) and a Hopf bifurcation that gives rise to a branch of periodic spiking solutions. In models of bursting in pituitary cells, we have recently used a different approach that focuses on the dynamics of the slow subsystem. Characteristic features of this approach are folded node singularities and a critical manifold. In this article, we investigate the relationships between the key structures of the two analysis techniques. We find that the z-curve and Hopf bifurcation of the two-fast/one-slow decomposition are closely related to the voltage nullcline and folded node singularity of the one-fast/two-slow decomposition, respectively. They become identical in the double singular limit in which voltage is infinitely fast and calcium is infinitely slow. PMID:23278052

Nonlinear Interaction of Detuned Instability Waves in Boundary-Layer Transition: Amplitude Equations

NASA Technical Reports Server (NTRS)

Lee, Sang Soo

1998-01-01

The non-equilibrium critical-layer analysis of a system of frequency-detuned resonant-triads is presented. In this part of the analysis, the system of partial differential critical-layer equations derived in Part I is solved analytically to yield the amplitude equations which are analyzed using a combination of asymptotic and numerical methods. Numerical solutions of the inviscid non-equilibrium oblique-mode amplitude equations show that the frequency-detuned self-interaction enhances the growth of the lower-frequency oblique modes more than the higher-frequency ones. All amplitudes become singular at the same finite downstream position. The frequency detuning delays the occurrence of the singularity. The spanwise-periodic mean-flow distortion and low-frequency nonlinear modes are generated by the critical-layer interaction between frequency-detuned oblique modes. The nonlinear mean flow and higher harmonics as well as the primary instabilities become as large as the base mean flow in the inviscid wall layer in the downstream region where the distance from the singularity is of the order of the wavelength scale.

Naked singularity, firewall, and Hawking radiation.

PubMed

Zhang, Hongsheng

2017-06-21

Spacetime singularity has always been of interest since the proof of the Penrose-Hawking singularity theorem. Naked singularity naturally emerges from reasonable initial conditions in the collapsing process. A recent interesting approach in black hole information problem implies that we need a firewall to break the surplus entanglements among the Hawking photons. Classically, the firewall becomes a naked singularity. We find some vacuum analytical solutions in R n -gravity of the firewall-type and use these solutions as concrete models to study the naked singularities. By using standard quantum theory, we investigate the Hawking radiation emitted from the black holes with naked singularities. Here we show that the singularity itself does not destroy information. A unitary quantum theory works well around a firewall-type singularity. We discuss the validity of our result in general relativity. Further our result demonstrates that the temperature of the Hawking radiation still can be expressed in the form of the surface gravity divided by 2π. This indicates that a naked singularity may not compromise the Hakwing evaporation process.

On the Weyl curvature hypothesis

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

Stoica, Ovidiu Cristinel, E-mail: holotronix@gmail.com

2013-11-15

The Weyl curvature hypothesis of Penrose attempts to explain the high homogeneity and isotropy, and the very low entropy of the early universe, by conjecturing the vanishing of the Weyl tensor at the Big-Bang singularity. In previous papers it has been proposed an equivalent form of Einstein’s equation, which extends it and remains valid at an important class of singularities (including in particular the Schwarzschild, FLRW, and isotropic singularities). Here it is shown that if the Big-Bang singularity is from this class, it also satisfies the Weyl curvature hypothesis. As an application, we study a very general example of cosmologicalmore » models, which generalizes the FLRW model by dropping the isotropy and homogeneity constraints. This model also generalizes isotropic singularities, and a class of singularities occurring in Bianchi cosmologies. We show that the Big-Bang singularity of this model is of the type under consideration, and satisfies therefore the Weyl curvature hypothesis. -- Highlights: •The singularities we introduce are described by finite geometric/physical objects. •Our singularities have smooth Riemann and Weyl curvatures. •We show they satisfy Penrose’s Weyl curvature hypothesis (Weyl=0 at singularities). •Examples: FLRW, isotropic singularities, an extension of Schwarzschild’s metric. •Example: a large class of singularities which may be anisotropic and inhomogeneous.« less

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

Strauss, Y.; Horwitz, L. P.; Eisenberg, E.

We discuss the quantum Lax-Phillips theory of scattering and unstable systems. In this framework, the decay of an unstable system is described by a semigroup. The spectrum of the generator of the semigroup corresponds to the singularities of the Lax-Phillips S-matrix. In the case of discrete (complex) spectrum of the generator of the semigroup, associated with resonances, the decay law is exactly exponential. The states corresponding to these resonances (eigenfunctions of the generator of the semigroup) lie in the Lax-Phillips Hilbert space, and therefore all physical properties of the resonant states can be computed. We show that the Lax-Phillips S-matrixmore » is unitarily related to the S-matrix of standard scattering theory by a unitary transformation parametrized by the spectral variable σ of the Lax-Phillips theory. Analytic continuation in σ has some of the properties of a method developed some time ago for application to dilation analytic potentials. We work out an illustrative example using a Lee-Friedrichs model for the underlying dynamical system.« less

Precise identification of Dirac-like point through a finite photonic crystal square matrix

PubMed Central

Dong, Guoyan; Zhou, Ji; Yang, Xiulun; Meng, Xiangfeng

2016-01-01

The phenomena of the minimum transmittance spectrum or the maximum reflection spectrum located around the Dirac frequency have been observed to demonstrate the 1/L scaling law near the Dirac-like point through the finite ribbon structure. However, so far there is no effective way to identify the Dirac-like point accurately. In this work we provide an effective measurement method to identify the Dirac-like point accurately through a finite photonic crystal square matrix. Based on the Dirac-like dispersion achieved by the accidental degeneracy at the centre of the Brillouin zone of dielectric photonic crystal, both the simulated and experimental results demonstrate that the transmittance spectra through a finite photonic crystal square matrix not only provide the clear evidence for the existence of Dirac-like point but also can be used to identify the precise location of Dirac-like point by the characteristics of sharp cusps embedded in the extremum spectra surrounding the conical singularity. PMID:27857145

Analysis of the cable equation with non-local and non-singular kernel fractional derivative

NASA Astrophysics Data System (ADS)

Karaagac, Berat

2018-02-01

Recently a new concept of differentiation was introduced in the literature where the kernel was converted from non-local singular to non-local and non-singular. One of the great advantages of this new kernel is its ability to portray fading memory and also well defined memory of the system under investigation. In this paper the cable equation which is used to develop mathematical models of signal decay in submarine or underwater telegraphic cables will be analysed using the Atangana-Baleanu fractional derivative due to the ability of the new fractional derivative to describe non-local fading memory. The existence and uniqueness of the more generalized model is presented in detail via the fixed point theorem. A new numerical scheme is used to solve the new equation. In addition, stability, convergence and numerical simulations are presented.

Horizon quantum fuzziness for non-singular black holes

NASA Astrophysics Data System (ADS)

Giugno, Andrea; Giusti, Andrea; Helou, Alexis

2018-03-01

We study the extent of quantum gravitational effects in the internal region of non-singular, Hayward-like solutions of Einstein's field equations according to the formalism known as horizon quantum mechanics. We grant a microscopic description to the horizon by considering a huge number of soft, off-shell gravitons, which superimpose in the same quantum state, as suggested by Dvali and Gomez. In addition to that, the constituents of such a configuration are understood as loosely confined in a binding harmonic potential. A simple analysis shows that the resolution of a central singularity through quantum physics does not tarnish the classical description, which is bestowed upon this extended self-gravitating system by General Relativity. Finally, we estimate the appearance of an internal horizon as being negligible, because of the suppression of the related probability caused by the large number of virtual gravitons.

Low-energy effective worldsheet theory of a non-Abelian vortex in high-density QCD revisited: A regular gauge construction

NASA Astrophysics Data System (ADS)

Chatterjee, Chandrasekhar; Nitta, Muneto

2017-04-01

Color symmetry is spontaneously broken in quark matter at high density as a consequence of di-quark condensations with exhibiting color superconductivity. Non-Abelian vortices or color magnetic flux tubes stably exist in the color-flavor locked phase at asymptotically high density. The effective worldsheet theory of a single non-Abelian vortex was previously calculated in the singular gauge to obtain the C P2 model [1,2]. Here, we reconstruct the effective theory in a regular gauge without taking a singular gauge, confirming the previous results in the singular gauge. As a byproduct of our analysis, we find that non-Abelian vortices in high-density QCD do not suffer from any obstruction for the global definition of a symmetry breaking.

Theoretical analysis of linearized acoustics and aerodynamics of advanced supersonic propellers

NASA Technical Reports Server (NTRS)

Farassat, F.

1985-01-01

The derivation of a formula for prediction of the noise of supersonic propellers using time domain analysis is presented. This formula is a solution of the Ffowcs Williams-Hawkings equation and does not have the Doppler singularity of some other formulations. The result presented involves some surface integrals over the blade and line integrals over the leading and trailing edges. The blade geometry, motion and surface pressure are needed for noise calculation. To obtain the blade surface pressure, the observer is moved onto the blade surface and a linear singular integral equation is derived which can be solved numerically. Two examples of acoustic calculations using a computer program are currently under development.

SIGN SINGULARITY AND FLARES IN SOLAR ACTIVE REGION NOAA 11158

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

Sorriso-Valvo, L.; De Vita, G.; Kazachenko, M. D.

Solar Active Region NOAA 11158 has hosted a number of strong flares, including one X2.2 event. The complexity of current density and current helicity are studied through cancellation analysis of their sign-singular measure, which features power-law scaling. Spectral analysis is also performed, revealing the presence of two separate scaling ranges with different spectral index. The time evolution of parameters is discussed. Sudden changes of the cancellation exponents at the time of large flares and the presence of correlation with Extreme-Ultra-Violet and X-ray flux suggest that eruption of large flares can be linked to the small-scale properties of the current structures.

Resolution of quantum singularities

NASA Astrophysics Data System (ADS)

Konkowski, Deborah; Helliwell, Thomas

2017-01-01

A review of quantum singularities in static and conformally static spacetimes is given. A spacetime is said to be quantum mechanically non-singular if a quantum wave packet does not feel, in some sense, the presence of a singularity; mathematically, this means that the wave operator is essentially self-adjoint on the space of square integrable functions. Spacetimes with classical mild singularities (quasiregular ones) to spacetimes with classical strong curvature singularities have been tested. Here we discuss the similarities and differences between classical singularities that are healed quantum mechanically and those that are not. Possible extensions of the mathematical technique to more physically realistic spacetimes are discussed.

The geometry of singularities and the black hole information paradox

NASA Astrophysics Data System (ADS)

Stoica, O. C.

2015-07-01

The information loss occurs in an evaporating black hole only if the time evolution ends at the singularity. But as we shall see, the black hole solutions admit analytical extensions beyond the singularities, to globally hyperbolic solutions. The method used is similar to that for the apparent singularity at the event horizon, but at the singularity, the resulting metric is degenerate. When the metric is degenerate, the covariant derivative, the curvature, and the Einstein equation become singular. However, recent advances in the geometry of spacetimes with singular metric show that there are ways to extend analytically the Einstein equation and other field equations beyond such singularities. This means that the information can get out of the singularity. In the case of charged black holes, the obtained solutions have nonsingular electromagnetic field. As a bonus, if particles are such black holes, spacetime undergoes dimensional reduction effects like those required by some approaches to perturbative Quantum Gravity.

Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers.

PubMed

Sochat, Vanessa V; Prybol, Cameron J; Kurtzer, Gregory M

2017-01-01

Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing metadata for, visualizing, and serving containers programmatically. Our novel metrics, based on custom filters of content hashes of container contents, allow for comparison of an entire container, including operating system, custom software, and metadata. First we will review Singularity Hub's primary use cases and how the infrastructure has been designed to support modern, common workflows. Next, we conduct three analyses to demonstrate build consistency, reproducibility metric and performance and interpretability, and potential for discovery. This is the first effort to demonstrate a rigorous assessment of measurable similarity between containers and operating systems. We provide these capabilities within Singularity Hub, as well as the source software singularity-python that provides the underlying functionality. Singularity Hub is available at https://singularity-hub.org, and we are excited to provide it as an openly available platform for building, and deploying scientific containers.

Enhancing reproducibility in scientific computing: Metrics and registry for Singularity containers

PubMed Central

Prybol, Cameron J.; Kurtzer, Gregory M.

2017-01-01

Here we present Singularity Hub, a framework to build and deploy Singularity containers for mobility of compute, and the singularity-python software with novel metrics for assessing reproducibility of such containers. Singularity containers make it possible for scientists and developers to package reproducible software, and Singularity Hub adds automation to this workflow by building, capturing metadata for, visualizing, and serving containers programmatically. Our novel metrics, based on custom filters of content hashes of container contents, allow for comparison of an entire container, including operating system, custom software, and metadata. First we will review Singularity Hub’s primary use cases and how the infrastructure has been designed to support modern, common workflows. Next, we conduct three analyses to demonstrate build consistency, reproducibility metric and performance and interpretability, and potential for discovery. This is the first effort to demonstrate a rigorous assessment of measurable similarity between containers and operating systems. We provide these capabilities within Singularity Hub, as well as the source software singularity-python that provides the underlying functionality. Singularity Hub is available at https://singularity-hub.org, and we are excited to provide it as an openly available platform for building, and deploying scientific containers. PMID:29186161

Multifractal and Singularity Maps of soil surface moisture distribution derived from 2D image analysis.

NASA Astrophysics Data System (ADS)

Cumbrera, Ramiro; Millán, Humberto; Martín-Sotoca, Juan Jose; Pérez Soto, Luis; Sanchez, Maria Elena; Tarquis, Ana Maria

2016-04-01

Soil moisture distribution usually presents extreme variation at multiple spatial scales. Image analysis could be a useful tool for investigating these spatial patterns of apparent soil moisture at multiple resolutions. The objectives of the present work were (i) to describe the local scaling of apparent soil moisture distribution and (ii) to define apparent soil moisture patterns from vertical planes of Vertisol pit images. Two soil pits (0.70 m long × 0.60 m width × 0.30 m depth) were excavated on a bare Mazic Pellic Vertisol. One was excavated in April/2011 and the other pit was established in May/2011 after 3 days of a moderate rainfall event. Digital photographs were taken from each Vertisol pit using a Kodak™ digital camera. The mean image size was 1600 × 945 pixels with one physical pixel ≈373 μm of the photographed soil pit. For more details see Cumbrera et al. (2012). Geochemical exploration have found with increasingly interests and benefits of using fractal (power-law) models to characterize geochemical distribution, using the concentration-area (C-A) model (Cheng et al., 1994; Cheng, 2012). This method is based on the singularity maps of a measure that at each point define areas with self-similar properties that are shown in power-law relationships in Concentration-Area plots (C-A method). The C-A method together with the singularity map ("Singularity-CA" method) define thresholds that can be applied to segment the map. We have applied it to each soil image. The results show that, in spite of some computational and practical limitations, image analysis of apparent soil moisture patterns could be used to study the dynamical change of soil moisture sampling in agreement with previous results (Millán et al., 2016). REFERENCES Cheng, Q., Agterberg, F. P. and Ballantyne, S. B. (1994). The separation of geochemical anomalies from background by fractal methods. Journal of Geochemical Exploration, 51, 109-130. Cheng, Q. (2012). Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. Journal of Geochemical Exploration, 122, 55-70. Cumbrera, R., Ana M. Tarquis, Gabriel Gascó, Humberto Millán (2012) Fractal scaling of apparent soil moisture estimated from vertical planes of Vertisol pit images. Journal of Hydrology (452-453), 205-212. Martin Sotoca; J.J. Antonio Saa-Requejo, Juan Grau and Ana M. Tarquis (2016). Segmentation of singularity maps in the context of soil porosity. Geophysical Research Abstracts, 18, EGU2016-11402. Millán, H., Cumbrera, R. and Ana M. Tarquis (2016) Multifractal and Levy-stable statistics of soil surface moisture distribution derived from 2D image analysis. Applied Mathematical Modelling, 40(3), 2384-2395.

Singular Stokes-polarimetry as new technique for metrology and inspection of polarized speckle fields

NASA Astrophysics Data System (ADS)

Soskin, Marat S.; Denisenko, Vladimir G.; Egorov, Roman I.

2004-08-01

Polarimetry is effective technique for polarized light fields characterization. It was shown recently that most full "finger-print" of light fields with arbitrary complexity is network of polarization singularities: C points with circular polarization and L lines with variable azimuth. The new singular Stokes-polarimetry was elaborated for such measurements. It allows define azimuth, eccentricity and handedness of elliptical vibrations in each pixel of receiving CCD camera in the range of mega-pixels. It is based on precise measurement of full set of Stokes parameters by the help of high quality analyzers and quarter-wave plates with λ/500 preciseness and 4" adjustment. The matrices of obtained data are processed in PC by special programs to find positions of polarization singularities and other needed topological features. The developed SSP technique was proved successfully by measurements of topology of polarized speckle-fields produced by multimode "photonic-crystal" fibers, double side rubbed polymer films, biomedical samples. Each singularity is localized with preciseness up to +/- 1 pixel in comparison with 500 pixels dimensions of typical speckle. It was confirmed that network of topological features appeared in polarized light field after its interaction with specimen under inspection is exact individual "passport" for its characterization. Therefore, SSP can be used for smart materials characterization. The presented data show that SSP technique is promising for local analysis of properties and defects of thin films, liquid crystal cells, optical elements, biological samples, etc. It is able discover heterogeneities and defects, which define essentially merits of specimens under inspection and can"t be checked by usual polarimetry methods. The detected extra high sensitivity of polarization singularities position and network to any changes of samples position and deformation opens quite new possibilities for sensing of deformations and displacement of checked elements in the sub-micron range.

Physics of singularities in pressure-impulse theory

NASA Astrophysics Data System (ADS)

Krechetnikov, R.

2018-05-01

The classical solution in the pressure-impulse theory for the inviscid, incompressible, and zero-surface-tension water impact of a flat plate at zero dead-rise angle exhibits both singular-in-time initial fluid acceleration, ∂v /∂ t |t =0˜δ (t ) , and a near-plate-edge spatial singularity in the velocity distribution, v ˜r-1 /2 , where r is the distance from the plate edge. The latter velocity divergence also leads to the interface being stretched infinitely right after the impact, which is another nonphysical artifact. From the point of view of matched asymptotic analysis, this classical solution is a singular limit when three physical quantities achieve limiting values: sound speed c0→∞ , fluid kinematic viscosity ν →0 , and surface tension σ →0 . This leaves open a question on how to resolve these singularities mathematically by including the neglected physical effects—compressibility, viscosity, and surface tension—first one by one and then culminating in the local compressible viscous solution valid for t →0 and r →0 , demonstrating a nontrivial flow structure that changes with the degree of the bulk compressibility. In the course of this study, by starting with the general physically relevant formulation of compressible viscous flow, we clarify the parameter range(s) of validity of the key analytical solutions including classical ones (inviscid incompressible and compressible, etc.) and understand the solution structure, its intermediate asymptotics nature, characteristics influencing physical processes, and the role of potential and rotational flow components. In particular, it is pointed out that sufficiently close to the plate edge surface tension must be taken into account. Overall, the idea is to highlight the interesting physics behind the singularities in the pressure-impulse theory.

Multiscale Resilience of Complex Systems

NASA Astrophysics Data System (ADS)

Tchiguirinskaia, I.; Schertzer, D. J. M.; Giangola-Murzyn, A.; Hoang Cong, T.

2014-12-01

We first argue the need for well defined resilience metrics to better evaluate the resilience of complex systems such as (peri-)urban flood management systems. We review both the successes and limitations of resilience metrics in the framework of dynamical systems and their generalization in the framework of the viability theory. We then point out that the most important step to achieve is to define resilience across scales instead of doing it at a given scale. Our preliminary, critical analysis of the series of attempts to define an operational resilience metrics led us to consider a scale invariant metrics based on the scale independent codimension of extreme singularities. Multifractal downscaling of climate scenarios can be considered as a first illustration. We focussed on a flood scenario evaluation method with the help of two singularities γ_s and γ_Max, corresponding respectively to an effective and a probable maximum singularity, that yield an innovative framework to address the issues of flood resilience systems in a scale independent manner. Indeed, the stationarity of the universal multifractal parameters would result into a rather stable value of probable maximum singularity γ_s. By fixing the limit of acceptability for a maximum flood water depth at a given scale, with a corresponding singularity, we effectively fix the threshold of the probable maximum singularity γ_s as a criterion of the flood resilience we accept. Then various scenarios of flood resilient measures could be simulated with the help of Multi-Hydro under upcoming climat scenarios. The scenarios that result in estimates of either γ_Max or γ_s below the pre-selected γ_s value will assure the effective flood resilience of the whole modeled system across scales. The research for this work was supported, in part, by the EU FP7 SMARTesT and INTERREG IVB RainGain projects.

HydroClimATe: hydrologic and climatic analysis toolkit

USGS Publications Warehouse

Dickinson, Jesse; Hanson, Randall T.; Predmore, Steven K.

2014-01-01

The potential consequences of climate variability and climate change have been identified as major issues for the sustainability and availability of the worldwide water resources. Unlike global climate change, climate variability represents deviations from the long-term state of the climate over periods of a few years to several decades. Currently, rich hydrologic time-series data are available, but the combination of data preparation and statistical methods developed by the U.S. Geological Survey as part of the Groundwater Resources Program is relatively unavailable to hydrologists and engineers who could benefit from estimates of climate variability and its effects on periodic recharge and water-resource availability. This report documents HydroClimATe, a computer program for assessing the relations between variable climatic and hydrologic time-series data. HydroClimATe was developed for a Windows operating system. The software includes statistical tools for (1) time-series preprocessing, (2) spectral analysis, (3) spatial and temporal analysis, (4) correlation analysis, and (5) projections. The time-series preprocessing tools include spline fitting, standardization using a normal or gamma distribution, and transformation by a cumulative departure. The spectral analysis tools include discrete Fourier transform, maximum entropy method, and singular spectrum analysis. The spatial and temporal analysis tool is empirical orthogonal function analysis. The correlation analysis tools are linear regression and lag correlation. The projection tools include autoregressive time-series modeling and generation of many realizations. These tools are demonstrated in four examples that use stream-flow discharge data, groundwater-level records, gridded time series of precipitation data, and the Multivariate ENSO Index.

Physical understanding of complex multiscale biochemical models via algorithmic simplification: Glycolysis in Saccharomyces cerevisiae

NASA Astrophysics Data System (ADS)

Kourdis, Panayotis D.; Steuer, Ralf; Goussis, Dimitris A.

2010-09-01

Large-scale models of cellular reaction networks are usually highly complex and characterized by a wide spectrum of time scales, making a direct interpretation and understanding of the relevant mechanisms almost impossible. We address this issue by demonstrating the benefits provided by model reduction techniques. We employ the Computational Singular Perturbation (CSP) algorithm to analyze the glycolytic pathway of intact yeast cells in the oscillatory regime. As a primary object of research for many decades, glycolytic oscillations represent a paradigmatic candidate for studying biochemical function and mechanisms. Using a previously published full-scale model of glycolysis, we show that, due to fast dissipative time scales, the solution is asymptotically attracted on a low dimensional manifold. Without any further input from the investigator, CSP clarifies several long-standing questions in the analysis of glycolytic oscillations, such as the origin of the oscillations in the upper part of glycolysis, the importance of energy and redox status, as well as the fact that neither the oscillations nor cell-cell synchronization can be understood in terms of glycolysis as a simple linear chain of sequentially coupled reactions.

Data-driven Applications for the Sun-Earth System

NASA Astrophysics Data System (ADS)

Kondrashov, D. A.

2016-12-01

Advances in observational and data mining techniques allow extracting information from the large volume of Sun-Earth observational data that can be assimilated into first principles physical models. However, equations governing Sun-Earth phenomena are typically nonlinear, complex, and high-dimensional. The high computational demand of solving the full governing equations over a large range of scales precludes the use of a variety of useful assimilative tools that rely on applied mathematical and statistical techniques for quantifying uncertainty and predictability. Effective use of such tools requires the development of computationally efficient methods to facilitate fusion of data with models. This presentation will provide an overview of various existing as well as newly developed data-driven techniques adopted from atmospheric and oceanic sciences that proved to be useful for space physics applications, such as computationally efficient implementation of Kalman Filter in radiation belts modeling, solar wind gap-filling by Singular Spectrum Analysis, and low-rank procedure for assimilation of low-altitude ionospheric magnetic perturbations into the Lyon-Fedder-Mobarry (LFM) global magnetospheric model. Reduced-order non-Markovian inverse modeling and novel data-adaptive decompositions of Sun-Earth datasets will be also demonstrated.

Data-Driven Modeling and Prediction of Arctic Sea Ice

NASA Astrophysics Data System (ADS)

Kondrashov, Dmitri; Chekroun, Mickael; Ghil, Michael

2016-04-01

We present results of data-driven predictive analyses of sea ice over the main Arctic regions. Our approach relies on the Multilayer Stochastic Modeling (MSM) framework of Kondrashov, Chekroun and Ghil [Physica D, 2015] and it leads to probabilistic prognostic models of sea ice concentration (SIC) anomalies on seasonal time scales. This approach is applied to monthly time series of state-of-the-art data-adaptive decompositions of SIC and selected climate variables over the Arctic. We evaluate the predictive skill of MSM models by performing retrospective forecasts with "no-look ahead" for up to 6-months ahead. It will be shown in particular that the memory effects included intrinsically in the formulation of our non-Markovian MSM models allow for improvements of the prediction skill of large-amplitude SIC anomalies in certain Arctic regions on the one hand, and of September Sea Ice Extent, on the other. Further improvements allowed by the MSM framework will adopt a nonlinear formulation and explore next-generation data-adaptive decompositions, namely modification of Principal Oscillation Patterns (POPs) and rotated Multichannel Singular Spectrum Analysis (M-SSA).

Monthly streamflow forecasting with auto-regressive integrated moving average

NASA Astrophysics Data System (ADS)

Nasir, Najah; Samsudin, Ruhaidah; Shabri, Ani

2017-09-01

Forecasting of streamflow is one of the many ways that can contribute to better decision making for water resource management. The auto-regressive integrated moving average (ARIMA) model was selected in this research for monthly streamflow forecasting with enhancement made by pre-processing the data using singular spectrum analysis (SSA). This study also proposed an extension of the SSA technique to include a step where clustering was performed on the eigenvector pairs before reconstruction of the time series. The monthly streamflow data of Sungai Muda at Jeniang, Sungai Muda at Jambatan Syed Omar and Sungai Ketil at Kuala Pegang was gathered from the Department of Irrigation and Drainage Malaysia. A ratio of 9:1 was used to divide the data into training and testing sets. The ARIMA, SSA-ARIMA and Clustered SSA-ARIMA models were all developed in R software. Results from the proposed model are then compared to a conventional auto-regressive integrated moving average model using the root-mean-square error and mean absolute error values. It was found that the proposed model can outperform the conventional model.

Wavelet-based unsupervised learning method for electrocardiogram suppression in surface electromyograms.

PubMed

Niegowski, Maciej; Zivanovic, Miroslav

2016-03-01

We present a novel approach aimed at removing electrocardiogram (ECG) perturbation from single-channel surface electromyogram (EMG) recordings by means of unsupervised learning of wavelet-based intensity images. The general idea is to combine the suitability of certain wavelet decomposition bases which provide sparse electrocardiogram time-frequency representations, with the capacity of non-negative matrix factorization (NMF) for extracting patterns from images. In order to overcome convergence problems which often arise in NMF-related applications, we design a novel robust initialization strategy which ensures proper signal decomposition in a wide range of ECG contamination levels. Moreover, the method can be readily used because no a priori knowledge or parameter adjustment is needed. The proposed method was evaluated on real surface EMG signals against two state-of-the-art unsupervised learning algorithms and a singular spectrum analysis based method. The results, expressed in terms of high-to-low energy ratio, normalized median frequency, spectral power difference and normalized average rectified value, suggest that the proposed method enables better ECG-EMG separation quality than the reference methods. Copyright © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.

The complexity of the HANG SENG Index and its constituencies during the 2007-2008 Great Recession

NASA Astrophysics Data System (ADS)

Argyroudis, G.; Siokis, F.

2018-04-01

We apply the multifractal detrended moving average (MF-DMA) procedure to the daily data from HANG SENG Index (HSI) and two sub-indices, the Properties Index which consists of 10 Real Estate Companies and the Finance Index with 12 companies respectively. Two major events are considered: the 2007 and the 1997 crises. Based on scaling exponents and the singularity spectrum analysis, we show that both events reveal multiscaling and the results are robust across different indices. Furthermore, by dividing the data into two equal sub-samples for prior and after the crisis periods, we reveal that for the 2007-2008 crisis, the complexity of the HSI and Properties index remain the same between periods, while for the Finance Index, the after crisis period exhibits richer multifractality and higher complexity. Especially for the Properties Index, the results indicate that the Real Estate sector was not affected as much, by the transitory shocks of the Great Recession. As for the 1997 event, the HS Index is impacted greatly in the after period crisis exhibiting higher degree of multifractality and heterogeneity.

Performance Analysis of ICA in Sensor Array

PubMed Central

Cai, Xin; Wang, Xiang; Huang, Zhitao; Wang, Fenghua

2016-01-01

As the best-known scheme in the field of Blind Source Separation (BSS), Independent Component Analysis (ICA) has been intensively used in various domains, including biomedical and acoustics applications, cooperative or non-cooperative communication, etc. While sensor arrays are involved in most of the applications, the influence on the performance of ICA of practical factors therein has not been sufficiently investigated yet. In this manuscript, the issue is researched by taking the typical antenna array as an illustrative example. Factors taken into consideration include the environment noise level, the properties of the array and that of the radiators. We analyze the analytic relationship between the noise variance, the source variance, the condition number of the mixing matrix and the optimal signal to interference-plus-noise ratio, as well as the relationship between the singularity of the mixing matrix and practical factors concerned. The situations where the mixing process turns (nearly) singular have been paid special attention to, since such circumstances are critical in applications. Results and conclusions obtained should be instructive when applying ICA algorithms on mixtures from sensor arrays. Moreover, an effective countermeasure against the cases of singular mixtures has been proposed, on the basis of previous analysis. Experiments validating the theoretical conclusions as well as the effectiveness of the proposed scheme have been included. PMID:27164100

An Improved Transformation and Optimized Sampling Scheme for the Numerical Evaluation of Singular and Near-Singular Potentials

NASA Technical Reports Server (NTRS)

Khayat, Michael A.; Wilton, Donald R.; Fink, Patrick W.

2007-01-01

Simple and efficient numerical procedures using singularity cancellation methods are presented for evaluating singular and near-singular potential integrals. Four different transformations are compared and the advantages of the Radial-angular transform are demonstrated. A method is then described for optimizing this integration scheme.

Topological dynamics of optical singularities in speckle-fields induced by photorefractive scattering in a LiNbO{sub 3} : Fe crystal

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

Vasil'ev, Vasilii I; Soskin, M S

2013-02-28

A natural singular dynamics of elliptically polarised speckle-fields induced by the 'optical damage' effect in a photorefractive crystal of lithium niobate by a passing beam of a helium - neon laser is studied by the developed methods of singular optics. For the polarisation singularities (C points), a new class of chain reactions, namely, singular chain reactions are discovered and studied. It is shown that they obey the topological charge and sum Poincare index conservation laws. In addition, they exist for all the time of crystal irradiation. They consist of a series of interlocking chains, where singularity pairs arising in amore » chain annihilate with singularities from neighbouring independently created chains. Less often singular 'loop' reactions are observed where arising pairs of singularities annihilate after reversible transformations in within the boundaries of a single speckle. The type of a singular reaction is determined by a topology and dynamics of the speckles, in which the reactions are developing. (laser optics 2012)« less

Are Singularities Integral to General Theory of Relativity?

NASA Astrophysics Data System (ADS)

Krori, K.; Dutta, S.

2011-11-01

Since the 1960s the general relativists have been deeply obsessed with the possibilities of GTR singularities - blackhole as well as cosmological singularities. Senovilla, for the first time, followed by others, showed that there are cylindrically symmetric cosmological space-times which are free of singularities. On the other hand, Krori et al. have presently shown that spherically symmetric cosmological space-times - which later reduce to FRW space-times may also be free of singularities. Besides, Mitra has in the mean-time come forward with some realistic calculations which seem to rule out the possibility of a blackhole singularity. So whether singularities are integral to GTR seems to come under a shadow.

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

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

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

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

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

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

Imaging a non-singular rotating black hole at the center of the Galaxy

NASA Astrophysics Data System (ADS)

Lamy, F.; Gourgoulhon, E.; Paumard, T.; Vincent, F. H.

2018-06-01

We show that the rotating generalization of Hayward’s non-singular black hole previously studied in the literature is geodesically incomplete, and that its straightforward extension leads to a singular spacetime. We present another extension, which is devoid of any curvature singularity. The obtained metric depends on three parameters and, depending on their values, yields an event horizon or not. These two regimes, named respectively regular rotating Hayward black hole and naked rotating wormhole, are studied both numerically and analytically. In preparation for the upcoming results of the Event Horizon Telescope, the images of an accretion torus around Sgr A*, the supermassive object at the center of the Galaxy, are computed. These images contain, even in the absence of a horizon, a central faint region which bears a resemblance to the shadow of Kerr black holes and emphasizes the difficulty of claiming the existence of an event horizon from the analysis of strong-field images. The frequencies of the co- and contra-rotating orbits at the innermost stable circular orbit (ISCO) in this geometry are also computed, in the hope that quasi-periodic oscillations may permit to compare this model with Kerr’s black hole on observational grounds.

On SYM theory and all order bulk singularity structures of BPS strings in type II theory

NASA Astrophysics Data System (ADS)

Hatefi, Ehsan

2018-06-01

The complete forms of the S-matrix elements of a transverse scalar field, two world volume gauge fields, and a Potential Cn-1 Ramond-Ramond (RR) form field are investigated. In order to find an infinite number of t , s , (t + s + u)-channel bulk singularity structures of this particular mixed open-closed amplitude, we employ all the conformal field theory techniques to , exploring all the entire correlation functions and all order α‧ contact interactions to these supersymmetric Yang-Mills (SYM) couplings. Singularity and contact term comparisons with the other symmetric analysis, and are also carried out in detail. Various couplings from pull-Back of branes, Myers terms and several generalized Bianchi identities should be taken into account to be able to reconstruct all order α‧ bulk singularities of type IIB (IIA) superstring theory. Finally, we make a comment on how to derive without any ambiguity all order α‧ contact terms of this S-matrix which carry momentum of RR in transverse directions.

On the dynamic singularities in the control of free-floating space manipulators

NASA Technical Reports Server (NTRS)

Papadopoulos, E.; Dubowsky, S.

1989-01-01

It is shown that free-floating space manipulator systems have configurations which are dynamically singular. At a dynamically singular position, the manipulator is unable to move its end effector in some direction. This problem appears in any free-floating space manipulator system that permits the vehicle to move in response to manipulator motion without correction from the vehicle's attitude control system. Dynamic singularities are functions of the dynamic properties of the system; their existence and locations cannot be predicted solely from the kinematic structure of the manipulator, unlike the singularities for fixed base manipulators. It is also shown that the location of these dynamic singularities in the workplace is dependent upon the path taken by the manipulator in reaching them. Dynamic singularities must be considered in the control, planning and design of free-floating space manipulator systems. A method for calculating these dynamic singularities is presented, and it is shown that the system parameters can be selected to reduce the effect of dynamic singularities on a system's performance.

The Hawking-Penrose Singularity Theorem for C 1,1-Lorentzian Metrics

NASA Astrophysics Data System (ADS)

Graf, Melanie; Grant, James D. E.; Kunzinger, Michael; Steinbauer, Roland

2018-06-01

We show that the Hawking-Penrose singularity theorem, and the generalisation of this theorem due to Galloway and Senovilla, continue to hold for Lorentzian metrics that are of C 1,1-regularity. We formulate appropriate weak versions of the strong energy condition and genericity condition for C 1,1-metrics, and of C 0-trapped submanifolds. By regularisation, we show that, under these weak conditions, causal geodesics necessarily become non-maximising. This requires a detailed analysis of the matrix Riccati equation for the approximating metrics, which may be of independent interest.

FREQ: A computational package for multivariable system loop-shaping procedures

NASA Technical Reports Server (NTRS)

Giesy, Daniel P.; Armstrong, Ernest S.

1989-01-01

Many approaches in the field of linear, multivariable time-invariant systems analysis and controller synthesis employ loop-sharing procedures wherein design parameters are chosen to shape frequency-response singular value plots of selected transfer matrices. A software package, FREQ, is documented for computing within on unified framework many of the most used multivariable transfer matrices for both continuous and discrete systems. The matrices are evaluated at user-selected frequency-response values, and singular values against frequency. Example computations are presented to demonstrate the use of the FREQ code.

Extreme value laws for fractal intensity functions in dynamical systems: Minkowski analysis

NASA Astrophysics Data System (ADS)

Mantica, Giorgio; Perotti, Luca

2016-09-01

Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase-space. In this paper we generalize this situation to fractal landscapes, i.e. intensity functions characterized by an uncountable set of singularities, located on a Cantor set. This reveals the dynamical rôle of classical quantities like the Minkowski dimension and content, whose definition we extend to account for singular continuous invariant measures. We also introduce the concept of extremely rare event, quantified by non-standard Minkowski constants and we study its consequences to extreme value statistics. Limit laws are derived from formal calculations and are verified by numerical experiments. Dedicated to the memory of Joseph Ford, on the twentieth anniversary of his departure.

Composite fuzzy sliding mode control of nonlinear singularly perturbed systems.

PubMed

Nagarale, Ravindrakumar M; Patre, B M

2014-05-01

This paper deals with the robust asymptotic stabilization for a class of nonlinear singularly perturbed systems using the fuzzy sliding mode control technique. In the proposed approach the original system is decomposed into two subsystems as slow and fast models by the singularly perturbed method. The composite fuzzy sliding mode controller is designed for stabilizing the full order system by combining separately designed slow and fast fuzzy sliding mode controllers. The two-time scale design approach minimizes the effect of boundary layer system on the full order system. A stability analysis allows us to provide sufficient conditions for the asymptotic stability of the full order closed-loop system. The simulation results show improved system performance of the proposed controller as compared to existing methods. The experimentation results validate the effectiveness of the proposed controller. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Ideal evolution of magnetohydrodynamic turbulence when imposing Taylor-Green symmetries.

PubMed

Brachet, M E; Bustamante, M D; Krstulovic, G; Mininni, P D; Pouquet, A; Rosenberg, D

2013-01-01

We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the fourfold symmetries of the Taylor-Green vortex generalized to MHD, leading to substantial computer time and memory savings at a given resolution; we also use a regridding method that allows for lower-resolution runs at early times, with no loss of spectral accuracy. One magnetic configuration is examined at an equivalent resolution of 6144(3) points and three different configurations on grids of 4096(3) points. At the highest resolution, two different current and vorticity sheet systems are found to collide, producing two successive accelerations in the development of small scales. At the latest time, a convergence of magnetic field lines to the location of maximum current is probably leading locally to a strong bending and directional variability of such lines. A novel analytical method, based on sharp analysis inequalities, is used to assess the validity of the finite-time singularity scenario. This method allows one to rule out spurious singularities by evaluating the rate at which the logarithmic decrement of the analyticity-strip method goes to zero. The result is that the finite-time singularity scenario cannot be ruled out, and the singularity time could be somewhere between t=2.33 and t=2.70. More robust conclusions will require higher resolution runs and grid-point interpolation measurements of maximum current and vorticity.

Finite element techniques applied to cracks interacting with selected singularities

NASA Technical Reports Server (NTRS)

Conway, J. C.

1975-01-01

The finite-element method for computing the extensional stress-intensity factor for cracks approaching selected singularities of varied geometry is described. Stress-intensity factors are generated using both displacement and J-integral techniques, and numerical results are compared to those obtained experimentally in a photoelastic investigation. The selected singularities considered are a colinear crack, a circular penetration, and a notched circular penetration. Results indicate that singularities greatly influence the crack-tip stress-intensity factor as the crack approaches the singularity. In addition, the degree of influence can be regulated by varying the overall geometry of the singularity. Local changes in singularity geometry have little effect on the stress-intensity factor for the cases investigated.

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

PubMed

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

2015-05-04

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

The effect of spherical aberration on the phase singularities of focused dark-hollow Gaussian beams

NASA Astrophysics Data System (ADS)

Luo, Yamei; Lü, Baida

2009-06-01

The phase singularities of focused dark-hollow Gaussian beams in the presence of spherical aberration are studied. It is shown that the evolution behavior of phase singularities of focused dark-hollow Gaussian beams in the focal region depends not only on the truncation parameter and beam order, but also on the spherical aberration. The spherical aberration leads to an asymmetric spatial distribution of singularities outside the focal plane and to a shift of singularities near the focal plane. The reorganization process of singularities and spatial distribution of singularities are additionally dependent on the sign of the spherical aberration. The results are illustrated by numerical examples.

Unidirectional spectral singularities.

PubMed

Ramezani, Hamidreza; Li, Hao-Kun; Wang, Yuan; Zhang, Xiang

2014-12-31

We propose a class of spectral singularities emerging from the coincidence of two independent singularities with highly directional responses. These spectral singularities result from resonance trapping induced by the interplay between parity-time symmetry and Fano resonances. At these singularities, while the system is reciprocal in terms of a finite transmission, a simultaneous infinite reflection from one side and zero reflection from the opposite side can be realized.

Mathematical analysis of the 1D model and reconstruction schemes for magnetic particle imaging

NASA Astrophysics Data System (ADS)

Erb, W.; Weinmann, A.; Ahlborg, M.; Brandt, C.; Bringout, G.; Buzug, T. M.; Frikel, J.; Kaethner, C.; Knopp, T.; März, T.; Möddel, M.; Storath, M.; Weber, A.

2018-05-01

Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

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…

Solving of the coefficient inverse problems for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time data

NASA Astrophysics Data System (ADS)

Lukyanenko, D. V.; Shishlenin, M. A.; Volkov, V. T.

2018-01-01

We propose the numerical method for solving coefficient inverse problem for a nonlinear singularly perturbed reaction-diffusion-advection equation with the final time observation data based on the asymptotic analysis and the gradient method. Asymptotic analysis allows us to extract a priory information about interior layer (moving front), which appears in the direct problem, and boundary layers, which appear in the conjugate problem. We describe and implement the method of constructing a dynamically adapted mesh based on this a priory information. The dynamically adapted mesh significantly reduces the complexity of the numerical calculations and improve the numerical stability in comparison with the usual approaches. Numerical example shows the effectiveness of the proposed method.

Considerations on the moving contact-line singularity, with application to frictional drag on a slender drop

NASA Technical Reports Server (NTRS)

Durbin, P. A.

1988-01-01

It has previously been shown that the no-slip boundary conditions leads to a singularity at a moving contact line and that this presumes some form of slip. Present considerations on the energetics of slip due to shear stress lead to a yield stress boundary condition. A model for the distortion of the liquid state near solid boundaries gives a physical basis for this boundary condition. The yield stress condition is illustrated by an analysis of a slender drop rolling down an incline. That analysis provides a formula for the frictional drag resisting the drop movement. With the present boundary condition, the length of the slip region becomes a property of the fluid flow.

A 1500-year record of climatic and environmental change in Elk Lake, Minnesota I: Varve thickness and gray-scale density

USGS Publications Warehouse

Dean, W.; Anderson, R.; Platt, Bradbury J.; Anderson, D.

2002-01-01

The deepest part (29.5 m) of Elk Lake, Clearwater County, northwestern Minnesota, contains a complete Holocene section that is continuously varved. The varve components are predominantly autochthonous (CaCO3, organic matter, biogenic silica, and several iron and manganese minerals), but the varves do contain a minor detrital-clastic (aluminosilicate) component that is predominantly wind-borne (eolian) and provides an important record of atmospheric conditions. Singular spectrum analysis (SSA) and wavelet analysis of varve thickness recognized significant periodicities in the multicentennial and multidecadal bands that varied in power (i.e., variable significance) and position (i.e., variable period) within the periodic bands. Persistent periodicities of about 10, 22, 40, and 90 years, and, in particular, multicentennial periodicities in varve thickness and other proxy variables are similar to those in spectra of radiocarbon production, a proxy for past solar activity. This suggests that there may be a solar control, perhaps through geomagnetic effects on atmospheric circulation. Multicentennial and multidecadal periodicities also occur in wavelet spectra of relative gray-scale density. However, gray-scale density does not appear to correlate with any of the measured proxy variables, and at this point we do not know what controlled gray scale.

A stacking method and its applications to Lanzarote tide gauge records

NASA Astrophysics Data System (ADS)

Zhu, Ping; van Ruymbeke, Michel; Cadicheanu, Nicoleta

2009-12-01

A time-period analysis tool based on stacking is introduced in this paper. The original idea comes from the classical tidal analysis method. It is assumed that the period of each major tidal component is precisely determined based on the astronomical constants and it is unchangeable with time at a given point in the Earth. We sum the tidal records at a fixed tidal component center period T then take the mean of it. The stacking could significantly increase the signal-to-noise ratio (SNR) if a certain number of stacking circles is reached. The stacking results were fitted using a sinusoidal function, the amplitude and phase of the fitting curve is computed by the least squares methods. The advantage of the method is that: (1) an individual periodical signal could be isolated by stacking; (2) one can construct a linear Stacking-Spectrum (SSP) by changing the stacking period Ts; (3) the time-period distribution of the singularity component could be approximated by a Sliding-Stacking approach. The shortcoming of the method is that in order to isolate a low energy frequency or separate the nearby frequencies, we need a long enough series with high sampling rate. The method was tested with a numeric series and then it was applied to 1788 days Lanzarote tide gauge records as an example.

Quantum gravitational collapse as a Dirac particle on the half line

NASA Astrophysics Data System (ADS)

Hassan, Syed Moeez; Husain, Viqar; Ziprick, Jonathan

2018-05-01

We show that the quantum dynamics of a thin spherical shell in general relativity is equivalent to the Coulomb-Dirac equation on the half line. The Hamiltonian has a one-parameter family of self-adjoint extensions with a discrete energy spectrum |E |m , where m is the rest mass of the shell and E is the Arnowitt-Deser-Misner mass. For sufficiently large m , the ground state energy level is negative. This suggests that classical positivity of energy does not survive quantization. The scattering states provide a realization of singularity avoidance. We speculate on the consequences of these results for black hole radiation.

Time-dependent mean-field theory for x-ray near-edge spectroscopy

NASA Astrophysics Data System (ADS)

Bertsch, G. F.; Lee, A. J.

2014-02-01

We derive equations of motion for calculating the near-edge x-ray absorption spectrum in molecules and condensed matter, based on a two-determinant approximation and Dirac's variational principle. The theory provides an exact solution for the linear response when the Hamiltonian or energy functional has only diagonal interactions in some basis. We numerically solve the equations to compare with the Mahan-Nozières-De Dominicis theory of the edge singularity in metallic conductors. Our extracted power-law exponents are similar to those of the analytic theory, but are not in quantitative agreement. The calculational method can be readily generalized to treat Kohn-Sham Hamiltonians with electron-electron interactions derived from correlation-exchange potentials.

Hyperasymptotics and quark-hadron duality violations in QCD

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Frequency-Independent Response of Self-Complementary Checkerboard Screens

NASA Astrophysics Data System (ADS)

Urade, Yoshiro; Nakata, Yosuke; Nakanishi, Toshihiro; Kitano, Masao

2015-06-01

This research resolves a long-standing problem on the electromagnetic response of self-complementary metallic screens with checkerboardlike geometry. Although Babinet's principle implies that they show a frequency-independent response, this unusual characteristic has not been observed yet due to the singularities of the metallic point contacts in the checkerboard geometry. We overcome this difficulty by replacing the point contacts with resistive sheets. The proposed structure is prepared and characterized by terahertz time-domain spectroscopy. It is experimentally confirmed that the resistive checkerboard structures exhibit a flat transmission spectrum over 0.1-1.1 THz. It is also demonstrated that self-complementarity can eliminate even the frequency-dependent transmission characteristics of resonant metamaterials.

Tachyon field in loop quantum cosmology: An example of traversable singularity

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

Li Lifang; Zhu Jianyang

2009-06-15

Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universe through a bounce in the high energy region. But LQC has an ambiguity about the quantization scheme. Recently, the authors in [Phys. Rev. D 77, 124008 (2008)] proposed a new quantization scheme. Similar to others, this new quantization scheme also replaces the big bang singularity with the quantum bounce. More interestingly, it introduces a quantum singularity, which is traversable. We investigate this novel dynamics quantitatively with a tachyon scalar field, which gives us a concrete example. Our result shows that our universe can evolve through the quantum singularity regularly,more » which is different from the classical big bang singularity. So this singularity is only a weak singularity.« less

Singular perturbation analysis of the steady-state Poisson–Nernst–Planck system: Applications to ion channels

PubMed Central

SINGER, A.; GILLESPIE, D.; NORBURY, J.; EISENBERG, R. S.

2009-01-01

Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst–Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current–voltage (I–V ) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I–V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages). PMID:19809600

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.

Features of the Percolation Scheme of Vibrational Spectrum Reconstruction in the Ga1 - x Al x P Alloy

NASA Astrophysics Data System (ADS)

Kozyrev, S. P.

2018-04-01

Specific features of the properties of Ga-P lattice vibrations have been investigated using the percolation model of a mixed Ga1 - x Al x P crystal (alloy) with zero lattice mismatch between binary components of the alloy. In contrast to other two-mode alloy systems, in Ga1 - x Al x P a percolation splitting of δ 13 cm-1 is observed for the low-frequency mode of GaP-like vibrations. An additional GaP mode (one of the percolation doublet components) split from the fundamental mode is observed for the GaP-rich alloy, which coincides in frequency with the gap corresponding to the zero density of one-phonon states of the GaP crystal. The vibrational spectrum of impurity Al in the GaP crystal has been calculated using the theory of crystal lattice dynamics. Upon substitution of lighter Al for the Ga atom, the calculated spectrum includes, along with the local mode, a singularity near the gap with the zero density of phonon states of the GaP crystal, which coincides with the mode observed experimentally at a frequency of 378 cm-1 in the Ga1 - x Al x P ( x < 0.4) alloy.

Local Self-Similarity and Finite-Time Singularity in a High-Symmetry Euler Flow

NASA Astrophysics Data System (ADS)

Ng, C. S.; Bhattacharjee, A.

1997-11-01

The dynamical consequence of a positive fourth-order pressure derivative (p_xxxx) at the origin [C. S. Ng and A. Bhattacharjee, Phys. Rev. E 54 1530, 1996] in a high-symmetry Euler flow (the Kida flow) is considered. It is shown that the third order spatial derivative u_xxx of the x component of the velocity u at the origin is always decreasing in this situation. By assuming that u_xxx always attains a minimum possible value consistent with a given spectral profile, it is found that the flow is locally self-similar near the origin and collapses as energy cascades to Fourier modes with higher wavenumbers k. Moreover, it is found that the self-similar p(x) and u(x) profiles (as well as their derivatives) near the origin are very similar in shape to what were found in numerical simulations [O. N. Boratav and R. B. Pelz, Phys. Fluids 6 2757, 1994]. It is shown that a finite-time singularity (FTS) must appear in this case if the spectral index ν of the energy spectrum E(k) ∝ k^-ν of the locally self-similar flow is less than 6. A self-similar solution satisfying the Kelvin's theorem of circulation trivially has ν = 2 with vortex filaments and a FTS.

Where Are the Logical Errors in the Theory of Big Bang?

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2015-04-01

The critical analysis of the foundations of the theory of Big Bang is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is argued that the starting point of the theory of Big Bang contains three fundamental logical errors. The first error is the assumption that a macroscopic object (having qualitative determinacy) can have an arbitrarily small size and can be in the singular state (i.e., in the state that has no qualitative determinacy). This assumption implies that the transition, (macroscopic object having the qualitative determinacy) --> (singular state of matter that has no qualitative determinacy), leads to loss of information contained in the macroscopic object. The second error is the assumption that there are the void and the boundary between matter and void. But if such boundary existed, then it would mean that the void has dimensions and can be measured. The third error is the assumption that the singular state of matter can make a transition into the normal state without the existence of the program of qualitative and quantitative development of the matter, without controlling influence of other (independent) object. However, these assumptions conflict with the practice and, consequently, formal logic, rational dialectics, and cybernetics. Indeed, from the point of view of cybernetics, the transition, (singular state of the Universe) -->(normal state of the Universe),would be possible only in the case if there was the Managed Object that is outside the Universe and have full, complete, and detailed information about the Universe. Thus, the theory of Big Bang is a scientific fiction.

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.

Singularities in loop quantum cosmology.

PubMed

Cailleteau, Thomas; Cardoso, Antonio; Vandersloot, Kevin; Wands, David

2008-12-19

We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of loop quantum cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of curvature singularities.

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.

Field singularities at lossless metal-dielectric arbitrary-angle edges and their ramifications to the numerical modeling of gratings.

PubMed

Li, Lifeng

2012-04-01

I extend a previous work [J. Opt. Soc. Am. A, 738 (2011)] on field singularities at lossless metal-dielectric right-angle edges and their ramifications to the numerical modeling of gratings to the case of arbitrary metallic wedge angles. Simple criteria are given that allow one knowing the lossless permittivities and the arbitrary wedge angles to determine if the electric field at the edges is nonsingular, can be regularly singular, or can be irregularly singular without calculating the singularity exponent. Furthermore, the knowledge of the singularity type enables one to predict immediately if a numerical method that uses Fourier expansions of the transverse electric field components at the edges will converge or not without making any numerical tests. All conclusions of the previous work about the general relationships between field singularities, Fourier representation of singular fields, and convergence of numerical methods for modeling lossless metal-dielectric gratings have been reconfirmed.

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.

Future singularity avoidance in phantom dark energy models

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

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

2012-07-01

Different approaches to quantum cosmology are studied in order to deal with the future singularity avoidance problem. Our results show that these future singularities will persist but could take different forms. As an example we have studied the big rip which appear when one considers the state equation P = ωρ with ω < −1, showing that it does not disappear in modified gravity. On the other hand, it is well-known that quantum geometric effects (holonomy corrections) in loop quantum cosmology introduce a quadratic modification, namely proportional to ρ{sup 2}, in Friedmann's equation that replace the big rip by amore » non-singular bounce. However this modified Friedmann equation could have been obtained in an inconsistent way, what means that the obtained results from this equation, in particular singularity avoidance, would be incorrect. In fact, we will show that instead of a non-singular bounce, the big rip singularity would be replaced, in loop quantum cosmology, by other kind of singularity.« less

Loop quantum cosmology and singularities.

PubMed

Struyve, Ward

2017-08-15

Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.

A novel equivalent definition of Caputo fractional derivative without singular kernel and superconvergent analysis

NASA Astrophysics Data System (ADS)

Liu, Zhengguang; Li, Xiaoli

2018-05-01

In this article, we present a new second-order finite difference discrete scheme for a fractal mobile/immobile transport model based on equivalent transformative Caputo formulation. The new transformative formulation takes the singular kernel away to make the integral calculation more efficient. Furthermore, this definition is also effective where α is a positive integer. Besides, the T-Caputo derivative also helps us to increase the convergence rate of the discretization of the α-order(0 < α < 1) Caputo derivative from O(τ2-α) to O(τ3-α), where τ is the time step. For numerical analysis, a Crank-Nicolson finite difference scheme to solve the fractal mobile/immobile transport model is introduced and analyzed. The unconditional stability and a priori estimates of the scheme are given rigorously. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

New singularities in unexpected places

NASA Astrophysics Data System (ADS)

Barrow, John D.; Graham, Alexander A. H.

2015-09-01

Spacetime singularities have been discovered which are physically much weaker than those predicted by the classical singularity theorems. Geodesics evolve through them and they only display infinities in the derivatives of their curvature invariants. So far, these singularities have appeared to require rather exotic and unphysical matter for their occurrence. Here, we show that a large class of singularities of this form can be found in a simple Friedmann cosmology containing only a scalar-field with a power-law self-interaction potential. Their existence challenges several preconceived ideas about the nature of spacetime singularities and has an impact upon the end of inflation in the early universe.

Low-thrust trajectory analysis for the geosynchronous mission

NASA Technical Reports Server (NTRS)

Jasper, T. P.

1973-01-01

Methodology employed in development of a computer program designed to analyze optimal low-thrust trajectories is described, and application of the program to a Solar Electric Propulsion Stage (SEPS) geosynchronous mission is discussed. To avoid the zero inclination and eccentricity singularities which plague many small-force perturbation techniques, a special set of state variables (equinoctial) is used. Adjoint equations are derived for the minimum time problem and are also free from the singularities. Solutions to the state and adjoint equations are obtained by both orbit averaging and precision numerical integration; an evaluation of these approaches is made.

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

NASA Technical Reports Server (NTRS)

Guzman, J. J.; Mailhe, L. M.; Schiff, C.; Hughes, S. P.; Folta, D. C.

2002-01-01

In this paper, a summary of primer vector theory is presented. The applicability of primer vector theory is examined in an effort to understand when and why the theory can fail. For example, since the Calculus of Variations is based on "small" variations, singularities in the linearized (variational) equations of motion along the arcs must be taken into account. These singularities are a recurring problem in analyse that employ small variations. Two examples, the initialization of an orbit and a line of apsides rotation, are presented. Recommendations, future work, and the possible addition of other optimization techniques are also discussed.

On a two-particle bound system on the half-line

NASA Astrophysics Data System (ADS)

Kerner, Joachim; Mühlenbruch, Tobias

2017-10-01

In this paper we provide an extension of the model discussed in [10] describing two singularly interacting particles on the half-line ℝ+. In this model, the particles are interacting only whenever at least one particle is situated at the origin. Stimulated by [11] we then provide a generalisation of this model in order to include additional interactions between the particles leading to a molecular-like state. We give a precise mathematical formulation of the Hamiltonian of the system and perform spectral analysis. In particular, we are interested in the effect of the singular two-particle interactions onto the molecule.

Vaidya spacetime in the diagonal coordinates

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

Berezin, V. A., E-mail: berezin@inr.ac.ru; Dokuchaev, V. I., E-mail: dokuchaev@inr.ac.ru; Eroshenko, Yu. N., E-mail: eroshenko@inr.ac.ru

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric andmore » cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g{sub 00} = 0 or g{sub 00} = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.« less

Dynamical singularities for complex initial conditions and the motion at a real separatrix.

PubMed

Shnerb, Tamar; Kay, K G

2006-04-01

This work investigates singularities occurring at finite real times in the classical dynamics of one-dimensional double-well systems with complex initial conditions. The objective is to understand the relationship between these singularities and the behavior of the systems for real initial conditions. An analytical treatment establishes that the dynamics of a quartic double well system possesses a doubly infinite sequence of singularities. These are associated with initial conditions that converge to those for the real separatrix as the singularity time becomes infinite. This confluence of singularities is shown to lead to the unstable behavior that characterizes the real motion at the separatrix. Numerical calculations confirm the existence of a large number of singularities converging to the separatrix for this and two additional double-well systems. The approach of singularities to the real axis is of particular interest since such behavior has been related to the formation of chaos in nonintegrable systems. The properties of the singular trajectories which cause this convergence to the separatrix are identified. The hyperbolic fixed point corresponding to the potential energy maximum, responsible for the characteristic motion at a separatrix, also plays a critical role in the formation of the complex singularities by delaying trajectories and then deflecting them into asymptotic regions of space from where they are directly repelled to infinity in a finite time.

Topological resolution of gauge theory singularities

NASA Astrophysics Data System (ADS)

Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

2013-08-01

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric SU(2) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit the singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.

Adaptive evolution of defense ability leads to diversification of prey species.

PubMed

Zu, Jian; Wang, Jinliang; Du, Jianqiang

2014-06-01

In this paper, by using the adaptive dynamics approach, we investigate how the adaptive evolution of defense ability promotes the diversity of prey species in an initial one-prey-two-predator community. We assume that the prey species can evolve to a safer strategy such that it can reduce the predation risk, but a prey with a high defense ability for one predator may have a low defense ability for the other and vice versa. First, by using the method of critical function analysis, we find that if the trade-off is convex in the vicinity of the evolutionarily singular strategy, then this singular strategy is a continuously stable strategy. However, if the trade-off is weakly concave near the singular strategy and the competition between the two predators is relatively weak, then the singular strategy may be an evolutionary branching point. Second, we find that after the branching has occurred in the prey strategy, if the trade-off curve is globally concave, then the prey species might eventually evolve into two specialists, each caught by only one predator species. However, if the trade-off curve is convex-concave-convex, the prey species might eventually branch into two partial specialists, each being caught by both of the two predators and they can stably coexist on the much longer evolutionary timescale.

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.

Super-nodal methods for space-time kinetics

NASA Astrophysics Data System (ADS)

Mertyurek, Ugur

The purpose of this research has been to develop an advanced Super-Nodal method to reduce the run time of 3-D core neutronics models, such as in the NESTLE reactor core simulator and FORMOSA nuclear fuel management optimization codes. Computational performance of the neutronics model is increased by reducing the number of spatial nodes used in the core modeling. However, as the number of spatial nodes decreases, the error in the solution increases. The Super-Nodal method reduces the error associated with the use of coarse nodes in the analyses by providing a new set of cross sections and ADFs (Assembly Discontinuity Factors) for the new nodalization. These so called homogenization parameters are obtained by employing consistent collapsing technique. During this research a new type of singularity, namely "fundamental mode singularity", is addressed in the ANM (Analytical Nodal Method) solution. The "Coordinate Shifting" approach is developed as a method to address this singularity. Also, the "Buckling Shifting" approach is developed as an alternative and more accurate method to address the zero buckling singularity, which is a more common and well known singularity problem in the ANM solution. In the course of addressing the treatment of these singularities, an effort was made to provide better and more robust results from the Super-Nodal method by developing several new methods for determining the transverse leakage and collapsed diffusion coefficient, which generally are the two main approximations in the ANM methodology. Unfortunately, the proposed new transverse leakage and diffusion coefficient approximations failed to provide a consistent improvement to the current methodology. However, improvement in the Super-Nodal solution is achieved by updating the homogenization parameters at several time points during a transient. The update is achieved by employing a refinement technique similar to pin-power reconstruction. A simple error analysis based on the relative residual in the 3-D few group diffusion equation at the fine mesh level is also introduced in this work.

The development of a mixing layer under the action of weak streamwise vortices

NASA Technical Reports Server (NTRS)

Goldstein, Marvin E.; Mathew, Joseph

1993-01-01

The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds-number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon(sup -1)), where epsilon is much less than 1 is the cross flow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by the appearance of a singularity. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the singular location.

Protein Aggregation/Folding: The Role of Deterministic Singularities of Sequence Hydrophobicity as Determined by Nonlinear Signal Analysis of Acylphosphatase and Aβ(1–40)

PubMed Central

Zbilut, Joseph P.; Colosimo, Alfredo; Conti, Filippo; Colafranceschi, Mauro; Manetti, Cesare; Valerio, MariaCristina; Webber, Charles L.; Giuliani, Alessandro

2003-01-01

The problem of protein folding vs. aggregation was investigated in acylphosphatase and the amyloid protein Aβ(1–40) by means of nonlinear signal analysis of their chain hydrophobicity. Numerical descriptors of recurrence patterns provided the basis for statistical evaluation of folding/aggregation distinctive features. Static and dynamic approaches were used to elucidate conditions coincident with folding vs. aggregation using comparisons with known protein secondary structure classifications, site-directed mutagenesis studies of acylphosphatase, and molecular dynamics simulations of amyloid protein, Aβ(1–40). The results suggest that a feature derived from principal component space characterized by the smoothness of singular, deterministic hydrophobicity patches plays a significant role in the conditions governing protein aggregation. PMID:14645049

7 CFR 46.1 - Words in singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the plural...

7 CFR 61.1 - Words in singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 3 2010-01-01 2010-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall be...

Transient infrared spectroscopy: a new approach to investigate valence tautomerism.

PubMed

Touceda, Patricia Tourón; Patricia, Tourón Touceda; Vázquez, Sandra Mosquera; Sandra, Mosquera Vázquez; Lima, Manuela; Manuela, Lima; Lapini, Andrea; Andrea, Lapini; Foggi, Paolo; Paolo, Foggi; Dei, Andrea; Andrea, Dei; Righini, Roberto; Roberto, Righini

2012-01-14

In this work we present, to our knowledge for the first time, the results of a transient infrared spectroscopic study of the photoinduced valence tautomerism process in cobalt-dioxolene complexes with sub-picosecond time resolution. The molecular systems investigated were [Co(tpa)(diox)]PF(6) (1) and [Co(Me(3)tpa)(diox)]PF(6) (2), where diox = 3,5-di-tert-butyl-1,2-dioxolene; tpa = tris(2-pyridylmethyl)amine and Me(3)tpa its 6-methylated analogue. Complex (1) is present in solution as ls-Co(III)(catecholate) (1-CAT), while (2) as hs-Co(II)(semiquinonate) (2-SQ). DFT calculation of the harmonic frequencies for (1) and (2) allowed us to identify the vibrational markers of catecholate and semiquinonate redox isomers. Irradiation with 405 and 810 nm pulses (~35 fs) of (1-CAT) induces the formation of an intermediate excited species from which the ground state population is recovered with a time constant of 1.5 ± 0.3 ns. Comparing the 1 ns transient infrared spectrum with the experimental difference spectrum FTIR(2-SQ)-FTIR(1-CAT) and with the calculated difference spectrum IR(c)(1-SQ)-IR(c)(1-CAT) we are able to unequivocally identify the long lived species as the semiquinonate redox isomer of (1). On the other hand, no evidence of photoconversion is observed upon irradiation of (2) with 405 nm. Temporal evolution of transient spectra was analyzed with the combined approach consisting of singular values decomposition and global fitting (global analysis). After 405 and 810 nm excitation of (1-CAT), the semiquinonate excited species is formed on an ultrafast time scale (<200 fs) and cools down within the first 50 ps. Excitation of (2-SQ) with 405 nm wavelength produces a short lived excited state in which the semiquinonate nature of dioxolene is preserved and the ground state recovery is completed within 30 ps.

Multifractal two-scale Cantor set model for slow solar wind turbulence in the outer heliosphere during solar maximum

NASA Astrophysics Data System (ADS)

Macek, W. M.; Wawrzaszek, A.

2011-05-01

To quantify solar wind turbulence, we consider a generalized two-scale weighted Cantor set with two different scales describing nonuniform distribution of the kinetic energy flux between cascading eddies of various sizes. We examine generalized dimensions and the corresponding multifractal singularity spectrum depending on one probability measure parameter and two rescaling parameters. In particular, we analyse time series of velocities of the slow speed streams of the solar wind measured in situ by Voyager 2 spacecraft in the outer heliosphere during solar maximum at various distances from the Sun: 10, 30, and 65 AU. This allows us to look at the evolution of multifractal intermittent scaling of the solar wind in the distant heliosphere. Namely, it appears that while the degree of multifractality for the solar wind during solar maximum is only weakly correlated with the heliospheric distance, but the multifractal spectrum could substantially be asymmetric in a very distant heliosphere beyond the planetary orbits. Therefore, one could expect that this scaling near the frontiers of the heliosphere should rather be asymmetric. It is worth noting that for the model with two different scaling parameters a better agreement with the solar wind data is obtained, especially for the negative index of the generalized dimensions. Therefore we argue that there is a need to use a two-scale cascade model. Hence we propose this model as a useful tool for analysis of intermittent turbulence in various environments and we hope that our general asymmetric multifractal model could shed more light on the nature of turbulence.

The Friedmann-Lemaître-Robertson-Walker Big Bang Singularities are Well Behaved

NASA Astrophysics Data System (ADS)

Stoica, Ovidiu Cristinel

2016-01-01

We show that the Big Bang singularity of the Friedmann-Lemaître-Robertson-Walker model does not raise major problems to General Relativity. We prove a theorem showing that the Einstein equation can be written in a non-singular form, which allows the extension of the spacetime before the Big Bang. The physical interpretation of the fields used is discussed. These results follow from our research on singular semi-Riemannian geometry and singular General Relativity.

Analysis of delamination in unidirectional and crossplied fiber composites containing surface cracks

NASA Technical Reports Server (NTRS)

Wang, S. S.; Mandell, J. F.

1977-01-01

A two-dimensional hybrid stress finite element analysis is described which was used to study the local stress field around delamination cracks in composite materials. The analysis employs a crack tip singularity element which is embedded in a matrix interlayer between plies of the laminate. Results are given for a unidirectional graphite/epoxy laminate containing a delamination emanating from a surface crack through the outside ply. The results illustrate several aspects of delamination cracks: (1) the localization of the singular stress domain within the interlayer; (2) the local concentration of stress in the ply adjacent to the crack; (3) the nature of the transverse normal and interlaminar shear stress distributions; and (4) the relative magnitudes of K sub 1 and K sub 2 associated with the delamination. A simple example of the use of the analysis in predicting delamination crack growth is demonstrated for a glass/epoxy laminate. The comparisons with experimental data show good agreement.

Cusp singularities in f(R) gravity: pros and cons

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

Chen, Pisin; Yeom, Dong-han

We investigate cusp singularities in f(R) gravity, especially for Starobinsky and Hu-Sawicki dark energy models. We illustrate that, by using double-null numerical simulations, a cusp singularity can be triggered by gravitational collapses. This singularity can be cured by adding a quadratic term, but this causes a Ricci scalar bump that can be observed by an observer outside the event horizon. Comparing with cosmological parameters, it seems that it would be difficult to see super-Planckian effects by astrophysical experiments. On the other hand, at once there exists a cusp singularity, it can be a mechanism to realize a horizon scale curvaturemore » singularity that can be interpreted by a firewall.« less

Propagation of the Lissajous singularity dipole emergent from non-paraxial polychromatic beams

NASA Astrophysics Data System (ADS)

Haitao, Chen; Gao, Zenghui; Wang, Wanqing

2017-06-01

The propagation of the Lissajous singularity dipole (LSD) emergent from the non-paraxial polychromatic beams is studied. It is found that the handedness reversal of Lissajous singularities, the change in the shape of Lissajous figures, as well as the creation and annihilation of the LSD may take place by varying the propagation distance, off-axis parameter, wavelength, or amplitude factor. Comparing with the LSD emergent from paraxial polychromatic beams, the output field of non-paraxial polychromatic beams is more complicated, which results in some richer dynamic behaviors of Lissajous singularities, such as more Lissajous singularities and no vanishing of a single Lissajous singularity at the plane z>0.

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.

Classical and quantum Big Brake cosmology for scalar field and tachyonic models

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

Kamenshchik, A. Yu.; Manti, S.

We study a relation between the cosmological singularities in classical and quantum theory, comparing the classical and quantum dynamics in some models possessing the Big Brake singularity - the model based on a scalar field and two models based on a tachyon-pseudo-tachyon field . It is shown that the effect of quantum avoidance is absent for the soft singularities of the Big Brake type while it is present for the Big Bang and Big Crunch singularities. Thus, there is some kind of a classical - quantum correspondence, because soft singularities are traversable in classical cosmology, while the strong Big Bangmore » and Big Crunch singularities are not traversable.« less

Quantum healing of spacetime singularities: A review

NASA Astrophysics Data System (ADS)

Konkowski, D. A.; Helliwell, T. M.

2018-02-01

Singularities are commonplace in general relativistic spacetimes. It is natural to hope that they might be “healed” (or resolved) by the inclusion of quantum mechanics, either in the theory itself (quantum gravity) or, more modestly, in the description of the spacetime geodesic paths used to define them. We focus here on the latter, mainly using a procedure proposed by Horowitz and Marolf to test whether singularities in broad classes of spacetimes can be resolved by replacing geodesic paths with quantum wave packets. We list the spacetime singularities that various authors have studied in this context, and distinguish those which are healed quantum mechanically (QM) from those which remain singular. Finally, we mention some alternative approaches to healing singularities.

Statistical mechanics of a single particle in a multiscale random potential: Parisi landscapes in finite-dimensional Euclidean spaces

NASA Astrophysics Data System (ADS)

Fyodorov, Yan V.; Bouchaud, Jean-Philippe

2008-08-01

We construct an N-dimensional Gaussian landscape with multiscale, translation invariant, logarithmic correlations and investigate the statistical mechanics of a single particle in this environment. In the limit of high dimension N → ∞ the free energy of the system and overlap function are calculated exactly using the replica trick and Parisi's hierarchical ansatz. In the thermodynamic limit, we recover the most general version of the Derrida's generalized random energy model (GREM). The low-temperature behaviour depends essentially on the spectrum of length scales involved in the construction of the landscape. If the latter consists of K discrete values, the system is characterized by a K-step replica symmetry breaking solution. We argue that our construction is in fact valid in any finite spatial dimensions N >= 1. We discuss the implications of our results for the singularity spectrum describing multifractality of the associated Boltzmann-Gibbs measure. Finally we discuss several generalizations and open problems, such as the dynamics in such a landscape and the construction of a generalized multifractal random walk.

The cosmological constant as an eigenvalue of a Sturm-Liouville problem

NASA Astrophysics Data System (ADS)

Astashenok, Artyom V.; Elizalde, Emilio; Yurov, Artyom V.

2014-01-01

It is observed that one of Einstein-Friedmann's equations has formally the aspect of a Sturm-Liouville problem, and that the cosmological constant, Λ, plays thereby the role of spectral parameter (what hints to its connection with the Casimir effect). The subsequent formulation of appropriate boundary conditions leads to a set of admissible values for Λ, considered as eigenvalues of the corresponding linear operator. Simplest boundary conditions are assumed, namely that the eigenfunctions belong to L 2 space, with the result that, when all energy conditions are satisfied, they yield a discrete spectrum for Λ>0 and a continuous one for Λ<0. A very interesting situation is seen to occur when the discrete spectrum contains only one point: then, there is the possibility to obtain appropriate cosmological conditions without invoking the anthropic principle. This possibility is shown to be realized in cyclic cosmological models, provided the potential of the matter field is similar to the potential of the scalar field. The dynamics of the universe in this case contains a sudden future singularity.

Study on sampling of continuous linear system based on generalized Fourier transform

NASA Astrophysics Data System (ADS)

Li, Huiguang

2003-09-01

In the research of signal and system, the signal's spectrum and the system's frequency characteristic can be discussed through Fourier Transform (FT) and Laplace Transform (LT). However, some singular signals such as impulse function and signum signal don't satisfy Riemann integration and Lebesgue integration. They are called generalized functions in Maths. This paper will introduce a new definition -- Generalized Fourier Transform (GFT) and will discuss generalized function, Fourier Transform and Laplace Transform under a unified frame. When the continuous linear system is sampled, this paper will propose a new method to judge whether the spectrum will overlap after generalized Fourier transform (GFT). Causal and non-causal systems are studied, and sampling method to maintain system's dynamic performance is presented. The results can be used on ordinary sampling and non-Nyquist sampling. The results also have practical meaning on research of "discretization of continuous linear system" and "non-Nyquist sampling of signal and system." Particularly, condition for ensuring controllability and observability of MIMO continuous systems in references 13 and 14 is just an applicable example of this paper.

On the r-mode spectrum of relativistic stars in the low-frequency approximation

NASA Astrophysics Data System (ADS)

Ruoff, Johannes; Kokkotas, Kostas D.

2001-12-01

The axial modes for non-barotropic relativistic rotating neutron stars with uniform angular velocity are studied, using the slow-rotation formalism together with the low-frequency approximation, first investigated by Kojima. The time-independent form of the equations leads to a singular eigenvalue problem, which admits a continuous spectrum. We show that for l=2, it is nevertheless also possible to find discrete mode solutions (the r modes). However, under certain conditions related to the equation of state and the compactness of the stellar model, the eigenfrequency lies inside the continuous band and the associated velocity perturbation is divergent; hence these solutions have to be discarded as being unphysical. We corroborate our results by explicitly integrating the time-dependent equations. For stellar models admitting a physical r-mode solution, it can indeed be excited by arbitrary initial data. For models admitting only an unphysical mode solution, the evolutions do not show any tendency to oscillate with the respective frequency. For higher values of l it seems that in certain cases there are no mode solutions at all.

New Fault Recognition Method for Rotary Machinery Based on Information Entropy and a Probabilistic Neural Network.

PubMed

Jiang, Quansheng; Shen, Yehu; Li, Hua; Xu, Fengyu

2018-01-24

Feature recognition and fault diagnosis plays an important role in equipment safety and stable operation of rotating machinery. In order to cope with the complexity problem of the vibration signal of rotating machinery, a feature fusion model based on information entropy and probabilistic neural network is proposed in this paper. The new method first uses information entropy theory to extract three kinds of characteristics entropy in vibration signals, namely, singular spectrum entropy, power spectrum entropy, and approximate entropy. Then the feature fusion model is constructed to classify and diagnose the fault signals. The proposed approach can combine comprehensive information from different aspects and is more sensitive to the fault features. The experimental results on simulated fault signals verified better performances of our proposed approach. In real two-span rotor data, the fault detection accuracy of the new method is more than 10% higher compared with the methods using three kinds of information entropy separately. The new approach is proved to be an effective fault recognition method for rotating machinery.

Singularities in water waves and Rayleigh-Taylor instability

NASA Technical Reports Server (NTRS)

Tanveer, S.

1991-01-01

Singularities in inviscid two-dimensional finite-amplitude water waves and inviscid Rayleigh-Taylor instability are discussed. For the deep water gravity waves of permanent form, through a combination of analytical and numerical methods, results describing the precise form, number, and location of singularities in the unphysical domain as the wave height is increased are presented. It is shown how the information on the singularity in the unphysical region has the same form as for deep water waves. However, associated with such a singularity is a series of image singularities at increasing distances from the physical plane with possibly different behavior. Furthermore, for the Rayleigh-Taylor problem of motion of fluid over a vacuum and for the unsteady water wave problem, integro-differential equations valid in the unphysical region are derived, and how these equations can give information on the nature of singularities for arbitrary initial conditions is shown.

Topological resolution of gauge theory singularities

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

Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

2013-08-21

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit themore » singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.« less

Genericity Distinctions and the Interpretation of Determiners in Second Language Acquisition

ERIC Educational Resources Information Center

Ionin, Tania; Montrul, Silvina; Kim, Ji-Hye; Philippov, Vadim

2011-01-01

English uses three types of generic NPs: bare plurals ("Lions are dangerous"), definite singulars ("The lion is dangerous"), and indefinite singulars ("A lion is dangerous"). These three NP types are not interchangeable: definite singulars and bare plurals can have generic reference at the NP-level, while indefinite singulars are compatible only…

7 CFR 900.36 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall be...

7 CFR 900.100 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

7 CFR 900.1 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

7 CFR 900.50 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

7 CFR 900.20 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed to...

7 CFR 1200.50 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

Singularities in the classical Rayleigh-Taylor flow - Formation and subsequent motion

NASA Technical Reports Server (NTRS)

Tanveer, S.

1993-01-01

The creation and subsequent motion of singularities of solution to classical Rayleigh-Taylor flow (two dimensional inviscid, incompressible fluid over a vacuum) are discussed. For a specific set of initial conditions, we give analytical evidence to suggest the instantaneous formation of one or more singularities at specific points in the unphysical plane, whose locations depend sensitively on small changes in initial conditions in the physical domain. One-half power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities are also possible. For a specific initial condition, we follow a numerical procedure in the unphysical plane to compute the motion of a one-half singularity. This computation confirms our previous conjecture that the approach of a one-half singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, we present analytical evidence to suggest that a singularity of the one-half type cannot impinge the physical domain in finite time.

Singularities in the classical Rayleigh-Taylor flow: Formation and subsequent motion

NASA Technical Reports Server (NTRS)

Tanveer, S.

1992-01-01

The creation and subsequent motion of singularities of solution to classical Rayleigh-Taylor flow (two dimensional inviscid, incompressible fluid over a vacuum) are discussed. For a specific set of initial conditions, we give analytical evidence to suggest the instantaneous formation of one or more singularities at specific points in the unphysical plane, whose locations depend sensitively on small changes in initial conditions in the physical domain. One-half power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities are also possible. For a specific initial condition, we follow a numerical procedure in the unphysical plane to compute the motion of a one-half singularity. This computation confirms our previous conjecture that the approach of a one-half singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, we present analytical evidence to suggest that a singularity of the one-half type cannot impinge the physical domain in finite time.

{lambda} elements for one-dimensional singular problems with known strength of singularity

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

Wong, K.K.; Surana, K.S.

1996-10-01

This paper presents a new and general procedure for designing special elements called {lambda} elements for one dimensional singular problems where the strength of the singularity is know. The {lambda} elements presented here are of type C{sup 0}. These elements also provide inter-element C{sup 0} continuity with p-version elements. The {lambda} elements do not require a precise knowledge of the extent of singular zone, i.e., their use may be extended beyond the singular zone. When {lambda} elements are used at the singularity, a singular problem behaves like a smooth problem thereby eliminating the need for h, p-adaptive processes all together.more » One dimensional steady state radial flow of an upper convected Maxwell fluid is considered as a sample problem. Least squares approach (or least squares finite element formulation: LSFEF) is used to construct the integral form (error functional I) from the differential equations. Numerical results presented for radially inward flow with inner radius r{sub i} = 0.1, 0.01, 0.001, 0.0001, 0.00001, and Deborah number of 2 (De = 2) demonstrate the accuracy, faster convergence of the iterative solution procedure, faster convergence rate of the error functional and mesh independent characteristics of the {lambda} elements regardless of the severity of the singularity.« less

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.

Control landscapes are almost always trap free: a geometric assessment

NASA Astrophysics Data System (ADS)

Russell, Benjamin; Rabitz, Herschel; Wu, Re-Bing

2017-05-01

A proof is presented that almost all closed, finite dimensional quantum systems have trap free (i.e. free from local optima) landscapes for a large and physically general class of circumstances, which includes qubit evolutions in quantum computing. This result offers an explanation for why gradient-based methods succeed so frequently in quantum control. The role of singular controls is analyzed using geometric tools in the case of the control of the propagator, and thus in the case of observables as well. Singular controls have been implicated as a source of landscape traps. The conditions under which singular controls can introduce traps, and thus interrupt the progress of a control optimization, are discussed and a geometrical characterization of the issue is presented. It is shown that a control being singular is not sufficient to cause control optimization progress to halt, and sufficient conditions for a trap free landscape are presented. It is further shown that the local surjectivity (full rank) assumption of landscape analysis can be refined to the condition that the end-point map is transverse to each of the level sets of the fidelity function. This mild condition is shown to be sufficient for a quantum system’s landscape to be trap free. The control landscape is shown to be trap free for all but a null set of Hamiltonians using a geometric technique based on the parametric transversality theorem. Numerical evidence confirming this analysis is also presented. This new result is the analogue of the work of Altifini, wherein it was shown that controllability holds for all but a null set of quantum systems in the dipole approximation. These collective results indicate that the availability of adequate control resources remains the most physically relevant issue for achieving high fidelity control performance while also avoiding landscape traps.

Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

PubMed Central

Donoho, David L.

1999-01-01

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1. PMID:10051554