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.

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.

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

DTIC Science & Technology

1991-08-01

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

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.

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.

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.

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.

Singularity spectrum of intermittent seismic tremor at Kilauea Volcano, Hawaii

USGS Publications Warehouse

Shaw, H.R.; Chouet, B.

1989-01-01

Fractal singularity analysis (FSA) is used to study a 22-yr record of deep seismic tremor (30-60 km depth) for regions below Kilauea Volcano on the assumption that magma transport and fracture can be treated as a system of coupled nonlinear oscillators. Tremor episodes range from 1 to 100 min (cumulative duration = 1.60 ?? 104 min; yearly average - 727 min yr-1; mean gradient = 24.2 min yr-1km-1). Partitioning of probabilities, Pi, in the phase space of normalized durations, xi, are expressed in terms of a function f(??), where ?? is a variable exponent of a length scale, l. Plots of f(??) vs. ?? are called multifractal singularity spectra. The spectrum for deep tremor durations is bounded by ?? values of about 0.4 and 1.9 at f = O; fmax ???1.0 for ?? ??? 1. Results for tremor are similar to those found for systems transitional between complete mode locking and chaos. -Authors

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

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.

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.

Excitation of Continuous and Discrete Modes in Incompressible Boundary Layers

NASA Technical Reports Server (NTRS)

Ashpis, David E.; Reshotko, Eli

1998-01-01

This report documents the full details of the condensed journal article by Ashpis & Reshotko (JFM, 1990) entitled "The Vibrating Ribbon Problem Revisited." A revised formal solution of the vibrating ribbon problem of hydrodynamic stability is presented. The initial formulation of Gaster (JFM, 1965) is modified by application of the Briggs method and a careful treatment of the complex double Fourier transform inversions. Expressions are obtained in a natural way for the discrete spectrum as well as for the four branches of the continuous spectra. These correspond to discrete and branch-cut singularities in the complex wave-number plane. The solutions from the continuous spectra decay both upstream and downstream of the ribbon, with the decay in the upstream direction being much more rapid than that in the downstream direction. Comments and clarification of related prior work are made.

The Singularity Mystery Associated with a Radially Continuous Maxwell Viscoelastic Structure

NASA Technical Reports Server (NTRS)

Fang, Ming; Hager, Bradford H.

1995-01-01

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

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.

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

A solid criterion based on strict LMI without invoking equality constraint for stabilization of continuous singular systems.

PubMed

Zhang, Xuefeng; Chen, YangQuan

2017-11-01

The paper considers the stabilization issue of linear continuous singular systems by dealing with strict linear matrix inequalities (LMIs) without invoking equality constraint and proposes a complete and effective solved LMIs formulation. The criterion is necessary and sufficient condition and can be directly solved the feasible solutions with LMI toolbox and is much more tractable and reliable in numerical simulation than existing results, which involve positive semi-definite LMIs with equality constraints. The most important property of the criterion proposed in the paper is that it can overcome the drawbacks of the invalidity caused by the singularity of Ω=PE T +SQ for stabilization of singular systems. Two counterexamples are presented to avoid the disadvantages of the existing condition of stabilization of continuous singular systems. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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.

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...

$$ \\mathcal{N} $$ = 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

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.

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.

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

PubMed

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

2018-02-26

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

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...

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.

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.

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.

Bifurcations and Singularities for Coupled Oscillators with Inertia and Frustration.

PubMed

Barré, J; Métivier, D

2016-11-18

We prove that any nonzero inertia, however small, is able to change the nature of the synchronization transition in Kuramoto-like models, either from continuous to discontinuous or from discontinuous to continuous. This result is obtained through an unstable manifold expansion in the spirit of Crawford, which features singularities in the vicinity of the bifurcation. Far from being unwanted artifacts, these singularities actually control the qualitative behavior of the system. Our numerical tests fully support this picture.

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

Time Series Imputation via L1 Norm-Based Singular Spectrum Analysis

NASA Astrophysics Data System (ADS)

Kalantari, Mahdi; Yarmohammadi, Masoud; Hassani, Hossein; Silva, Emmanuel Sirimal

Missing values in time series data is a well-known and important problem which many researchers have studied extensively in various fields. In this paper, a new nonparametric approach for missing value imputation in time series is proposed. The main novelty of this research is applying the L1 norm-based version of Singular Spectrum Analysis (SSA), namely L1-SSA which is robust against outliers. The performance of the new imputation method has been compared with many other established methods. The comparison is done by applying them to various real and simulated time series. The obtained results confirm that the SSA-based methods, especially L1-SSA can provide better imputation in comparison to other methods.

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

Singular-value demodulation of phase-shifted holograms.

PubMed

Lopes, Fernando; Atlan, Michael

2015-06-01

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

Study on a kind of ϕ-Laplacian Liénard equation with attractive and repulsive singularities.

PubMed

Xin, Yun; Cheng, Zhibo

2017-01-01

In this paper, by application of the Manasevich-Mawhin continuation theorem, we investigate the existence of a positive periodic solution for a kind of ϕ -Laplacian singular Liénard equation with attractive and repulsive singularities.

Excited-state quantum phase transitions in systems with two degrees of freedom: Level density, level dynamics, thermal properties

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

Stránský, Pavel; Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510, México, D.F.; Macek, Michal

2014-06-15

Quantum systems with a finite number of freedom degrees f develop robust singularities in the energy spectrum of excited states as the system’s size increases to infinity. We analyze the general form of these singularities for low f, particularly f=2, clarifying the relation to classical stationary points of the corresponding potential. Signatures in the smoothed energy dependence of the quantum state density and in the flow of energy levels with an arbitrary control parameter are described along with the relevant thermodynamical consequences. The general analysis is illustrated with specific examples of excited-state singularities accompanying the first-order quantum phase transition. --more » Highlights: •ESQPTs found in infinite-size limit of systems with low numbers of freedom degrees f. •ESQPTs related to non-analytical evolutions of classical phase–space properties. •ESQPT signatures analyzed for general f, particularly f=2, extending known case f=1. •ESQPT signatures identified in smoothened density and flow of energy spectrum. •ESQPTs shown to induce a new type of thermodynamic anomalies.« less

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

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

Kotoku, J; Kumagai, S; Nakabayashi, S

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

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.

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.

Contracting singular horseshoe

NASA Astrophysics Data System (ADS)

Morales, C. A.; San Martín, B.

2017-11-01

We suggest a notion of hyperbolicity adapted to the geometric Rovella attractor (Robinson 2012 An Introduction to Dynamical Systems—Continuous and Discrete (Pure and Applied Undergraduate Texts vol 19) 2nd edn (Providence, RI: American Mathematical Society)) . More precisely, we call a partially hyperbolic set asymptotically sectional-hyperbolic if its singularities are hyperbolic and if its central subbundle is asymptotically sectional expanding outside the stable manifolds of the singularities. We prove that there are highly chaotic flows with Rovella-like singularities exhibiting this kind of hyperbolicity. We shall call them contracting singular horseshoes.

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.

On the continuity of the stationary state distribution of DPCM

NASA Astrophysics Data System (ADS)

Naraghi-Pour, Morteza; Neuhoff, David L.

1990-03-01

Continuity and singularity properties of the stationary state distribution of differential pulse code modulation (DPCM) are explored. Two-level DPCM (i.e., delta modulation) operating on a first-order autoregressive source is considered, and it is shown that, when the magnitude of the DPCM prediciton coefficient is between zero and one-half, the stationary state distribution is singularly continuous; i.e., it is not discrete but concentrates on an uncountable set with a Lebesgue measure of zero. Consequently, it cannot be represented with a probability density function. For prediction coefficients with magnitude greater than or equal to one-half, the distribution is pure, i.e., either absolutely continuous and representable with a density function, or singular. This problem is compared to the well-known and still substantially unsolved problem of symmetric Bernoulli convolutions.

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.

Noncolocated Time-Reversal MUSIC: High-SNR Distribution of Null Spectrum

NASA Astrophysics Data System (ADS)

Ciuonzo, Domenico; Rossi, Pierluigi Salvo

2017-04-01

We derive the asymptotic distribution of the null spectrum of the well-known Multiple Signal Classification (MUSIC) in its computational Time-Reversal (TR) form. The result pertains to a single-frequency non-colocated multistatic scenario and several TR-MUSIC variants are here investigated. The analysis builds upon the 1st-order perturbation of the singular value decomposition and allows a simple characterization of null-spectrum moments (up to the 2nd order). This enables a comparison in terms of spectrums stability. Finally, a numerical analysis is provided to confirm the theoretical findings.

7 CFR 1200.1 - 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. 1200.1 Section 1200.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Governing Proceedings To Formulate and Amend an Order § 1200.1 Words in the singular form. Words in this...

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.

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

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.

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

NASA Astrophysics Data System (ADS)

Kwon, Ohsung; Kweon, Jae Ryong

2018-06-01

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

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.

The Singular Set of Solutions to Non-Differentiable Elliptic Systems

NASA Astrophysics Data System (ADS)

Mingione, Giuseppe

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

Null cosmological singularities and free strings

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

Narayan, K.

2010-03-15

We continue exploring free strings in the background of null Kasner-like cosmological singularities, following K. Narayan, arXiv:0904.4532. We study the free string Schrodinger wave functional along the lines of K. Narayan, arXiv:0807.1517. We find the wave functional to be nonsingular in the vicinity of singularities whose Kasner exponents satisfy certain relations. We compare this with the description in other variables. We then study certain regulated versions of these singularities where the singular region is replaced by a substringy but nonsingular region and study the string spectra in these backgrounds. The string modes can again be solved for exactly, giving somemore » insight into how string oscillator states get excited near the singularity.« less

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.

Singular spectrum analysis in nonlinear dynamics, with applications to paleoclimatic time series

NASA Technical Reports Server (NTRS)

Vautard, R.; Ghil, M.

1989-01-01

Two dimensions of a dynamical system given by experimental time series are distinguished. Statistical dimension gives a theoretical upper bound for the minimal number of degrees of freedom required to describe the attractor up to the accuracy of the data, taking into account sampling and noise problems. The dynamical dimension is the intrinsic dimension of the attractor and does not depend on the quality of the data. Singular Spectrum Analysis (SSA) provides estimates of the statistical dimension. SSA also describes the main physical phenomena reflected by the data. It gives adaptive spectral filters associated with the dominant oscillations of the system and clarifies the noise characteristics of the data. SSA is applied to four paleoclimatic records. The principal climatic oscillations and the regime changes in their amplitude are detected. About 10 degrees of freedom are statistically significant in the data. Large noise and insufficient sample length do not allow reliable estimates of the dynamical dimension.

Singular Spectrum Analysis for Astronomical Time Series: Constructing a Parsimonious Hypothesis Test

NASA Astrophysics Data System (ADS)

Greco, G.; Kondrashov, D.; Kobayashi, S.; Ghil, M.; Branchesi, M.; Guidorzi, C.; Stratta, G.; Ciszak, M.; Marino, F.; Ortolan, A.

We present a data-adaptive spectral method - Monte Carlo Singular Spectrum Analysis (MC-SSA) - and its modification to tackle astrophysical problems. Through numerical simulations we show the ability of the MC-SSA in dealing with 1/f β power-law noise affected by photon counting statistics. Such noise process is simulated by a first-order autoregressive, AR(1) process corrupted by intrinsic Poisson noise. In doing so, we statistically estimate a basic stochastic variation of the source and the corresponding fluctuations due to the quantum nature of light. In addition, MC-SSA test retains its effectiveness even when a significant percentage of the signal falls below a certain level of detection, e.g., caused by the instrument sensitivity. The parsimonious approach presented here may be broadly applied, from the search for extrasolar planets to the extraction of low-intensity coherent phenomena probably hidden in high energy transients.

Singular spectrum decomposition of Bouligand-Minkowski fractal descriptors: an application to the classification of texture Images

NASA Astrophysics Data System (ADS)

Florindo, João. Batista

2018-04-01

This work proposes the use of Singular Spectrum Analysis (SSA) for the classification of texture images, more specifically, to enhance the performance of the Bouligand-Minkowski fractal descriptors in this task. Fractal descriptors are known to be a powerful approach to model and particularly identify complex patterns in natural images. Nevertheless, the multiscale analysis involved in those descriptors makes them highly correlated. Although other attempts to address this point was proposed in the literature, none of them investigated the relation between the fractal correlation and the well-established analysis employed in time series. And SSA is one of the most powerful techniques for this purpose. The proposed method was employed for the classification of benchmark texture images and the results were compared with other state-of-the-art classifiers, confirming the potential of this analysis in image classification.

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

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.

Continuous family of finite-dimensional representations of a solvable Lie algebra arising from singularities

PubMed Central

Yau, Stephen S.-T.

1983-01-01

A natural mapping from the set of complex analytic isolated hypersurface singularities to the set of finite dimensional Lie algebras is first defined. It is proven that the image under this natural mapping is contained in the set of solvable Lie algebras. This approach gives rise to a continuous inequivalent family of finite dimensional representations of a solvable Lie algebra. PMID:16593401

Gauge theories with time dependent couplings and their cosmological duals

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

Awad, Adel; Center for Theoretical Physics, British University of Egypt, Sherouk City 11837, P.O. Box 43; Das, Sumit R.

2009-02-15

We consider the N=4 super Yang-Mills theory in flat 3+1-dimensional space-time with a time dependent coupling constant which vanishes at t=0, like g{sub YM}{sup 2}=t{sup p}. In an analogous quantum mechanics toy model we find that the response is singular. The energy diverges at t=0, for a generic state. In addition, if p>1 the phase of the wave function has a wildly oscillating behavior, which does not allow it to be continued past t=0. A similar effect would make the gauge theory singular as well, though nontrivial effects of renormalization could tame this singularity and allow a smooth continuation beyondmore » t=0. The gravity dual in some cases is known to be a time dependent cosmology which exhibits a spacelike singularity at t=0. Our results, if applicable in the gauge theory for the case of the vanishing coupling, imply that the singularity is a genuine sickness and does not admit a meaningful continuation. When the coupling remains nonzero and becomes small at t=0, the curvature in the bulk becomes of order string scale. The gauge theory now admits a time evolution beyond this point. In this case, a finite amount of energy is produced which possibly thermalizes and leads to a black hole in the bulk.« less

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.

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.

A New Continuous-Time Equality-Constrained Optimization to Avoid Singularity.

PubMed

Quan, Quan; Cai, Kai-Yuan

2016-02-01

In equality-constrained optimization, a standard regularity assumption is often associated with feasible point methods, namely, that the gradients of constraints are linearly independent. In practice, the regularity assumption may be violated. In order to avoid such a singularity, a new projection matrix is proposed based on which a feasible point method to continuous-time, equality-constrained optimization is developed. First, the equality constraint is transformed into a continuous-time dynamical system with solutions that always satisfy the equality constraint. Second, a new projection matrix without singularity is proposed to realize the transformation. An update (or say a controller) is subsequently designed to decrease the objective function along the solutions of the transformed continuous-time dynamical system. The invariance principle is then applied to analyze the behavior of the solution. Furthermore, the proposed method is modified to address cases in which solutions do not satisfy the equality constraint. Finally, the proposed optimization approach is applied to three examples to demonstrate its effectiveness.

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

Transformations between Jordan and Einstein frames: Bounces, antigravity, and crossing singularities

NASA Astrophysics Data System (ADS)

Kamenshchik, Alexander Yu.; Pozdeeva, Ekaterina O.; Vernov, Sergey Yu.; Tronconi, Alessandro; Venturi, Giovanni

2016-09-01

We study the relation between the Jordan-Einstein frame transition and the possible description of the crossing of singularities in flat Friedmann universes, using the fact that the regular evolution in one frame can correspond to crossing singularities in the other frame. We show that some interesting effects arise in simple models such as one with a massless scalar field or another wherein the potential is constant in the Einstein frame. The dynamics in these models and in their conformally coupled counterparts are described in detail, and a method for the continuation of such cosmological evolutions beyond the singularity is developed. We compare our approach with some other, recently developed, approaches to the problem of the crossing of singularities.

Tight-binding chains with off-diagonal disorder: Bands of extended electronic states induced by minimal quasi-one-dimensionality

NASA Astrophysics Data System (ADS)

Nandy, Atanu; Pal, Biplab; Chakrabarti, Arunava

2016-08-01

It is shown that an entire class of off-diagonally disordered linear lattices composed of two basic building blocks and described within a tight-binding model can be tailored to generate absolutely continuous energy bands. It can be achieved if linear atomic clusters of an appropriate size are side-coupled to a suitable subset of sites in the backbone, and if the nearest-neighbor hopping integrals, in the backbone and in the side-coupled cluster, bear a certain ratio. We work out the precise relationship between the number of atoms in one of the building blocks in the backbone and that in the side attachment. In addition, we also evaluate the definite correlation between the numerical values of the hopping integrals at different subsections of the chain, that can convert an otherwise point spectrum (or a singular continuous one for deterministically disordered lattices) with exponentially (or power law) localized eigenfunctions to an absolutely continuous spectrum comprising one or more bands (subbands) populated by extended, totally transparent eigenstates. The results, which are analytically exact, put forward a non-trivial variation of the Anderson localization (Anderson P. W., Phys. Rev., 109 (1958) 1492), pointing towards its unusual sensitivity to the numerical values of the system parameters and, go well beyond the other related models such as the Random Dimer Model (RDM) (Dunlap D. H. et al., Phys. Rev. Lett., 65 (1990) 88).

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.

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.

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.

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.

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.

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.

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 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.

Positive periodic solution for p-Laplacian neutral Rayleigh equation with singularity of attractive type.

PubMed

Xin, Yun; Liu, Hongmin; Cheng, Zhibo

2018-01-01

In this paper, we consider a kind of p -Laplacian neutral Rayleigh equation with singularity of attractive type, [Formula: see text] By applications of an extension of Mawhin's continuation theorem, sufficient conditions for the existence of periodic solution are established.

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 analysis and forecasting of male cycling time trial records established within England and Wales.

PubMed

Dyer, Bryce; Hassani, Hossein; Shadi, Mehran

2016-01-01

The format of cycling time trials in England, Wales and Northern Ireland, involves riders competing individually over several fixed race distances of 10-100 miles in length and using time constrained formats of 12 and 24 h in duration. Drawing on data provided by the national governing body that covers the regions of England and Wales, an analysis of six male competition record progressions was undertaken to illustrate its progression. Future forecasts are then projected through use of the Singular Spectrum Analysis technique. This method has not been applied to sport-based time series data before. All six records have seen a progressive improvement and are non-linear in nature. Five records saw their highest level of record change during the 1950-1969 period. Whilst new record frequency generally has reduced since this period, the magnitude of performance improvement has generally increased. The Singular Spectrum Analysis technique successfully provided forecasted projections in the short to medium term with a high level of fit to the time series data.

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.

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.

{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

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.

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.

New conformal mapping for adaptive resolving of the complex singularities of Stokes wave

PubMed Central

Dyachenko, Sergey A.; A. Silantyev, Denis

2017-01-01

A new highly efficient method is developed for computation of travelling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularities above the free surface for the analytical continuation of the travelling wave into the complex plane. An auxiliary conformal mapping is introduced which moves singularities away from the free surface thus dramatically speeding up numerical convergence by adapting the numerical grid for resolving singularities while being consistent with the fluid dynamics. The efficiency of that conformal mapping is demonstrated for the Stokes wave approaching the limiting Stokes wave (the wave of the greatest height) which significantly expands the family of numerically accessible solutions. It allows us to provide a detailed study of the oscillatory approach of these solutions to the limiting wave. Generalizations of the conformal mapping to resolve multiple singularities are also introduced. PMID:28690418

New conformal mapping for adaptive resolving of the complex singularities of Stokes wave.

PubMed

Lushnikov, Pavel M; Dyachenko, Sergey A; A Silantyev, Denis

2017-06-01

A new highly efficient method is developed for computation of travelling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularities above the free surface for the analytical continuation of the travelling wave into the complex plane. An auxiliary conformal mapping is introduced which moves singularities away from the free surface thus dramatically speeding up numerical convergence by adapting the numerical grid for resolving singularities while being consistent with the fluid dynamics. The efficiency of that conformal mapping is demonstrated for the Stokes wave approaching the limiting Stokes wave (the wave of the greatest height) which significantly expands the family of numerically accessible solutions. It allows us to provide a detailed study of the oscillatory approach of these solutions to the limiting wave. Generalizations of the conformal mapping to resolve multiple singularities are also introduced.

New method for detecting singularities in experimental incompressible flows

NASA Astrophysics Data System (ADS)

Kuzzay, Denis; Saw, Ewe-Wei; Martins, Fabio J. W. A.; Faranda, Davide; Foucaut, Jean-Marc; Daviaud, François; Dubrulle, Bérengère

2017-06-01

We introduce two new criteria based on the work of Duchon and Robert (2000 Nonlinearity 13 249) and Eyink (2006 Phys. Rev. E 74 066302), which allow for the local detection of Navier-Stokes singularities in experimental flows. We discuss the difference between non-dissipative or dissipative Euler quasi-singularities and genuine Navier-Stokes dissipative singularites, and classify them with respect to their Hölder exponent h. We show that our criteria allow us to detect areas in a flow where the velocity field is no more regular than Hölder continuous with some Hölder exponent h ≤slant 1/2 . We illustrate our discussion using classical tomographic particle image velocimetry (TPIV) measurements obtained inside a high Reynolds number flow generated in the boundary layer of a wind tunnel. Our study shows that, in order to detect singularities or quasi-singularities, one does not need to have access to the whole velocity field inside a volume, but can instead look for them from stereoscopic PIV data on a plane. We also provide a discussion about the link between areas detected by our criteria and areas corresponding to large vorticity. We argue that this link might provide either a clue about the genesis of these quasi-singularities or a way to discriminate dissipative Euler quasi-singularities and genuine Navier-Stokes singularities.

A study of the application of singular perturbation theory. [development of a real time algorithm for optimal three dimensional aircraft maneuvers

NASA Technical Reports Server (NTRS)

Mehra, R. K.; Washburn, R. B.; Sajan, S.; Carroll, J. V.

1979-01-01

A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.

Timelike naked singularity

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

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

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

Recollection is a continuous process: Evidence from plurality memory receiver operating characteristics.

PubMed

Slotnick, Scott D; Jeye, Brittany M; Dodson, Chad S

2016-01-01

Is recollection a continuous/graded process or a threshold/all-or-none process? Receiver operating characteristic (ROC) analysis can answer this question as the continuous model and the threshold model predict curved and linear recollection ROCs, respectively. As memory for plurality, an item's previous singular or plural form, is assumed to rely on recollection, the nature of recollection can be investigated by evaluating plurality memory ROCs. The present study consisted of four experiments. During encoding, words (singular or plural) or objects (single/singular or duplicate/plural) were presented. During retrieval, old items with the same plurality or different plurality were presented. For each item, participants made a confidence rating ranging from "very sure old", which was correct for same plurality items, to "very sure new", which was correct for different plurality items. Each plurality memory ROC was the proportion of same versus different plurality items classified as "old" (i.e., hits versus false alarms). Chi-squared analysis revealed that all of the plurality memory ROCs were adequately fit by the continuous unequal variance model, whereas none of the ROCs were adequately fit by the two-high threshold model. These plurality memory ROC results indicate recollection is a continuous process, which complements previous source memory and associative memory ROC findings.

[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.

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.

Modeling meander morphodynamics over self-formed heterogeneous floodplains

NASA Astrophysics Data System (ADS)

Bogoni, Manuel; Putti, Mario; Lanzoni, Stefano

2017-06-01

This work addresses the signatures embedded in the planform geometry of meandering rivers consequent to the formation of floodplain heterogeneities as the river bends migrate. Two geomorphic features are specifically considered: scroll bars produced by lateral accretion of point bars at convex banks and oxbow lake fills consequent to neck cutoffs. The sedimentary architecture of these geomorphic units depends on the type and amount of sediment, and controls bank erodibility as the river impinges on them, favoring or contrasting the river migration. The geometry of numerically generated planforms obtained for different scenarios of floodplain heterogeneity is compared to that of natural meandering paths. Half meander metrics and spatial distribution of channel curvatures are used to disclose the complexity embedded in meandering geometry. Fourier Analysis, Principal Component Analysis, Singular Spectrum Analysis and Multivariate Singular Spectrum Analysis are used to emphasize the subtle but crucial differences which may emerge between apparently similar configurations. A closer similarity between observed and simulated planforms is attained when fully coupling flow and sediment dynamics (fully-coupled models) and when considering self-formed heterogeneities that are less erodible than the surrounding floodplain.

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 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.

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.

A singularity free approach to post glacial rebound calculations

NASA Technical Reports Server (NTRS)

Fang, Ming; Hager, Bradford H.

1994-01-01

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

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

NASA Astrophysics Data System (ADS)

Rostworowski, A.

2007-01-01

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

Geometric and Topological Methods for Quantum Field Theory

NASA Astrophysics Data System (ADS)

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

2013-05-01

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

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.

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.

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.

A note on singularities of the 3-D Euler equation

NASA Technical Reports Server (NTRS)

Tanveer, S.

1994-01-01

In this paper, we consider analytic initial conditions with finite energy, whose complex spatial continuation is a superposition of a smooth background flow and a singular field. Through explicit calculation in the complex plane, we show that under some assumptions, the solution to the 3-D Euler equation ceases to be analytic in the real domain in finite time.

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

NASA Technical Reports Server (NTRS)

Juarez, M. de la Torre

2002-01-01

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

Aerodynamic influence coefficient method using singularity splines.

NASA Technical Reports Server (NTRS)

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

1973-01-01

A new numerical formulation with computed results, is presented. This formulation combines the adaptability to complex shapes offered by paneling schemes with the smoothness and accuracy of the loading function methods. The formulation employs a continuous distribution of singularity strength over a set of panels on a paneled wing. The basic distributions are independent, and each satisfies all of the continuity conditions required of the final solution. These distributions are overlapped both spanwise and chordwise (termed 'spline'). Boundary conditions are satisfied in a least square error sense over the surface using a finite summing technique to approximate the integral.

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.

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.

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.

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.

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.

MIB Galerkin method for elliptic interface problems.

PubMed

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

2014-12-15

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

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.

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).

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

NASA Astrophysics Data System (ADS)

Das, Siddhartha; Siopsis, George; Weedbrook, Christian

2018-02-01

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

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.

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.

Global Resolution of the Physical Vacuum Singularity for Three-Dimensional Isentropic Inviscid Flows with Damping in Spherically Symmetric Motions

NASA Astrophysics Data System (ADS)

Zeng, Huihui

2017-10-01

For the gas-vacuum interface problem with physical singularity and the sound speed being {C^{{1}/{2}}}-Hölder continuous near vacuum boundaries of the isentropic compressible Euler equations with damping, the global existence of smooth solutions and the convergence to Barenblatt self-similar solutions of the corresponding porous media equation are proved in this paper for spherically symmetric motions in three dimensions; this is done by overcoming the analytical difficulties caused by the coordinate's singularity near the center of symmetry, and the physical vacuum singularity to which standard methods of symmetric hyperbolic systems do not apply. Various weights are identified to resolve the singularity near the vacuum boundary and the center of symmetry globally in time. The results obtained here contribute to the theory of global solutions to vacuum boundary problems of compressible inviscid fluids, for which the currently available results are mainly for the local-in-time well-posedness theory, and also to the theory of global smooth solutions of dissipative hyperbolic systems which fail to be strictly hyperbolic.

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.

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.

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.

Treatment of charge singularities in implicit solvent models.

PubMed

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-21

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2 A for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.

Treatment of charge singularities in implicit solvent models

NASA Astrophysics Data System (ADS)

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-01

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2Å for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.

On a class of unsteady three-dimensional Navier Stokes solutions relevant to rotating disc flows: Threshold amplitudes and finite time singularities

NASA Technical Reports Server (NTRS)

Hall, Philip; Balakumar, P.

1990-01-01

A class of exact steady and unsteady solutions of the Navier Stokes equations in cylindrical polar coordinates is given. The flows correspond to the motion induced by an infinite disc rotating with constant angular velocity about the z-axis in a fluid occupying a semi-infinite region which, at large distances from the disc, has velocity field proportional to (x,-y,O) with respect to a Cartesian coordinate system. It is shown that when the rate of rotation is large, Karman's exact solution for a disc rotating in an otherwise motionless fluid is recovered. In the limit of zero rotation rate a particular form of Howarth's exact solution for three-dimensional stagnation point flow is obtained. The unsteady form of the partial differential system describing this class of flow may be generalized to time-periodic equilibrium flows. In addition the unsteady equations are shown to describe a strongly nonlinear instability of Karman's rotating disc flow. It is shown that sufficiently large perturbations lead to a finite time breakdown of that flow whilst smaller disturbances decay to zero. If the stagnation point flow at infinity is sufficiently strong, the steady basic states become linearly unstable. In fact there is then a continuous spectrum of unstable eigenvalues of the stability equations but, if the initial value problem is considered, it is found that, at large values of time, the continuous spectrum leads to a velocity field growing exponentially in time with an amplitude decaying algebraically in time.

Continuation through Singularity of Continuum Multiphase Algorithms

DTIC Science & Technology

2013-03-01

capturing simulation of two-phase flow ; a singularity- free mesoscopic simulation that bridges atomic and continuum scales; and a physics-based closure...for free surface flow . The full two-way coupling was found to be irrelevant to the overall objective of developing a closure model to allow...The method can be used for the study of single species free - surface flow , for instance, in the case of pinch-off of a liquid thread during the

Polarization singularity indices in Gaussian laser beams

NASA Astrophysics Data System (ADS)

Freund, Isaac

2002-01-01

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

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.

Quantum supersymmetric Bianchi IX cosmology

NASA Astrophysics Data System (ADS)

Damour, Thibault; Spindel, Philippe

2014-11-01

We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D =4 simple supergravity for a S U (2 ) -homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a 64-component spinor of spin(8,4) depending on the three squashing parameters, which satisfies Dirac-like, and Klein-Gordon-like, wave equations describing the propagation of a "quantum spinning particle" reflecting off spin-dependent potential walls. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact subalgebra of the rank-3 hyperbolic Kac-Moody algebra A E3 . The (quartic-in-fermions) squared-mass term μ^ 2 entering the Klein-Gordon-like equation has several remarkable properties: (i) it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; (ii) it is a quadratic function of the fermion number NF; and (iii) it is negative in most of the Hilbert space. The latter property leads to a possible quantum avoidance of the singularity ("cosmological bounce"), and suggests imposing the boundary condition that the wave function of the Universe vanish when the volume of space tends to zero (a type of boundary condition which looks like a final-state condition when considering the big crunch inside a black hole). The space of solutions is a mixture of "discrete-spectrum states" (parametrized by a few constant parameters, and known in explicit form) and of continuous-spectrum states (parametrized by arbitrary functions entering some initial-value problem). The predominantly negative values of the squared-mass term lead to a "bottle effect" between small-volume universes and large-volume ones, and to a possible reduction of the continuous spectrum to a discrete spectrum of quantum states looking like excited versions of the Planckian-size universes described by the discrete states at fermionic levels NF=0 and 1.

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.

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.

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.

Hierarchical and non-hierarchical {lambda} elements for one dimensional problems with unknown 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 hierarchical and non-hierarchical special elements called {lambda} elements for one dimensional singular problems where the strength of the singularity is unknown. The {lambda} element formulations presented here permit correct numerical simulation of linear as well as non-linear singular problems without a priori knowledge of the strength of the singularity. A procedure is also presented for determining the exact strength of the singularity using the converged solution. It is shown that in special instances, the general formulation of {lambda} elements can also be made hierarchical. The {lambda} elements presented here aremore » of type C{sup 0} and provide C{sup 0} inter-element continuity with p-version elements. One dimensional steady state radial flow of an upper convected Maxwell fluid is considered as a sample problem. Since in this case {lambda}{sub i} are known, this problem provides a good example for investigating the performance of the formulation proposed here. 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 studies are presented for radially inward flow of an upper convected Maxwell fluid with inner radius r{sub i} = .1 and .01 etc. and Deborah number De = 2.« less

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

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.

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

The numerical calculation of laminar boundary-layer separation

NASA Technical Reports Server (NTRS)

Klineberg, J. M.; Steger, J. L.

1974-01-01

Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for several separated flows and the accuracy of the method is verified. A computer program listing and complete solution case are included.

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.

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.

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.

Singularity resolution in string theory and new quantum condensed matter phases

NASA Astrophysics Data System (ADS)

Fidkowski, Lukasz

2007-12-01

In the first part of this thesis (chapters 1 through 4) we study singularity resolution in string theory. We employ an array of techniques, including the AdS-CFT correspondence, exact solvability of low dimensional models, and supersymmetry. We are able to detect a signature of the black hole singularity by analytically continuing certain AdS-CFT correlators. Also in AdS-CFT, we are able to study a D-brane snapping transition on both sides of the correspondence. In the second part (chapters 5 through 7) we study topological phases in condensed matter systems. We investigate theoretical lattice models realizing such phases, use these to derive nontrivial mathematical physics results, and study an idealized quantum interferometer designed to detect such a phase in quantum Hall systems.

Reduced rank regression via adaptive nuclear norm penalization

PubMed Central

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

2014-01-01

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

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.

On the Lagrangian description of unsteady boundary-layer separation. I - General theory

NASA Technical Reports Server (NTRS)

Van Dommelen, Leon L.; Cowley, Stephen J.

1990-01-01

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

On the Lagrangian description of unsteady boundary layer separation. Part 1: General theory

NASA Technical Reports Server (NTRS)

Vandommelen, Leon L.; Cowley, Stephen J.

1989-01-01

Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.

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.

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.

Calculation of periodic flows in a continuously stratified fluid

NASA Astrophysics Data System (ADS)

Vasiliev, A.

2012-04-01

Analytic theory of disturbances generated by an oscillating compact source in a viscous continuously stratified fluid was constructed. Exact solution of the internal waves generation problem was constructed taking into account diffusivity effects. This analysis is based on set of fundamental equations of incompressible flows. The linearized problem of periodic flows in a continuously stratified fluid, generated by an oscillating part of the inclined plane was solved by methods of singular perturbation theory. A rectangular or disc placed on a sloping plane and oscillating linearly in an arbitrary direction was selected as a source of disturbances. The solutions include regularly perturbed on dissipative component functions describing internal waves and a family of singularly perturbed functions. One of the functions from the singular components family has an analogue in a homogeneous fluid that is a periodic or Stokes' flow. Its thickness is defined by a universal micro scale depending on kinematics viscosity coefficient and a buoyancy frequency with a factor depending on the wave slope. Other singular perturbed functions are specific for stratified flows. Their thickness are defined the diffusion coefficient, kinematic viscosity and additional factor depending on geometry of the problem. Fields of fluid density, velocity, vorticity, pressure, energy density and flux as well as forces acting on the source are calculated for different types of the sources. It is shown that most effective source of waves is the bi-piston. Complete 3D problem is transformed in various limiting cases that are into 2D problem for source in stratified or homogeneous fluid and the Stokes problem for an oscillating infinite plane. The case of the "critical" angle that is equality of the emitting surface and the wave cone slope angles needs in separate investigations. In this case, the number of singular component is saved. Patterns of velocity and density fields were constructed and analyzed by methods of computational mathematics. Singular components of the solution affect the flow pattern of the inhomogeneous stratified fluid, not only near the source of the waves, but at a large distance. Analytical calculations of the structure of wave beams are matched with laboratory experiments. Some deviations at large distances from the source are formed due to the contribution of background wave field associated with seiches in the laboratory tank. In number of the experiments vortices with closed contours were observed on some distances from the disk. The work was supported by Ministry of Education and Science RF (Goscontract No. 16.518.11.7059), experiments were performed on set up USU "HPC IPMec RAS".

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

NASA Technical Reports Server (NTRS)

Baker, Gregory; Siegel, Michael; Tanveer, Saleh

1995-01-01

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

MHD memes

NASA Astrophysics Data System (ADS)

Dewar, R. L.; Mills, R.; Hole, M. J.

2009-05-01

The celebration of Allan Kaufman's 80th birthday was an occasion to reflect on a career that has stimulated the mutual exchange of ideas (or memes in the terminology of Richard Dawkins) between many researchers. This paper will revisit a meme Allan encountered in his early career in magnetohydrodynamics, the continuation of a magnetohydrodynamic mode through a singularity, and will also mention other problems where Allan's work has had a powerful cross-fertilizing effect in plasma physics and other areas of physics and mathematics. To resolve the continuation problem we regularize the Newcomb equation, solve it in terms of Legendre functions of imaginary argument, and define the small weak solutions of the Newcomb equation as generalized functions in the manner of Lighthill, i.e. via a limiting sequence of analytic functions that connect smoothly across the singularity.

Singular value decomposition for the truncated Hilbert transform

NASA Astrophysics Data System (ADS)

Katsevich, A.

2010-11-01

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

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

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 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.

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.

Translational control of a graphically simulated robot arm by kinematic rate equations that overcome elbow joint singularity

NASA Technical Reports Server (NTRS)

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

1984-01-01

An operator commands a robot hand to move in a certain direction relative to its own axis system by specifying a velocity in that direction. This velocity command is then resolved into individual joint rotational velocities in the robot arm to effect the motion. However, the usual resolved-rate equations become singular when the robot arm is straightened. To overcome this elbow joint singularity, equations were developed which allow continued translational control of the robot hand even though the robot arm is (or is nearly) fully extended. A feature of the equations near full arm extension is that an operator simply extends and retracts the robot arm to reverse the direction of the elbow bend (difficult maneuver for the usual resolved-rate equations). Results show successful movement of a graphically simulated robot arm.

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

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

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.

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.

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.

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

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.

Variations in the Parameters of Background Seismic Noise during the Preparation Stages of Strong Earthquakes in the Kamchatka Region

NASA Astrophysics Data System (ADS)

Kasimova, V. A.; Kopylova, G. N.; Lyubushin, A. A.

2018-03-01

The results of the long (2011-2016) investigation of background seismic noise (BSN) in Kamchatka by the method suggested by Doct. Sci. (Phys.-Math.) A.A. Lyubushin with the use of the data from the network of broadband seismic stations of the Geophysical Survey of the Russian Academy of Sciences are presented. For characterizing the BSN field and its variability, continuous time series of the statistical parameters of the multifractal singularity spectra and wavelet expansion calculated from the records at each station are used. These parameters include the generalized Hurst exponent α*, singularity spectrum support width Δα, wavelet spectral exponent β, minimal normalized entropy of wavelet coefficients En, and spectral measure of their coherent behavior. The peculiarities in the spatiotemporal distribution of the BSN parameters as a probable response to the earthquakes with M w = 6.8-8.3 that occurred in Kamchatka in 2013 and 2016 are considered. It is established that these seismic events were preceded by regular variations in the BSN parameters, which lasted for a few months and consisted in the reduction of the median and mean α*, Δα, and β values estimated over all the stations and in the increase of the En values. Based on the increase in the spectral measure of the coherent behavior of the four-variate time series of the median and mean values of the considered statistics, the effect of the enhancement of the synchronism in the joint (collective) behavior of these parameters during a certain period prior to the mantle earthquake in the Sea of Okhotsk (May 24, 2013, M w = 8.3) is diagnosed. The procedures for revealing the precursory effects in the variations of the BSN parameters are described and the examples of these effects are presented.

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

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

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

1995-09-01

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

The 6D superswirl

NASA Astrophysics Data System (ADS)

Parameswaran, S. L.; Tasinato, G.; Zavala, I.

2006-03-01

We present a novel supersymmetric solution to a nonlinear sigma model coupled to supergravity. The solution represents a static, supersymmetric, codimension-two object, which is different to the familiar cosmic strings. In particular, we consider 6D chiral gauged supergravity, whose spectrum contains a number of hypermultiplets. The scalar components of the hypermultiplet are charged under a gauge field, and supersymmetry implies that they experience a simple paraboloid-like (or 2D infinite well) potential, which is minimised when they vanish. Unlike conventional vortices, the energy density of our configuration is not localized to a string-like core. The solutions have two timelike singularities in the internal manifold, which provide the necessary boundary conditions to ensure that the scalars do not lie at the minimum of their potential. The 4D spacetime is flat, and the solution is a continuous deformation of the so-called "rugby ball" solution, which has been studied in the context of the cosmological constant problem. It represents an unexpected class of supersymmetric solutions to the 6D theory, which have gravity, gauge fluxes and hyperscalars all active in the background.

Structured optical vortices with broadband comb-like optical spectra in Yb:Y3Al5O12/YVO4 Raman microchip laser

NASA Astrophysics Data System (ADS)

Dong, Jun; Wang, Xiaolei; Zhang, Mingming; Wang, Xiaojie; He, Hongsen

2018-04-01

Structured optical vortices with 4 phase singularities have been generated in a laser diode pumped continuous-wave Yb:Y3Al5O12/YVO4 (Yb:YAG/YVO4) Raman microchip laser. The broadband comb-like first order Stokes laser emitting spectrum including 30 longitudinal modes covers from 1072.49 nm to 1080.13 nm with a bandwidth of 7.64 nm, which is generated with the Raman shift 259 cm-1 of the c-cut YVO4 crystal converted from the fundamental laser around 1.05 μm. Pump power dependent optical vortex beams are attributed to overlap of the Stokes laser field with the fundamental laser field caused by dynamically changing the coupling losses of the fundamental laser field. The maximum output power is 1.16 W, and the optical-to-optical efficiency is 18.4%. This work provides a method for generating structured optical vortices with an optical frequency comb in solid-state Raman microchip lasers, which have potential applications in quantum computations, micro-machining, and information processing.

A new class of asymptotically non-chaotic vacuum singularities

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

Klinger, Paul, E-mail: paul.klinger@univie.ac.at

2015-12-15

The BKL conjecture, stated in the 1960s and early 1970s by Belinski, Khalatnikov and Lifschitz, proposes a detailed description of the generic asymptotic dynamics of spacetimes as they approach a spacelike singularity. It predicts complicated chaotic behaviour in the generic case, but simpler non-chaotic one in cases with symmetry assumptions or certain kinds of matter fields. Here we construct a new class of four-dimensional vacuum spacetimes containing spacelike singularities which show non-chaotic behaviour. In contrast with previous constructions, no symmetry assumptions are made. Rather, the metric is decomposed in Iwasawa variables and conditions on the asymptotic evolution of some ofmore » them are imposed. The constructed solutions contain five free functions of all space coordinates, two of which are constrained by inequalities. We investigate continuous and discrete isometries and compare the solutions to previous constructions. Finally, we give the asymptotic behaviour of the metric components and curvature.« less

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

PubMed

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

2016-05-26

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

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

PubMed Central

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

2016-01-01

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

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

NASA Astrophysics Data System (ADS)

Mantica, Giorgio; Perotti, Luca

2016-09-01

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

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

PubMed

Hooper, I R; Philbin, T G

2013-12-30

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

On the Existence of Star Products on Quotient Spaces of Linear Hamiltonian Torus Actions

NASA Astrophysics Data System (ADS)

Herbig, Hans-Christian; Iyengar, Srikanth B.; Pflaum, Markus J.

2009-08-01

We discuss BFV deformation quantization (Bordemann et al. in A homological approach to singular reduction in deformation quantization, singularity theory, pp. 443-461. World Scientific, Hackensack, 2007) in the special case of a linear Hamiltonian torus action. In particular, we show that the Koszul complex on the moment map of an effective linear Hamiltonian torus action is acyclic. We rephrase the nonpositivity condition of Arms and Gotay (Adv Math 79(1):43-103, 1990) for linear Hamiltonian torus actions. It follows that reduced spaces of such actions admit continuous star products.

Multi-Level Adaptive Techniques (MLAT) for singular-perturbation problems

NASA Technical Reports Server (NTRS)

Brandt, A.

1978-01-01

The multilevel (multigrid) adaptive technique, a general strategy of solving continuous problems by cycling between coarser and finer levels of discretization is described. It provides very fast general solvers, together with adaptive, nearly optimal discretization schemes. In the process, boundary layers are automatically either resolved or skipped, depending on a control function which expresses the computational goal. The global error decreases exponentially as a function of the overall computational work, in a uniform rate independent of the magnitude of the singular-perturbation terms. The key is high-order uniformly stable difference equations, and uniformly smoothing relaxation schemes.

Through the big bang: Continuing Einstein's equations beyond a cosmological singularity

NASA Astrophysics Data System (ADS)

Koslowski, Tim A.; Mercati, Flavio; Sloan, David

2018-03-01

All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a non-trivial prediction of the relational description; the big bang/crunch is not the end of physics - it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einstein's equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Analytic Evolution of Singular Distribution Amplitudes in QCD

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

Tandogan Kunkel, Asli

2014-08-01

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

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).

Trajectory phase transitions and dynamical Lee-Yang zeros of the Glauber-Ising chain.

PubMed

Hickey, James M; Flindt, Christian; Garrahan, Juan P

2013-07-01

We examine the generating function of the time-integrated energy for the one-dimensional Glauber-Ising model. At long times, the generating function takes on a large-deviation form and the associated cumulant generating function has singularities corresponding to continuous trajectory (or "space-time") phase transitions between paramagnetic trajectories and ferromagnetically or antiferromagnetically ordered trajectories. In the thermodynamic limit, the singularities make up a whole curve of critical points in the complex plane of the counting field. We evaluate analytically the generating function by mapping the generator of the biased dynamics to a non-Hermitian Hamiltonian of an associated quantum spin chain. We relate the trajectory phase transitions to the high-order cumulants of the time-integrated energy which we use to extract the dynamical Lee-Yang zeros of the generating function. This approach offers the possibility to detect continuous trajectory phase transitions from the finite-time behavior of measurable quantities.

Regularity results for the minimum time function with Hörmander vector fields

NASA Astrophysics Data System (ADS)

Albano, Paolo; Cannarsa, Piermarco; Scarinci, Teresa

2018-03-01

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

A Singular Differential Equation Stemming from an Optimal Control Problem in Financial Economics

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

Brunovsky, Pavol, E-mail: brunovsky@fmph.uniba.sk; Cerny, Ales, E-mail: ales.cerny.1@city.ac.uk; Winkler, Michael, E-mail: michael.winkler@uni-due.de

2013-10-15

We consider the ordinary differential equation x{sup 2} u'' = axu'+bu-c(u'-1){sup 2}, x Element-Of (0,x{sub 0}), with a Element-Of R, b Element-Of R , c>0 and the singular initial condition u(0)=0, which in financial economics describes optimal disposal of an asset in a market with liquidity effects. It is shown in the paper that if a+b<0 then no continuous solutions exist, whereas if a+b>0 then there are infinitely many continuous solutions with indistinguishable asymptotics near 0. Moreover, it is proved that in the latter case there is precisely one solution u corresponding to the choice x{sub 0}={infinity} which is suchmore » that 0{<=}u(x){<=}x for all x>0, and that this solution is strictly increasing and concave.« less

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.

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.

Computation at a coordinate singularity

NASA Astrophysics Data System (ADS)

Prusa, Joseph M.

2018-05-01

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

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.

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

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.

Stress intensity factors of composite orthotropic plates containing periodic buffer strips

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.

1978-01-01

The fracture problem of laminated plates which consist of bonded orthotropic layers is studied. The fields equations for an elastic orthotropic body are transformed to give the displacement and stress expressions for each layer or strip. The unknown functions in these expressions are found by satisfying the remaining boundary and continuity conditions. A system of singular integral equations is obtained from the mixed boundary conditions. The singular behavior around the crack tip and at the bimaterial interface is studied. The stress intensity factors are computed for various material combinations and various crack geometries. The results are discussed and are compared with those for isotropic materials.

Inference of strata separation and gas emission paths in longwall overburden using continuous wavelet transform of well logs and geostatistical simulation

NASA Astrophysics Data System (ADS)

Karacan, C. Özgen; Olea, Ricardo A.

2014-06-01

Prediction of potential methane emission pathways from various sources into active mine workings or sealed gobs from longwall overburden is important for controlling methane and for improving mining safety. The aim of this paper is to infer strata separation intervals and thus gas emission pathways from standard well log data. The proposed technique was applied to well logs acquired through the Mary Lee/Blue Creek coal seam of the Upper Pottsville Formation in the Black Warrior Basin, Alabama, using well logs from a series of boreholes aligned along a nearly linear profile. For this purpose, continuous wavelet transform (CWT) of digitized gamma well logs was performed by using Mexican hat and Morlet, as the mother wavelets, to identify potential discontinuities in the signal. Pointwise Hölder exponents (PHE) of gamma logs were also computed using the generalized quadratic variations (GQV) method to identify the location and strength of singularities of well log signals as a complementary analysis. PHEs and wavelet coefficients were analyzed to find the locations of singularities along the logs. Using the well logs in this study, locations of predicted singularities were used as indicators in single normal equation simulation (SNESIM) to generate equi-probable realizations of potential strata separation intervals. Horizontal and vertical variograms of realizations were then analyzed and compared with those of indicator data and training image (TI) data using the Kruskal-Wallis test. A sum of squared differences was employed to select the most probable realization representing the locations of potential strata separations and methane flow paths. Results indicated that singularities located in well log signals reliably correlated with strata transitions or discontinuities within the strata. Geostatistical simulation of these discontinuities provided information about the location and extents of the continuous channels that may form during mining. If there is a gas source within their zone of influence, paths may develop and allow methane movement towards sealed or active gobs under pressure differentials. Knowledge gained from this research will better prepare mine operations for potential methane inflows, thus improving mine safety.

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%.

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.

Solitons and black holes in non-Abelian Einstein-Born-Infeld theory

NASA Astrophysics Data System (ADS)

Dyadichev, V. V.; Gal'tsov, D. V.

2000-08-01

Recently it was shown that the Born-Infeld modification of the quadratic Yang-Mills action gives rise to classical particle-like solutions in the flat space which have a striking similarity with the Bartnik-McKinnon solutions obtained within the gravity coupled Yang-Mills theory. We show that both families of solutions are continuously related within the framework of the Einstein-Born-Infeld theory via interpolating sequences of parameters. We also investigate an internal structure of the associated black holes and find that the Born-Infeld non-linearity changes drastically the black hole interior typical for the usual quadratic Yang-Mills theory. In the latter case a generic solution exhibits violent metric oscillations near the singularity. In the Born-Infeld case the generic interior solution is smooth, the metric tends to the standard Schwarzschild type singularity, and we did not observe internal horizons. Smoothing of the `violent' EYM singularity may be interpreted as a result of non-gravitational quantum effects.

Numerical methods for coupled fracture problems

NASA Astrophysics Data System (ADS)

Viesca, Robert C.; Garagash, Dmitry I.

2018-04-01

We consider numerical solutions in which the linear elastic response to an opening- or sliding-mode fracture couples with one or more processes. Classic examples of such problems include traction-free cracks leading to stress singularities or cracks with cohesive-zone strength requirements leading to non-singular stress distributions. These classical problems have characteristic square-root asymptotic behavior for stress, relative displacement, or their derivatives. Prior work has shown that such asymptotics lead to a natural quadrature of the singular integrals at roots of Chebyhsev polynomials of the first, second, third, or fourth kind. We show that such quadratures lead to convenient techniques for interpolation, differentiation, and integration, with the potential for spectral accuracy. We further show that these techniques, with slight amendment, may continue to be used for non-classical problems which lack the classical asymptotic behavior. We consider solutions to example problems of both the classical and non-classical variety (e.g., fluid-driven opening-mode fracture and fault shear rupture driven by thermal weakening), with comparisons to analytical solutions or asymptotes, where available.

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

NASA Astrophysics Data System (ADS)

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

2017-10-01

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

Computational analysis of drop formation before and after the first singularity: the fate of free and satellite drops during simple dripping and DOD drop formation

NASA Astrophysics Data System (ADS)

Chen, Alvin U.; Basaran, Osman A.

2000-11-01

Drop formation from a capillary --- dripping mode --- or an ink jet nozzle --- drop-on-demand (DOD) mode --- falls into a class of scientifically challenging yet practically useful free surface flows that exhibit a finite time singularity, i.e. the breakup of an initially single liquid mass into two or more fragments. While computational tools to model such problems have been developed recently, they lack the accuracy needed to quantitatively predict all the dynamics observed in experiments. Here we present a new finite element method (FEM) based on a robust algorithm for elliptic mesh generation and remeshing to handle extremely large interface deformations. The new algorithm allows continuation of computations beyond the first singularity to track fates of both primary and any satellite drops. The accuracy of the computations is demonstrated by comparison of simulations with experimental measurements made possible with an ultra high-speed digital imager capable of recording 100 million frames per second.

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.

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.

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.

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.

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.

Eigensensitivity analysis of rotating clamped uniform beams with the asymptotic numerical method

NASA Astrophysics Data System (ADS)

Bekhoucha, F.; Rechak, S.; Cadou, J. M.

2016-12-01

In this paper, free vibrations of a rotating clamped Euler-Bernoulli beams with uniform cross section are studied using continuation method, namely asymptotic numerical method. The governing equations of motion are derived using Lagrange's method. The kinetic and strain energy expression are derived from Rayleigh-Ritz method using a set of hybrid variables and based on a linear deflection assumption. The derived equations are transformed in two eigenvalue problems, where the first is a linear gyroscopic eigenvalue problem and presents the coupled lagging and stretch motions through gyroscopic terms. While the second is standard eigenvalue problem and corresponds to the flapping motion. Those two eigenvalue problems are transformed into two functionals treated by continuation method, the Asymptotic Numerical Method. New method proposed for the solution of the linear gyroscopic system based on an augmented system, which transforms the original problem to a standard form with real symmetric matrices. By using some techniques to resolve these singular problems by the continuation method, evolution curves of the natural frequencies against dimensionless angular velocity are determined. At high angular velocity, some singular points, due to the linear elastic assumption, are computed. Numerical tests of convergence are conducted and the obtained results are compared to the exact values. Results obtained by continuation are compared to those computed with discrete eigenvalue problem.

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

NASA Astrophysics Data System (ADS)

Jitomirskaya, S.; Marx, C. A.

2012-11-01

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

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.

Transitions in Pediatrics: A Segmental Analysis.

ERIC Educational Resources Information Center

Pawluch, Dorothy.

1983-01-01

Examines how, as medical advances drastically reduced infant and child mortality rates, the field of pediatrics expanded from singular concern with treating children's diseases to include involvement in managing troublesome behavior. Considers the continued involvement of pediatricians in ministering to the psychosocial and behavioral needs of…

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

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.

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.

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.

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.

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

Some Theoretical Aspects of Nonzero Sum Differential Games and Applications to Combat Problems

DTIC Science & Technology

1971-06-01

the Equilibrium Solution . 7 Hamilton-Jacobi-Bellman Partial Differential Equations ............. .............. 9 Influence Function Differential...Linearly .......... ............ 18 Problem Statement .......... ............ 18 Formulation of LJB Equations, Influence Function Equations and the TPBVP...19 Control Lawe . . .. ...... ........... 21 Conditions for Influence Function Continuity along Singular Surfaces

The best of both Reps—Diabatized Gaussians on adiabatic surfaces

NASA Astrophysics Data System (ADS)

Meek, Garrett A.; Levine, Benjamin G.

2016-11-01

When simulating nonadiabatic molecular dynamics, choosing an electronic representation requires consideration of well-known trade-offs. The uniqueness and spatially local couplings of the adiabatic representation come at the expense of an electronic wave function that changes discontinuously with nuclear motion and associated singularities in the nonadiabatic coupling matrix elements. The quasi-diabatic representation offers a smoothly varying wave function and finite couplings, but identification of a globally well-behaved quasi-diabatic representation is a system-specific challenge. In this work, we introduce the diabatized Gaussians on adiabatic surfaces (DGAS) approximation, a variant of the ab initio multiple spawning (AIMS) method that preserves the advantages of both electronic representations while avoiding their respective pitfalls. The DGAS wave function is expanded in a basis of vibronic functions that are continuous in both electronic and nuclear coordinates, but potentially discontinuous in time. Because the time-dependent Schrödinger equation contains only first-order derivatives with respect to time, singularities in the second-derivative nonadiabatic coupling terms (i.e., diagonal Born-Oppenheimer correction; DBOC) at conical intersections are rigorously absent, though singular time-derivative couplings remain. Interpolation of the electronic wave function allows the accurate prediction of population transfer probabilities even in the presence of the remaining singularities. We compare DGAS calculations of the dynamics of photoexcited ethene to AIMS calculations performed in the adiabatic representation, including the DBOC. The 28 fs excited state lifetime observed in DGAS simulations is considerably shorter than the 50 fs lifetime observed in the adiabatic simulations. The slower decay in the adiabatic representation is attributable to the large, repulsive DBOC in the neighborhood of conical intersections. These repulsive DBOC terms are artifacts of the discontinuities in the individual adiabatic vibronic basis functions and therefore cannot reflect the behavior of the exact molecular wave function, which must be continuous.

Sampling Singular and Aggregate Point Sources of Carbon Dioxide from Space Using OCO-2

NASA Astrophysics Data System (ADS)

Schwandner, F. M.; Gunson, M. R.; Eldering, A.; Miller, C. E.; Nguyen, H.; Osterman, G. B.; Taylor, T.; O'Dell, C.; Carn, S. A.; Kahn, B. H.; Verhulst, K. R.; Crisp, D.; Pieri, D. C.; Linick, J.; Yuen, K.; Sanchez, R. M.; Ashok, M.

2016-12-01

Anthropogenic carbon dioxide (CO2) sources increasingly tip the natural balance between natural carbon sources and sinks. Space-borne measurements offer opportunities to detect and analyze point source emission signals anywhere on Earth. Singular continuous point source plumes from power plants or volcanoes turbulently mix into their proximal background fields. In contrast, plumes of aggregate point sources such as cities, and transportation or fossil fuel distribution networks, mix into each other and may therefore result in broader and more persistent excess signals of total column averaged CO2 (XCO2). NASA's first satellite dedicated to atmospheric CO2observation, the Orbiting Carbon Observatory-2 (OCO-2), launched in July 2014 and now leads the afternoon constellation of satellites (A-Train). While continuously collecting measurements in eight footprints across a narrow ( < 10 km) wide swath it occasionally cross-cuts coincident emission plumes. For singular point sources like volcanoes and coal fired power plants, we have developed OCO-2 data discovery tools and a proxy detection method for plumes using SO2-sensitive TIR imaging data (ASTER). This approach offers a path toward automating plume detections with subsequent matching and mining of OCO-2 data. We found several distinct singular source CO2signals. For aggregate point sources, we investigated whether OCO-2's multi-sounding swath observing geometry can reveal intra-urban spatial emission structures in the observed variability of XCO2 data. OCO-2 data demonstrate that we can detect localized excess XCO2 signals of 2 to 6 ppm against suburban and rural backgrounds. Compared to single-shot GOSAT soundings which detected urban/rural XCO2differences in megacities (Kort et al., 2012), the OCO-2 swath geometry opens up the path to future capabilities enabling urban characterization of greenhouse gases using hundreds of soundings over a city at each satellite overpass. California Institute of Technology

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.

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

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.

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

NASA Astrophysics Data System (ADS)

Dubovskii, L. B.

2018-05-01

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

Fractional charge and inter-Landau-level states at points of singular curvature.

PubMed

Biswas, Rudro R; Son, Dam Thanh

2016-08-02

The quest for universal properties of topological phases is fundamentally important because these signatures are robust to variations in system-specific details. Aspects of the response of quantum Hall states to smooth spatial curvature are well-studied, but challenging to observe experimentally. Here we go beyond this prevailing paradigm and obtain general results for the response of quantum Hall states to points of singular curvature in real space; such points may be readily experimentally actualized. We find, using continuum analytical methods, that the point of curvature binds an excess fractional charge and sequences of quantum states split away, energetically, from the degenerate bulk Landau levels. Importantly, these inter-Landau-level states are bound to the topological singularity and have energies that are universal functions of bulk parameters and the curvature. Our exact diagonalization of lattice tight-binding models on closed manifolds demonstrates that these results continue to hold even when lattice effects are significant. An important technological implication of these results is that these inter-Landau-level states, being both energetically and spatially isolated quantum states, are promising candidates for constructing qubits for quantum computation.

Singularity in the positive Hall coeffcient near pre-onset temperatures in high-Tc superconductors

NASA Astrophysics Data System (ADS)

Vezzoli, G. C.; Chen, M. F.; Craver, F.; Moon, B. M.; Safari, A.; Burke, T.; Stanley, W.

1990-10-01

Hall measurements using continuous extremely slow cooling and reheating rates as well as employing eqiulibrium point-by-point conventional techniques reveals a clear anomally in RH at pre-onset temperatures near Tc in polycrystalline samples Y1Ba2Cu3O7 and Bi2Sr2Ca2Cu3O10. The anomaly has the appearance of a singularity of Dirac-delta function which parallels earlier work on La1-xSrxCuO4. Recent single crystal work on the Bi-containing high-Tc superconductor is in accord with a clearcut anomaly. The singularity is tentatively interpreted to be associated (upon cooling) with initially the removal of positive holes from the hopping conduction system of the normal state such as from the increased concentration of bound virtual excitons due to increased exciton and hole lifetimes at low temperature. Subsequently the formation of Cooper pairs by mediation from these centers (bound-holes) and/or bound excitons) may cause an ionization of these bound virtual excitons thereby re-introducing holes and electrons into the conduction system at Tc.

Legacies of Immigration: Children of Immigrants' Experiences Navigating Higher Education

ERIC Educational Resources Information Center

Yeung, Fanny P.F.

2011-01-01

Immigration, as a continuous phenomenon, extends beyond a singular migratory event that an individual experiences. The purpose of this research project was to explore the college experiences of second-generation immigrants and how their family relationships, immigrant histories, and socioeconomic status directly and indirectly shaped their…

7 CFR 201.1 - Meaning of words.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 3 2010-01-01 2010-01-01 false Meaning of words. 201.1 Section 201.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... REGULATIONS Definitions § 201.1 Meaning of words. Words in the regulations in this part in the singular form...

7 CFR 202.1 - Meaning of words.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 3 2010-01-01 2010-01-01 false Meaning of words. 202.1 Section 202.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... RULES OF PRACTICE General § 202.1 Meaning of words. As used in this part, words in the singular form...

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.

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.

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.

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.

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.

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.

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.

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.

Teaching and Learning Jewish History in the 21st Century: New Priorities and Opportunities

ERIC Educational Resources Information Center

Jacobs, Benjamin M.

2018-01-01

New 21st-century circumstances in the Jewish world--including the changing nature of Jewish identification, the retreat from identity and continuity as singular aims of Jewish education, the democratization of Jewish learning opportunities, increased emphasis on informal and experiential Jewish education activities, and demonstrable interest among…

DISTINCTIVE FEATURES IN THE PLURALIZATION RULES OF ENGLISH SPEAKERS.

ERIC Educational Resources Information Center

ANISFELD, MOSHE; AND OTHERS

FIRST AND SECOND GRADERS, GIVEN "CVC" SINGULAR NONSENSE WORDS (E.G., NAR) ORALLY AND ASKED TO CHOOSE BETWEEN TWO PLURALS (NARF-NARK), PREFERRED FINAL SOUNDS SHARING WITH /Z/ (THE MOST COMMON SHAPE OF THE PLURAL MORPHEME IN ENGLISH) THE STRIDENCY OR CONTINUANCE FEATURES. THIS SUGGESTS THAT THEIR PLURALIZATION RULES ARE FORMULATED IN TERMS OF…

7 CFR 283.1 - Meaning of words.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 4 2010-01-01 2010-01-01 false Meaning of words. 283.1 Section 283.1 Agriculture Regulations of the Department of Agriculture (Continued) FOOD AND NUTRITION SERVICE, DEPARTMENT OF AGRICULTURE... Meaning of words. As used in this part, words in the singular form shall be deemed to import the plural...

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…

Continuous spin representations from group contraction

NASA Astrophysics Data System (ADS)

Khan, Abu M.; Ramond, Pierre

2005-05-01

We consider how the continuous spin representation (CSR) of the Poincaré group in four dimensions can be generated by dimensional reduction. The analysis uses the front-form little group in five dimensions, which must yield the Euclidean group E(2), the little group of the CSR. We consider two cases, one is the single spin massless representation of the Poincaré group in five dimensions, the other is the infinite component Majorana equation, which describes an infinite tower of massive states in five dimensions. In the first case, the double singular limit j, R →∞, with j /R fixed, where R is the Kaluza-Klein radius of the fifth dimension, and j is the spin of the particle in five dimensions, yields the CSR in four dimensions. It amounts to the Inönü-Wigner contraction, with the inverse Kaluza-Klein radius as contraction parameter. In the second case, the CSR appears only by taking a triple singular limit, where an internal coordinate of the Majorana theory goes to infinity, while leaving its ratio to the Kaluza-Klein radius fixed.

Solving regularly and singularly perturbed reaction-diffusion equations in three space dimensions

NASA Astrophysics Data System (ADS)

Moore, Peter K.

2007-06-01

In [P.K. Moore, Effects of basis selection and h-refinement on error estimator reliability and solution efficiency for higher-order methods in three space dimensions, Int. J. Numer. Anal. Mod. 3 (2006) 21-51] a fixed, high-order h-refinement finite element algorithm, Href, was introduced for solving reaction-diffusion equations in three space dimensions. In this paper Href is coupled with continuation creating an automatic method for solving regularly and singularly perturbed reaction-diffusion equations. The simple quasilinear Newton solver of Moore, (2006) is replaced by the nonlinear solver NITSOL [M. Pernice, H.F. Walker, NITSOL: a Newton iterative solver for nonlinear systems, SIAM J. Sci. Comput. 19 (1998) 302-318]. Good initial guesses for the nonlinear solver are obtained using continuation in the small parameter ɛ. Two strategies allow adaptive selection of ɛ. The first depends on the rate of convergence of the nonlinear solver and the second implements backtracking in ɛ. Finally a simple method is used to select the initial ɛ. Several examples illustrate the effectiveness of the algorithm.

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.

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).

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.

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.

Hybrid Inflation: Multi-field Dynamics and Cosmological Constraints

NASA Astrophysics Data System (ADS)

Clesse, Sébastien

2011-09-01

The dynamics of hybrid models is usually approximated by the evolution of a scalar field slowly rolling along a nearly flat valley. Inflation ends with a waterfall phase, due to a tachyonic instability. This final phase is usually assumed to be nearly instantaneous. In this thesis, we go beyond these approximations and analyze the exact 2-field dynamics of hybrid models. Several effects are put in evidence: 1) the possible slow-roll violations along the valley induce the non existence of inflation at small field values. Provided super-planckian fields, the scalar spectrum of the original model is red, in agreement with observations. 2) The initial field values are not fine-tuned along the valley but also occupy a considerable part of the field space exterior to it. They form a structure with fractal boundaries. Using bayesian methods, their distribution in the whole parameter space is studied. Natural bounds on the potential parameters are derived. 3) For the original model, inflation is found to continue for more than 60 e-folds along waterfall trajectories in some part of the parameter space. The scalar power spectrum of adiabatic perturbations is modified and is generically red, possibly in agreement with CMB observations. Topological defects are conveniently stretched outside the observable Universe. 4) The analysis of the initial conditions is extended to the case of a closed Universe, in which the initial singularity is replaced by a classical bounce. In the third part of the thesis, we study how the present CMB constraints on the cosmological parameters could be ameliorated with the observation of the 21cm cosmic background, by future giant radio-telescopes. Forecasts are determined for a characteristic Fast Fourier Transform Telescope, by using both Fisher matrix and MCMC methods.

Truly self-consistent solution of Kohn-Sham equations for extended systems with inhomogeneous electron gas

NASA Astrophysics Data System (ADS)

Shul'man, A. Ya; Posvyanskii, D. V.

2014-05-01

The density functional approach in the Kohn-Sham approximation is widely used to study properties of many-electron systems. Due to the nonlinearity of the Kohn-Sham equations, the general self-consistent solution method for infinite systems involves iterations with alternate solutions of the Poisson and Schrödinger equations. One of problems with such an approach is that the charge distribution, updated by solving the Schrodinger equation, may be incompatible with the boundary conditions of the Poisson equation for Coulomb potential. The resulting instability or divergence manifests itself most appreciably in the case of infinitely extended systems because the corresponding boundary-value problem becomes singular. In this work the stable iterative scheme for solving the Kohn-Sham equations for infinite systems with inhomogeneous electron gas is described based on eliminating the long-range character of the Coulomb interaction, which causes the tight coupling of the charge distribution with the boundary conditions. This algorithm has been previously successfully implemented in the calculation of work function and surface energy of simple metals in the jellium model. Here it is used to calculate the energy spectrum of quasi-two-dimensional electron gas in the accumulation layer at the semiconductor surface n-InAs. The electrons in such a structure occupy states that belong to both discrete and continuous parts of the energy spectrum. This causes the problems of convergence in the usually used approaches, which do not exist in our case. Because of the narrow bandgap of InAs, it is necessary to take the nonparabolicity of the conduction band into account; this is done by means of a new effective mass method. The calculated quasi-two-dimensional energy bands correspond well to experimental data measured by the angle resolved photoelectron spectroscopy technique.

An approach for the regularization of a power flow solution around the maximum loading point

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

Kataoka, Y.

1992-08-01

In the conventional power flow solution, the boundary conditions are directly specified by active power and reactive power at each node, so that the singular point coincided with the maximum loading point. For this reason, the computations are often disturbed by ill-condition. This paper proposes a new method for getting the wide-range regularity by giving some modifications to the conventional power flow solution method, thereby eliminating the singular point or shifting it to the region with the voltage lower than that of the maximum loading point. Then, the continuous execution of V-P curves including maximum loading point is realized. Themore » efficiency and effectiveness of the method are tested in practical 598-nodes system in comparison with the conventional method.« less

Efficient scheme for parametric fitting of data in arbitrary dimensions.

PubMed

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

2008-07-01

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

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.

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.

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.

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.

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.

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.

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.

EDITORIAL: The plurality of optical singularities

NASA Astrophysics Data System (ADS)

Berry, Michael; Dennis, Mark; Soskin, Marat

2004-05-01

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

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.

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.

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.

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

Mass hierarchy, mass gap and corrections to Newton's law on thick branes with Poincaré symmetry

NASA Astrophysics Data System (ADS)

Barbosa-Cendejas, Nandinii; Herrera-Aguilar, Alfredo; Kanakoglou, Konstantinos; Nucamendi, Ulises; Quiros, Israel

2014-01-01

We consider a scalar thick brane configuration arising in a 5D theory of gravity coupled to a self-interacting scalar field in a Riemannian manifold. We start from known classical solutions of the corresponding field equations and elaborate on the physics of the transverse traceless modes of linear fluctuations of the classical background, which obey a Schrödinger-like equation. We further consider two special cases in which this equation can be solved analytically for any massive mode with , in contrast with numerical approaches, allowing us to study in closed form the massive spectrum of Kaluza-Klein (KK) excitations and to analytically compute the corrections to Newton's law in the thin brane limit. In the first case we consider a novel solution with a mass gap in the spectrum of KK fluctuations with two bound states—the massless 4D graviton free of tachyonic instabilities and a massive KK excitation—as well as a tower of continuous massive KK modes which obey a Legendre equation. The mass gap is defined by the inverse of the brane thickness, allowing us to get rid of the potentially dangerous multiplicity of arbitrarily light KK modes. It is shown that due to this lucky circumstance, the solution of the mass hierarchy problem is much simpler and transparent than in the thin Randall-Sundrum (RS) two-brane configuration. In the second case we present a smooth version of the RS model with a single massless bound state, which accounts for the 4D graviton, and a sector of continuous fluctuation modes with no mass gap, which obey a confluent Heun equation in the Ince limit. (The latter seems to have physical applications for the first time within braneworld models). For this solution the mass hierarchy problem is solved with positive branes as in the Lykken-Randall (LR) model and the model is completely free of naked singularities. We also show that the scalar-tensor system is stable under scalar perturbations with no scalar modes localized on the braneworld configuration.

Continuous analogues of matrix factorizations

PubMed Central

Townsend, Alex; Trefethen, Lloyd N.

2015-01-01

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

38 CFR 18b.11 - Use of number.

Code of Federal Regulations, 2012 CFR

2012-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 2 2012-07-01 2012-07-01 false Use of number. 18b.11 Section 18b.11 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS AFFAIRS (CONTINUED) PRACTICE... § 18b.11 Use of number. As used in this part, words importing the singular number may extend and be...

38 CFR 18b.11 - Use of number.

Code of Federal Regulations, 2010 CFR

2010-07-01

... 38 Pensions, Bonuses, and Veterans' Relief 2 2010-07-01 2010-07-01 false Use of number. 18b.11 Section 18b.11 Pensions, Bonuses, and Veterans' Relief DEPARTMENT OF VETERANS AFFAIRS (CONTINUED) PRACTICE... § 18b.11 Use of number. As used in this part, words importing the singular number may extend and be...

Digging Deeper: Understanding Non-Proficient Students through an Understanding of Reading and Motivational Profiles

ERIC Educational Resources Information Center

Smith, Hiawatha D.

2017-01-01

With the continued emphasis on accountability for students, schools are working to increase the reading academic performance of their non-proficient students. Many remedial approaches fail to identify the individual strengths and weaknesses and tend to treat these students with a singular remedial focus on word identification (Allington, 2001). In…

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.

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

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 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.

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.

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

Phenomenological implications of the blown-up orbifolds

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

Cvetic, M.

1987-05-01

We discuss the structure of the effective Lagrangian for the (2,2) Z/sub N/ orbifolds and the corresponding Calabi-Yau manifolds which are obtained by ''blowing-up'' the orbifold singularities. The method to ''blow-up'' such singularities is reviewed. Results are exact at the string tree-level. In particular, the question of generating an intermediate scale M/sub I/ in such models is addressed. It is shown that for Z/sub N/ orbifolds (except one) and the corresponding blown-up orbifolds which are compactified on any six-torus T/sup 6/ which can be obtained by continuously deforming T/sup 4/ circle times T/sup 2/, all the terms of the typemore » (2727)/sup K/ are absent from the effective superpotential, thus questioning the mechanism for generating a large intermediate scale for such compactifications.« less

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.

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.

Top predators induce the evolutionary diversification of intermediate predator species.

PubMed

Zu, Jian; Yuan, Bo; Du, Jianqiang

2015-12-21

We analyze the evolutionary branching phenomenon of intermediate predator species in a tritrophic food chain model by using adaptive dynamics theory. Specifically, we consider the adaptive diversification of an intermediate predator species that feeds on a prey species and is fed upon by a top predator species. We assume that the intermediate predator׳s ability to forage on the prey can adaptively improve, but this comes at the cost of decreased defense ability against the top predator. First, we identify the general properties of trade-off relationships that lead to a continuously stable strategy or to evolutionary branching in the intermediate predator species. We find that if there is an accelerating cost near the singular strategy, then that strategy is continuously stable. In contrast, if there is a mildly decelerating cost near the singular strategy, then that strategy may be an evolutionary branching point. Second, we find that after branching has occurred, depending on the specific shape and strength of the trade-off relationship, the intermediate predator species may reach an evolutionarily stable dimorphism or one of the two resultant predator lineages goes extinct. Crown Copyright © 2015. Published by Elsevier Ltd. All rights reserved.

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.

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.

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…

Abrupt current switching in graphene bilayer tunnel transistors enabled by van Hove singularities.

PubMed

Alymov, Georgy; Vyurkov, Vladimir; Ryzhii, Victor; Svintsov, Dmitry

2016-04-21

In a continuous search for the energy-efficient electronic switches, a great attention is focused on tunnel field-effect transistors (TFETs) demonstrating an abrupt dependence of the source-drain current on the gate voltage. Among all TFETs, those based on one-dimensional (1D) semiconductors exhibit the steepest current switching due to the singular density of states near the band edges, though the current in 1D structures is pretty low. In this paper, we propose a TFET based on 2D graphene bilayer which demonstrates a record steep subthreshold slope enabled by van Hove singularities in the density of states near the edges of conduction and valence bands. Our simulations show the accessibility of 3.5 × 10(4) ON/OFF current ratio with 150 mV gate voltage swing, and a maximum subthreshold slope of (20 μV/dec)(-1) just above the threshold. The high ON-state current of 0.8 mA/μm is enabled by a narrow (~0.3 eV) extrinsic band gap, while the smallness of the leakage current is due to an all-electrical doping of the source and drain contacts which suppresses the band tailing and trap-assisted tunneling.

Abrupt current switching in graphene bilayer tunnel transistors enabled by van Hove singularities

PubMed Central

Alymov, Georgy; Vyurkov, Vladimir; Ryzhii, Victor; Svintsov, Dmitry

2016-01-01

In a continuous search for the energy-efficient electronic switches, a great attention is focused on tunnel field-effect transistors (TFETs) demonstrating an abrupt dependence of the source-drain current on the gate voltage. Among all TFETs, those based on one-dimensional (1D) semiconductors exhibit the steepest current switching due to the singular density of states near the band edges, though the current in 1D structures is pretty low. In this paper, we propose a TFET based on 2D graphene bilayer which demonstrates a record steep subthreshold slope enabled by van Hove singularities in the density of states near the edges of conduction and valence bands. Our simulations show the accessibility of 3.5 × 104 ON/OFF current ratio with 150 mV gate voltage swing, and a maximum subthreshold slope of (20 μV/dec)−1 just above the threshold. The high ON-state current of 0.8 mA/μm is enabled by a narrow (~0.3 eV) extrinsic band gap, while the smallness of the leakage current is due to an all-electrical doping of the source and drain contacts which suppresses the band tailing and trap-assisted tunneling. PMID:27098051

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.

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.

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.

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.

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

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.

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.

Bridging the gap between the technological singularity and mainstream medicine: highlighting a course on technology and the future of medicine.

PubMed

Solez, Kim; Bernier, Ashlyn; Crichton, Joel; Graves, Heather; Kuttikat, Preeti; Lockwood, Ross; Marovitz, William F; Monroe, Damon; Pallen, Mark; Pandya, Shawna; Pearce, David; Saleh, Abdullah; Sandhu, Neelam; Sergi, Consolato; Tuszynski, Jack; Waugh, Earle; White, Jonathan; Woodside, Michael; Wyndham, Roger; Zaiane, Osmar; Zakus, David

2013-09-09

The "technological singularity" is defined as that putative point in time forecasted to occur in the mid twenty-first century when machines will become smarter than humans, leading humans and machines to merge. It is hypothesized that this event will have a profound influence on medicine and population health. This work describes a new course on Technology and the Future of Medicine developed by a diverse, multi-disciplinary group of faculty members at a Canadian university. The course began as a continuous professional learning course and was later established as a recognized graduate course. We describe the philosophy of the course, the barriers encountered in course development, and some of the idiosyncratic solutions that were developed to overcome these, including the use of YouTube audience retention analytics. We hope that this report might provide a useful template for other institutions attempting to set up similar programs.

Forward and inverse solutions for three-element Risley prism beam scanners.

PubMed

Li, Anhu; Liu, Xingsheng; Sun, Wansong

2017-04-03

Scan blind zone and control singularity are two adverse issues for the beam scanning performance in double-prism Risley systems. In this paper, a theoretical model which introduces a third prism is developed. The critical condition for a fully eliminated scan blind zone is determined through a geometric derivation, providing several useful formulae for three-Risley-prism system design. Moreover, inverse solutions for a three-prism system are established, based on the damped least-squares iterative refinement by a forward ray tracing method. It is shown that the efficiency of this iterative calculation of the inverse solutions can be greatly enhanced by a numerical differentiation method. In order to overcome the control singularity problem, the motion law of any one prism in a three-prism system needs to be conditioned, resulting in continuous and steady motion profiles for the other two prisms.

Perturbations of non-resonant satellite orbits due to a rotating earth. [tesseral harmonics and the Von Ziepel method

NASA Technical Reports Server (NTRS)

Mueller, A.

1978-01-01

The dominant perturbations of the motion of a satellite near the earth are due to atmospheric drag and the non-symmetrical gravitational field. Atmospheric drag perturbation continually pulls the satellite in and out of the different long period resonant frequencies. The result is that the resonances never become apparent and may be neglected. The tesseral harmonics have no true secular perturbation but the periodicities in the mean motion induce a secular perturbation in the mean anomaly. This secular perturbation may be determined by simply using the average mean motion instead of the osculating mean motion. The Von Ziepel method is used to determine tesseral perturbations. The solution is found first in the singular DS phi elements and then rewritten in the PS phi elements to remove singularities. The notation used in the development is described in the appendix.

Topology of three-dimensional separated flows

NASA Technical Reports Server (NTRS)

Tobak, M.; Peake, D. J.

1981-01-01

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

Wavelet maxima curves of surface latent heat flux associated with two recent Greek earthquakes

NASA Astrophysics Data System (ADS)

Cervone, G.; Kafatos, M.; Napoletani, D.; Singh, R. P.

2004-05-01

Multi sensor data available through remote sensing satellites provide information about changes in the state of the oceans, land and atmosphere. Recent studies have shown anomalous changes in oceans, land, atmospheric and ionospheric parameters prior to earthquakes events. This paper introduces an innovative data mining technique to identify precursory signals associated with earthquakes. The proposed methodology is a multi strategy approach which employs one dimensional wavelet transformations to identify singularities in the data, and an analysis of the continuity of the wavelet maxima in time and space to identify the singularities associated with earthquakes. The proposed methodology has been employed using Surface Latent Heat Flux (SLHF) data to study the earthquakes which occurred on 14 August 2003 and on 1 March 2004 in Greece. A single prominent SLHF anomaly has been found about two weeks prior to each of the earthquakes.

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.

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

NASA Technical Reports Server (NTRS)

Chen, B. M.; Saber, A.

1993-01-01

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

Regularization of the big bang singularity with random perturbations

NASA Astrophysics Data System (ADS)

Belbruno, Edward; Xue, BingKan

2018-03-01

We show how to regularize the big bang singularity in the presence of random perturbations modeled by Brownian motion using stochastic methods. We prove that the physical variables in a contracting universe dominated by a scalar field can be continuously and uniquely extended through the big bang as a function of time to an expanding universe only for a discrete set of values of the equation of state satisfying special co-prime number conditions. This result significantly generalizes a previous result (Xue and Belbruno 2014 Class. Quantum Grav. 31 165002) that did not model random perturbations. This result implies that the extension from a contracting to an expanding universe for the discrete set of co-prime equation of state is robust, which is a surprising result. Implications for a purely expanding universe are discussed, such as a non-smooth, randomly varying scale factor near the big bang.

Fault detection for singular switched linear systems with multiple time-varying delay in finite frequency domain

NASA Astrophysics Data System (ADS)

Zhai, Ding; Lu, Anyang; Li, Jinghao; Zhang, Qingling

2016-10-01

This paper deals with the problem of the fault detection (FD) for continuous-time singular switched linear systems with multiple time-varying delay. In this paper, the actuator fault is considered. Besides, the systems faults and unknown disturbances are assumed in known frequency domains. Some finite frequency performance indices are initially introduced to design the switched FD filters which ensure that the filtering augmented systems under switching signal with average dwell time are exponentially admissible and guarantee the fault input sensitivity and disturbance robustness. By developing generalised Kalman-Yakubovic-Popov lemma and using Parseval's theorem and Fourier transform, finite frequency delay-dependent sufficient conditions for the existence of such a filter which can guarantee the finite-frequency H- and H∞ performance are derived and formulated in terms of linear matrix inequalities. Four examples are provided to illustrate the effectiveness of the proposed finite frequency method.

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.

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 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.

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

NASA Astrophysics Data System (ADS)

Bernard, Patrick; Suhr, Stefan

2018-03-01

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

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects

DOE PAGES

Argyres, Philip C.; Uensal, Mithat

2012-08-10

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a massmore » gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics — which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription — to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion-anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Écalle’s resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.« less

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.

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)

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.

On the contact interaction of two identical stringers with an elastic semi-infinite continuous or vertically cracked plate

NASA Astrophysics Data System (ADS)

Grigoryan, M. S.

2018-04-01

This paper considers two connected contact problems on the interaction of stringers with an elastic semi-infinite plate. In the first problem, an elastic half-infinite continuous plate is reinforced on its boundary by two identical stringers exposed to a tensile external force. In the second problem, in the presence of the same stringers, the plate contains a collinear system of cracks on its vertical axis. The solution of both problems is reduced to the solution of singular integral equations (SIE) that are solved by a known numerical-analytical method.

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.

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

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

NASA Astrophysics Data System (ADS)

Khan, Abu M. A. S.

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

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.

Temperament and character as endophenotype in adults with autism spectrum disorders or attention deficit/hyperactivity disorder.

PubMed

Sizoo, Bram B; van der Gaag, Rutger Jan; van den Brink, Wim

2015-05-01

Autism spectrum disorder and attention deficit/hyperactivity disorder overlap in several ways, raising questions about the nature of this comorbidity. Rommelse et al. published an innovative review of candidate endophenotypes for autism spectrum disorder and attention deficit/hyperactivity disorder in cognitive and brain domains. They found that all the endophenotypic impairments that were reviewed in attention deficit/hyperactivity disorder were also present in autism spectrum disorder, suggesting a continuity model with attention deficit/hyperactivity disorder as "a light form of autism spectrum disorder." Using existing data, 75 adults with autism spectrum disorder and 53 with attention deficit/hyperactivity disorder were directly compared on autistic symptoms with the autism spectrum quotient, and on the endophenotypic measure of temperament and character, using the Abbreviated (Dutch: Verkorte) Temperament and Character Inventory. Based on the hypothesis that attention deficit/hyperactivity disorder and autism spectrum disorder are disorders on a continuous spectrum, autism spectrum quotient scores and abbreviated Temperament and Character Inventory scores were expected to be different from normal controls in both disorders in a similar direction. In addition, the autism spectrum quotient and abbreviated Temperament and Character Inventory scores were expected to be closely correlated. These conditions applied to only two of the seven Abbreviated Temperament and Character Inventory scales (harm avoidance and self-directedness), suggesting that temperament and character as an endophenotype of autism spectrum disorder and attention deficit/hyperactivity disorder provides only partial support for the continuity hypothesis of autism spectrum disorder and attention deficit/hyperactivity disorder. © The Author(s) 2014.

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.

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.

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...

On the initial value problem for the wave equation in Friedmann-Robertson-Walker space-times.

PubMed

Abbasi, Bilal; Craig, Walter

2014-09-08

The propagator W ( t 0 , t 1 )( g , h ) for the wave equation in a given space-time takes initial data ( g ( x ), h ( x )) on a Cauchy surface {( t , x ) :  t = t 0 } and evaluates the solution ( u ( t 1 , x ),∂ t u ( t 1 , x )) at other times t 1 . The Friedmann-Robertson-Walker space-times are defined for t 0 , t 1 >0, whereas for t 0 →0, there is a metric singularity. There is a spherical means representation for the general solution of the wave equation with the Friedmann-Robertson-Walker background metric in the three spatial dimensional cases of curvature K =0 and K =-1 given by S. Klainerman and P. Sarnak. We derive from the expression of their representation three results about the wave propagator for the Cauchy problem in these space-times. First, we give an elementary proof of the sharp rate of time decay of solutions with compactly supported data. Second, we observe that the sharp Huygens principle is not satisfied by solutions, unlike in the case of three-dimensional Minkowski space-time (the usual Huygens principle of finite propagation speed is satisfied, of course). Third, we show that for 0< t 0 < t the limit, [Formula: see text] exists, it is independent of h ( x ), and for all reasonable initial data g ( x ), it gives rise to a well-defined solution for all t >0 emanating from the space-time singularity at t =0. Under reflection t →- t , the Friedmann-Robertson-Walker metric gives a space-time metric for t <0 with a singular future at t =0, and the same solution formulae hold. We thus have constructed solutions u ( t , x ) of the wave equation in Friedmann-Robertson-Walker space-times which exist for all [Formula: see text] and [Formula: see text], where in conformally regularized coordinates, these solutions are continuous through the singularity t =0 of space-time, taking on specified data u (0,⋅)= g (⋅) at the singular time.

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.

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.

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.

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

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.

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

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…

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.

Efficient Kinematic Computations For 7-DOF Manipulators

NASA Technical Reports Server (NTRS)

Seraji, Homayoun; Long, Mark K.; Kreutz-Delgado, Kenneth

1994-01-01

Efficient algorithms for forward kinematic mappings of seven-degree-of-freedom (7-DOF) robotic manipulator having revolute joints developed on basis of representation of redundant DOF in terms of parameter called "arm angle." Continuing effort to exploit redundancy in manipulator according to concept of basic and additional tasks. Concept also discussed in "Configuration-Control Scheme Copes With Singularities" (NPO-18556) and "Increasing the Dexterity of Redundant Robots" (NPO-17801).

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.

Metric dimensional reduction at singularities with implications to Quantum Gravity

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

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

2014-08-15

A series of old and recent theoretical observations suggests that the quantization of gravity would be feasible, and some problems of Quantum Field Theory would go away if, somehow, the spacetime would undergo a dimensional reduction at high energy scales. But an identification of the deep mechanism causing this dimensional reduction would still be desirable. The main contribution of this article is to show that dimensional reduction effects are due to General Relativity at singularities, and do not need to be postulated ad-hoc. Recent advances in understanding the geometry of singularities do not require modification of General Relativity, being justmore » non-singular extensions of its mathematics to the limit cases. They turn out to work fine for some known types of cosmological singularities (black holes and FLRW Big-Bang), allowing a choice of the fundamental geometric invariants and physical quantities which remain regular. The resulting equations are equivalent to the standard ones outside the singularities. One consequence of this mathematical approach to the singularities in General Relativity is a special, (geo)metric type of dimensional reduction: at singularities, the metric tensor becomes degenerate in certain spacetime directions, and some properties of the fields become independent of those directions. Effectively, it is like one or more dimensions of spacetime just vanish at singularities. This suggests that it is worth exploring the possibility that the geometry of singularities leads naturally to the spontaneous dimensional reduction needed by Quantum Gravity. - Highlights: • The singularities we introduce are described by finite geometric/physical objects. • Our singularities are accompanied by dimensional reduction effects. • They affect the metric, the measure, the topology, the gravitational DOF (Weyl = 0). • Effects proposed in other approaches to Quantum Gravity are obtained naturally. • The geometric dimensional reduction obtained opens new ways for Quantum Gravity.« less

Calculating the electron temperature in the lightning channel by continuous spectrum

NASA Astrophysics Data System (ADS)

Xiangcheng, DONG; Jianhong, CHEN; Xiufang, WEI; Ping, YUAN

2017-12-01

Based on the theory of plasma continuous radiation, the relationship between the emission intensity of bremsstrahlung and recombination radiation and the plasma electron temperature is obtained. During the development process of a return stroke of ground flash, the intensity of continuous radiation spectrum is separated on the basis of the spectrums with obviously different luminous intensity at two moments. The electron temperature of the lightning discharge channel is obtained through the curve fitting of the continuous spectrum intensity. It is found that electron temperature increases with the increase of wavelength and begins to reduce after the peak. The peak temperature of the two spectra is close to 25 000 K. To be compared with the result of discrete spectrum, the electron temperature is fitted by the O I line and N II line of the spectrum respectively. The comparison shows that the high temperature value is in good agreement with the temperature of the lightning core current channel obtained from the ion line information, and the low temperature at the high band closes to the calculation result of the atomic line, at a low band is lower than the calculation of the atomic line, which reflects the temperature of the luminous channel of the outer corona.

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

NASA Astrophysics Data System (ADS)

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

2008-02-01

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

Spectral singularities and Bragg scattering in complex crystals

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

Longhi, S.

2010-02-15

Spectral singularities that spoil the completeness of Bloch-Floquet states may occur in non-Hermitian Hamiltonians with complex periodic potentials. Here an equivalence is established between spectral singularities in complex crystals and secularities that arise in Bragg diffraction patterns. Signatures of spectral singularities in a scattering process with wave packets are elucidated for a PT-symmetric complex crystal.

On the splash and splat singularities for the one-phase inhomogeneous Muskat Problem

NASA Astrophysics Data System (ADS)

Córdoba, Diego; Pernas-Castaño, Tania

2017-10-01

In this paper, we study finite time splash and splat singularities formation for the interface of one fluid in a porous media with two different permeabilities. We prove that the smoothness of the interface breaks down in finite time into a splash singularity but this is not going to happen into a splat singularity.

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 embedding method in potential flow calculations

NASA Technical Reports Server (NTRS)

Jou, W. H.; Huynh, H.

1982-01-01

The so-called H-type mesh is used in a finite-element (or finite-volume) calculation of the potential flow past an airfoil. Due to coordinate singularity at the leading edge, a special singular trial function is used for the elements neighboring the leading edge. The results using the special singular elements are compared to those using the regular elements. It is found that the unreasonable pressure distribution obtained by the latter is removed by the embedding of the singular element. Suggestions to extend the present method to transonic cases are given.

Naked singularities are not singular in distorted gravity

NASA Astrophysics Data System (ADS)

Garattini, Remo; Majumder, Barun

2014-07-01

We compute the Zero Point Energy (ZPE) induced by a naked singularity with the help of a reformulation of the Wheele-DeWitt equation. A variational approach is used for the calculation with Gaussian Trial Wave Functionals. The one loop contribution of the graviton to the ZPE is extracted keeping under control the UltraViolet divergences by means of a distorted gravitational field. Two examples of distortion are taken under consideration: Gravity's Rainbow and Noncommutative Geometry. Surprisingly, we find that the ZPE is no more singular when we approach the singularity.

Probing the degenerate states of V-point singularities.

PubMed

Ram, B S Bhargava; Sharma, Anurag; Senthilkumaran, Paramasivam

2017-09-15

V-points are polarization singularities in spatially varying linearly polarized optical fields and are characterized by the Poincare-Hopf index η. Each V-point singularity is a superposition of two oppositely signed orbital angular momentum states in two orthogonal spin angular momentum states. Hence, a V-point singularity has zero net angular momentum. V-points with given |η| have the same (amplitude) intensity distribution but have four degenerate polarization distributions. Each of these four degenerate states also produce identical diffraction patterns. Hence to distinguish these degenerate states experimentally, we present in this Letter a method involving a combination of polarization transformation and diffraction. This method also shows the possibility of using polarization singularities in place of phase singularities in optical communication and quantum information processing.

Phase singularities of the transverse field component of high numerical aperture dark-hollow Gaussian beams in the focal region

NASA Astrophysics Data System (ADS)

Liu, Pusheng; Lü, Baida

2007-04-01

By using the vectorial Debye diffraction theory, phase singularities of high numerical aperture (NA) dark-hollow Gaussian beams in the focal region are studied. The dependence of phase singularities on the truncation parameter δ and semi-aperture angle α (or equally, NA) is illustrated numerically. A comparison of phase singularities of high NA dark-hollow Gaussian beams with those of scalar paraxial Gaussian beams and high NA Gaussian beams is made. For high NA dark-hollow Gaussian beams the beam order n additionally affects the spatial distribution of phase singularities, and there exist phase singularities outside the focal plane, which may be created or annihilated by variation of the semi-aperture angle in a certain region.

Singularity: Scientific containers for mobility of compute.

PubMed

Kurtzer, Gregory M; Sochat, Vanessa; Bauer, Michael W

2017-01-01

Here we present Singularity, software developed to bring containers and reproducibility to scientific computing. Using Singularity containers, developers can work in reproducible environments of their choosing and design, and these complete environments can easily be copied and executed on other platforms. Singularity is an open source initiative that harnesses the expertise of system and software engineers and researchers alike, and integrates seamlessly into common workflows for both of these groups. As its primary use case, Singularity brings mobility of computing to both users and HPC centers, providing a secure means to capture and distribute software and compute environments. This ability to create and deploy reproducible environments across these centers, a previously unmet need, makes Singularity a game changing development for computational science.

Singularity: Scientific containers for mobility of compute

PubMed Central

Kurtzer, Gregory M.; Bauer, Michael W.

2017-01-01

Here we present Singularity, software developed to bring containers and reproducibility to scientific computing. Using Singularity containers, developers can work in reproducible environments of their choosing and design, and these complete environments can easily be copied and executed on other platforms. Singularity is an open source initiative that harnesses the expertise of system and software engineers and researchers alike, and integrates seamlessly into common workflows for both of these groups. As its primary use case, Singularity brings mobility of computing to both users and HPC centers, providing a secure means to capture and distribute software and compute environments. This ability to create and deploy reproducible environments across these centers, a previously unmet need, makes Singularity a game changing development for computational science. PMID:28494014

Managing focal fields of vector beams with multiple polarization singularities.

PubMed

Han, Lei; Liu, Sheng; Li, Peng; Zhang, Yi; Cheng, Huachao; Gan, Xuetao; Zhao, Jianlin

2016-11-10

We explore the tight focusing behavior of vector beams with multiple polarization singularities, and analyze the influences of the number, position, and topological charge of the singularities on the focal fields. It is found that the ellipticity of the local polarization states at the focal plane could be determined by the spatial distribution of the polarization singularities of the vector beam. When the spatial location and topological charge of singularities have even-fold rotation symmetry, the transverse fields at the focal plane are locally linearly polarized. Otherwise, the polarization state becomes a locally hybrid one. By appropriately arranging the distribution of the polarization singularities in the vector beam, the polarization distributions of the focal fields could be altered while the intensity maintains unchanged.

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.

Predictor-based multivariable closed-loop system identification of the EXTRAP T2R reversed field pinch external plasma response

NASA Astrophysics Data System (ADS)

Olofsson, K. Erik J.; Brunsell, Per R.; Rojas, Cristian R.; Drake, James R.; Hjalmarsson, Håkan

2011-08-01

The usage of computationally feasible overparametrized and nonregularized system identification signal processing methods is assessed for automated determination of the full reversed-field pinch external plasma response spectrum for the experiment EXTRAP T2R. No assumptions on the geometry of eigenmodes are imposed. The attempted approach consists of high-order autoregressive exogenous estimation followed by Markov block coefficient construction and Hankel matrix singular value decomposition. It is seen that the obtained 'black-box' state-space models indeed can be compared with the commonplace ideal magnetohydrodynamics (MHD) resistive thin-shell model in cylindrical geometry. It is possible to directly map the most unstable autodetected empirical system pole to the corresponding theoretical resistive shell MHD eigenmode.

The multifractal nature of plume structure in high-Rayleigh-number convection

NASA Astrophysics Data System (ADS)

Puthenveettil, Baburaj A.; Ananthakrishna, G.; Arakeri, Jaywant H.

2005-03-01

The geometrically different planforms of near-wall plume structure in turbulent natural convection, visualized by driving the convection using concentration differences across a membrane, are shown to have a common multifractal spectrum of singularities for Rayleigh numbers in the range 1010-1011 at Schmidt number of 602. The scaling is seen for a length scale range of 25 and is independent of the Rayleigh number, the flux, the strength and nature of the large-scale flow, and the aspect ratio. Similar scaling is observed for the plume structures obtained in the presence of a weak flow across the membrane. This common non-trivial spatial scaling is proposed to be due to the same underlying generating process for the near-wall plume structures.

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

Recollection is a continuous process: implications for dual-process theories of recognition memory.

PubMed

Mickes, Laura; Wais, Peter E; Wixted, John T

2009-04-01

Dual-process theory, which holds that recognition decisions can be based on recollection or familiarity, has long seemed incompatible with signal detection theory, which holds that recognition decisions are based on a singular, continuous memory-strength variable. Formal dual-process models typically regard familiarity as a continuous process (i.e., familiarity comes in degrees), but they construe recollection as a categorical process (i.e., recollection either occurs or does not occur). A continuous process is characterized by a graded relationship between confidence and accuracy, whereas a categorical process is characterized by a binary relationship such that high confidence is associated with high accuracy but all lower degrees of confidence are associated with chance accuracy. Using a source-memory procedure, we found that the relationship between confidence and source-recollection accuracy was graded. Because recollection, like familiarity, is a continuous process, dual-process theory is more compatible with signal detection theory than previously thought.

Singular perturbation and time scale approaches in discrete control systems

NASA Technical Reports Server (NTRS)

Naidu, D. S.; Price, D. B.

1988-01-01

After considering a singularly perturbed discrete control system, a singular perturbation approach is used to obtain outer and correction subsystems. A time scale approach is then applied via block diagonalization transformations to decouple the system into slow and fast subsystems. To a zeroth-order approximation, the singular perturbation and time-scale approaches are found to yield equivalent results.

Overcoming Robot-Arm Joint Singularities

NASA Technical Reports Server (NTRS)

Barker, L. K.; Houck, J. A.

1986-01-01

Kinematic equations allow arm to pass smoothly through singular region. Report discusses mathematical singularities in equations of robotarm control. Operator commands robot arm to move in direction relative to its own axis system by specifying velocity in that direction. Velocity command then resolved into individual-joint rotational velocities in robot arm to effect motion. However, usual resolved-rate equations become singular when robot arm is straightened.

7 CFR 900.80 - 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. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice versa...

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

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1983-01-01

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

Singular trajectories: space-time domain topology of developing speckle fields

NASA Astrophysics Data System (ADS)

Vasil'ev, Vasiliy; Soskin, Marat S.

2010-02-01

It is shown the space-time dynamics of optical singularities is fully described by singularities trajectories in space-time domain, or evolution of transverse coordinates(x, y) in some fixed plane z0. The dynamics of generic developing speckle fields was realized experimentally by laser induced scattering in LiNbO3:Fe photorefractive crystal. The space-time trajectories of singularities can be divided topologically on two classes with essentially different scenario and duration. Some of them (direct topological reactions) consist from nucleation of singularities pair at some (x, y, z0, t) point, their movement and annihilation. They possess form of closed loops with relatively short time of existence. Another much more probable class of trajectories are chain topological reactions. Each of them consists from sequence of links, i.e. of singularities nucleation in various points (xi yi, ti) and following annihilation of both singularities in other space-time points with alien singularities of opposite topological indices. Their topology and properties are established. Chain topological reactions can stop on the borders of a developing speckle field or go to infinity. Examples of measured both types of topological reactions for optical vortices (polarization C points) in scalar (elliptically polarized) natural developing speckle fields are presented.

On the Absolutely Continuous Spectrum of Stark Operators

NASA Astrophysics Data System (ADS)

Perelman, Galina

The stability of the absolutely continuous spectrum of the one-dimensional Stark operator under perturbations of the potential is discussed. The focus is on proving this stability under minimal assumptions on smoothness of the perturbation. A general criterion is presented together with some applications. These include the case of periodic perturbations where we show that any perturbation vL1()∩H-1/2() preserves the a.c. spectrum.

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.

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.

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).

Infinite derivative gravity: non-singular cosmology & blackhole solutions

NASA Astrophysics Data System (ADS)

Mazumdar, A.

Both Einstein’s theory of General Relativity and Newton’s theory of gravity possess a short distance and small time scale catastrophe. The blackhole singularity and cosmological Big Bang singularity problems highlight that current theories of gravity are incomplete description at early times and small distances. I will discuss how one can potentially resolve these fundamental problems at a classical level and quantum level. In particular, I will discuss infinite derivative theories of gravity, where gravitational interactions become weaker in the ultraviolet, and therefore resolving some of the classical singularities, such as Big Bang and Schwarzschild singularity for compact non-singular objects with mass up to 1025 grams. In this lecture, I will discuss quantum aspects of infinite derivative gravity and discuss few aspects which can make the theory asymptotically free in the UV.

Three dimensional canonical singularity and five dimensional N = 1 SCFT

NASA Astrophysics Data System (ADS)

Xie, Dan; Yau, Shing-Tung

2017-06-01

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

Sharp bounds for singular values of fractional integral operators

NASA Astrophysics Data System (ADS)

Burman, Prabir

2007-03-01

From the results of Dostanic [M.R. Dostanic, Asymptotic behavior of the singular values of fractional integral operators, J. Math. Anal. Appl. 175 (1993) 380-391] and Vu and Gorenflo [Kim Tuan Vu, R. Gorenflo, Singular values of fractional and Volterra integral operators, in: Inverse Problems and Applications to Geophysics, Industry, Medicine and Technology, Ho Chi Minh City, 1995, Ho Chi Minh City Math. Soc., Ho Chi Minh City, 1995, pp. 174-185] it is known that the jth singular value of the fractional integral operator of order [alpha]>0 is approximately ([pi]j)-[alpha] for all large j. In this note we refine this result by obtaining sharp bounds for the singular values and use these bounds to show that the jth singular value is ([pi]j)-[alpha][1+O(j-1)].

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.

Diffraction of V-point singularities through triangular apertures.

PubMed

Ram, B S Bhargava; Sharma, Anurag; Senthilkumaran, P

2017-05-01

In this paper we present experimental studies on diffraction of V-point singularities through equilateral and isosceles right triangular apertures. When V-point index, also called Poincare-Hopf index (η), of the optical field is +1, the diffraction disintegrates it into two monstars/lemons. When V-point index η is -1, diffraction produces two stars. The diffraction pattern, unlike phase singularity, is insensitive to polarity of the polarization singularity and the intensity pattern remains invariant. Higher order V-point singularities are generated using Sagnac interferometer and it is observed that the diffraction disintegrates them into lower order C-points.

Dynamics of a linear system coupled to a chain of light nonlinear oscillators analyzed through a continuous approximation

NASA Astrophysics Data System (ADS)

Charlemagne, S.; Ture Savadkoohi, A.; Lamarque, C.-H.

2018-07-01

The continuous approximation is used in this work to describe the dynamics of a nonlinear chain of light oscillators coupled to a linear main system. A general methodology is applied to an example where the chain has local nonlinear restoring forces. The slow invariant manifold is detected at fast time scale. At slow time scale, equilibrium and singular points are sought around this manifold in order to predict periodic regimes and strongly modulated responses of the system. Analytical predictions are in good accordance with numerical results and represent a potent tool for designing nonlinear chains for passive control purposes.

Survey and Introduction to Modern Martingale Theory (Stopping Times, Semi-Martingales and Stochastic Integration)

DTIC Science & Technology

1986-10-01

35 ~- 2.3.12. Remark: Let X. Y be the processes given in the example :after Lemma 2.3.3. Take the same probability space as in that example and...z(s) =zjO) + ’ A zis).1als) + ’~ zsMs 0O<s<t 0O<s<t 0<~ Fix n>1I; then if s Is a point of increase of a, (that is. if Aa(s)=Al). then ri(s) = q(s...Absolute Continuity and Singularity of Locally Absolutely Continuous Probability Distributions. I. Math USSR Sbornik Vol. 35 , No 5, 631-680. Kabanov

Optimisation of strain selection in evolutionary continuous culture

NASA Astrophysics Data System (ADS)

Bayen, T.; Mairet, F.

2017-12-01

In this work, we study a minimal time control problem for a perfectly mixed continuous culture with n ≥ 2 species and one limiting resource. The model that we consider includes a mutation factor for the microorganisms. Our aim is to provide optimal feedback control laws to optimise the selection of the species of interest. Thanks to Pontryagin's Principle, we derive optimality conditions on optimal controls and introduce a sub-optimal control law based on a most rapid approach to a singular arc that depends on the initial condition. Using adaptive dynamics theory, we also study a simplified version of this model which allows to introduce a near optimal strategy.

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

NASA Technical Reports Server (NTRS)

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

2005-01-01

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

Plastic zone size and crack tip opening displacement of a Dugdale crack interacting with a coated circular inclusion

NASA Astrophysics Data System (ADS)

Hoh, H. J.; Xiao, Z. M.; Luo, J.

2010-09-01

An analytical investigation on the plastic zone size of a crack near a coated circular inclusion under three different loading conditions of uniaxial tension, uniform tension and pure shear was carried out. Both the crack and coated circular inclusion are embedded in an infinite matrix, with the crack oriented along the radial direction of the inclusion. In the solution procedure, the crack is simulated as a continuous distribution of edge dislocations. With the Dugdale model of small-scale yielding [J. Mech. Phys. Solids 8 (1960) p. 100], two thin strips of yielded plastic zones are introduced at both crack tips. Using the solution for a coated circular inclusion interacting with a single dislocation as the Green's function, the physical problem is formulated into a set of singular integral equations. Using the method of Erdogan and Gupta [Q. J. Appl. Math. 29 (1972) p. 525] and iterative numerical procedures, the singular integral equations are solved numerically for the plastic zone sizes and crack tip opening displacement.

Unsteady free convection flow of viscous fluids with analytical results by employing time-fractional Caputo-Fabrizio derivative (without singular kernel)

NASA Astrophysics Data System (ADS)

Ali Shah, Nehad; Mahsud, Yasir; Ali Zafar, Azhar

2017-10-01

This article introduces a theoretical study for unsteady free convection flow of an incompressible viscous fluid. The fluid flows near an isothermal vertical plate. The plate has a translational motion with time-dependent velocity. The equations governing the fluid flow are expressed in fractional differential equations by using a newly defined time-fractional Caputo-Fabrizio derivative without singular kernel. Explicit solutions for velocity, temperature and solute concentration are obtained by applying the Laplace transform technique. As the fractional parameter approaches to one, solutions for the ordinary fluid model are extracted from the general solutions of the fractional model. The results showed that, for the fractional model, the obtained solutions for velocity, temperature and concentration exhibit stationary jumps discontinuity across the plane at t=0 , while the solutions are continuous functions in the case of the ordinary model. Finally, numerical results for flow features at small-time are illustrated through graphs for various pertinent parameters.

FAST TRACK COMMUNICATION: Shear coordinate description of the quantized versal unfolding of a D4 singularity

NASA Astrophysics Data System (ADS)

Chekhov, Leonid; Mazzocco, Marta

2010-11-01

In this communication, by using Teichmüller theory of a sphere with four holes/orbifold points, we obtain a system of flat coordinates on the general affine cubic surface having a D4 singularity at the origin. We show that the Goldman bracket on the geodesic functions on the four-holed/orbifold sphere coincides with the Etingof-Ginzburg Poisson bracket on the affine D4 cubic. We prove that this bracket is the image under the Riemann-Hilbert map of the Poisson-Lie bracket on \\oplus _{1}^3\\mathfrak {sl}^\\ast (2,{{\\bb C}}) . We realize the action of the mapping class group by the action of the braid group on the geodesic functions. This action coincides with the procedure of analytic continuation of solutions of the sixth Painlevé equation. Finally, we produce the explicit quantization of the Goldman bracket on the geodesic functions on the four-holed/orbifold sphere and of the braid group action.

A robust adaptive observer for a class of singular nonlinear uncertain systems

NASA Astrophysics Data System (ADS)

Arefinia, Elaheh; Talebi, Heidar Ali; Doustmohammadi, Ali

2017-05-01

This paper proposes a robust adaptive observer for a class of singular nonlinear non-autonomous uncertain systems with unstructured unknown system and derivative matrices, and unknown bounded nonlinearities. Unlike many existing observers, no strong assumption such as Lipschitz condition is imposed on the recommended system. An augmented system is constructed, and the unknown bounds are calculated online using adaptive bounding technique. Considering the continuous nonlinear gain removes the chattering which may appear in practical applications such as analysis of electrical circuits and estimation of interaction force in beating heart robotic-assisted surgery. Moreover, a simple yet precise structure is attained which is easy to implement in many systems with significant uncertainties. The existence conditions of the standard form observer are obtained in terms of linear matrix inequality and the constrained generalised Sylvester's equations, and global stability is ensured. Finally, simulation results are obtained to evaluate the performance of the proposed estimator and demonstrate the effectiveness of the developed scheme.

Sensitivity analysis of reactive ecological dynamics.

PubMed

Verdy, Ariane; Caswell, Hal

2008-08-01

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

Coplanar three-beam interference and phase edge dislocations

NASA Astrophysics Data System (ADS)

Patorski, Krzysztof; SłuŻewski, Łukasz; Trusiak, Maciej; Pokorski, Krzysztof

2016-12-01

We present a comprehensive analysis of grating three-beam interference to discover a broad range of the ratio of amplitudes A of +/-1 diffraction orders and the zero order amplitude C providing phase edge dislocations. We derive a condition A/C > 0.5 for the occurrence of phase edge dislocations in three-beam interference self-image planes. In the boundary case A/C = 0.5 singularity conditions are met in those planes (once per interference field period), but the zero amplitude condition is not accompanied by an abrupt phase change. For A/C > 0.5 two adjacent singularities in a single field period show opposite sign topological charges. The occurrence of edge dislocations for selected values of A/C was verified by processing fork fringes obtained by introducing the fourth beam in the plane perpendicular to the one containing three coplanar diffraction orders. Two fork pattern processing methods are described, 2D CWT (two-dimensional continuous wavelet transform) and 2D spatial differentiation.

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.

Autism Spectrum Disorder (ASD): Related Topics

MedlinePlus

... Facebook Tweet Share Compartir Q: Do vaccines cause autism spectrum disorder (ASD)? A: Many studies that have ... whether there is a relationship between vaccines and autism spectrum disorder (ASD). To date, the studies continue ...

Naked shell singularities on the brane

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

Seahra, Sanjeev S.

By utilizing nonstandard slicings of 5-dimensional Schwarzschild and Schwarzschild-AdS manifolds based on isotropic coordinates, we generate static and spherically-symmetric braneworld spacetimes containing shell-like naked null singularities. For planar slicings, we find that the brane-matter sourcing the solution is a perfect fluid with an exotic equation of state and a pressure singularity where the brane crosses the bulk horizon. From a relativistic point of view, such a singularity is required to maintain matter infinitesimally above the surface of a black hole. From the point of view of the AdS/CFT conjecture, the singular horizon can be seen as one possible quantum correctionmore » to a classical black hole geometry. Various generalizations of planar slicings are also considered for a Ricci-flat bulk, and we find that singular horizons and exotic matter distributions are common features.« less

Experimental verification of free-space singular boundary conditions in an invisibility cloak

NASA Astrophysics Data System (ADS)

Wu, Qiannan; Gao, Fei; Song, Zhengyong; Lin, Xiao; Zhang, Youming; Chen, Huanyang; Zhang, Baile

2016-04-01

A major issue in invisibility cloaking, which caused intense mathematical discussions in the past few years but still remains physically elusive, is the plausible singular boundary conditions associated with the singular metamaterials at the inner boundary of an invisibility cloak. The perfect cloaking phenomenon, as originally proposed by Pendry et al for electromagnetic waves, cannot be treated as physical before a realistic inner boundary of a cloak is demonstrated. Although a recent demonstration has been done in a waveguide environment, the exotic singular boundary conditions should apply to a general environment as in free space. Here we fabricate a metamaterial surface that exhibits the singular boundary conditions and demonstrate its performance in free space. Particularly, the phase information of waves reflected from this metamaterial surface is explicitly measured, confirming the singular responses of boundary conditions for an invisibility cloak.

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

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1983-01-01

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

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.

Spectral singularities of complex scattering potentials and infinite reflection and transmission coefficients at real energies.

PubMed

Mostafazadeh, Ali

2009-06-05

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a waveguide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic waveguide.

Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems

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

Oshemkov, Andrey A

2010-10-06

A complete invariant is constructed that is a solution of the problem of semilocal classification of saddle singularities of integrable Hamiltonian systems. Namely, a certain combinatorial object (an f{sub n}-graph) is associated with every nondegenerate saddle singularity of rank zero; as a result, the problem of semilocal classification of saddle singularities of rank zero is reduced to the problem of enumeration of the f{sub n}-graphs. This enables us to describe a simple algorithm for obtaining the lists of saddle singularities of rank zero for a given number of degrees of freedom and a given complexity. Bibliography: 24 titles.

Boundary-layer effects in composite laminates: Free-edge stress singularities, part 6

NASA Technical Reports Server (NTRS)

Wanag, S. S.; Choi, I.

1981-01-01

A rigorous mathematical model was obtained for the boundary-layer free-edge stress singularity in angleplied and crossplied fiber composite laminates. The solution was obtained using a method consisting of complex-variable stress function potentials and eigenfunction expansions. The required order of the boundary-layer stress singularity is determined by solving the transcendental characteristic equation obtained from the homogeneous solution of the partial differential equations. Numerical results obtained show that the boundary-layer stress singularity depends only upon material elastic constants and fiber orientation of the adjacent plies. For angleplied and crossplied laminates the order of the singularity is weak in general.

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.

Spectral Singularities of Complex Scattering Potentials and Infinite Reflection and Transmission Coefficients at Real Energies

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

Mostafazadeh, Ali

2009-06-05

Spectral singularities are spectral points that spoil the completeness of the eigenfunctions of certain non-Hermitian Hamiltonian operators. We identify spectral singularities of complex scattering potentials with the real energies at which the reflection and transmission coefficients tend to infinity, i.e., they correspond to resonances having a zero width. We show that a waveguide modeled using such a potential operates like a resonator at the frequencies of spectral singularities. As a concrete example, we explore the spectral singularities of an imaginary PT-symmetric barrier potential and demonstrate the above resonance phenomenon for a certain electromagnetic waveguide.

Elasto-plastic flow in cracked bodies using a new finite element model. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Karabin, M. E., Jr.

1977-01-01

Cracked geometries were studied by finite element techniques with the aid of a new special element embedded at the crack tip. This model seeked to accurately represent the singular stresses and strains associated with the elasto-plastic flow process. The present model was not restricted to a material type and did not predetermine a singularity. Rather the singularity was treated as an unknown. For each step of the incremental process the nodal degrees of freedom and the unknown singularity were found through minimization of an energy-like functional. The singularity and nodal degrees of freedom were determined by means of an iterative process.

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

The strong energy condition and the S-brane singularity problem

NASA Astrophysics Data System (ADS)

McInnes, Brett

2003-06-01

Recently it has been argued that, because tachyonic matter satisfies the Strong Energy Condition [SEC], there is little hope of avoiding the singularities which plague S-Brane spacetimes. Meanwhile, however, Townsend and Wohlfarth have suggested an ingenious way of circumventing the SEC in such situations, and other suggestions for actually violating it in the S-Brane context have recently been proposed. Of course, the natural context for discussions of [effective or actual] violations of the SEC is the theory of asymptotically deSitter spacetimes, which tend to be less singular than ordinary FRW spacetimes. However, while violating or circumventing the SEC is necessary if singularities are to be avoided, it is not at all clear that it is sufficient. That is, we can ask: would an asymptotically deSitter S-brane spacetime be non-singular? We show that this is difficult to achieve; this result is in the spirit of the recently proved "S-brane singularity theorem". Essentially our results suggest that circumventing or violating the SEC may not suffice to solve the S-Brane singularity problem, though we do propose two ways of avoiding this conclusion.

Singularity computations. [finite element methods for elastoplastic flow

NASA Technical Reports Server (NTRS)

Swedlow, J. L.

1978-01-01

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

Transmutation of planar media singularities in a conformal cloak.

PubMed

Liu, Yichao; Mukhtar, Musawwadah; Ma, Yungui; Ong, C K

2013-11-01

Invisibility cloaking based on optical transformation involves materials singularity at the branch cut points. Many interesting optical devices, such as the Eaton lens, also require planar media index singularities in their implementation. We show a method to transmute two singularities simultaneously into harmless topological defects formed by anisotropic permittivity and permeability tensors. Numerical simulation is performed to verify the functionality of the transmuted conformal cloak consisting of two kissing Maxwell fish eyes.

Computing singularities of perturbation series

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

Kvaal, Simen; Jarlebring, Elias; Michiels, Wim

2011-03-15

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

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

PubMed

Zhang, Weixuan; Wu, Tong; Zhang, Xiangdong

2017-09-12

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

Stress singularities at the vertex of a cylindrically anisotropic wedge

NASA Technical Reports Server (NTRS)

Delale, F.; Erdogan, F.; Boduroglu, H.

1980-01-01

The plane elasticity problem for a cylindrically anisotropic solid is formulated. The form of the solution for an infinite wedge shaped domain with various homogeneous boundary conditions is derived and the nature of the stress singularity at the vertex of the wedge is studied. The characteristic equations giving the stress singularity and the angular distribution of the stresses around the vertex of the wedge are obtained for three standard homogeneous boundary conditions. The numerical examples show that the singular behavior of the stresses around the vertex of an anisotropic wedge may be significantly different from that of the isotropic material. Some of the results which may be of practical importance are that for a half plane the stress state at r = 0 may be singular and for a crack the power of stress singularity may be greater or less than 1/2.

Stanley Corrsin Award Talk: The role of singularities in hydrodynamics

NASA Astrophysics Data System (ADS)

Eggers, Jens

2017-11-01

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

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

NASA Technical Reports Server (NTRS)

Mukhopadhyay, V.; Newsom, J. R.

1982-01-01

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

Discrete cilia modelling with singularity distributions: application to the embryonic node and the airway surface liquid.

PubMed

Smith, D J; Gaffney, E A; Blake, J R

2007-07-01

We discuss in detail techniques for modelling flows due to finite and infinite arrays of beating cilia. An efficient technique, based on concepts from previous 'singularity models' is described, that is accurate in both near and far-fields. Cilia are modelled as curved slender ellipsoidal bodies by distributing Stokeslet and potential source dipole singularities along their centrelines, leading to an integral equation that can be solved using a simple and efficient discretisation. The computed velocity on the cilium surface is found to compare favourably with the boundary condition. We then present results for two topics of current interest in biology. 1) We present the first theoretical results showing the mechanism by which rotating embryonic nodal cilia produce a leftward flow by a 'posterior tilt,' and track particle motion in an array of three simulated nodal cilia. We find that, contrary to recent suggestions, there is no continuous layer of negative fluid transport close to the ciliated boundary. The mean leftward particle transport is found to be just over 1 mum/s, within experimentally measured ranges. We also discuss the accuracy of models that represent the action of cilia by steady rotlet arrays, in particular, confirming the importance of image systems in the boundary in establishing the far-field fluid transport. Future modelling may lead to understanding of the mechanisms by which morphogen gradients or mechanosensing cilia convert a directional flow to asymmetric gene expression. 2) We develop a more complex and detailed model of flow patterns in the periciliary layer of the airway surface liquid. Our results confirm that shear flow of the mucous layer drives a significant volume of periciliary liquid in the direction of mucus transport even during the recovery stroke of the cilia. Finally, we discuss the advantages and disadvantages of the singularity technique and outline future theoretical and experimental developments required to apply this technique to various other biological problems, particularly in the reproductive system.

The Production of FRW Universe and Decay to Particles in Multiverse

NASA Astrophysics Data System (ADS)

Ghaffary, Tooraj

2017-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

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.

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle

PubMed Central

Brzezicki, Samuel J.

2017-01-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function. PMID:28690412

Analytical solutions for two-dimensional Stokes flow singularities in a no-slip wedge of arbitrary angle.

PubMed

Crowdy, Darren G; Brzezicki, Samuel J

2017-06-01

An analytical method to find the flow generated by the basic singularities of Stokes flow in a wedge of arbitrary angle is presented. Specifically, we solve a biharmonic equation for the stream function of the flow generated by a point stresslet singularity and satisfying no-slip boundary conditions on the two walls of the wedge. The method, which is readily adapted to any other singularity type, takes full account of any transcendental singularities arising at the corner of the wedge. The approach is also applicable to problems of plane strain/stress of an elastic solid where the biharmonic equation also governs the Airy stress function.

Looking for a bulk point

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

Maldacena, Juan; Simmons-Duffin, David; Zhiboedov, Alexander

Here, we consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We also argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of double-trace operators. In the exact nonperturbative theory, we expect no singularity at thesemore » locations. Finally, we prove this statement in 1+1 dimensions by CFT methods.« less

Looking for a bulk point

DOE PAGES

Maldacena, Juan; Simmons-Duffin, David; Zhiboedov, Alexander

2017-01-03

Here, we consider Lorentzian correlators of local operators. In perturbation theory, singularities occur when we can draw a position-space Landau diagram with null lines. In theories with gravity duals, we can also draw Landau diagrams in the bulk. We also argue that certain singularities can arise only from bulk diagrams, not from boundary diagrams. As has been previously observed, these singularities are a clear diagnostic of bulk locality. We analyze some properties of these perturbative singularities and discuss their relation to the OPE and the dimensions of double-trace operators. In the exact nonperturbative theory, we expect no singularity at thesemore » locations. Finally, we prove this statement in 1+1 dimensions by CFT methods.« less

Steering law design for redundant single-gimbal control moment gyroscopes. [for spacecraft attitude control

NASA Technical Reports Server (NTRS)

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

1990-01-01

Two steering laws are presented for single-gimbal control moment gyroscopes. An approach using the Moore-Penrose pseudoinverse with a nondirectional null-motion algorithm is shown by example to avoid internal singularities for unidirectional torque commands, for which existing algorithms fail. Because this is still a tangent-based approach, however, singularity avoidance cannot be guaranteed. The singularity robust inverse is introduced as an alternative to the pseudoinverse for computing torque-producing gimbal rates near singular states. This approach, coupled with the nondirectional null algorithm, is shown by example to provide better steering law performance by allowing torque errors to be produced in the vicinity of singular states.

Observer-dependent sign inversions of polarization singularities.

PubMed

Freund, Isaac

2014-10-15

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

w-cosmological singularities

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

Fernandez-Jambrina, L.

2010-12-15

In this paper we characterize barotropic index singularities of homogeneous isotropic cosmological models [M. P. Dabrowski and T. Denkiewicz, Phys. Rev. D 79, 063521 (2009).]. They are shown to appear in cosmologies for which the scale factor is analytical with a Taylor series in which the linear and quadratic terms are absent. Though the barotropic index of the perfect fluid is singular, the singularities are weak, as it happens for other models for which the density and the pressure are regular.

Optical spectral singularities as threshold resonances

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

Mostafazadeh, Ali

2011-04-15

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

Three-body spectrum in a finite volume: The role of cubic symmetry

DOE PAGES

Doring, M.; Hammer, H. -W.; Mai, M.; ...

2018-06-15

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allowmore » for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.« less

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

Three-body spectrum in a finite volume: The role of cubic symmetry

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

Doring, M.; Hammer, H. -W.; Mai, M.

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allowmore » for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.« less

Investigation of local modification and luminescence of a carbon nanotube by scanning tunneling microscopy

NASA Astrophysics Data System (ADS)

Katano, Satoshi; Fujita, Hiroto; Uehara, Yoichi

2018-01-01

We have studied the nanoscale luminescence from a multiwalled carbon nanotube (CNT) adsorbed on Au(111) using a scanning tunneling microscope (STM). STM images revealed that a number of isolated chains of CNTs can be deposited by dry contact transfer while keeping the surface clean. By injecting tunneling electrons from the STM tip to the CNT, we observed STM light emission (STM-LE) from the CNT in the visible-light range, showing electronic transitions between the bands associated with the van Hove singularity in the density of states of the CNT. The STM-LE spectrum was obviously changed after introducing the local defect created by the STM tip, indicating the controllability of the nanoscale luminescence within a single chain of a CNT.

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.

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).

What distinguishes the small fraction of tropical ocean storms with lightning? An examination of the environment, organization, and evolution of radar features over Kwajalein

NASA Astrophysics Data System (ADS)

Bang, S. D.; Zipser, E. J.

2017-12-01

Lightning over the tropical ocean, though much rarer than over land, is predominantly observed in large, mostly mature convective systems. The implication is that these may require external forcing or organization in order to develop updrafts sufficiently strong to loft and sustain graupel and supercooled water above the freezing level and thereby produce lightning. We examine three years of radar data from the Kwajalein Atoll in the Marshall Islands in the tropical Pacific Ocean, which we subject to the Warning Decisions Support System - Integrated Information (WDSS-II) tracking algorithm in order to create an evolutionary radar feature dataset. In conjunction with ERA-interim reanalysis environmental data and World Wide Lightning Location Network (WWLLN) lightning data, we are able to observe the lifecycles of electrified convection over Kwajalein and examine the characteristics leading up to a lightning flash for radar features throughout the intensity spectrum. We find that lightning over Kwajalein exhibits the same tendency to occur in large, mature radar features, and the probability of lightning increases with increasing size and, to a certain extent, age. However, there is little evidence to support the role of singular environmental parameters in the development into large features. We continue to struggle to find the reasons that may influence or control the evolution of small features into large, organized convective systems, a major issue that has importance well beyond whether the feature is electrified.

Singularity-free dislocation dynamics with strain gradient elasticity

NASA Astrophysics Data System (ADS)

Po, Giacomo; Lazar, Markus; Seif, Dariush; Ghoniem, Nasr

2014-08-01

The singular nature of the elastic fields produced by dislocations presents conceptual challenges and computational difficulties in the implementation of discrete dislocation-based models of plasticity. In the context of classical elasticity, attempts to regularize the elastic fields of discrete dislocations encounter intrinsic difficulties. On the other hand, in gradient elasticity, the issue of singularity can be removed at the outset and smooth elastic fields of dislocations are available. In this work we consider theoretical and numerical aspects of the non-singular theory of discrete dislocation loops in gradient elasticity of Helmholtz type, with interest in its applications to three dimensional dislocation dynamics (DD) simulations. The gradient solution is developed and compared to its singular and non-singular counterparts in classical elasticity using the unified framework of eigenstrain theory. The fundamental equations of curved dislocation theory are given as non-singular line integrals suitable for numerical implementation using fast one-dimensional quadrature. These include expressions for the interaction energy between two dislocation loops and the line integral form of the generalized solid angle associated with dislocations having a spread core. The single characteristic length scale of Helmholtz elasticity is determined from independent molecular statics (MS) calculations. The gradient solution is implemented numerically within our variational formulation of DD, with several examples illustrating the viability of the non-singular solution. The displacement field around a dislocation loop is shown to be smooth, and the loop self-energy non-divergent, as expected from atomic configurations of crystalline materials. The loop nucleation energy barrier and its dependence on the applied shear stress are computed and shown to be in good agreement with atomistic calculations. DD simulations of Lome-Cottrell junctions in Al show that the strength of the junction and its configuration are easily obtained, without ad-hoc regularization of the singular fields. Numerical convergence studies related to the implementation of the non-singular theory in DD are presented.

Einstein-Langevin and Einstein-Fokker-Planck equations for Oppenheimer-Snyder gravitational collapse in a spacetime with conformal vacuum fluctuations

NASA Astrophysics Data System (ADS)

Miller, Steven David

1999-10-01

A consistent extension of the Oppenheimer-Snyder gravitational collapse formalism is presented which incorporates stochastic, conformal, vacuum fluctuations of the metric tensor. This results in a tractable approach to studying the possible effects of vacuum fluctuations on collapse and singularity formation. The motivation here, is that it is known that coupling stochastic noise to a classical field theory can lead to workable methodologies that accommodate or reproduce many aspects of quantum theory, turbulence or structure formation. The effect of statistically averaging over the metric fluctuations gives the appearance of a deterministic Riemannian structure, with an induced non-vanishing cosmological constant arising from the nonlinearity. The Oppenheimer-Snyder collapse of a perfect fluid or dust star in the fluctuating or `turbulent' spacetime, is reformulated in terms of nonlinear Einstein-Langevin field equations, with an additional noise source in the energy-momentum tensor. The smooth deterministic worldlines of collapsing matter within the classical Oppenheimer-Snyder model, now become nonlinear Brownian motions due to the backreaction induced by vacuum fluctuations. As the star collapses, the matter worldlines become increasingly randomized since the backreaction coupling to the vacuum fluctuations is nonlinear; the input assumptions of the Hawking-Penrose singularity theorems should then be violated. Solving the nonlinear Einstein-Langevin field equation for collapse - via the Ito interpretation - gives a singularity-free solution, which is equivalent to the original Oppenheimer solution but with higher-order stochastic corrections; the original singular solution is recovered in the limit of zero vacuum fluctuations. The `geometro-hydrodynamics' of noisy gravitational collapse, were also translated into an equivalent mathematical formulation in terms of nonlinear Einstein-Fokker-Planck (EFP) continuity equations with respect to comoving coordinates: these describe the collapse as a conserved flow of probability. A solution was found in the dilute limit of weak fluctuations where the EFP equation is linearized. There is zero probability that the star collapses to a singular state in the presence of background vacuum fluctuations, but the singularity returns with unit probability when the fluctuations are reduced to zero. Finally, an EFP equation was considered with respect to standard exterior coordinates. Using the thermal Brownian motion paradigm, an exact stationary or equilibrium solution was found in the infinite standard time relaxation limit. The solution gives the conditions required for the final collapsed object (a black hole) to be in thermal equilibrium with the background vacuum fluctuations. From this solution, one recovers the Hawking temperature without using field theory. The stationary solution then seems to correspond to a black hole in thermal equilibrium with a fluctuating conformal scalar field; or the Hawking-Hartle state.

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.

Quantum singularities in (2+1) dimensional matter coupled black hole spacetimes

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

Unver, O.; Gurtug, O.

2010-10-15

Quantum singularities considered in the 3D Banados-Teitelboim-Zanelli (BTZ) spacetime by Pitelli and Letelier [Phys. Rev. D 77, 124030 (2008)] is extended to charged BTZ and 3D Einstein-Maxwell-dilaton gravity spacetimes. The occurrence of naked singularities in the Einstein-Maxwell extension of the BTZ spacetime both in linear and nonlinear electrodynamics as well as in the Einstein-Maxwell-dilaton gravity spacetimes are analyzed with the quantum test fields obeying the Klein-Gordon and Dirac equations. We show that with the inclusion of the matter fields, the conical geometry near r=0 is removed and restricted classes of solutions are admitted for the Klein-Gordon and Dirac equations. Hence,more » the classical central singularity at r=0 turns out to be quantum mechanically singular for quantum particles obeying the Klein-Gordon equation but nonsingular for fermions obeying the Dirac equation. Explicit calculations reveal that the occurrence of the timelike naked singularities in the considered spacetimes does not violate the cosmic censorship hypothesis as far as the Dirac fields are concerned. The role of horizons that clothes the singularity in the black hole cases is replaced by repulsive potential barrier against the propagation of Dirac fields.« less

Multivalued classical mechanics arising from singularity loops in complex time

NASA Astrophysics Data System (ADS)

Koch, Werner; Tannor, David J.

2018-02-01

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

Exact solutions, finite time singularities and non-singular universe models from a variety of Λ(t) cosmologies

NASA Astrophysics Data System (ADS)

Pan, Supriya

2018-01-01

Cosmological models with time-dependent Λ (read as Λ(t)) have been investigated widely in the literature. Models that solve background dynamics analytically are of special interest. Additionally, the allowance of past or future singularities at finite cosmic time in a specific model signals for a generic test on its viabilities with the current observations. Following these, in this work we consider a variety of Λ(t) models focusing on their evolutions and singular behavior. We found that a series of models in this class can be exactly solved when the background universe is described by a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) line element. The solutions in terms of the scale factor of the FLRW universe offer different universe models, such as power-law expansion, oscillating, and the singularity free universe. However, we also noticed that a large number of the models in this series permit past or future cosmological singularities at finite cosmic time. At last we close the work with a note that the avoidance of future singularities is possible for certain models under some specific restrictions.

Generation of phase singularity through diffracting a plane or Gaussian beam by a spiral phase plate.

PubMed

Kotlyar, Victor V; Almazov, Anton A; Khonina, Svetlana N; Soifer, Victor A; Elfstrom, Henna; Turunen, Jari

2005-05-01

We deduce and study an analytical expression for Fresnel diffraction of a plane wave by a spiral phase plate (SPP) that imparts an arbitrary-order phase singularity on the light field. Estimates for the optical vortex radius that depends on the singularity's integer order n (also termed topological charge, or order of the dislocation) have been derived. The near-zero vortex intensity is shown to be proportional to rho2n, where p is the radial coordinate. Also, an analytical expression for Fresnel diffraction of the Gaussian beam by a SPP with nth-order singularity is analyzed. The far-field intensity distribution is derived. The radius of maximal intensity is shown to depend on the singularity number. The behavior of the Gaussian beam intensity after a SPP with second-order singularity (n = 2) is studied in more detail. The parameters of the light beams generated numerically with the Fresnel transform and via analytical formulas are in good agreement. In addition, the light fields with first- and second-order singularities were generated by a 32-level SPP fabricated on the resist by use of the electron-beam lithography technique.

Observational constraints on cosmological future singularities

NASA Astrophysics Data System (ADS)

Beltrán Jiménez, Jose; Lazkoz, Ruth; Sáez-Gómez, Diego; Salzano, Vincenzo

2016-11-01

In this work we consider a family of cosmological models featuring future singularities. This type of cosmological evolution is typical of dark energy models with an equation of state violating some of the standard energy conditions (e.g. the null energy condition). Such a kind of behavior, widely studied in the literature, may arise in cosmologies with phantom fields, theories of modified gravity or models with interacting dark matter/dark energy. We briefly review the physical consequences of these cosmological evolution regarding geodesic completeness and the divergence of tidal forces in order to emphasize under which circumstances the singularities in some cosmological quantities correspond to actual singular spacetimes. We then introduce several phenomenological parameterizations of the Hubble expansion rate to model different singularities existing in the literature and use SN Ia, BAO and H( z) data to constrain how far in the future the singularity needs to be (under some reasonable assumptions on the behavior of the Hubble factor). We show that, for our family of parameterizations, the lower bound for the singularity time cannot be smaller than about 1.2 times the age of the universe, what roughly speaking means {˜ }2.8 Gyrs from the present time.

A study of non-local holography in the AdS/CFT correspondence

NASA Astrophysics Data System (ADS)

Hamilton, Alex

This thesis is broadly composed of three topics. After giving a brief overview of the origins of the AdS/CFT duality, we describe a way of representing local bulk fields as quasi-local CFT operators. We show how these smeared boundary operators encode the holographic radial-scale duality, and how this can lead to degrees of freedom consistent with Bekenstein's entropy. We also gain insight into the BTZ black hole, with the horizon, singularity, and thermality arising naturally via these operators. As another aspect of AdS/CFT, we will be interested in the fate of giant gravitons under a marginal deformation. We review the construction and fluctuation spectrum of giants, and then proceed to evaluate them in two different Penrose limits of Lunin and Maldacena's gamma deformed geometry. We find only one to be stable, and describe how the degeneracy of the spectrum is partially broken. Finally, we make a first step towards cosmological particle production in string theory by introducing a first quantized alternative approach to the standard method of calculation. We show how the same calculation can be done with Green's Functions---objects which are well defined in a first quantized setting (such as string theory).

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.

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)

Simulation of generation and dynamics of polarization singularities with circular Airy beams.

PubMed

Ye, Dong; Peng, Xinyu; Zhou, Muchun; Xin, Yu; Song, Minmin

2017-11-01

The generation and dynamics of polarization singularities have been underresearched for years, while the focusing property of the topological configuration has not been explored much. In this paper, we simulated the generation of low-order polarization singularities with a circular Airy beam and explored the focusing property of the synthetic light field during propagation due to the autofocusing of the component. Our work researched the focusing properties of the polarization singularity configuration, which may help to develop its application prospect.

Wave-front singularities for two-dimensional anisotropic elastic waves.

NASA Technical Reports Server (NTRS)

Payton, R. G.

1972-01-01

Wavefront singularities for the displacement functions, associated with the radiation of linear elastic waves from a point source embedded in a finitely strained two-dimensional elastic solid, are examined in detail. It is found that generally the singularities are of order d to the -1/2 power, where d measures distance away from the front. However, in certain exceptional cases singularities of order d to the -n power, where n = 1/4, 2/3, 3/4, may be encountered.

Nonlinear spectral singularities for confined nonlinearities.

PubMed

Mostafazadeh, Ali

2013-06-28

We introduce a notion of spectral singularity that applies for a general class of nonlinear Schrödinger operators involving a confined nonlinearity. The presence of the nonlinearity does not break the parity-reflection symmetry of spectral singularities but makes them amplitude dependent. Nonlinear spectral singularities are, therefore, associated with a resonance effect that produces amplified waves with a specific amplitude-wavelength profile. We explore the consequences of this phenomenon for a complex δ-function potential that is subject to a general confined nonlinearity.

Computation of Incompressible Potential Flow over an Airfoil Using a High Order Aerodynamic Panel Method Based on Circular Arc Panels.

DTIC Science & Technology

1982-08-01

Vortex Sheet Figure 4 - Properties of Singularity Sheets they may be used to model different types of flow. Transfer of boundary... Vortex Sheet Equivalence Singularity Behavior Using Green’s theorem it is clear that the problem of potential flow over a body can be modeled using ...that source, doublet, or vortex singularities can be used to model potential flow problems, and that the doublet and vortex singularities are