On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

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

A study of methods to predict and measure the transmission of sound through the walls of light aircraft. Integration of certain singular boundary element integrals for applications in linear acoustics

NASA Technical Reports Server (NTRS)

Zimmerle, D.; Bernhard, R. J.

1985-01-01

An alternative method for performing singular boundary element integrals for applications in linear acoustics is discussed. The method separates the integral of the characteristic solution into a singular and nonsingular part. The singular portion is integrated with a combination of analytic and numerical techniques while the nonsingular portion is integrated with standard Gaussian quadrature. The method may be generalized to many types of subparametric elements. The integrals over elements containing the root node are considered, and the characteristic solution for linear acoustic problems are examined. The method may be generalized to most characteristic solutions.

Numerical evaluation of multi-loop integrals for arbitrary kinematics with SecDec 2.0

NASA Astrophysics Data System (ADS)

Borowka, Sophia; Carter, Jonathon; Heinrich, Gudrun

2013-02-01

We present the program SecDec 2.0, which contains various new features. First, it allows the numerical evaluation of multi-loop integrals with no restriction on the kinematics. Dimensionally regulated ultraviolet and infrared singularities are isolated via sector decomposition, while threshold singularities are handled by a deformation of the integration contour in the complex plane. As an application, we present numerical results for various massive two-loop four-point diagrams. SecDec 2.0 also contains new useful features for the calculation of more general parameter integrals, related for example to phase space integrals. Program summaryProgram title: SecDec 2.0 Catalogue identifier: AEIR_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIR_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 156829 No. of bytes in distributed program, including test data, etc.: 2137907 Distribution format: tar.gz Programming language: Wolfram Mathematica, Perl, Fortran/C++. Computer: From a single PC to a cluster, depending on the problem. Operating system: Unix, Linux. RAM: Depending on the complexity of the problem Classification: 4.4, 5, 11.1. Catalogue identifier of previous version: AEIR_v1_0 Journal reference of previous version: Comput. Phys. Comm. 182(2011)1566 Does the new version supersede the previous version?: Yes Nature of problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in gauge theories. Numerical integration in the presence of integrable singularities (e.g., kinematic thresholds). Solution method: Algebraic extraction of singularities in dimensional regularization using iterated sector decomposition. This leads to a Laurent series in the dimensional regularization parameter ɛ, where the coefficients are finite integrals over the unit hypercube. Those integrals are evaluated numerically by Monte Carlo integration. The integrable singularities are handled by choosing a suitable integration contour in the complex plane, in an automated way. Reasons for new version: In the previous version the calculation of multi-scale integrals was restricted to the Euclidean region. Now multi-loop integrals with arbitrary physical kinematics can be evaluated. Another major improvement is the possibility of full parallelization. Summary of revisions: No restriction on the kinematics for multi-loop integrals. The integrand can be constructed from the topological cuts of the diagram. Possibility of full parallelization. Numerical integration of multi-loop integrals written in C++ rather than Fortran. Possibility to loop over ranges of parameters. Restrictions: Depending on the complexity of the problem, limited by memory and CPU time. The restriction that multi-scale integrals could only be evaluated at Euclidean points is superseded in version 2.0. Running time: Between a few minutes and several days, depending on the complexity of the problem. Test runs provided take only seconds.

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

PubMed

Tudor, Tiberiu

2016-04-20

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

Reduction by symmetries in singular quantum-mechanical problems: General scheme and application to Aharonov-Bohm model

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

Smirnov, A. G., E-mail: smirnov@lpi.ru

2015-12-15

We develop a general technique for finding self-adjoint extensions of a symmetric operator that respects a given set of its symmetries. Problems of this type naturally arise when considering two- and three-dimensional Schrödinger operators with singular potentials. The approach is based on constructing a unitary transformation diagonalizing the symmetries and reducing the initial operator to the direct integral of a suitable family of partial operators. We prove that symmetry preserving self-adjoint extensions of the initial operator are in a one-to-one correspondence with measurable families of self-adjoint extensions of partial operators obtained by reduction. The general scheme is applied to themore » three-dimensional Aharonov-Bohm Hamiltonian describing the electron in the magnetic field of an infinitely thin solenoid. We construct all self-adjoint extensions of this Hamiltonian, invariant under translations along the solenoid and rotations around it, and explicitly find their eigenfunction expansions.« 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.

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.

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

NASA Astrophysics Data System (ADS)

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

2012-10-01

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

On the solution of integral equations with a generalized cauchy kernal

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

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

On the efficiency of treating singularities in triatomic variational vibrational computations. The vibrational states of H(+)3 up to dissociation.

PubMed

Szidarovszky, Tamás; Császár, Attila G; Czakó, Gábor

2010-08-01

Several techniques of varying efficiency are investigated, which treat all singularities present in the triatomic vibrational kinetic energy operator given in orthogonal internal coordinates of the two distances-one angle type. The strategies are based on the use of a direct-product basis built from one-dimensional discrete variable representation (DVR) bases corresponding to the two distances and orthogonal Legendre polynomials, or the corresponding Legendre-DVR basis, corresponding to the angle. The use of Legendre functions ensures the efficient treatment of the angular singularity. Matrix elements of the singular radial operators are calculated employing DVRs using the quadrature approximation as well as special DVRs satisfying the boundary conditions and thus allowing for the use of exact DVR expressions. Potential optimized (PO) radial DVRs, based on one-dimensional Hamiltonians with potentials obtained by fixing or relaxing the two non-active coordinates, are also studied. The numerical calculations employed Hermite-DVR, spherical-oscillator-DVR, and Bessel-DVR bases as the primitive radial functions. A new analytical formula is given for the determination of the matrix elements of the singular radial operator using the Bessel-DVR basis. The usually claimed failure of the quadrature approximation in certain singular integrals is revisited in one and three dimensions. It is shown that as long as no potential optimization is carried out the quadrature approximation works almost as well as the exact DVR expressions. If wave functions with finite amplitude at the boundary are to be computed, the basis sets need to meet the required boundary conditions. The present numerical results also confirm that PO-DVRs should be constructed employing relaxed potentials and PO-DVRs can be useful for optimizing quadrature points for calculations applying large coordinate intervals and describing large-amplitude motions. The utility and efficiency of the different algorithms is demonstrated by the computation of converged near-dissociation vibrational energy levels for the H molecular ion.

On the solution of integral equations with a generalized cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

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

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

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

Kalay, Berfin; Demiralp, Metin

2014-10-06

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

Classification of singularities in the problem of motion of the Kovalevskaya top in a double force field

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

Ryabov, Pavel E; Kharlamov, Mikhail P

2012-02-28

The problem of motion of the Kovalevskaya top in a double force field is investigated (the integrable case of A.G. Reyman and M.A. Semenov-Tian-Shansky without a gyrostatic momentum). It is a completely integrable Hamiltonian system with three degrees of freedom not reducible to a family of systems with two degrees of freedom. The critical set of the integral map is studied. The critical subsystems and bifurcation diagrams are described. The classification of all nondegenerate critical points is given. The set of these points consists of equilibria (nondegenerate singularities of rank 0), of singular periodic motions (nondegenerate singularities of rank 1),more » and also of critical two-frequency motions (nondegenerate singularities of rank 2). Bibliography: 32 titles.« less

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.

Non-homogeneous harmonic analysis: 16 years of development

NASA Astrophysics Data System (ADS)

Volberg, A. L.; Èiderman, V. Ya

2013-12-01

This survey contains results and methods in the theory of singular integrals, a theory which has been developing dramatically in the last 15-20 years. The central (although not the only) topic of the paper is the connection between the analytic properties of integrals and operators with Calderón-Zygmund kernels and the geometric properties of the measures. The history is traced of the classical Painlevé problem of describing removable singularities of bounded analytic functions, which has provided a strong incentive for the development of this branch of harmonic analysis. The progress of recent decades has largely been based on the creation of an apparatus for dealing with non-homogeneous measures, and much attention is devoted to this apparatus here. Several open questions are stated, first and foremost in the multidimensional case, where the method of curvature of a measure is not available. Bibliography: 128 titles.

Singularity Preserving Numerical Methods for Boundary Integral Equations

NASA Technical Reports Server (NTRS)

Kaneko, Hideaki (Principal Investigator)

1996-01-01

In the past twelve months (May 8, 1995 - May 8, 1996), under the cooperative agreement with Division of Multidisciplinary Optimization at NASA Langley, we have accomplished the following five projects: a note on the finite element method with singular basis functions; numerical quadrature for weakly singular integrals; superconvergence of degenerate kernel method; superconvergence of the iterated collocation method for Hammersteion equations; and singularity preserving Galerkin method for Hammerstein equations with logarithmic kernel. This final report consists of five papers describing these projects. Each project is preceeded by a brief abstract.

Simple and Efficient Numerical Evaluation of Near-Hypersingular Integrals

NASA Technical Reports Server (NTRS)

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

2007-01-01

Recently, significant progress has been made in the handling of singular and nearly-singular potential integrals that commonly arise in the Boundary Element Method (BEM). To facilitate object-oriented programming and handling of higher order basis functions, cancellation techniques are favored over techniques involving singularity subtraction. However, gradients of the Newton-type potentials, which produce hypersingular kernels, are also frequently required in BEM formulations. As is the case with the potentials, treatment of the near-hypersingular integrals has proven more challenging than treating the limiting case in which the observation point approaches the surface. Historically, numerical evaluation of these near-hypersingularities has often involved a two-step procedure: a singularity subtraction to reduce the order of the singularity, followed by a boundary contour integral evaluation of the extracted part. Since this evaluation necessarily links basis function, Green s function, and the integration domain (element shape), the approach ill fits object-oriented programming concepts. Thus, there is a need for cancellation-type techniques for efficient numerical evaluation of the gradient of the potential. Progress in the development of efficient cancellation-type procedures for the gradient potentials was recently presented. To the extent possible, a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. However, since the gradient kernel involves singularities of different orders, we also require that the transformation leaves remaining terms that are analytic. The terms "normal" and "tangential" are used herein with reference to the source element. Also, since computational formulations often involve the numerical evaluation of both potentials and their gradients, it is highly desirable that a single integration procedure efficiently handles both.

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

PubMed

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

2018-07-01

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

The detection of flaws in austenitic welds using the decomposition of the time-reversal operator

NASA Astrophysics Data System (ADS)

Cunningham, Laura J.; Mulholland, Anthony J.; Tant, Katherine M. M.; Gachagan, Anthony; Harvey, Gerry; Bird, Colin

2016-04-01

The non-destructive testing of austenitic welds using ultrasound plays an important role in the assessment of the structural integrity of safety critical structures. The internal microstructure of these welds is highly scattering and can lead to the obscuration of defects when investigated by traditional imaging algorithms. This paper proposes an alternative objective method for the detection of flaws embedded in austenitic welds based on the singular value decomposition of the time-frequency domain response matrices. The distribution of the singular values is examined in the cases where a flaw exists and where there is no flaw present. A lower threshold on the singular values, specific to austenitic welds, is derived which, when exceeded, indicates the presence of a flaw. The detection criterion is successfully implemented on both synthetic and experimental data. The datasets arising from welds containing a flaw are further interrogated using the decomposition of the time-reversal operator (DORT) method and the total focusing method (TFM), and it is shown that images constructed via the DORT algorithm typically exhibit a higher signal-to-noise ratio than those constructed by the TFM algorithm.

The detection of flaws in austenitic welds using the decomposition of the time-reversal operator

PubMed Central

Cunningham, Laura J.; Mulholland, Anthony J.; Gachagan, Anthony; Harvey, Gerry; Bird, Colin

2016-01-01

The non-destructive testing of austenitic welds using ultrasound plays an important role in the assessment of the structural integrity of safety critical structures. The internal microstructure of these welds is highly scattering and can lead to the obscuration of defects when investigated by traditional imaging algorithms. This paper proposes an alternative objective method for the detection of flaws embedded in austenitic welds based on the singular value decomposition of the time-frequency domain response matrices. The distribution of the singular values is examined in the cases where a flaw exists and where there is no flaw present. A lower threshold on the singular values, specific to austenitic welds, is derived which, when exceeded, indicates the presence of a flaw. The detection criterion is successfully implemented on both synthetic and experimental data. The datasets arising from welds containing a flaw are further interrogated using the decomposition of the time-reversal operator (DORT) method and the total focusing method (TFM), and it is shown that images constructed via the DORT algorithm typically exhibit a higher signal-to-noise ratio than those constructed by the TFM algorithm. PMID:27274683

Space-time domain solutions of the wave equation by a non-singular boundary integral method and Fourier transform.

PubMed

Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C

2017-08-01

The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.

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.

Hybrid normed ideal perturbations of n-tuples of operators I

NASA Astrophysics Data System (ADS)

Voiculescu, Dan-Virgil

2018-06-01

In hybrid normed ideal perturbations of n-tuples of operators, the normed ideal is allowed to vary with the component operators. We begin extending to this setting the machinery we developed for normed ideal perturbations based on the modulus of quasicentral approximation and an adaptation of our non-commutative generalization of the Weyl-von Neumann theorem. For commuting n-tuples of hermitian operators, the modulus of quasicentral approximation remains essentially the same when Cn- is replaced by a hybrid n-tuple Cp1,…- , … , Cpn- , p1-1 + ⋯ + pn-1 = 1. The proof involves singular integrals of mixed homogeneity.

The problem of a finite strip compressed between two rough rigid stamps

NASA Technical Reports Server (NTRS)

Gupta, G. D.

1975-01-01

A finite strip compressed between two rough rigid stamps is considered. The elastostatic problem is formulated in terms of a singular integral equation from which the proper stress singularities at the corners are determined. The singular integral equation is solved numerically to determine the stresses along the fixed ends of the strip. The effect of material properties and strip geometry on the stress-intensity factor is presented graphically.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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

Modeling of Graphene Planar Grating in the THz Range by the Method of Singular Integral Equations

NASA Astrophysics Data System (ADS)

Kaliberda, Mstislav E.; Lytvynenko, Leonid M.; Pogarsky, Sergey A.

2018-04-01

Diffraction of the H-polarized electromagnetic wave by the planar graphene grating in the THz range is considered. The scattering and absorption characteristics are studied. The scattered field is represented in the spectral domain via unknown spectral function. The mathematical model is based on the graphene surface impedance and the method of singular integral equations. The numerical solution is obtained by the Nystrom-type method of discrete singularities.

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.

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.

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

NASA Astrophysics Data System (ADS)

Tyni, Teemu

2018-04-01

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

Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities

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

Zhou, Yao

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

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

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

Landau singularities and symbology: One- and two-loop MHV amplitudes in SYM theory

DOE PAGES

Dennen, Tristan; Spradlin, Marcus; Volovich, Anastasia

2016-03-14

We apply the Landau equations, whose solutions parameterize the locus of possible branch points, to the one- and two-loop Feynman integrals relevant to MHV amplitudes in planar N = 4 super-Yang-Mills theory. We then identify which of the Landau singularities appear in the symbols of the amplitudes, and which do not. Finally, we observe that all of the symbol entries in the two-loop MHV amplitudes are already present as Landau singularities of one-loop pentagon integrals.

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

Classification of almost toric singularities of Lagrangian foliations

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

Izosimov, Anton M

2011-07-31

The topological classification is given of almost toric singularities of integrable Hamiltonian systems with a large number of degrees of freedom, that is, of nondegenerate singularities without hyperbolic components. A descriptive geometric model is constructed, which makes it possible to perform effective calculations. Bibliography: 10 titles.

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.

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.

Leading singularities and off-shell conformal integrals

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

Drummond, James; Duhr, Claude; Eden, Burkhard

2013-08-29

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

Hörmander multipliers on two-dimensional dyadic Hardy spaces

NASA Astrophysics Data System (ADS)

Daly, J.; Fridli, S.

2008-12-01

In this paper we are interested in conditions on the coefficients of a two-dimensional Walsh multiplier operator that imply the operator is bounded on certain of the Hardy type spaces Hp, 0

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.

Asymptotic Behaviour of the Ground State of Singularly Perturbed Elliptic Equations

NASA Astrophysics Data System (ADS)

Piatnitski, Andrey L.

The ground state of a singularly perturbed nonselfadjoint elliptic operator defined on a smooth compact Riemannian manifold with metric aij(x)=(aij(x))-1, is studied. We investigate the limiting behaviour of the first eigenvalue of this operator as μ goes to zero, and find the logarithmic asymptotics of the first eigenfunction everywhere on the manifold. The results are formulated in terms of auxiliary variational problems on the manifold. This approach also allows to study the general singularly perturbed second order elliptic operator on a bounded domain in Rn.

Asymptotics of action variables near semi-toric singularities

NASA Astrophysics Data System (ADS)

Wacheux, Christophe

2015-12-01

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

Path optimization method for the sign problem

NASA Astrophysics Data System (ADS)

Ohnishi, Akira; Mori, Yuto; Kashiwa, Kouji

2018-03-01

We propose a path optimization method (POM) to evade the sign problem in the Monte-Carlo calculations for complex actions. Among many approaches to the sign problem, the Lefschetz-thimble path-integral method and the complex Langevin method are promising and extensively discussed. In these methods, real field variables are complexified and the integration manifold is determined by the flow equations or stochastically sampled. When we have singular points of the action or multiple critical points near the original integral surface, however, we have a risk to encounter the residual and global sign problems or the singular drift term problem. One of the ways to avoid the singular points is to optimize the integration path which is designed not to hit the singular points of the Boltzmann weight. By specifying the one-dimensional integration-path as z = t +if(t)(f ɛ R) and by optimizing f(t) to enhance the average phase factor, we demonstrate that we can avoid the sign problem in a one-variable toy model for which the complex Langevin method is found to fail. In this proceedings, we propose POM and discuss how we can avoid the sign problem in a toy model. We also discuss the possibility to utilize the neural network to optimize the path.

Singular vectors for the WN algebras

NASA Astrophysics Data System (ADS)

Ridout, David; Siu, Steve; Wood, Simon

2018-03-01

In this paper, we use free field realisations of the A-type principal, or Casimir, WN algebras to derive explicit formulae for singular vectors in Fock modules. These singular vectors are constructed by applying screening operators to Fock module highest weight vectors. The action of the screening operators is then explicitly evaluated in terms of Jack symmetric functions and their skew analogues. The resulting formulae depend on sequences of pairs of integers that completely determine the Fock module as well as the Jack symmetric functions.

Calculating corner singularities by boundary integral equations.

PubMed

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

2017-06-01

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

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

Integrating the Gradient of the Thin Wire Kernel

NASA Technical Reports Server (NTRS)

Champagne, Nathan J.; Wilton, Donald R.

2008-01-01

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

Stability effects of singularities in force-controlled robotic assist devices

NASA Astrophysics Data System (ADS)

Luecke, Greg R.

2002-02-01

Force feedback is being used as an interface between humans and material handling equipment to provide an intuitive method to control large and bulky payloads. Powered actuation in the lift assist device compensates for the inertial characteristics of the manipulator and the payload to provide effortless control and handling of manufacturing parts, components, and assemblies. The use of these Intelligent Assist Devices (IAD) is being explored to prevent worker injury, enhance material handling performance, and increase productivity in the workplace. The IAD also provides the capability to shape and control motion in the workspace during routine operations. Virtual barriers can be developed to protect fixed objects in the workspace, and regions can be programmed that attract the work piece to a certain position and orientation. However, the robot is still under complete control of the human operator, with the trajectory being determined and commanded using the judgment of the operator to complete a given task. In many cases, the IAD is built in a configuration that may have singular points inside the workspace. These singularities can cause problems when the unstructured trajectory commands from the human cause interaction between the IAD and the virtual walls and fixtures at positions close to these singularities. The research presented here explores the stability effects of the interactions between the powered manipulator and the virtual surfaces when controlled by the operator. Because of the flexible nature of the human decisions determining the real time work piece paths, manipulator singularities that occur in conjunction with the virtual surfaces raise stability issues in the performance around these singularities. We examine these stability issues in the context of a particular IAD configuration, and present analytic results for the performance and stability of these systems in response to the real-time trajectory modification of the human operator.

Singularities in Dromo formulation. Analysis of deep flybys

NASA Astrophysics Data System (ADS)

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

2015-08-01

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

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.

Modelling the spread of Ebola virus with Atangana-Baleanu fractional operators

NASA Astrophysics Data System (ADS)

Koca, Ilknur

2018-03-01

The model of Ebola spread within a targeted population is extended to the concept of fractional differentiation and integration with non-local and non-singular fading memory introduced by Atangana and Baleanu. It is expected that the proposed model will show better approximation than the models established before. The existence and uniqueness of solutions for the spread of Ebola disease model is given via the Picard-Lindelof method. Finally, numerical solutions for the model are given by using different parameter values.

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.

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.

Stable, high-order computation of impedance-impedance operators for three-dimensional layered medium simulations.

PubMed

Nicholls, David P

2018-04-01

The faithful modelling of the propagation of linear waves in a layered, periodic structure is of paramount importance in many branches of the applied sciences. In this paper, we present a novel numerical algorithm for the simulation of such problems which is free of the artificial singularities present in related approaches. We advocate for a surface integral formulation which is phrased in terms of impedance-impedance operators that are immune to the Dirichlet eigenvalues which plague the Dirichlet-Neumann operators that appear in classical formulations. We demonstrate a high-order spectral algorithm to simulate these latter operators based upon a high-order perturbation of surfaces methodology which is rapid, robust and highly accurate. We demonstrate the validity and utility of our approach with a sequence of numerical simulations.

Stable, high-order computation of impedance-impedance operators for three-dimensional layered medium simulations

NASA Astrophysics Data System (ADS)

Nicholls, David P.

2018-04-01

The faithful modelling of the propagation of linear waves in a layered, periodic structure is of paramount importance in many branches of the applied sciences. In this paper, we present a novel numerical algorithm for the simulation of such problems which is free of the artificial singularities present in related approaches. We advocate for a surface integral formulation which is phrased in terms of impedance-impedance operators that are immune to the Dirichlet eigenvalues which plague the Dirichlet-Neumann operators that appear in classical formulations. We demonstrate a high-order spectral algorithm to simulate these latter operators based upon a high-order perturbation of surfaces methodology which is rapid, robust and highly accurate. We demonstrate the validity and utility of our approach with a sequence of numerical simulations.

Spontaneous generation of singularities in paraxial optical fields.

PubMed

Aiello, Andrea

2016-04-01

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

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

NASA Astrophysics Data System (ADS)

Kamimoto, Shingo; Kawai, Takahiro; Koike, Tatsuya

2016-12-01

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

Interaction between a circular inclusion and an arbitrarily oriented crack

NASA Technical Reports Server (NTRS)

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

1975-01-01

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

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.

Perturbed dark and singular optical solitons in polarization preserving fibers by modified simple equation method

NASA Astrophysics Data System (ADS)

Yaşar, Emrullah; Yıldırım, Yakup; Zhou, Qin; Moshokoa, Seithuti P.; Ullah, Malik Zaka; Triki, Houria; Biswas, Anjan; Belic, Milivoj

2017-11-01

This paper obtains optical soliton solution to perturbed nonlinear Schrödinger's equation by modified simple equation method. There are four types of nonlinear fibers studied in this paper. They are Anti-cubic law, Quadratic-cubic law, Cubic-quintic-septic law and Triple-power law. Dark and singular soliton solutions are derived. Additional solutions such as singular periodic solutions also fall out of the integration scheme.

Solving differential equations for Feynman integrals by expansions near singular points

NASA Astrophysics Data System (ADS)

Lee, Roman N.; Smirnov, Alexander V.; Smirnov, Vladimir A.

2018-03-01

We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter ɛ.

Scattering of elastic waves from thin shapes in three dimensions using the composite boundary integral equation formulation

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

Liu, Y.; Rizzo, F.J.

1997-08-01

In this paper, the composite boundary integral equation (BIE) formulation is applied to scattering of elastic waves from thin shapes with small but {ital finite} thickness (open cracks or thin voids, thin inclusions, thin-layer interfaces, etc.), which are modeled with {ital two surfaces}. This composite BIE formulation, which is an extension of the Burton and Miller{close_quote}s formulation for acoustic waves, uses a linear combination of the conventional BIE and the hypersingular BIE. For thin shapes, the conventional BIE, as well as the hypersingular BIE, will degenerate (or nearly degenerate) if they are applied {ital individually} on the two surfaces. Themore » composite BIE formulation, however, will not degenerate for such problems, as demonstrated in this paper. Nearly singular and hypersingular integrals, which arise in problems involving thin shapes modeled with two surfaces, are transformed into sums of weakly singular integrals and nonsingular line integrals. Thus, no finer mesh is needed to compute these nearly singular integrals. Numerical examples of elastic waves scattered from penny-shaped cracks with varying openings are presented to demonstrate the effectiveness of the composite BIE formulation. {copyright} {ital 1997 Acoustical Society of America.}« less

27 CFR 46.163 - Meaning of terms.

Code of Federal Regulations, 2010 CFR

2010-04-01

... singular, words in the singular form shall include the plural, and words importing the masculine gender... warehouse with respect to the operation of such warehouse. Package. The container in which tobacco products...

27 CFR 46.163 - Meaning of terms.

Code of Federal Regulations, 2011 CFR

2011-04-01

... singular, words in the singular form shall include the plural, and words importing the masculine gender... warehouse with respect to the operation of such warehouse. Package. The container in which tobacco products...

27 CFR 46.163 - Meaning of terms.

Code of Federal Regulations, 2014 CFR

2014-04-01

... singular, words in the singular form shall include the plural, and words importing the masculine gender... warehouse with respect to the operation of such warehouse. Package. The container in which tobacco products...

27 CFR 46.163 - Meaning of terms.

Code of Federal Regulations, 2012 CFR

2012-04-01

... singular, words in the singular form shall include the plural, and words importing the masculine gender... warehouse with respect to the operation of such warehouse. Package. The container in which tobacco products...

27 CFR 46.163 - Meaning of terms.

Code of Federal Regulations, 2013 CFR

2013-04-01

... singular, words in the singular form shall include the plural, and words importing the masculine gender... warehouse with respect to the operation of such warehouse. Package. The container in which tobacco products...

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

NASA Astrophysics Data System (ADS)

Zhou, Yajun

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

Singularity now: using the ventricular assist device as a model for future human-robotic physiology.

PubMed

Martin, Archer K

2016-04-01

In our 21 st century world, human-robotic interactions are far more complicated than Asimov predicted in 1942. The future of human-robotic interactions includes human-robotic machine hybrids with an integrated physiology, working together to achieve an enhanced level of baseline human physiological performance. This achievement can be described as a biological Singularity. I argue that this time of Singularity cannot be met by current biological technologies, and that human-robotic physiology must be integrated for the Singularity to occur. In order to conquer the challenges we face regarding human-robotic physiology, we first need to identify a working model in today's world. Once identified, this model can form the basis for the study, creation, expansion, and optimization of human-robotic hybrid physiology. In this paper, I present and defend the line of argument that currently this kind of model (proposed to be named "IshBot") can best be studied in ventricular assist devices - VAD.

Singularity now: using the ventricular assist device as a model for future human-robotic physiology

PubMed Central

Martin, Archer K.

2016-01-01

In our 21st century world, human-robotic interactions are far more complicated than Asimov predicted in 1942. The future of human-robotic interactions includes human-robotic machine hybrids with an integrated physiology, working together to achieve an enhanced level of baseline human physiological performance. This achievement can be described as a biological Singularity. I argue that this time of Singularity cannot be met by current biological technologies, and that human-robotic physiology must be integrated for the Singularity to occur. In order to conquer the challenges we face regarding human-robotic physiology, we first need to identify a working model in today’s world. Once identified, this model can form the basis for the study, creation, expansion, and optimization of human-robotic hybrid physiology. In this paper, I present and defend the line of argument that currently this kind of model (proposed to be named “IshBot”) can best be studied in ventricular assist devices – VAD. PMID:28913480

Decomposition of the Multistatic Response Matrix and Target Characterization

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

Chambers, D H

2008-02-14

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

Exact solution for an optimal impermeable parachute problem

NASA Astrophysics Data System (ADS)

Lupu, Mircea; Scheiber, Ernest

2002-10-01

In the paper there are solved direct and inverse boundary problems and analytical solutions are obtained for optimization problems in the case of some nonlinear integral operators. It is modeled the plane potential flow of an inviscid, incompressible and nonlimited fluid jet, witch encounters a symmetrical, curvilinear obstacle--the deflector of maximal drag. There are derived integral singular equations, for direct and inverse problems and the movement in the auxiliary canonical half-plane is obtained. Next, the optimization problem is solved in an analytical manner. The design of the optimal airfoil is performed and finally, numerical computations concerning the drag coefficient and other geometrical and aerodynamical parameters are carried out. This model corresponds to the Helmholtz impermeable parachute problem.

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

NASA Astrophysics Data System (ADS)

Ghosh, Somnath

2018-05-01

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

Fredholm-Volterra Integral Equation with a Generalized Singular Kernel and its Numerical Solutions

NASA Astrophysics Data System (ADS)

El-Kalla, I. L.; Al-Bugami, A. M.

2010-11-01

In this paper, the existence and uniqueness of solution of the Fredholm-Volterra integral equation (F-VIE), with a generalized singular kernel, are discussed and proved in the spaceL2(Ω)×C(0,T). The Fredholm integral term (FIT) is considered in position while the Volterra integral term (VIT) is considered in time. Using a numerical technique we have a system of Fredholm integral equations (SFIEs). This system of integral equations can be reduced to a linear algebraic system (LAS) of equations by using two different methods. These methods are: Toeplitz matrix method and Product Nyström method. A numerical examples are considered when the generalized kernel takes the following forms: Carleman function, logarithmic form, Cauchy kernel, and Hilbert kernel.

Conformal anomaly of generalized form factors and finite loop integrals

NASA Astrophysics Data System (ADS)

Chicherin, Dmitry; Sokatchev, Emery

2018-04-01

We reveal a new mechanism of conformal symmetry breaking at Born level. It occurs in generalized form factors with several local operators and an on-shell state of massless particles. The effect is due to hidden singularities on collinear configurations of the momenta. This conformal anomaly is different from the holomorphic anomaly of amplitudes. We present a number of examples in four and six dimensions. We find an application of the new conformal anomaly to finite loop momentum integrals with one or more massless legs. The collinear region around a massless leg creates a contact anomaly, made visible by the loop integration. The anomalous conformal Ward identity for an ℓ-loop integral is a 2nd-order differential equation whose right-hand side is an (ℓ - 1)-loop integral. It could serve as a new useful tool to find/test analytic expressions for conformal integrals. We illustrate this point with several examples of known integrals. We propose a new differential equation for the four-dimensional scalar double box.

Boundary Element Method in a Self-Gravitating Elastic Half-Space and Its Application to Deformation Induced by Magma Chambers

NASA Astrophysics Data System (ADS)

Fang, M.; Hager, B. H.

2014-12-01

In geophysical applications the boundary element method (BEM) often carries the essential physics in addition to being an efficient numerical scheme. For use of the BEM in a self-gravitating uniform half-space, we made extra effort and succeeded in deriving the fundamental solution analytically in closed-form. A problem that goes deep into the heart of the classic BEM is encountered when we try to apply the new fundamental solution in BEM for deformation field induced by a magma chamber or a fluid-filled reservoir. The central issue of the BEM is the singular integral arising from determination of the boundary values. A widely employed technique is to rescale the singular boundary point into a small finite volume and then shrink it to extract the limits. This operation boils down to the calculation of the so-called C-matrix. Authors in the past take the liberty of either adding or subtracting a small volume. By subtracting a small volume, the C-matrix is (1/2)I on a smooth surface, where I is the identity matrix; by adding a small volume, we arrive at the same C-matrix in the form of I - (1/2)I. This evenness is a result of the spherical symmetry of Kelvin's fundamental solution employed. When the spherical symmetry is broken by gravity, the C-matrix is polarized. And we face the choice between right and wrong, for adding and subtracting a small volume yield different C-matrices. Close examination reveals that both derivations, addition and subtraction of a small volume, are ad hoc. To resolve the issue we revisit the Somigliana identity with a new derivation and careful step-by-step anatomy. The result proves that even though both adding and subtracting a small volume appear to twist the original boundary, only addition essentially modifies the original boundary and consequently modifies the physics of the original problem in a subtle way. The correct procedure is subtraction. We complete a new BEM theory by introducing in full analytical form what we call the singular stress tensor for the fundamental solution. We partition the stress tensor of the fundamental solution into a singular part and a regular part. In this way all singular integrals systematically shift into the easy singular stress tensor. Applications of this new BEM to deformation and gravitational perturbation induced by magma chambers of finite volume will be presented.

Numerical techniques in radiative heat transfer for general, scattering, plane-parallel media

NASA Technical Reports Server (NTRS)

Sharma, A.; Cogley, A. C.

1982-01-01

The study of radiative heat transfer with scattering usually leads to the solution of singular Fredholm integral equations. The present paper presents an accurate and efficient numerical method to solve certain integral equations that govern radiative equilibrium problems in plane-parallel geometry for both grey and nongrey, anisotropically scattering media. In particular, the nongrey problem is represented by a spectral integral of a system of nonlinear integral equations in space, which has not been solved previously. The numerical technique is constructed to handle this unique nongrey governing equation as well as the difficulties caused by singular kernels. Example problems are solved and the method's accuracy and computational speed are analyzed.

Multi-particle phase space integration with arbitrary set of singularities in CompHEP

NASA Astrophysics Data System (ADS)

Kovalenko, D. N.; Pukhov, A. E.

1997-02-01

We describe an algorithm of multi-particle phase space integration for collision and decay processes realized in CompHEP package version 3.2. In the framework of this algorithm it is possible to regularize an arbitrary set of singularities caused by virtual particle propagators. The algorithm is based on the method of the recursive representation of kinematics and on the multichannel Monte Carlo approach. CompHEP package is available by WWW: http://theory.npi.msu.su/pukhov/comphep.html

Confining potential in momentum space

NASA Technical Reports Server (NTRS)

Norbury, John W.; Kahana, David E.; Maung, Khin Maung

1992-01-01

A method is presented for the solution in momentum space of the bound state problem with a linear potential in r space. The potential is unbounded at large r leading to a singularity at small q. The singularity is integrable, when regulated by exponentially screening the r-space potential, and is removed by a subtraction technique. The limit of zero screening is taken analytically, and the numerical solution of the subtracted integral equation gives eigenvalues and wave functions in good agreement with position space calculations.

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.

{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

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

PubMed Central

Ran, Changyan; Cheng, Xianghong

2016-01-01

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

On the complete and partial integrability of non-Hamiltonian systems

NASA Astrophysics Data System (ADS)

Bountis, T. C.; Ramani, A.; Grammaticos, B.; Dorizzi, B.

1984-11-01

The methods of singularity analysis are applied to several third order non-Hamiltonian systems of physical significance including the Lotka-Volterra equations, the three-wave interaction and the Rikitake dynamo model. Complete integrability is defined and new completely integrable systems are discovered by means of the Painlevé property. In all these cases we obtain integrals, which reduce the equations either to a final quadrature or to an irreducible second order ordinary differential equation (ODE) solved by Painlevé transcendents. Relaxing the Painlevé property we find many partially integrable cases whose movable singularities are poles at leading order, with In( t- t0) terms entering at higher orders. In an Nth order, generalized Rössler model a precise relation is established between the partial fulfillment of the Painlevé conditions and the existence of N - 2 integrals of the motion.

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

PubMed

Ghosh, Somnath

2018-05-10

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

On the singular perturbations for fractional differential equation.

PubMed

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method.

Quantum probe of Hořava-Lifshitz gravity

NASA Astrophysics Data System (ADS)

Gurtug, O.; Mangut, M.

2018-04-01

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

Regularization with numerical extrapolation for finite and UV-divergent multi-loop integrals

NASA Astrophysics Data System (ADS)

de Doncker, E.; Yuasa, F.; Kato, K.; Ishikawa, T.; Kapenga, J.; Olagbemi, O.

2018-03-01

We give numerical integration results for Feynman loop diagrams such as those covered by Laporta (2000) and by Baikov and Chetyrkin (2010), and which may give rise to loop integrals with UV singularities. We explore automatic adaptive integration using multivariate techniques from the PARINT package for multivariate integration, as well as iterated integration with programs from the QUADPACK package, and a trapezoidal method based on a double exponential transformation. PARINT is layered over MPI (Message Passing Interface), and incorporates advanced parallel/distributed techniques including load balancing among processes that may be distributed over a cluster or a network/grid of nodes. Results are included for 2-loop vertex and box diagrams and for sets of 2-, 3- and 4-loop self-energy diagrams with or without UV terms. Numerical regularization of integrals with singular terms is achieved by linear and non-linear extrapolation methods.

Object detection with a multistatic array using singular value decomposition

DOEpatents

Hallquist, Aaron T.; Chambers, David H.

2014-07-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-01-01

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

Building blocks for subleading helicity operators

DOE PAGES

Kolodrubetz, Daniel W.; Moult, Ian; Stewart, Iain W.

2016-05-24

On-shell helicity methods provide powerful tools for determining scattering amplitudes, which have a one-to-one correspondence with leading power helicity operators in the Soft-Collinear Effective Theory (SCET) away from singular regions of phase space. We show that helicity based operators are also useful for enumerating power suppressed SCET operators, which encode subleading amplitude information about singular limits. In particular, we present a complete set of scalar helicity building blocks that are valid for constructing operators at any order in the SCET power expansion. In conclusion, we also describe an interesting angular momentum selection rule that restricts how these building blocks canmore » be assembled.« less

Some boundary-value problems for anisotropic quarter plane

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Application of singular value decomposition to structural dynamics systems with constraints

NASA Technical Reports Server (NTRS)

Juang, J.-N.; Pinson, L. D.

1985-01-01

Singular value decomposition is used to construct a coordinate transformation for a linear dynamic system subject to linear, homogeneous constraint equations. The method is compared with two commonly used methods, namely classical Gaussian elimination and Walton-Steeves approach. Although the classical method requires fewer numerical operations, the singular value decomposition method is more accurate and convenient in eliminating the dependent coordinates. Numerical examples are presented to demonstrate the application of the method.

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

NASA Technical Reports Server (NTRS)

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

1977-01-01

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

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.

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.

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

NASA Technical Reports Server (NTRS)

Atluri, Satya N.; Shen, Shengping

2002-01-01

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

On the Singular Perturbations for Fractional Differential Equation

PubMed Central

Atangana, Abdon

2014-01-01

The goal of this paper is to examine the possible extension of the singular perturbation differential equation to the concept of fractional order derivative. To achieve this, we presented a review of the concept of fractional calculus. We make use of the Laplace transform operator to derive exact solution of singular perturbation fractional linear differential equations. We make use of the methodology of three analytical methods to present exact and approximate solution of the singular perturbation fractional, nonlinear, nonhomogeneous differential equation. These methods are including the regular perturbation method, the new development of the variational iteration method, and the homotopy decomposition method. PMID:24683357

Holographic signatures of cosmological singularities.

PubMed

Engelhardt, Netta; Hertog, Thomas; Horowitz, Gary T

2014-09-19

To gain insight into the quantum nature of cosmological singularities, we study anisotropic Kasner solutions in gauge-gravity duality. The dual description of the bulk evolution towards the singularity involves N=4 super Yang-Mills theory on the expanding branch of deformed de Sitter space and is well defined. We compute two-point correlators of Yang-Mills operators of large dimensions using spacelike geodesics anchored on the boundary. The correlators show a strong signature of the singularity around horizon scales and decay at large boundary separation at different rates in different directions. More generally, the boundary evolution exhibits a process of particle creation similar to that in inflation. This leads us to conjecture that information on the quantum nature of cosmological singularities is encoded in long-wavelength features of the boundary wave function.

Classification of subsurface objects using singular values derived from signal frames

DOEpatents

Chambers, David H; Paglieroni, David W

2014-05-06

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

Theoretical analysis of linearized acoustics and aerodynamics of advanced supersonic propellers

NASA Technical Reports Server (NTRS)

Farassat, F.

1985-01-01

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

Vertically integrated (Ga, In)N nanostructures for future single photon emitters operating in the telecommunication wavelength range

NASA Astrophysics Data System (ADS)

Winden, A.; Mikulics, M.; Grützmacher, D.; Hardtdegen, H.

2013-10-01

Important technological steps are discussed and realized for future room-temperature operation of III-nitride single photon emitters. First, the growth technology of positioned single pyramidal InN nanostructures capped by Mg-doped GaN is presented. The optimization of their optical characteristics towards narrowband emission in the telecommunication wavelength range is demonstrated. In addition, a device concept and technology was developed so that the nanostructures became singularly addressable. It was found that the nanopyramids emit in the telecommunication wavelength range if their size is chosen appropriately. A p-GaN contacting layer was successfully produced as a cap to the InN pyramids and the top p-contact was achievable using an intrinsically conductive polymer PEDOT:PSS, allowing a 25% increase in light transmittance compared to standard Ni/Au contact technology. Single nanopyramids were successfully integrated into a high-frequency device layout. These decisive technology steps provide a promising route to electrically driven and room-temperature operating InN based single photon emitters in the telecommunication wavelength range.

Computational singular perturbation analysis of stochastic chemical systems with stiffness

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Solving the hypersingular boundary integral equation for the Burton and Miller formulation.

PubMed

Langrenne, Christophe; Garcia, Alexandre; Bonnet, Marc

2015-11-01

This paper presents an easy numerical implementation of the Burton and Miller (BM) formulation, where the hypersingular Helmholtz integral is regularized by identities from the associated Laplace equation and thus needing only the evaluation of weakly singular integrals. The Helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes not used when the surface is not smooth. The hypersingular operators arising in this process are regularized and then evaluated by an indirect procedure based on discretized versions of the Calderón identities linking the integral operators for associated Laplace problems. The method is valid for acoustic radiation and scattering problems involving arbitrarily shaped three-dimensional bodies. Unlike other approaches using direct evaluation of hypersingular integrals, collocation points still coincide with mesh nodes, as is usual when using conforming elements. Using higher-order shape functions (with the boundary element method model size kept fixed) reduces the overall numerical integration effort while increasing the solution accuracy. To reduce the condition number of the resulting BM formulation at low frequencies, a regularized version α = ik/(k(2 )+ λ) of the classical BM coupling factor α = i/k is proposed. Comparisons with the combined Helmholtz integral equation Formulation method of Schenck are made for four example configurations, two of them featuring non-smooth surfaces.

Towards timelike singularity via AdS dual

NASA Astrophysics Data System (ADS)

Bhowmick, Samrat; Chatterjee, Soumyabrata

2017-07-01

It is well known that Kasner geometry with spacelike singularity can be extended to bulk AdS-like geometry, furthermore, one can study field theory on this Kasner space via its gravity dual. In this paper, we show that there exists a Kasner-like geometry with timelike singularity for which one can construct a dual gravity description. We then study various extremal surfaces including spacelike geodesics in the dual gravity description. Finally, we compute correlators of highly massive operators in the boundary field theory with a geodesic approximation.

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

PubMed

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

2013-08-01

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

Constructing Current Singularity in a 3D Line-tied Plasma

DOE PAGES

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

2017-12-27

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

Burton-Miller-type singular boundary method for acoustic radiation and scattering

NASA Astrophysics Data System (ADS)

Fu, Zhuo-Jia; Chen, Wen; Gu, Yan

2014-08-01

This paper proposes the singular boundary method (SBM) in conjunction with Burton and Miller's formulation for acoustic radiation and scattering. The SBM is a strong-form collocation boundary discretization technique using the singular fundamental solutions, which is mathematically simple, easy-to-program, meshless and introduces the concept of source intensity factors (SIFs) to eliminate the singularities of the fundamental solutions. Therefore, it avoids singular numerical integrals in the boundary element method (BEM) and circumvents the troublesome placement of the fictitious boundary in the method of fundamental solutions (MFS). In the present method, we derive the SIFs of exterior Helmholtz equation by means of the SIFs of exterior Laplace equation owing to the same order of singularities between the Laplace and Helmholtz fundamental solutions. In conjunction with the Burton-Miller formulation, the SBM enhances the quality of the solution, particularly in the vicinity of the corresponding interior eigenfrequencies. Numerical illustrations demonstrate efficiency and accuracy of the present scheme on some benchmark examples under 2D and 3D unbounded domains in comparison with the analytical solutions, the boundary element solutions and Dirichlet-to-Neumann finite element solutions.

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Anisotropic singularities in modified gravity models

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

Figueiro, Michele Ferraz; Saa, Alberto; Departamento de Matematica Aplicada, IMECC-UNICAMP, C.P. 6065, 13083-859 Campinas, SP

2009-09-15

We show that the common singularities present in generic modified gravity models governed by actions of the type S={integral}d{sup 4}x{radical}(-g)f(R,{phi},X), with X=-(1/2)g{sup ab}{partial_derivative}{sub a}{phi}{partial_derivative}{sub b}{phi}, are essentially the same anisotropic instabilities associated to the hypersurface F({phi})=0 in the case of a nonminimal coupling of the type F({phi})R, enlightening the physical origin of such singularities that typically arise in rather complex and cumbersome inhomogeneous perturbation analyses. We show, moreover, that such anisotropic instabilities typically give rise to dynamically unavoidable singularities, precluding completely the possibility of having physically viable models for which the hypersurface ({partial_derivative}f/{partial_derivative}R)=0 is attained. Some examples are explicitly discussed.

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

ERIC Educational Resources Information Center

McDonald, Roderick P.; And Others

1979-01-01

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

Employment of a Dual Status Commander in a Multi-State Disaster Operation

DTIC Science & Technology

2016-06-10

propagates parallel commands among affected states without a singular organization to synchronize and prioritize efforts. Thus, the central research ...without a singular organization to synchronize and prioritize efforts. Thus, the central research question is: How can laws be changed to support the...1 The Research Question

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.

Gauge boson exchange in AdS d+1

NASA Astrophysics Data System (ADS)

D'Hoker, Eric; Freedman, Daniel Z.

1999-04-01

We study the amplitude for exchange of massless gauge bosons between pairs of massive scalar fields in anti-de Sitter space. In the AdS/CFT correspondence this amplitude describes the contribution of conserved flavor symmetry currents to 4-point functions of scalar operators in the boundary conformal theory. A concise, covariant, Y2K compatible derivation of the gauge boson propagator in AdS d + 1 is given. Techniques are developed to calculate the two bulk integrals over AdS space leading to explicit expressions or convenient, simple integral representations for the amplitude. The amplitude contains leading power and sub-leading logarithmic singularities in the gauge boson channel and leading logarithms in the crossed channel. The new methods of this paper are expected to have other applications in the study of the Maldacena conjecture.

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

Volume-preserving normal forms of Hopf-zero singularity

NASA Astrophysics Data System (ADS)

Gazor, Majid; Mokhtari, Fahimeh

2013-10-01

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

A high-order boundary integral method for surface diffusions on elastically stressed axisymmetric rods.

PubMed

Li, Xiaofan; Nie, Qing

2009-07-01

Many applications in materials involve surface diffusion of elastically stressed solids. Study of singularity formation and long-time behavior of such solid surfaces requires accurate simulations in both space and time. Here we present a high-order boundary integral method for an elastically stressed solid with axi-symmetry due to surface diffusions. In this method, the boundary integrals for isotropic elasticity in axi-symmetric geometry are approximated through modified alternating quadratures along with an extrapolation technique, leading to an arbitrarily high-order quadrature; in addition, a high-order (temporal) integration factor method, based on explicit representation of the mean curvature, is used to reduce the stability constraint on time-step. To apply this method to a periodic (in axial direction) and axi-symmetric elastically stressed cylinder, we also present a fast and accurate summation method for the periodic Green's functions of isotropic elasticity. Using the high-order boundary integral method, we demonstrate that in absence of elasticity the cylinder surface pinches in finite time at the axis of the symmetry and the universal cone angle of the pinching is found to be consistent with the previous studies based on a self-similar assumption. In the presence of elastic stress, we show that a finite time, geometrical singularity occurs well before the cylindrical solid collapses onto the axis of symmetry, and the angle of the corner singularity on the cylinder surface is also estimated.

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.

Symmetry breaking and singularity structure in Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

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

2012-08-01

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

A 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.

Singular perturbations with boundary conditions and the Casimir effect in the half space

NASA Astrophysics Data System (ADS)

Albeverio, S.; Cognola, G.; Spreafico, M.; Zerbini, S.

2010-06-01

We study the self-adjoint extensions of a class of nonmaximal multiplication operators with boundary conditions. We show that these extensions correspond to singular rank 1 perturbations (in the sense of Albeverio and Kurasov [Singular Perturbations of Differential Operaters (Cambridge University Press, Cambridge, 2000)]) of the Laplace operator, namely, the formal Laplacian with a singular delta potential, on the half space. This construction is the appropriate setting to describe the Casimir effect related to a massless scalar field in the flat space-time with an infinite conducting plate and in the presence of a pointlike "impurity." We use the relative zeta determinant (as defined in the works of Müller ["Relative zeta functions, relative determinants and scattering theory," Commun. Math. Phys. 192, 309 (1998)] and Spreafico and Zerbini ["Finite temperature quantum field theory on noncompact domains and application to delta interactions," Rep. Math. Phys. 63, 163 (2009)]) in order to regularize the partition function of this model. We study the analytic extension of the associated relative zeta function, and we present explicit results for the partition function and for the Casimir force.

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.

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

NASA Technical Reports Server (NTRS)

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

1982-01-01

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

Nonplanar on-shell diagrams and leading singularities of scattering amplitudes

NASA Astrophysics Data System (ADS)

Chen, Baoyi; Chen, Gang; Cheung, Yeuk-Kwan E.; Li, Yunxuan; Xie, Ruofei; Xin, Yuan

2017-02-01

Bipartite on-shell diagrams are the latest tool in constructing scattering amplitudes. In this paper we prove that a Britto-Cachazo-Feng-Witten (BCFW) decomposable on-shell diagram process a rational top form if and only if the algebraic ideal comprised the geometrical constraints are shifted linearly during successive BCFW integrations. With a proper geometric interpretation of the constraints in the Grassmannian manifold, the rational top form integration contours can thus be obtained, and understood, in a straightforward way. All rational top form integrands of arbitrary higher loops leading singularities can therefore be derived recursively, as long as the corresponding on-shell diagram is BCFW decomposable.

Torsion analysis of cracked circular bars actuated by a piezoelectric coating

NASA Astrophysics Data System (ADS)

Hassani, A. R.; Faal, R. T.

2016-12-01

This study presents a formulation for a bar with circular cross-section, coated by a piezoelectric layer and subjected to Saint-Venant torsion loading. The bar is weakened by a Volterra-type screw dislocation. First, with aid of the finite Fourier transform, the stress fields in the circular bar and the piezoelectric layer are obtained. The problem is then reduced to a set of singular integral equations with a Cauchy-type singularity. Unknown dislocation density is achieved by numerical solution of these integral equations. Numerical results are discussed, to reveal the effect of the piezoelectric layer on the reduction of the mechanical stress intensity factor in the bar.

Sigmoid function based integral-derivative observer and application to autopilot design

NASA Astrophysics Data System (ADS)

Shao, Xingling; Wang, Honglun; Liu, Jun; Tang, Jun; Li, Jie; Zhang, Xiaoming; Shen, Chong

2017-02-01

To handle problems of accurate signal reconstruction and controller implementation with integral and derivative components in the presence of noisy measurement, motivated by the design principle of sigmoid function based tracking differentiator and nonlinear continuous integral-derivative observer, a novel integral-derivative observer (SIDO) using sigmoid function is developed. The key merit of the proposed SIDO is that it can simultaneously provide continuous integral and differential estimates with almost no drift phenomena and chattering effect, as well as acceptable noise-tolerance performance from output measurement, and the stability is established based on exponential stability and singular perturbation theory. In addition, the effectiveness of SIDO in suppressing drift phenomena and high frequency noises is firstly revealed using describing function and confirmed through simulation comparisons. Finally, the theoretical results on SIDO are demonstrated with application to autopilot design: 1) the integral and tracking estimates are extracted from the sensed pitch angular rate contaminated by nonwhite noises in feedback loop, 2) the PID(proportional-integral-derivative) based attitude controller is realized by adopting the error estimates offered by SIDO instead of using the ideal integral and derivative operator to achieve satisfactory tracking performance under control constraint.

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.

Computational singular perturbation analysis of stochastic chemical systems with stiffness

DOE PAGES

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

2017-01-25

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

A multi-domain spectral method for time-fractional differential equations

NASA Astrophysics Data System (ADS)

Chen, Feng; Xu, Qinwu; Hesthaven, Jan S.

2015-07-01

This paper proposes an approach for high-order time integration within a multi-domain setting for time-fractional differential equations. Since the kernel is singular or nearly singular, two main difficulties arise after the domain decomposition: how to properly account for the history/memory part and how to perform the integration accurately. To address these issues, we propose a novel hybrid approach for the numerical integration based on the combination of three-term-recurrence relations of Jacobi polynomials and high-order Gauss quadrature. The different approximations used in the hybrid approach are justified theoretically and through numerical examples. Based on this, we propose a new multi-domain spectral method for high-order accurate time integrations and study its stability properties by identifying the method as a generalized linear method. Numerical experiments confirm hp-convergence for both time-fractional differential equations and time-fractional partial differential equations.

Ultra-Dense Quantum Communication Using Integrated Photonic Architecture

DTIC Science & Technology

2012-02-03

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

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

NASA Technical Reports Server (NTRS)

Paduano, James D.; Downing, David R.

1987-01-01

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

Second-order relativistic corrections for the S(L=0) states in one- and two-electron atomic systems

NASA Astrophysics Data System (ADS)

Frolov, A. M.; Mitelut, C. C.; Zhong, Z.

2005-01-01

An analytical approach is developed to compute the first- (similar to alpha(2)) and second-order (similar to alpha(4)) relativistic corrections in one- and two-electron atomic systems. The approach is based on the reduction of all operators to divergent (singular) and nondivergent (regular) parts. Then, we show that all the divergent parts from the differentmatrix elements cancel each other. The remaining expression contains only regular operators and its expectation value can be easily computed. Analysis of the S(L = 0) states in such systems is of specific interest since the corresponding operators for these states contain a large number of singularities. For one-electron systems the computed relativistic corrections coincide exactly with the appropriate result that follows from the Taylor expansion of the relativistic (i.e., Dirac) energy. We also discuss an alternative approach that allows one to cancel all singularities by using the so-called operator-compensation technique. This second approach is found to be very effective in applications of more complex systems, such as helium-like atoms and ions, H-2(+)-like ions, and some exotic three-body systems.

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

NASA Astrophysics Data System (ADS)

Hai, Kuo; Yu, Ning; Jia, Jiangping

2018-06-01

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

Integrated ensemble noise-reconstructed empirical mode decomposition for mechanical fault detection

NASA Astrophysics Data System (ADS)

Yuan, Jing; Ji, Feng; Gao, Yuan; Zhu, Jun; Wei, Chenjun; Zhou, Yu

2018-05-01

A new branch of fault detection is utilizing the noise such as enhancing, adding or estimating the noise so as to improve the signal-to-noise ratio (SNR) and extract the fault signatures. Hereinto, ensemble noise-reconstructed empirical mode decomposition (ENEMD) is a novel noise utilization method to ameliorate the mode mixing and denoised the intrinsic mode functions (IMFs). Despite the possibility of superior performance in detecting weak and multiple faults, the method still suffers from the major problems of the user-defined parameter and the powerless capability for a high SNR case. Hence, integrated ensemble noise-reconstructed empirical mode decomposition is proposed to overcome the drawbacks, improved by two noise estimation techniques for different SNRs as well as the noise estimation strategy. Independent from the artificial setup, the noise estimation by the minimax thresholding is improved for a low SNR case, which especially shows an outstanding interpretation for signature enhancement. For approximating the weak noise precisely, the noise estimation by the local reconfiguration using singular value decomposition (SVD) is proposed for a high SNR case, which is particularly powerful for reducing the mode mixing. Thereinto, the sliding window for projecting the phase space is optimally designed by the correlation minimization. Meanwhile, the reasonable singular order for the local reconfiguration to estimate the noise is determined by the inflection point of the increment trend of normalized singular entropy. Furthermore, the noise estimation strategy, i.e. the selection approaches of the two estimation techniques along with the critical case, is developed and discussed for different SNRs by means of the possible noise-only IMF family. The method is validated by the repeatable simulations to demonstrate the synthetical performance and especially confirm the capability of noise estimation. Finally, the method is applied to detect the local wear fault from a dual-axis stabilized platform and the gear crack from an operating electric locomotive to verify its effectiveness and feasibility.

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.

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

NASA Astrophysics Data System (ADS)

Hutterer, Victoria; Ramlau, Ronny

2018-03-01

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

Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid

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

Prochnow, Bo; O'Reilly, Ossian; Dunham, Eric M.

In this paper, we develop a high-order finite difference scheme for axisymmetric wave propagation in a cylindrical conduit filled with a viscous fluid. The scheme is provably stable, and overcomes the difficulty of the polar coordinate singularity in the radial component of the diffusion operator. The finite difference approximation satisfies the principle of summation-by-parts (SBP), which is used to establish stability using the energy method. To treat the coordinate singularity without losing the SBP property of the scheme, a staggered grid is introduced and quadrature rules with weights set to zero at the endpoints are considered. Finally, the accuracy ofmore » the scheme is studied both for a model problem with periodic boundary conditions at the ends of the conduit and its practical utility is demonstrated by modeling acoustic-gravity waves in a magmatic conduit.« less

Quantum space and quantum completeness

NASA Astrophysics Data System (ADS)

Jurić, Tajron

2018-05-01

Motivated by the question whether quantum gravity can "smear out" the classical singularity we analyze a certain quantum space and its quantum-mechanical completeness. Classical singularity is understood as a geodesic incompleteness, while quantum completeness requires a unique unitary time evolution for test fields propagating on an underlying background. Here the crucial point is that quantum completeness renders the Hamiltonian (or spatial part of the wave operator) to be essentially self-adjoint in order to generate a unique time evolution. We examine a model of quantum space which consists of a noncommutative BTZ black hole probed by a test scalar field. We show that the quantum gravity (noncommutative) effect is to enlarge the domain of BTZ parameters for which the relevant wave operator is essentially self-adjoint. This means that the corresponding quantum space is quantum complete for a larger range of BTZ parameters rendering the conclusion that in the quantum space one observes the effect of "smearing out" the singularity.

Treatment of the polar coordinate singularity in axisymmetric wave propagation using high-order summation-by-parts operators on a staggered grid

DOE PAGES

Prochnow, Bo; O'Reilly, Ossian; Dunham, Eric M.; ...

2017-03-16

In this paper, we develop a high-order finite difference scheme for axisymmetric wave propagation in a cylindrical conduit filled with a viscous fluid. The scheme is provably stable, and overcomes the difficulty of the polar coordinate singularity in the radial component of the diffusion operator. The finite difference approximation satisfies the principle of summation-by-parts (SBP), which is used to establish stability using the energy method. To treat the coordinate singularity without losing the SBP property of the scheme, a staggered grid is introduced and quadrature rules with weights set to zero at the endpoints are considered. Finally, the accuracy ofmore » the scheme is studied both for a model problem with periodic boundary conditions at the ends of the conduit and its practical utility is demonstrated by modeling acoustic-gravity waves in a magmatic conduit.« less

Robust penalty method for structural synthesis

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1983-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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

NASA Astrophysics Data System (ADS)

Erb, W.; Weinmann, A.; Ahlborg, M.; Brandt, C.; Bringout, G.; Buzug, T. M.; Frikel, J.; Kaethner, C.; Knopp, T.; März, T.; Möddel, M.; Storath, M.; Weber, A.

2018-05-01

Magnetic particle imaging (MPI) is a promising new in vivo medical imaging modality in which distributions of super-paramagnetic nanoparticles are tracked based on their response in an applied magnetic field. In this paper we provide a mathematical analysis of the modeled MPI operator in the univariate situation. We provide a Hilbert space setup, in which the MPI operator is decomposed into simple building blocks and in which these building blocks are analyzed with respect to their mathematical properties. In turn, we obtain an analysis of the MPI forward operator and, in particular, of its ill-posedness properties. We further get that the singular values of the MPI core operator decrease exponentially. We complement our analytic results by some numerical studies which, in particular, suggest a rapid decay of the singular values of the MPI operator.

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

NASA Astrophysics Data System (ADS)

Li, Dafa

2018-06-01

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

On quantum integrability of the Landau-Lifshitz model

NASA Astrophysics Data System (ADS)

Melikyan, A.; Pinzul, A.

2009-10-01

We investigate the quantum integrability of the Landau-Lifshitz (LL) model and solve the long-standing problem of finding the local quantum Hamiltonian for the arbitrary n-particle sector. The particular difficulty of the LL model quantization, which arises due to the ill-defined operator product, is dealt with by simultaneously regularizing the operator product and constructing the self-adjoint extensions of a very particular structure. The diagonalizibility difficulties of the Hamiltonian of the LL model, due to the highly singular nature of the quantum-mechanical Hamiltonian, are also resolved in our method for the arbitrary n-particle sector. We explicitly demonstrate the consistency of our construction with the quantum inverse scattering method due to Sklyanin [Lett. Math. Phys. 15, 357 (1988)] and give a prescription to systematically construct the general solution, which explains and generalizes the puzzling results of Sklyanin for the particular two-particle sector case. Moreover, we demonstrate the S-matrix factorization and show that it is a consequence of the discontinuity conditions on the functions involved in the construction of the self-adjoint extensions.

Recovering a function from its trigonometric integral

NASA Astrophysics Data System (ADS)

Sworowska, Tat'yana A.

2010-09-01

The approximate symmetric Henstock-Kurzweil integral is shown as solving the problem of the recovery of a function from its trigonometric integral. This being so, we generalize Offord's theorem, which is an analogue of de la Vallée Poussin's theorem for trigonometric series. A new condition for a function to be representable by a singular Fourier integral is also obtained.Bibliography: 10 titles.

Opening of an interface flaw in a layered elastic half-plane under compressive loading

NASA Technical Reports Server (NTRS)

Kennedy, J. M.; Fichter, W. B.; Goree, J. G.

1984-01-01

A static analysis is given of the problem of an elastic layer perfectly bonded, except for a frictionless interface crack, to a dissimilar elastic half-plane. The free surface of the layer is loaded by a finite pressure distribution directly over the crack. The problem is formulated using the two dimensional linear elasticity equations. Using Fourier transforms, the governing equations are converted to a pair of coupled singular integral equations. The integral equations are reduced to a set of simultaneous algebraic equations by expanding the unknown functions in a series of Jacobi polynomials and then evaluating the singular Cauchy-type integrals. The resulting equations are found to be ill-conditioned and, consequently, are solved in the least-squares sense. Results from the analysis show that, under a normal pressure distribution on the free surface of the layer and depending on the combination of geometric and material parameters, the ends of the crack can open. The resulting stresses at the crack-tips are singular, implying that crack growth is possible. The extent of the opening and the crack-top stress intensity factors depend on the width of the pressure distribution zone, the layer thickness, and the relative material properties of the layer and half-plane.

Finite-surface method for the Maxwell equations with corner singularities

NASA Technical Reports Server (NTRS)

Vinokur, Marcel; Yarrow, Maurice

1994-01-01

The finite-surface method for the two-dimensional Maxwell equations in generalized coordinates is extended to treat perfect conductor boundaries with sharp corners. Known singular forms of the grid and the electromagnetic fields in the neighborhood of each corner are used to obtain accurate approximations to the surface and line integrals appearing in the method. Numerical results are presented for a harmonic plane wave incident on a finite flat plate. Comparisons with exact solutions show good agreement.

Problems of interaction longitudinal shear waves with V-shape tunnels defect

NASA Astrophysics Data System (ADS)

Popov, V. G.

2018-04-01

The problem of determining the two-dimensional dynamic stress state near a tunnel defect of V-shaped cross-section is solved. The defect is located in an infinite elastic medium, where harmonic longitudinal shear waves are propagating. The initial problem is reduced to a system of two singular integral or integro-differential equations with fixed singularities. A numerical method for solving these systems with regard to the true asymptotics of the unknown functions is developed.

Milne, a routine for the numerical solution of Milne's problem

NASA Astrophysics Data System (ADS)

Rawat, Ajay; Mohankumar, N.

2010-11-01

The routine Milne provides accurate numerical values for the classical Milne's problem of neutron transport for the planar one speed and isotropic scattering case. The solution is based on the Case eigen-function formalism. The relevant X functions are evaluated accurately by the Double Exponential quadrature. The calculated quantities are the extrapolation distance and the scalar and the angular fluxes. Also, the H function needed in astrophysical calculations is evaluated as a byproduct. Program summaryProgram title: Milne Catalogue identifier: AEGS_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGS_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 701 No. of bytes in distributed program, including test data, etc.: 6845 Distribution format: tar.gz Programming language: Fortran 77 Computer: PC under Linux or Windows Operating system: Ubuntu 8.04 (Kernel version 2.6.24-16-generic), Windows-XP Classification: 4.11, 21.1, 21.2 Nature of problem: The X functions are integral expressions. The convergence of these regular and Cauchy Principal Value integrals are impaired by the singularities of the integrand in the complex plane. The DE quadrature scheme tackles these singularities in a robust manner compared to the standard Gauss quadrature. Running time: The test included in the distribution takes a few seconds to run.

Conformal Galilei algebras, symmetric polynomials and singular vectors

NASA Astrophysics Data System (ADS)

Křižka, Libor; Somberg, Petr

2018-01-01

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

Nonlinear bending models for beams and plates

PubMed Central

Antipov, Y. A.

2014-01-01

A new nonlinear model for large deflections of a beam is proposed. It comprises the Euler–Bernoulli boundary value problem for the deflection and a nonlinear integral condition. When bending does not alter the beam length, this condition guarantees that the deflected beam has the original length and fixes the horizontal displacement of the free end. The numerical results are in good agreement with the ones provided by the elastica model. Dynamic and two-dimensional generalizations of this nonlinear one-dimensional static model are also discussed. The model problem for an inextensible rectangular Kirchhoff plate, when one side is clamped, the opposite one is subjected to a shear force, and the others are free of moments and forces, is reduced to a singular integral equation with two fixed singularities. The singularities of the unknown function are examined, and a series-form solution is derived by the collocation method in terms of the associated Jacobi polynomials. The procedure requires solving an infinite system of linear algebraic equations for the expansion coefficients subject to the inextensibility condition. PMID:25294960

High order Nyström method for elastodynamic scattering

NASA Astrophysics Data System (ADS)

Chen, Kun; Gurrala, Praveen; Song, Jiming; Roberts, Ron

2016-02-01

Elastic waves in solids find important applications in ultrasonic non-destructive evaluation. The scattering of elastic waves has been treated using many approaches like the finite element method, boundary element method and Kirchhoff approximation. In this work, we propose a novel accurate and efficient high order Nyström method to solve the boundary integral equations for elastodynamic scattering problems. This approach employs high order geometry description for the element, and high order interpolation for fields inside each element. Compared with the boundary element method, this approach makes the choice of the nodes for interpolation based on the Gaussian quadrature, which renders matrix elements for far field interaction free from integration, and also greatly simplifies the process for singularity and near singularity treatment. The proposed approach employs a novel efficient near singularity treatment that makes the solver able to handle extreme geometries like very thin penny-shaped crack. Numerical results are presented to validate the approach. By using the frequency domain response and performing the inverse Fourier transform, we also report the time domain response of flaw scattering.

Phases of unstable conifolds

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

Narayan, K.

2007-03-15

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

Fast algorithms for Quadrature by Expansion I: Globally valid expansions

NASA Astrophysics Data System (ADS)

Rachh, Manas; Klöckner, Andreas; O'Neil, Michael

2017-09-01

The use of integral equation methods for the efficient numerical solution of PDE boundary value problems requires two main tools: quadrature rules for the evaluation of layer potential integral operators with singular kernels, and fast algorithms for solving the resulting dense linear systems. Classically, these tools were developed separately. In this work, we present a unified numerical scheme based on coupling Quadrature by Expansion, a recent quadrature method, to a customized Fast Multipole Method (FMM) for the Helmholtz equation in two dimensions. The method allows the evaluation of layer potentials in linear-time complexity, anywhere in space, with a uniform, user-chosen level of accuracy as a black-box computational method. Providing this capability requires geometric and algorithmic considerations beyond the needs of standard FMMs as well as careful consideration of the accuracy of multipole translations. We illustrate the speed and accuracy of our method with various numerical examples.

Quadrature rules with multiple nodes for evaluating integrals with strong singularities

NASA Astrophysics Data System (ADS)

Milovanovic, Gradimir V.; Spalevic, Miodrag M.

2006-05-01

We present a method based on the Chakalov-Popoviciu quadrature formula of Lobatto type, a rather general case of quadrature with multiple nodes, for approximating integrals defined by Cauchy principal values or by Hadamard finite parts. As a starting point we use the results obtained by L. Gori and E. Santi (cf. On the evaluation of Hilbert transforms by means of a particular class of Turan quadrature rules, Numer. Algorithms 10 (1995), 27-39; Quadrature rules based on s-orthogonal polynomials for evaluating integrals with strong singularities, Oberwolfach Proceedings: Applications and Computation of Orthogonal Polynomials, ISNM 131, Birkhauser, Basel, 1999, pp. 109-119). We generalize their results by using some of our numerical procedures for stable calculation of the quadrature formula with multiple nodes of Gaussian type and proposed methods for estimating the remainder term in such type of quadrature formulae. Numerical examples, illustrations and comparisons are also shown.

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.

Singular instantons in Eddington-inspired-Born-Infeld gravity

DOE PAGES

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

2017-03-23

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

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

NASA Astrophysics Data System (ADS)

You, J. H.; Bolt, H.

2001-10-01

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

Singular boundary method for wave propagation analysis in periodic structures

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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.

ZZ-Type a posteriori error estimators for adaptive boundary element methods on a curve☆

PubMed Central

Feischl, Michael; Führer, Thomas; Karkulik, Michael; Praetorius, Dirk

2014-01-01

In the context of the adaptive finite element method (FEM), ZZ-error estimators named after Zienkiewicz and Zhu (1987) [52] are mathematically well-established and widely used in practice. In this work, we propose and analyze ZZ-type error estimators for the adaptive boundary element method (BEM). We consider weakly singular and hyper-singular integral equations and prove, in particular, convergence of the related adaptive mesh-refining algorithms. Throughout, the theoretical findings are underlined by numerical experiments. PMID:24748725

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

NASA Technical Reports Server (NTRS)

Adams, Richard J.

1993-01-01

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

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

Non-Singular Dislocation Elastic Fields and Linear Elastic Fracture Mechanics

NASA Astrophysics Data System (ADS)

Korsunsky, Alexander M.

2010-03-01

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

Tunnel junctions with multiferroic barriers

NASA Astrophysics Data System (ADS)

Gajek, Martin; Bibes, Manuel; Fusil, Stéphane; Bouzehouane, Karim; Fontcuberta, Josep; Barthélémy, Agnès; Fert, Albert

2007-04-01

Multiferroics are singular materials that can exhibit simultaneously electric and magnetic orders. Some are ferroelectric and ferromagnetic and provide the opportunity to encode information in electric polarization and magnetization to obtain four logic states. However, such materials are rare and schemes allowing a simple electrical readout of these states have not been demonstrated in the same device. Here, we show that films of La0.1Bi0.9MnO3 (LBMO) are ferromagnetic and ferroelectric, and retain both ferroic properties down to a thickness of 2nm. We have integrated such ultrathin multiferroic films as barriers in spin-filter-type tunnel junctions that exploit the magnetic and ferroelectric degrees of freedom of LBMO. Whereas ferromagnetism permits read operations reminiscent of magnetic random access memories (MRAM), the electrical switching evokes a ferroelectric RAM write operation. Significantly, our device does not require the destructive ferroelectric readout, and therefore represents an advance over the original four-state memory concept based on multiferroics.

Tunnel junctions with multiferroic barriers.

PubMed

Gajek, Martin; Bibes, Manuel; Fusil, Stéphane; Bouzehouane, Karim; Fontcuberta, Josep; Barthélémy, Agnès; Fert, Albert

2007-04-01

Multiferroics are singular materials that can exhibit simultaneously electric and magnetic orders. Some are ferroelectric and ferromagnetic and provide the opportunity to encode information in electric polarization and magnetization to obtain four logic states. However, such materials are rare and schemes allowing a simple electrical readout of these states have not been demonstrated in the same device. Here, we show that films of La(0.1)Bi(0.9)MnO(3) (LBMO) are ferromagnetic and ferroelectric, and retain both ferroic properties down to a thickness of 2 nm. We have integrated such ultrathin multiferroic films as barriers in spin-filter-type tunnel junctions that exploit the magnetic and ferroelectric degrees of freedom of LBMO. Whereas ferromagnetism permits read operations reminiscent of magnetic random access memories (MRAM), the electrical switching evokes a ferroelectric RAM write operation. Significantly, our device does not require the destructive ferroelectric readout, and therefore represents an advance over the original four-state memory concept based on multiferroics.

Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes

NASA Astrophysics Data System (ADS)

Saini, Sahil; Singh, Parampreet

2018-03-01

We study the generic resolution of strong singularities in loop quantized effective Bianchi-IX spacetime in two different quantizations—the connection operator based ‘A’ quantization and the extrinsic curvature based ‘K’ quantization. We show that in the effective spacetime description with arbitrary matter content, it is necessary to include inverse triad corrections to resolve all the strong singularities in the ‘A’ quantization. Whereas in the ‘K’ quantization these results can be obtained without including inverse triad corrections. Under these conditions, the energy density, expansion and shear scalars for both of the quantization prescriptions are bounded. Notably, both the quantizations can result in potentially curvature divergent events if matter content allows divergences in the partial derivatives of the energy density with respect to the triad variables at a finite energy density. Such events are found to be weak curvature singularities beyond which geodesics can be extended in the effective spacetime. Our results show that all potential strong curvature singularities of the classical theory are forbidden in Bianchi-IX spacetime in loop quantum cosmology and geodesic evolution never breaks down for such events.

Giant enhancement in Goos-Hänchen shift at the singular phase of a nanophotonic cavity

NASA Astrophysics Data System (ADS)

Sreekanth, Kandammathe Valiyaveedu; Ouyang, Qingling; Han, Song; Yong, Ken-Tye; Singh, Ranjan

2018-04-01

In this letter, we experimentally demonstrate thirtyfold enhancement in Goos-Hänchen shift at the Brewster angle of a nanophotonic cavity that operates at the wavelength of 632.8 nm. In particular, the point-of-darkness and the singular phase are achieved using a four-layered metal-dielectric-dielectric-metal asymmetric Fabry-Perot cavity. A highly absorbing ultra-thin layer of germanium in the stack gives rise to the singular phase and the enhanced Goos-Hänchen shift at the point-of-darkness. The obtained giant Goos-Hänchen shift in the lithography-free nanophotonic cavity could enable many intriguing applications including cost-effective label-free biosensors.

Finite-dimensional integrable systems: A collection of research problems

NASA Astrophysics Data System (ADS)

Bolsinov, A. V.; Izosimov, A. M.; Tsonev, D. M.

2017-05-01

This article suggests a series of problems related to various algebraic and geometric aspects of integrability. They reflect some recent developments in the theory of finite-dimensional integrable systems such as bi-Poisson linear algebra, Jordan-Kronecker invariants of finite dimensional Lie algebras, the interplay between singularities of Lagrangian fibrations and compatible Poisson brackets, and new techniques in projective geometry.

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

Kanna, T.; Sakkaravarthi, K.; Kumar, C. Senthil

In this paper, we have studied the integrability nature of a system of three-coupled Gross-Pitaevskii type nonlinear evolution equations arising in the context of spinor Bose-Einstein condensates by applying the Painleve singularity structure analysis. We show that only for two sets of parametric choices, corresponding to the known integrable cases, the system passes the Painleve test.

How to Integrate Bilingual Education without Tracking.

ERIC Educational Resources Information Center

Glenn, Charles L.

1990-01-01

Integrated schools that stress learning among students in two languages are called two-way schools. They provide a singularly rich educational environment and avoid the negative effects of educational segregation by tracking. A Chelsea, Massachusetts, bilingual elementary school focused on team building to use existing resources more effectively.…

Formation of current singularity in a topologically constrained plasma

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

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

2016-02-01

Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the Hahm-Kulsrud-Taylor problem, which considers the response of a 2D plasma magnetized by a sheared field under sinusoidal boundary forcing. We obtain an equilibrium solution that preserves the magnetic topology of the initial field exactly, with a fluid mapping that is non-differentiable. Unlike previous studies that examine the current density output, we identify a singular current sheet from the fluid mapping. These results are benchmarked with a constrained Grad-Shafranovmore » solver. The same signature of current singularity can be found in other cases with more complex magnetic topologies.« less

Dynamics of magnetic shells and information loss problem

NASA Astrophysics Data System (ADS)

Lee, Bum-Hoon; Lee, Wonwoo; Yeom, Dong-han

2015-07-01

We investigate dynamics of magnetic thin-shells in three dimensional anti-de Sitter background. Because of the magnetic field, an oscillatory solution is possible. This oscillating shell can tunnel to a collapsing shell or a bouncing shell, where both tunnelings induce an event horizon and a singularity. In the entire path integral, via the oscillating solution, there is a nonzero probability to maintain a trivial causal structure without a singularity. Therefore, due to the path integral, the entire wave function can conserve information. Since an oscillating shell can tunnel after a number of oscillations, in the end, it will allow an infinite number of different branchings to classical histories. This system can be a good model of the effective loss of information, where information is conserved by a solution that is originated from gauge fields.

A robust direct-integration method for rotorcraft maneuver and periodic response

NASA Technical Reports Server (NTRS)

Panda, Brahmananda

1992-01-01

The Newmark-Beta method and the Newton-Raphson iteration scheme are combined to develop a direct-integration method for evaluating the maneuver and periodic-response expressions for rotorcraft. The method requires the generation of Jacobians and includes higher derivatives in the formulation of the geometric stiffness matrix to enhance the convergence of the system. The method leads to effective convergence with nonlinear structural dynamics and aerodynamic terms. Singularities in the matrices can be addressed with the method as they arise from a Lagrange multiplier approach for coupling equations with nonlinear constraints. The method is also shown to be general enough to handle singularities from quasisteady control-system models. The method is shown to be more general and robust than the similar 2GCHAS method for analyzing rotorcraft dynamics.

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

NASA Astrophysics Data System (ADS)

Zhao, Huaqing

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

{lambda} elements for singular problems in CFD: Viscoelastic fluids

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

Wong, K.K.; Surana, K.S.

1996-10-01

This paper presents two dimensional {lambda} element formulation for viscoelastic fluid flow containing point singularities in the flow field. The flow of viscoelastic fluid even without singularities are a difficult class of problems for increasing Deborah number or Weissenburg number due to increased dominance of convective terms and thus increased hyperbolicity. In the present work the equations of fluid motion and the constitutive laws are recast in the form of a first order system of coupled equations with the use of auxiliary variables. The velocity, pressure and stresses are interpolated using equal order C{sup 0} {lambda} element approximations. The Leastmore » Squares Finite Element Method (LSFEM) is used to construct the integral form (error functional I) corresponding to these equations. The error functional is constructed by taking the integrated sum of the squares of the errors or residuals (over the whole discretization) resulting when the element approximation is substituted into these equations. The conditions resulting from the minimization of the error functional are satisfied by using Newton`s method with line search. LSFEM has much superior performance when dealing with non-linear and convection dominated problems.« less

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

PubMed

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

2017-01-01

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

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

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

Adachi, Satoshi; Toda, Mikito; Kubotani, Hiroto

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

40 CFR 112.1 - General applicability.

Code of Federal Regulations, 2013 CFR

2013-07-01

... the singular also include the plural and words in the masculine gender also include the feminine and... does not apply to: (1) The owner or operator of any facility, equipment, or operation that is not.... (ii) Any equipment, or operation of a vessel or transportation-related onshore or offshore facility...

Accelerator-feasible N -body nonlinear integrable system

DOE PAGES

Danilov, V.; Nagaitsev, S.

2014-12-23

Nonlinear N-body integrable Hamiltonian systems, where N is an arbitrary number, attract the attention of mathematical physicists for the last several decades, following the discovery of some number of these systems. This research presents a new integrable system, which can be realized in facilities such as particle accelerators. This feature makes it more attractive than many of the previous such systems with singular or unphysical forces.

Rotating black holes in the teleparallel equivalent of general relativity

NASA Astrophysics Data System (ADS)

Nashed, Gamal G. L.

2016-05-01

We derive set of solutions with flat transverse sections in the framework of a teleparallel equivalent of general relativity which describes rotating black holes. The singularities supported from the invariants of torsion and curvature are explained. We investigate that there appear more singularities in the torsion scalars than in the curvature ones. The conserved quantities are discussed using Einstein-Cartan geometry. The physics of the constants of integration is explained through the calculations of conserved quantities. These calculations show that there is a unique solution that may describe true physical black hole.

Nonlinear wave choked inlets

NASA Technical Reports Server (NTRS)

1979-01-01

The quasi-one dimensional flow program was modified in two ways. The Runge-Kutta subroutine was replaced with a subroutine which used a modified divided difference form of the Adams Pece method and the matrix inversion routine was replaced with a pseudo inverse routine. Calculations were run using both the original and modified programs. Comparison of the calculations showed that the original Runge-Kutta routine could not detect singularity near the throat and was integrating across it. The modified version was able to detect the singularity and therefore gave more valid calculations.

Renormalized asymptotic enumeration of Feynman diagrams

NASA Astrophysics Data System (ADS)

Borinsky, Michael

2017-10-01

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

Maslov indices, Poisson brackets, and singular differential forms

NASA Astrophysics Data System (ADS)

Esterlis, I.; Haggard, H. M.; Hedeman, A.; Littlejohn, R. G.

2014-06-01

Maslov indices are integers that appear in semiclassical wave functions and quantization conditions. They are often notoriously difficult to compute. We present methods of computing the Maslov index that rely only on typically elementary Poisson brackets and simple linear algebra. We also present a singular differential form, whose integral along a curve gives the Maslov index of that curve. The form is closed but not exact, and transforms by an exact differential under canonical transformations. We illustrate the method with the 6j-symbol, which is important in angular-momentum theory and in quantum gravity.

A fast collocation method for a variable-coefficient nonlocal diffusion model

NASA Astrophysics Data System (ADS)

Wang, Che; Wang, Hong

2017-02-01

We develop a fast collocation scheme for a variable-coefficient nonlocal diffusion model, for which a numerical discretization would yield a dense stiffness matrix. The development of the fast method is achieved by carefully handling the variable coefficients appearing inside the singular integral operator and exploiting the structure of the dense stiffness matrix. The resulting fast method reduces the computational work from O (N3) required by a commonly used direct solver to O (Nlog ⁡ N) per iteration and the memory requirement from O (N2) to O (N). Furthermore, the fast method reduces the computational work of assembling the stiffness matrix from O (N2) to O (N). Numerical results are presented to show the utility of the fast method.

3D Higher Order Modeling in the BEM/FEM Hybrid Formulation

NASA Technical Reports Server (NTRS)

Fink, P. W.; Wilton, D. R.

2000-01-01

Higher order divergence- and curl-conforming bases have been shown to provide significant benefits, in both convergence rate and accuracy, in the 2D hybrid finite element/boundary element formulation (P. Fink and D. Wilton, National Radio Science Meeting, Boulder, CO, Jan. 2000). A critical issue in achieving the potential for accuracy of the approach is the accurate evaluation of all matrix elements. These involve products of high order polynomials and, in some instances, singular Green's functions. In the 2D formulation, the use of a generalized Gaussian quadrature method was found to greatly facilitate the computation and to improve the accuracy of the boundary integral equation self-terms. In this paper, a 3D, hybrid electric field formulation employing higher order bases and higher order elements is presented. The improvements in convergence rate and accuracy, compared to those resulting from lower order modeling, are established. Techniques developed to facilitate the computation of the boundary integral self-terms are also shown to improve the accuracy of these terms. Finally, simple preconditioning techniques are used in conjunction with iterative solution procedures to solve the resulting linear system efficiently. In order to handle the boundary integral singularities in the 3D formulation, the parent element- either a triangle or rectangle-is subdivided into a set of sub-triangles with a common vertex at the singularity. The contribution to the integral from each of the sub-triangles is computed using the Duffy transformation to remove the singularity. This method is shown to greatly facilitate t'pe self-term computation when the bases are of higher order. In addition, the sub-triangles can be further divided to achieve near arbitrary accuracy in the self-term computation. An efficient method for subdividing the parent element is presented. The accuracy obtained using higher order bases is compared to that obtained using lower order bases when the number of unknowns is approximately equal. Also, convergence rates obtained using higher order bases are compared to those obtained with lower order bases for selected sample

Normal forms for Hopf-Zero singularities with nonconservative nonlinear part

NASA Astrophysics Data System (ADS)

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

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

Plates and shells containing a surface crack under general loading conditions

NASA Technical Reports Server (NTRS)

Joseph, Paul F.; Erdogan, Fazil

1986-01-01

The severity of the underlying assumptions of the line-spring model (LSM) are such that verification with three-dimensional solutions is necessary. Such comparisons show that the model is quite accurate, and therefore, its use in extensive parameter studies is justified. Investigations into the endpoint behavior of the line-spring model have led to important conclusions about the ability of the model to predict stresses in front of the crack tip. An important application of the LSM was to solve the contact plate bending problem. Here the flexibility of the model to allow for any crack shape is exploited. The use of displacement quantities as unknowns in the formulation of the problem leads to strongly singular integral equations, rather than singular integral equations which result from using displacement derivatives. The collocation method of solving the integral equations was found to be better and more convenient than the quadrature technique. Orthogonal polynomials should be used as fitting functions when using the LSM as opposed to simpler functions such as power series.

Implementation of equivalent domain integral method in the two-dimensional analysis of mixed mode problems

NASA Technical Reports Server (NTRS)

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

1989-01-01

An equivalent domain integral (EDI) method for calculating J-intergrals for two-dimensional cracked elastic bodies is presented. The details of the method and its implementation are presented for isoparametric elements. The total and product integrals consist of the sum of an area of domain integral and line integrals on the crack faces. The line integrals vanish only when the crack faces are traction free and the loading is either pure mode 1 or pure mode 2 or a combination of both with only the square-root singular term in the stress field. The EDI method gave accurate values of the J-integrals for two mode I and two mixed mode problems. Numerical studies showed that domains consisting of one layer of elements are sufficient to obtain accurate J-integral values. Two procedures for separating the individual modes from the domain integrals are presented. The procedure that uses the symmetric and antisymmetric components of the stress and displacement fields to calculate the individual modes gave accurate values of the integrals for all problems analyzed. The EDI method when applied to a problem of an interface crack in two different materials showed that the mode 1 and mode 2 components are domain dependent while the total integral is not. This behavior is caused by the presence of the oscillatory part of the singularity in bimaterial crack problems. The EDI method, thus, shows behavior similar to the virtual crack closure method for bimaterial problems.

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

NASA Astrophysics Data System (ADS)

Vieira Martins, R.

1999-05-01

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

Comninou contact zones for a crack parallel to an interface

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

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

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

Integrability in conformally coupled gravity: Taub-NUT spacetimes and rotating black holes

NASA Astrophysics Data System (ADS)

Bardoux, Yannis; Caldarelli, Marco M.; Charmousis, Christos

2014-05-01

We consider four dimensional stationary and axially symmetric spacetimes for conformally coupled scalar-tensor theories. We show that, in analogy to the Lewis-Papapetrou problem in General Relativity (GR), the theory at hand can be recast in an analogous integrable form. We give the relevant rod formalism, introduced by Weyl for vacuum GR, explicitly giving the rod structure of the black hole of Bocharova et al. and Bekenstein (BBMB), in complete analogy to the Schwarzschild solution. The additional scalar field is shown to play the role of an extra Weyl potential. We then employ the Ernst method as a concrete solution generating example to obtain the Taub-NUT version of the BBMB hairy black hole. The solution is easily extended to include a cosmological constant. We show that the anti-de Sitter hyperbolic version of this solution is free of closed timelike curves that plague usual Taub-NUT metrics, and thus consists of a rotating, asymptotically locally anti-de Sitter black hole. This stationary solution has no curvature singularities whatsoever in the conformal frame, and the NUT charge is shown here to regularize the central curvature singularity of the corresponding static black hole. Given our findings we discuss the anti-de Sitter hyperbolic version of Taub-NUT in four dimensions, and show that the curvature singularity of the NUT-less solution is now replaced by a neighbouring chronological singularity screened by horizons. We argue that the properties of this rotating black hole are very similar to those of the rotating BTZ black hole in three dimensions.

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

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

Kalay, Berfin; Demiralp, Metin

2015-03-10

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

Reliable and efficient a posteriori error estimation for adaptive IGA boundary element methods for weakly-singular integral equations

PubMed Central

Feischl, Michael; Gantner, Gregor; Praetorius, Dirk

2015-01-01

We consider the Galerkin boundary element method (BEM) for weakly-singular integral equations of the first-kind in 2D. We analyze some residual-type a posteriori error estimator which provides a lower as well as an upper bound for the unknown Galerkin BEM error. The required assumptions are weak and allow for piecewise smooth parametrizations of the boundary, local mesh-refinement, and related standard piecewise polynomials as well as NURBS. In particular, our analysis gives a first contribution to adaptive BEM in the frame of isogeometric analysis (IGABEM), for which we formulate an adaptive algorithm which steers the local mesh-refinement and the multiplicity of the knots. Numerical experiments underline the theoretical findings and show that the proposed adaptive strategy leads to optimal convergence. PMID:26085698

Solution of Grad-Shafranov equation by the method of fundamental solutions

NASA Astrophysics Data System (ADS)

Nath, D.; Kalra, M. S.; Kalra

2014-06-01

In this paper we have used the Method of Fundamental Solutions (MFS) to solve the Grad-Shafranov (GS) equation for the axisymmetric equilibria of tokamak plasmas with monomial sources. These monomials are the individual terms appearing on the right-hand side of the GS equation if one expands the nonlinear terms into polynomials. Unlike the Boundary Element Method (BEM), the MFS does not involve any singular integrals and is a meshless boundary-alone method. Its basic idea is to create a fictitious boundary around the actual physical boundary of the computational domain. This automatically removes the involvement of singular integrals. The results obtained by the MFS match well with the earlier results obtained using the BEM. The method is also applied to Solov'ev profiles and it is found that the results are in good agreement with analytical results.

Wavelets on the Group SO(3) and the Sphere S3

NASA Astrophysics Data System (ADS)

Bernstein, Swanhild

2007-09-01

The construction of wavelets relies on translations and dilations which are perfectly given in R. On the sphere translations can be considered as rotations but it difficult to say what are dilations. For the 2-dimensional sphere there exist two different approaches to obtain wavelets which are worth to be considered. The first concept goes back to Freeden and collaborators [2] which defines wavelets by means of kernels of spherical singular integrals. The other concept developed by Antoine and Vandergheynst and coworkers [3] is a purely group theoretical approach and defines dilations as dilations in the tangent plane. Surprisingly both concepts coincides for zonal functions. We will define wavelets on the 3-dimensional sphere by means of kernels of singular integrals and demonstrate that wavelets constructed by Antoine and Vandergheynst for zonal functions meet our definition.

Purely Singular Continuous Spectrum for CMV Operators Generated by Subshifts

NASA Astrophysics Data System (ADS)

Ong, Darren C.

2014-03-01

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

Smart built-in test

NASA Technical Reports Server (NTRS)

Richards, Dale W.

1990-01-01

The work which built-in test (BIT) is asked to perform in today's electronic systems increases with every insertion of new technology or introduction of tighter performance criteria. Yet the basic purpose remains unchanged -- to determine with high confidence the operational capability of that equipment. Achievement of this level of BIT performance requires the management and assimilation of a large amount of data, both realtime and historical. Smart BIT has taken advantage of advanced techniques from the field of artificial intelligence (AI) in order to meet these demands. The Smart BIT approach enhances traditional functional BIT by utilizing AI techniques to incorporate environmental stress data, temporal BIT information and maintenance data, and realtime BIT reports into an integrated test methodology for increased BIT effectiveness and confidence levels. Future research in this area will incorporate onboard fault-logging of BIT output, stress data and Smart BIT decision criteria in support of a singular, integrated and complete test and maintenance capability. The state of this research is described along with a discussion of directions for future development.

Smart built-in test

NASA Astrophysics Data System (ADS)

Richards, Dale W.

1990-03-01

The work which built-in test (BIT) is asked to perform in today's electronic systems increases with every insertion of new technology or introduction of tighter performance criteria. Yet the basic purpose remains unchanged -- to determine with high confidence the operational capability of that equipment. Achievement of this level of BIT performance requires the management and assimilation of a large amount of data, both realtime and historical. Smart BIT has taken advantage of advanced techniques from the field of artificial intelligence (AI) in order to meet these demands. The Smart BIT approach enhances traditional functional BIT by utilizing AI techniques to incorporate environmental stress data, temporal BIT information and maintenance data, and realtime BIT reports into an integrated test methodology for increased BIT effectiveness and confidence levels. Future research in this area will incorporate onboard fault-logging of BIT output, stress data and Smart BIT decision criteria in support of a singular, integrated and complete test and maintenance capability. The state of this research is described along with a discussion of directions for future development.

Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications

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

Du, Qiang, E-mail: jyanghkbu@gmail.com; Yang, Jiang, E-mail: qd2125@columbia.edu

This work is concerned with the Fourier spectral approximation of various integral differential equations associated with some linear nonlocal diffusion and peridynamic operators under periodic boundary conditions. For radially symmetric kernels, the nonlocal operators under consideration are diagonalizable in the Fourier space so that the main computational challenge is on the accurate and fast evaluation of their eigenvalues or Fourier symbols consisting of possibly singular and highly oscillatory integrals. For a large class of fractional power-like kernels, we propose a new approach based on reformulating the Fourier symbols both as coefficients of a series expansion and solutions of some simplemore » ODE models. We then propose a hybrid algorithm that utilizes both truncated series expansions and high order Runge–Kutta ODE solvers to provide fast evaluation of Fourier symbols in both one and higher dimensional spaces. It is shown that this hybrid algorithm is robust, efficient and accurate. As applications, we combine this hybrid spectral discretization in the spatial variables and the fourth-order exponential time differencing Runge–Kutta for temporal discretization to offer high order approximations of some nonlocal gradient dynamics including nonlocal Allen–Cahn equations, nonlocal Cahn–Hilliard equations, and nonlocal phase-field crystal models. Numerical results show the accuracy and effectiveness of the fully discrete scheme and illustrate some interesting phenomena associated with the nonlocal models.« less

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.

Van Hove singularities in the paramagnetic phase of the Hubbard model: DMFT study

NASA Astrophysics Data System (ADS)

Žitko, Rok; Bonča, Janez; Pruschke, Thomas

2009-12-01

Using the dynamical mean-field theory (DMFT) with the numerical renormalization-group impurity solver we study the paramagnetic phase of the Hubbard model with the density of states (DOS) corresponding to the three-dimensional (3D) cubic lattice and the two-dimensional (2D) square lattice, as well as a DOS with inverse square-root singularity. We show that the electron correlations rapidly smooth out the square-root van Hove singularities (kinks) in the spectral function for the 3D lattice and that the Mott metal-insulator transition (MIT) as well as the magnetic-field-induced MIT differ only little from the well-known results for the Bethe lattice. The consequences of the logarithmic singularity in the DOS for the 2D lattice are more dramatic. At half filling, the divergence pinned at the Fermi level is not washed out, only its integrated weight decreases as the interaction is increased. While the Mott transition is still of the usual kind, the magnetic-field-induced MIT falls into a different universality class as there is no field-induced localization of quasiparticles. In the case of a power-law singularity in the DOS at the Fermi level, the power-law singularity persists in the presence of interaction, albeit with a different exponent, and the effective impurity model in the DMFT turns out to be a pseudogap Anderson impurity model with a hybridization function which vanishes at the Fermi level. The system is then a generalized Fermi liquid. At finite doping, regular Fermi-liquid behavior is recovered.

Unitary Operators on the Document Space.

ERIC Educational Resources Information Center

Hoenkamp, Eduard

2003-01-01

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

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

NASA Technical Reports Server (NTRS)

Bossel, H. H.

1972-01-01

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

Non-free gas of dipoles of non-singular screw dislocations and the shear modulus near the melting

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

Malyshev, Cyril, E-mail: malyshev@pdmi.ras.ru

2014-12-15

The behavior of the shear modulus caused by proliferation of dipoles of non-singular screw dislocations with finite-sized core is considered. The representation of two-dimensional Coulomb gas with smoothed-out coupling is used, and the stress–stress correlation function is calculated. A convolution integral expressed in terms of the modified Bessel function K{sub 0} is derived in order to obtain the shear modulus in approximation of interacting dipoles. Implications are demonstrated for the shear modulus near the melting transition which are due to the singularityless character of the dislocations. - Highlights: • Thermodynamics of dipoles of non-singular screw dislocations is studied below themore » melting. • The renormalization of the shear modulus is obtained for interacting dipoles. • Dependence of the shear modulus on the system scales is presented near the melting.« less

Accurate ω-ψ Spectral Solution of the Singular Driven Cavity Problem

NASA Astrophysics Data System (ADS)

Auteri, F.; Quartapelle, L.; Vigevano, L.

2002-08-01

This article provides accurate spectral solutions of the driven cavity problem, calculated in the vorticity-stream function representation without smoothing the corner singularities—a prima facie impossible task. As in a recent benchmark spectral calculation by primitive variables of Botella and Peyret, closed-form contributions of the singular solution for both zero and finite Reynolds numbers are subtracted from the unknown of the problem tackled here numerically in biharmonic form. The method employed is based on a split approach to the vorticity and stream function equations, a Galerkin-Legendre approximation of the problem for the perturbation, and an evaluation of the nonlinear terms by Gauss-Legendre numerical integration. Results computed for Re=0, 100, and 1000 compare well with the benchmark steady solutions provided by the aforementioned collocation-Chebyshev projection method. The validity of the proposed singularity subtraction scheme for computing time-dependent solutions is also established.

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.

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.

Low-thrust trajectory analysis for the geosynchronous mission

NASA Technical Reports Server (NTRS)

Jasper, T. P.

1973-01-01

Methodology employed in development of a computer program designed to analyze optimal low-thrust trajectories is described, and application of the program to a Solar Electric Propulsion Stage (SEPS) geosynchronous mission is discussed. To avoid the zero inclination and eccentricity singularities which plague many small-force perturbation techniques, a special set of state variables (equinoctial) is used. Adjoint equations are derived for the minimum time problem and are also free from the singularities. Solutions to the state and adjoint equations are obtained by both orbit averaging and precision numerical integration; an evaluation of these approaches is made.

Fingering patterns in Hele-Shaw flows are density shock wave solutions of dispersionless KdV hierarchy

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

Teodorescu, Razvan; Lee, S - Y; Wiegmann, P

We investigate the hydrodynamics of a Hele-Shaw flow as the free boundary evolves from smooth initial conditions into a generic cusp singularity (of local geometry type x{sup 3} {approx} y{sup 2}), and then into a density shock wave. This novel solution preserves the integrability of the dynamics and, unlike all the weak solutions proposed previously, is not underdetermined. The evolution of the shock is such that the net vorticity remains zero, as before the critical time, and the shock can be interpreted as a singular line distribution of fluid deficit.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1974-01-01

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

Contact and crack problems for an elastic wedge. [stress concentration in elastic half spaces

NASA Technical Reports Server (NTRS)

Erdogan, F.; Gupta, G. D.

1974-01-01

The contact and the crack problems for an elastic wedge of arbitrary angle are considered. The problem is reduced to a singular integral equation which, in the general case, may have a generalized Cauchy kernel. The singularities under the stamp as well as at the wedge apex were studied, and the relevant stress intensity factors are defined. The problem was solved for various wedge geometries and loading conditions. The results may be applicable to certain foundation problems and to crack problems in symmetrically loaded wedges in which cracks initiate from the apex.

Fracture and contact problems for an elastic wedge

NASA Technical Reports Server (NTRS)

Erdogan, F.; Arin, K.

1976-01-01

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

Diffraction of Nondiverging Bessel Beams by Fork-Shaped and Rectilinear Grating

NASA Astrophysics Data System (ADS)

Janicijevic, Ljiljana; Topuzoski, Suzana

2007-04-01

We present an investigation about Fresnel diffraction of Bessel beams, propagating as nondiverging within a distance Ln, with or without phase singularities, by rectilinear and fork-shaped gratings. The common general transmission function of these gratings is defined and specialized for three different cases: binary amplitude gratings, amplitude holograms and their phase versions. Solving the Fresnel diffraction integral in cylindrical coordinates, we obtain analytical expressions for the diffracted wave amplitude for all types of proposed gratings, and make conclusions about the existence of phase singularities and corresponding topological charges in the created by the gratings beams of different diffraction orders.

Algorithms for computing the geopotential using a simple density layer

NASA Technical Reports Server (NTRS)

Morrison, F.

1976-01-01

Several algorithms have been developed for computing the potential and attraction of a simple density layer. These are numerical cubature, Taylor series, and a mixed analytic and numerical integration using a singularity-matching technique. A computer program has been written to combine these techniques for computing the disturbing acceleration on an artificial earth satellite. A total of 1640 equal-area, constant surface density blocks on an oblate spheroid are used. The singularity-matching algorithm is used in the subsatellite region, Taylor series in the surrounding zone, and numerical cubature on the rest of the earth.

Integrable discrete PT symmetric model.

PubMed

Ablowitz, Mark J; Musslimani, Ziad H

2014-09-01

An exactly solvable discrete PT invariant nonlinear Schrödinger-like model is introduced. It is an integrable Hamiltonian system that exhibits a nontrivial nonlinear PT symmetry. A discrete one-soliton solution is constructed using a left-right Riemann-Hilbert formulation. It is shown that this pure soliton exhibits unique features such as power oscillations and singularity formation. The proposed model can be viewed as a discretization of a recently obtained integrable nonlocal nonlinear Schrödinger equation.

Spontaneous emission in the presence of a realistically sized cylindrical waveguide

NASA Astrophysics Data System (ADS)

Dung, Ho Trung

2016-02-01

Various quantities characterizing the spontaneous emission process of a dipole emitter including the emission rate and the emission pattern can be expressed in terms of the Green tensor of the surrounding environment. By expanding the Green tensor around some analytically known background one as a Born series, and truncating it under appropriate conditions, complicated boundaries can be tackled with ease. However, when the emitter is embedded in the medium, even the calculation of the first-order term in the Born series is problematic because of the presence of a singularity. We show how to eliminate this singularity for a medium of arbitrary size and shape by expanding around the bulk medium rather than vacuum. In the highly symmetric configuration of an emitter located on the axis of a realistically sized cylinder, it is shown that the singularity can be removed by changing the integral variables and then the order of integration. Using both methods, we investigate the spontaneous emission rate of an initially excited two-level dipole emitter, embedded in a realistically sized cylinder, which can be a common optical fiber in the long-length limit and a disk in the short-length limit. The spatial distribution of the emitted light is calculated using the Born-expansion approach, and local-field corrections to the spontaneous emission rate are briefly discussed.

Information hiding techniques for infrared images: exploring the state-of-the art and challenges

NASA Astrophysics Data System (ADS)

Pomponiu, Victor; Cavagnino, Davide; Botta, Marco; Nejati, Hossein

2015-10-01

The proliferation of Infrared technology and imaging systems enables a different perspective to tackle many computer vision problems in defense and security applications. Infrared images are widely used by the law enforcement, Homeland Security and military organizations to achieve a significant advantage or situational awareness, and thus is vital to protect these data against malicious attacks. Concurrently, sophisticated malware are developed which are able to disrupt the security and integrity of these digital media. For instance, illegal distribution and manipulation are possible malicious attacks to the digital objects. In this paper we explore the use of a new layer of defense for the integrity of the infrared images through the aid of information hiding techniques such as watermarking. In this context, we analyze the efficiency of several optimal decoding schemes for the watermark inserted into the Singular Value Decomposition (SVD) domain of the IR images using an additive spread spectrum (SS) embedding framework. In order to use the singular values (SVs) of the IR images with the SS embedding we adopt several restrictions that ensure that the values of the SVs will maintain their statistics. For both the optimal maximum likelihood decoder and sub-optimal decoders we assume that the PDF of SVs can be modeled by the Weibull distribution. Furthermore, we investigate the challenges involved in protecting and assuring the integrity of IR images such as data complexity and the error probability behavior, i.e., the probability of detection and the probability of false detection, for the applied optimal decoders. By taking into account the efficiency and the necessary auxiliary information for decoding the watermark, we discuss the suitable decoder for various operating situations. Experimental results are carried out on a large dataset of IR images to show the imperceptibility and efficiency of the proposed scheme against various attack scenarios.

Conical twist fields and null polygonal Wilson loops

NASA Astrophysics Data System (ADS)

Castro-Alvaredo, Olalla A.; Doyon, Benjamin; Fioravanti, Davide

2018-06-01

Using an extension of the concept of twist field in QFT to space-time (external) symmetries, we study conical twist fields in two-dimensional integrable QFT. These create conical singularities of arbitrary excess angle. We show that, upon appropriate identification between the excess angle and the number of sheets, they have the same conformal dimension as branch-point twist fields commonly used to represent partition functions on Riemann surfaces, and that both fields have closely related form factors. However, we show that conical twist fields are truly different from branch-point twist fields. They generate different operator product expansions (short distance expansions) and form factor expansions (large distance expansions). In fact, we verify in free field theories, by re-summing form factors, that the conical twist fields operator product expansions are correctly reproduced. We propose that conical twist fields are the correct fields in order to understand null polygonal Wilson loops/gluon scattering amplitudes of planar maximally supersymmetric Yang-Mills theory.

Exact finite volume expectation values of local operators in excited states

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

"Listen to the Voice of Reason": The "New Orleans Tribune" as Advocate for Public, Integrated Education

ERIC Educational Resources Information Center

Melancon, Kristi Richard; Hendry, Petra Munro

2015-01-01

The "New Orleans Tribune" (1864-1870), the first black daily newspaper in the United States, was the singular text in the public South at its time to staunchly advocate for public, integrated education, anticipating the ruling of "Brown v. Board of Education," and arguing that separate education would always be synonymous with…

Applicability of integrated cell culture reverse transcriptase quantitative PCR (ICC-RTqPCR) for the simultaneous detection of the four human enteric enterovirus species in disinfection studies

EPA Science Inventory

A newly developed integrated cell culture reverse transcriptase quantitative PCR (ICC-RTqPCR) method and its applicability in UV disinfection studies is described. This method utilizes a singular cell culture system coupled with four RTqPCR assays to detect infectious serotypes t...

Formation of Singularities for a Conservation Law with Memory.

DTIC Science & Technology

1983-04-01

respectively. Intetchanging the order of integration in the double integrals in (4.4) yields -10- I.I.... ..... , t su8 (0 + 011(011 ft JI) + SCOW)d + 64...molten polymers , meology 2 ory and pp lioatioona, 5 (1969), 57-92. Ovwi..’ " Is UsmIUTY CLANKFCATWN @’ TunS PA.. 010f bo~W _____________ WORT 0OOIM ATMO

Analytical and numerical solutions for heat transfer and effective thermal conductivity of cracked media

NASA Astrophysics Data System (ADS)

Tran, A. B.; Vu, M. N.; Nguyen, S. T.; Dong, T. Q.; Le-Nguyen, K.

2018-02-01

This paper presents analytical solutions to heat transfer problems around a crack and derive an adaptive model for effective thermal conductivity of cracked materials based on singular integral equation approach. Potential solution of heat diffusion through two-dimensional cracked media, where crack filled by air behaves as insulator to heat flow, is obtained in a singular integral equation form. It is demonstrated that the temperature field can be described as a function of temperature and rate of heat flow on the boundary and the temperature jump across the cracks. Numerical resolution of this boundary integral equation allows determining heat conduction and effective thermal conductivity of cracked media. Moreover, writing this boundary integral equation for an infinite medium embedding a single crack under a far-field condition allows deriving the closed-form solution of temperature discontinuity on the crack and particularly the closed-form solution of temperature field around the crack. These formulas are then used to establish analytical effective medium estimates. Finally, the comparison between the developed numerical and analytical solutions allows developing an adaptive model for effective thermal conductivity of cracked media. This model takes into account both the interaction between cracks and the percolation threshold.

A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation method.

PubMed

Chen, I L; Chen, J T; Kuo, S R; Liang, M T

2001-03-01

Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.

Integrated tools for control-system analysis

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

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.

Rotation forms and local Hamiltonian monodromy

NASA Astrophysics Data System (ADS)

Efstathiou, K.; Giacobbe, A.; Mardešić, P.; Sugny, D.

2017-02-01

The monodromy of torus bundles associated with completely integrable systems can be computed using geometric techniques (constructing homology cycles) or analytic arguments (computing discontinuities of abelian integrals). In this article, we give a general approach to the computation of monodromy that resembles the analytical one, reducing the problem to the computation of residues of polar 1-forms. We apply our technique to three celebrated examples of systems with monodromy (the champagne bottle, the spherical pendulum, the hydrogen atom) and to the case of non-degenerate focus-focus singularities, re-obtaining the classical results. An advantage of this approach is that the residue-like formula can be shown to be local in a neighborhood of a singularity, hence allowing the definition of monodromy also in the case of non-compact fibers. This idea has been introduced in the literature under the name of scattering monodromy. We prove the coincidence of the two definitions with the monodromy of an appropriately chosen compactification.

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

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

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

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

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

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

27 CFR 447.11 - Meaning of terms.

Code of Federal Regulations, 2012 CFR

2012-04-01

... singular, and vice versa, and words imparting the masculine gender shall include the feminine. The terms..., operation, overhaul, repair, maintenance, modification, or reconstruction of defense articles, whether in...

27 CFR 447.11 - Meaning of terms.

Code of Federal Regulations, 2010 CFR

2010-04-01

... singular, and vice versa, and words imparting the masculine gender shall include the feminine. The terms..., operation, overhaul, repair, maintenance, modification, or reconstruction of defense articles, whether in...

27 CFR 447.11 - Meaning of terms.

Code of Federal Regulations, 2014 CFR

2014-04-01

... singular, and vice versa, and words imparting the masculine gender shall include the feminine. The terms..., operation, overhaul, repair, maintenance, modification, or reconstruction of defense articles, whether in...

27 CFR 447.11 - Meaning of terms.

Code of Federal Regulations, 2013 CFR

2013-04-01

... singular, and vice versa, and words imparting the masculine gender shall include the feminine. The terms..., operation, overhaul, repair, maintenance, modification, or reconstruction of defense articles, whether in...

27 CFR 447.11 - Meaning of terms.

Code of Federal Regulations, 2011 CFR

2011-04-01

... singular, and vice versa, and words imparting the masculine gender shall include the feminine. The terms..., operation, overhaul, repair, maintenance, modification, or reconstruction of defense articles, whether in...

Conditional symmetries in axisymmetric quantum cosmologies with scalar fields and the fate of the classical singularities

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

Zampeli, Adamantia; Pailas, Theodoros; Terzis, Petros A.

2016-05-01

In this paper, the classical and quantum solutions of some axisymmetric cosmologies coupled to a massless scalar field are studied in the context of minisuperspace approximation. In these models, the singular nature of the Lagrangians entails a search for possible conditional symmetries. These have been proven to be the simultaneous conformal symmetries of the supermetric and the superpotential. The quantization is performed by adopting the Dirac proposal for constrained systems, i.e. promoting the first-class constraints to operators annihilating the wave function. To further enrich the approach, we follow [1] and impose the operators related to the classical conditional symmetries onmore » the wave function. These additional equations select particular solutions of the Wheeler-DeWitt equation. In order to gain some physical insight from the quantization of these cosmological systems, we perform a semiclassical analysis following the Bohmian approach to quantum theory. The generic result is that, in all but one model, one can find appropriate ranges of the parameters, so that the emerging semiclassical geometries are non-singular. An attempt for physical interpretation involves the study of the effective energy-momentum tensor which corresponds to an imperfect fluid.« less

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

NASA Astrophysics Data System (ADS)

Chen, Guoxiong; Cheng, Qiuming

2016-02-01

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

An extension of the QZ algorithm for solving the generalized matrix eigenvalue problem

NASA Technical Reports Server (NTRS)

Ward, R. C.

1973-01-01

This algorithm is an extension of Moler and Stewart's QZ algorithm with some added features for saving time and operations. Also, some additional properties of the QR algorithm which were not practical to implement in the QZ algorithm can be generalized with the combination shift QZ algorithm. Numerous test cases are presented to give practical application tests for algorithm. Based on results, this algorithm should be preferred over existing algorithms which attempt to solve the class of generalized eigenproblems where both matrices are singular or nearly singular.

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

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

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

1993-08-01

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

An Integrated Theory of Everything (TOE)

NASA Astrophysics Data System (ADS)

Colella, Antonio

2014-03-01

An Integrated TOE unifies all known physical phenomena from the Planck cube to the Super Universe (multiverse). Each matter/force particle is represented by a Planck cube string. Any Super Universe object is a volume of contiguous Planck cubes. Super force Planck cube string singularities existed at the start of all universes. An Integrated TOE foundations are twenty independent existing theories and without sacrificing their integrities, are replaced by twenty interrelated amplified theories. Amplifications of Higgs force theory are key to an Integrated TOE and include: 64 supersymmetric Higgs particles; super force condensations to 17 matter particles/associated Higgs forces; spontaneous symmetry breaking is bidirectional; and the sum of 8 permanent Higgs force energies is dark energy. Stellar black hole theory was amplified to include a quark star (matter) with mass, volume, near zero temperature, and maximum entropy. A black hole (energy) has energy, minimal volume (singularity), near infinite temperature, and minimum entropy. Our precursor universe's super supermassive quark star (matter) evaporated to a super supermassive black hole (energy). This transferred total conserved energy/mass and transformed entropy from maximum to minimum. Integrated Theory of Everything Book Video: https://www.youtube.com/watch?v=4a1c9IvdoGY Research Article Video: http://www.youtube.com/watch?v=CD-QoLeVbSY Research Article: http://toncolella.files.wordpress.com/2012/07/m080112.pdf.

A highly accurate boundary integral equation method for surfactant-laden drops in 3D

NASA Astrophysics Data System (ADS)

Sorgentone, Chiara; Tornberg, Anna-Karin

2018-05-01

The presence of surfactants alters the dynamics of viscous drops immersed in an ambient viscous fluid. This is specifically true at small scales, such as in applications of droplet based microfluidics, where the interface dynamics become of increased importance. At such small scales, viscous forces dominate and inertial effects are often negligible. Considering Stokes flow, a numerical method based on a boundary integral formulation is presented for simulating 3D drops covered by an insoluble surfactant. The method is able to simulate drops with different viscosities and close interactions, automatically controlling the time step size and maintaining high accuracy also when substantial drop deformation appears. To achieve this, the drop surfaces as well as the surfactant concentration on each surface are represented by spherical harmonics expansions. A novel reparameterization method is introduced to ensure a high-quality representation of the drops also under deformation, specialized quadrature methods for singular and nearly singular integrals that appear in the formulation are evoked and the adaptive time stepping scheme for the coupled drop and surfactant evolution is designed with a preconditioned implicit treatment of the surfactant diffusion.

Multi-domain boundary element method for axi-symmetric layered linear acoustic systems

NASA Astrophysics Data System (ADS)

Reiter, Paul; Ziegelwanger, Harald

2017-12-01

Homogeneous porous materials like rock wool or synthetic foam are the main tool for acoustic absorption. The conventional absorbing structure for sound-proofing consists of one or multiple absorbers placed in front of a rigid wall, with or without air-gaps in between. Various models exist to describe these so called multi-layered acoustic systems mathematically for incoming plane waves. However, there is no efficient method to calculate the sound field in a half space above a multi layered acoustic system for an incoming spherical wave. In this work, an axi-symmetric multi-domain boundary element method (BEM) for absorbing multi layered acoustic systems and incoming spherical waves is introduced. In the proposed BEM formulation, a complex wave number is used to model absorbing materials as a fluid and a coordinate transformation is introduced which simplifies singular integrals of the conventional BEM to non-singular radial and angular integrals. The radial and angular part are integrated analytically and numerically, respectively. The output of the method can be interpreted as a numerical half space Green's function for grounds consisting of layered materials.

The Riemann-Hilbert problem for nonsymmetric systems

NASA Astrophysics Data System (ADS)

Greenberg, W.; Zweifel, P. F.; Paveri-Fontana, S.

1991-12-01

A comparison of the Riemann-Hilbert problem and the Wiener-Hopf factorization problem arising in the solution of half-space singular integral equations is presented. Emphasis is on the factorization of functions lacking the reflection symmetry usual in transport theory.

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.

Topics in Bethe Ansatz

NASA Astrophysics Data System (ADS)

Wang, Chunguang

Integrable quantum spin chains have close connections to integrable quantum field. theories, modern condensed matter physics, string and Yang-Mills theories. Bethe. ansatz is one of the most important approaches for solving quantum integrable spin. chains. At the heart of the algebraic structure of integrable quantum spin chains is. the quantum Yang-Baxter equation and the boundary Yang-Baxter equation. This. thesis focuses on four topics in Bethe ansatz. The Bethe equations for the isotropic periodic spin-1/2 Heisenberg chain with N. sites have solutions containing ±i/2 that are singular: both the corresponding energy and the algebraic Bethe ansatz vector are divergent. Such solutions must be carefully regularized. We consider a regularization involving a parameter that can be. determined using a generalization of the Bethe equations. These generalized Bethe. equations provide a practical way of determining which singular solutions correspond. to eigenvectors of the model. The Bethe equations for the periodic XXX and XXZ spin chains admit singular. solutions, for which the corresponding eigenvalues and eigenvectors are ill-defined. We use a twist regularization to derive conditions for such singular solutions to bephysical, in which case they correspond to genuine eigenvalues and eigenvectors of. the Hamiltonian. We analyze the ground state of the open spin-1/2 isotropic quantum spin chain. with a non-diagonal boundary term using a recently proposed Bethe ansatz solution. As the coefficient of the non-diagonal boundary term tends to zero, the Bethe roots. split evenly into two sets: those that remain finite, and those that become infinite. We. argue that the former satisfy conventional Bethe equations, while the latter satisfy a. generalization of the Richardson-Gaudin equations. We derive an expression for the. leading correction to the boundary energy in terms of the boundary parameters. We argue that the Hamiltonians for A(2) 2n open quantum spin chains corresponding. to two choices of integrable boundary conditions have the symmetries Uq(Bn) and. Uq(Cn), respectively. The deformation of Cn is novel, with a nonstandard coproduct. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of. each type. With the help of this formula, we verify numerically (for a generic value of. the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.

27 CFR 45.11 - Meaning of terms.

Code of Federal Regulations, 2010 CFR

2010-04-01

... the singular, and vice versa, and words indicating the masculine gender shall include the feminine... with respect to the operation of such warehouse. Package. The immediate container in which tobacco...

Integrated Multiscale Modeling of Molecular Computing Devices

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

Gregory Beylkin

2012-03-23

Significant advances were made on all objectives of the research program. We have developed fast multiresolution methods for performing electronic structure calculations with emphasis on constructing efficient representations of functions and operators. We extended our approach to problems of scattering in solids, i.e. constructing fast algorithms for computing above the Fermi energy level. Part of the work was done in collaboration with Robert Harrison and George Fann at ORNL. Specific results (in part supported by this grant) are listed here and are described in greater detail. (1) We have implemented a fast algorithm to apply the Green's function for themore » free space (oscillatory) Helmholtz kernel. The algorithm maintains its speed and accuracy when the kernel is applied to functions with singularities. (2) We have developed a fast algorithm for applying periodic and quasi-periodic, oscillatory Green's functions and those with boundary conditions on simple domains. Importantly, the algorithm maintains its speed and accuracy when applied to functions with singularities. (3) We have developed a fast algorithm for obtaining and applying multiresolution representations of periodic and quasi-periodic Green's functions and Green's functions with boundary conditions on simple domains. (4) We have implemented modifications to improve the speed of adaptive multiresolution algorithms for applying operators which are represented via a Gaussian expansion. (5) We have constructed new nearly optimal quadratures for the sphere that are invariant under the icosahedral rotation group. (6) We obtained new results on approximation of functions by exponential sums and/or rational functions, one of the key methods that allows us to construct separated representations for Green's functions. (7) We developed a new fast and accurate reduction algorithm for obtaining optimal approximation of functions by exponential sums and/or their rational representations.« less

Healthcare system resiliency: The case for taking disaster plans further - Part 2.

PubMed

Hiller, Michael; Bone, Eric A; Timmins, Michael L

2015-01-01

For the most part, top management is aware of the costs of healthcare downtime. They recognise that minimising downtime while fulfilling risk management standards, namely, 'duty of care' and 'standard of care', are among the most difficult challenges they face, especially when coupled with the increasing pressure for continued service availability with the frequency of incidents. Through continuous operational availability and greater resiliency demands a new, combined approach has emerged, which necessitates that the disciplines of: (1) enterprise risk management; (2) emergency response planning; (3) business continuity management including IT disaster recovery; (4) crisis communications be addressed with strategies and techniques designed and integrated into a singular, seamless approach. It is no longer feasible to separate these disciplines. By integrating them as the gateway for service continuity, the organisation can enhance its ability to run as a business by helping to identify risks and prepare for change, prioritise work efforts, flag problems and pinpoint important areas that underpin the overarching business continuity processes. The driver of change in staying ahead of the risk curve, and the entry point of a true resiliency strategy, begins with identifying the synergies of the aforementioned disciplines and integrating each of them to jointly contribute to service continuance.

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.

The Homotopic Probability Distribution and the Partition Function for the Entangled System Around a Ribbon Segment Chain

NASA Astrophysics Data System (ADS)

Qian, Shang-Wu; Gu, Zhi-Yu

2001-12-01

Using the Feynman's path integral with topological constraints arising from the presence of one singular line, we find the homotopic probability distribution P_L^n for the winding number n and the partition function P_L of the entangled system around a ribbon segment chain. We find that when the width of the ribbon segment chain 2a increases,the partition function exponentially decreases, whereas the free energy increases an amount, which is proportional to the square of the width. When the width tends to zero we obtain the same results as those of a single chain with one singular point.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Recent developments in rotary-wing aerodynamic theory

NASA Technical Reports Server (NTRS)

Johnson, W.

1986-01-01

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

27 CFR 45.11 - Meaning of terms.

Code of Federal Regulations, 2012 CFR

2012-04-01

... the singular, and vice versa, and words indicating the masculine gender shall include the feminine... warehouse with respect to the operation of such warehouse. Package. The immediate container in which tobacco...

27 CFR 45.11 - Meaning of terms.

Code of Federal Regulations, 2011 CFR

2011-04-01

... the singular, and vice versa, and words indicating the masculine gender shall include the feminine... warehouse with respect to the operation of such warehouse. Package. The immediate container in which tobacco...

27 CFR 45.11 - Meaning of terms.

Code of Federal Regulations, 2013 CFR

2013-04-01

... the singular, and vice versa, and words indicating the masculine gender shall include the feminine... warehouse with respect to the operation of such warehouse. Package. The immediate container in which tobacco...

27 CFR 45.11 - Meaning of terms.

Code of Federal Regulations, 2014 CFR

2014-04-01

... the singular, and vice versa, and words indicating the masculine gender shall include the feminine... warehouse with respect to the operation of such warehouse. Package. The immediate container in which tobacco...

$$ \\mathcal{N} $$ = 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

27 CFR 44.11 - Meaning of terms.

Code of Federal Regulations, 2013 CFR

2013-04-01

... singular, and vice versa, and words indicating the masculine gender shall include the feminine. The terms... warehouse with respect to the operation of such warehouse. Package. The immediate container in which tobacco...

27 CFR 44.11 - Meaning of terms.

Code of Federal Regulations, 2011 CFR

2011-04-01

... singular, and vice versa, and words indicating the masculine gender shall include the feminine. The terms... warehouse with respect to the operation of such warehouse. Package. The immediate container in which tobacco...

27 CFR 44.11 - Meaning of terms.

Code of Federal Regulations, 2012 CFR

2012-04-01

... singular, and vice versa, and words indicating the masculine gender shall include the feminine. The terms... warehouse with respect to the operation of such warehouse. Package. The immediate container in which tobacco...

Typical event horizons in AdS/CFT

NASA Astrophysics Data System (ADS)

Avery, Steven G.; Lowe, David A.

2016-01-01

We consider the construction of local bulk operators in a black hole background dual to a pure state in conformal field theory. The properties of these operators in a microcanonical ensemble are studied. It has been argued in the literature that typical states in such an ensemble contain firewalls, or otherwise singular horizons. We argue this conclusion can be avoided with a proper definition of the interior operators.

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

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

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

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

Selectively enhanced photocurrent generation in twisted bilayer graphene with van Hove singularity

PubMed Central

Yin, Jianbo; Wang, Huan; Peng, Han; Tan, Zhenjun; Liao, Lei; Lin, Li; Sun, Xiao; Koh, Ai Leen; Chen, Yulin; Peng, Hailin; Liu, Zhongfan

2016-01-01

Graphene with ultra-high carrier mobility and ultra-short photoresponse time has shown remarkable potential in ultrafast photodetection. However, the broad and weak optical absorption (∼2.3%) of monolayer graphene hinders its practical application in photodetectors with high responsivity and selectivity. Here we demonstrate that twisted bilayer graphene, a stack of two graphene monolayers with an interlayer twist angle, exhibits a strong light–matter interaction and selectively enhanced photocurrent generation. Such enhancement is attributed to the emergence of unique twist-angle-dependent van Hove singularities, which are directly revealed by spatially resolved angle-resolved photoemission spectroscopy. When the energy interval between the van Hove singularities of the conduction and valance bands matches the energy of incident photons, the photocurrent generated can be significantly enhanced (up to ∼80 times with the integration of plasmonic structures in our devices). These results provide valuable insight for designing graphene photodetectors with enhanced sensitivity for variable wavelength. PMID:26948537

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.

Fuel optimal maneuvers for spacecraft with fixed thrusters

NASA Technical Reports Server (NTRS)

Carter, T. C.

1982-01-01

Several mathematical models, including a minimum integral square criterion problem, were used for the qualitative investigation of fuel optimal maneuvers for spacecraft with fixed thrusters. The solutions consist of intervals of "full thrust" and "coast" indicating that thrusters do not need to be designed as "throttleable" for fuel optimal performance. For the primary model considered, singular solutions occur only if the optimal solution is "pure translation". "Time optimal" singular solutions can be found which consist of intervals of "coast" and "full thrust". The shape of the optimal fuel consumption curve as a function of flight time was found to depend on whether or not the initial state is in the region admitting singular solutions. Comparisons of fuel optimal maneuvers in deep space with those relative to a point in circular orbit indicate that qualitative differences in the solutions can occur. Computation of fuel consumption for certain "pure translation" cases indicates that considerable savings in fuel can result from the fuel optimal maneuvers.

27 CFR 44.11 - Meaning of terms.

Code of Federal Regulations, 2014 CFR

2014-04-01

... singular, and vice versa, and words indicating the masculine gender shall include the feminine. The terms... respect to the operation of such warehouse. (2) The term “Manufacturer of tobacco products” includes any...

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.

Hierarchical random cellular neural networks for system-level brain-like signal processing.

PubMed

Kozma, Robert; Puljic, Marko

2013-09-01

Sensory information processing and cognition in brains are modeled using dynamic systems theory. The brain's dynamic state is described by a trajectory evolving in a high-dimensional state space. We introduce a hierarchy of random cellular automata as the mathematical tools to describe the spatio-temporal dynamics of the cortex. The corresponding brain model is called neuropercolation which has distinct advantages compared to traditional models using differential equations, especially in describing spatio-temporal discontinuities in the form of phase transitions. Phase transitions demarcate singularities in brain operations at critical conditions, which are viewed as hallmarks of higher cognition and awareness experience. The introduced Monte-Carlo simulations obtained by parallel computing point to the importance of computer implementations using very large-scale integration (VLSI) and analog platforms. Copyright © 2013 Elsevier Ltd. All rights reserved.

Dopamine prediction error responses integrate subjective value from different reward dimensions

PubMed Central

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

2014-01-01

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

Numerically stable formulas for a particle-based explicit exponential integrator

NASA Astrophysics Data System (ADS)

Nadukandi, Prashanth

2015-05-01

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

A fast numerical solution of scattering by a cylinder: Spectral method for the boundary integral equations

NASA Technical Reports Server (NTRS)

Hu, Fang Q.

1994-01-01

It is known that the exact analytic solutions of wave scattering by a circular cylinder, when they exist, are not in a closed form but in infinite series which converges slowly for high frequency waves. In this paper, we present a fast number solution for the scattering problem in which the boundary integral equations, reformulated from the Helmholtz equation, are solved using a Fourier spectral method. It is shown that the special geometry considered here allows the implementation of the spectral method to be simple and very efficient. The present method differs from previous approaches in that the singularities of the integral kernels are removed and dealt with accurately. The proposed method preserves the spectral accuracy and is shown to have an exponential rate of convergence. Aspects of efficient implementation using FFT are discussed. Moreover, the boundary integral equations of combined single and double-layer representation are used in the present paper. This ensures the uniqueness of the numerical solution for the scattering problem at all frequencies. Although a strongly singular kernel is encountered for the Neumann boundary conditions, we show that the hypersingularity can be handled easily in the spectral method. Numerical examples that demonstrate the validity of the method are also presented.

Asymptotics of bivariate generating functions with algebraic singularities

NASA Astrophysics Data System (ADS)

Greenwood, Torin

Flajolet and Odlyzko (1990) derived asymptotic formulae the coefficients of a class of uni- variate generating functions with algebraic singularities. Gao and Richmond (1992) and Hwang (1996, 1998) extended these results to classes of multivariate generating functions, in both cases by reducing to the univariate case. Pemantle and Wilson (2013) outlined new multivariate ana- lytic techniques and used them to analyze the coefficients of rational generating functions. After overviewing these methods, we use them to find asymptotic formulae for the coefficients of a broad class of bivariate generating functions with algebraic singularities. Beginning with the Cauchy integral formula, we explicity deform the contour of integration so that it hugs a set of critical points. The asymptotic contribution to the integral comes from analyzing the integrand near these points, leading to explicit asymptotic formulae. Next, we use this formula to analyze an example from current research. In the following chapter, we apply multivariate analytic techniques to quan- tum walks. Bressler and Pemantle (2007) found a (d + 1)-dimensional rational generating function whose coefficients described the amplitude of a particle at a position in the integer lattice after n steps. Here, the minimal critical points form a curve on the (d + 1)-dimensional unit torus. We find asymptotic formulae for the amplitude of a particle in a given position, normalized by the number of steps n, as n approaches infinity. Each critical point contributes to the asymptotics for a specific normalized position. Using Groebner bases in Maple again, we compute the explicit locations of peak amplitudes. In a scaling window of size the square root of n near the peaks, each amplitude is asymptotic to an Airy function.

Cosmology of the closed string tachyon

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

Swanson, Ian

2008-09-15

The spacetime physics of bulk closed string tachyon condensation is studied at the level of a two-derivative effective action. We derive the unique perturbative tachyon potential consistent with a full class of linearized tachyonic deformations of supercritical string theory. The solutions of interest deform a general linear dilaton background by the insertion of purely exponential tachyon vertex operators. In spacetime, the evolution of the tachyon drives an accelerated contraction of the universe and, absent higher-order corrections, the theory collapses to a cosmological singularity in finite time, at arbitrarily weak string coupling. When the tachyon exhibits a null symmetry, the worldsheetmore » dynamics is known to be exact and well defined at tree level. We prove that if the two-derivative effective action is free of nongravitational singularities, higher-order corrections always resolve the spacetime curvature singularity of the null tachyon. The resulting theory provides an explicit mechanism by which tachyon condensation can generate or terminate the flow of cosmological time in string theory. Additional particular solutions can resolve an initial singularity with a tachyonic phase at weak coupling, or yield solitonic configurations that localize the universe along spatial directions.« less

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

NASA Astrophysics Data System (ADS)

Cai, Zhishan

2016-10-01

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

Quantum propagation across cosmological singularities

NASA Astrophysics Data System (ADS)

Gielen, Steffen; Turok, Neil

2017-05-01

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

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

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

Pachikara, J.; Portmann, G.

2007-01-01

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

A General Theory of Unsteady Compressible Potential Aerodynamics

NASA Technical Reports Server (NTRS)

Morino, L.

1974-01-01

The general theory of potential aerodynamic flow around a lifting body having arbitrary shape and motion is presented. By using the Green function method, an integral representation for the potential is obtained for both supersonic and subsonic flow. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface, sigma, of the body. Hence, if the point P approaches the surface of the body, the representation reduces to an integro-differential equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface sigma. For the important practical case of small harmonic oscillation around a rest position, the equation reduces to a two-dimensional Fredholm integral equation of second-type. It is shown that this equation reduces properly to the lifting surface theories as well as other classical mathematical formulas. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings.

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.

Multiscale Resilience of Complex Systems

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

Typical event horizons in AdS/CFT

DOE PAGES

Avery, Steven G.; Lowe, David A.

2016-01-14

We consider the construction of local bulk operators in a black hole background dual to a pure state in conformal field theory. The properties of these operators in a microcanonical ensemble are studied. It has been argued in the literature that typical states in such an ensemble contain firewalls, or otherwise singular horizons. Here, we argue this conclusion can be avoided with a proper definition of the interior operators.

About CIB | Division of Cancer Prevention

Cancer.gov

The Consortium was created to improve cancer screening, early detection of aggressive cancer, assessment of cancer risk and cancer diagnosis aimed at integrating multi-modality imaging strategies and multiplexed biomarker methodologies into a singular complementary approach. Investigator perform collaborative studies, exchange information, share knowledge and leverage common

Modeling of thin-walled structures interacting with acoustic media as constrained two-dimensional continua

NASA Astrophysics Data System (ADS)

Rabinskiy, L. N.; Zhavoronok, S. I.

2018-04-01

The transient interaction of acoustic media and elastic shells is considered on the basis of the transition function approach. The three-dimensional hyperbolic initial boundary-value problem is reduced to a two-dimensional problem of shell theory with integral operators approximating the acoustic medium effect on the shell dynamics. The kernels of these integral operators are determined by the elementary solution of the problem of acoustic waves diffraction at a rigid obstacle with the same boundary shape as the wetted shell surface. The closed-form elementary solution for arbitrary convex obstacles can be obtained at the initial interaction stages on the background of the so-called “thin layer hypothesis”. Thus, the shell–wave interaction model defined by integro-differential dynamic equations with analytically determined kernels of integral operators becomes hence two-dimensional but nonlocal in time. On the other hand, the initial interaction stage results in localized dynamic loadings and consequently in complex strain and stress states that require higher-order shell theories. Here the modified theory of I.N.Vekua–A.A.Amosov-type is formulated in terms of analytical continuum dynamics. The shell model is constructed on a two-dimensional manifold within a set of field variables, Lagrangian density, and constraint equations following from the boundary conditions “shifted” from the shell faces to its base surface. Such an approach allows one to construct consistent low-order shell models within a unified formal hierarchy. The equations of the N th-order shell theory are singularly perturbed and contain second-order partial derivatives with respect to time and surface coordinates whereas the numerical integration of systems of first-order equations is more efficient. Such systems can be obtained as Hamilton–de Donder–Weyl-type equations for the Lagrangian dynamical system. The Hamiltonian formulation of the elementary N th-order shell theory is here briefly described.

Weak-noise limit of a piecewise-smooth stochastic differential equation.

PubMed

Chen, Yaming; Baule, Adrian; Touchette, Hugo; Just, Wolfram

2013-11-01

We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a simple model of Brownian motion with solid friction. For this model, we show that the weak-noise approximation of the path integral correctly reproduces the known propagator of the SDE at lowest order in the noise power, as well as the main features of the exact propagator with higher-order corrections, provided the singularity of the path integral associated with the nonsmooth SDE is treated with some heuristics. We also show that, as in the case of smooth SDEs, the deterministic paths of the noiseless system correctly describe the behavior of the nonsmooth SDE in the low-noise limit. Finally, we consider a smooth regularization of the piecewise-constant SDE and study to what extent this regularization can rectify some of the problems encountered when dealing with discontinuous drifts and singularities in SDEs.

On singular and highly oscillatory properties of the Green function for ship motions

NASA Astrophysics Data System (ADS)

Chen, Xiao-Bo; Xiong Wu, Guo

2001-10-01

The Green function used for analysing ship motions in waves is the velocity potential due to a point source pulsating and advancing at a uniform forward speed. The behaviour of this function is investigated, in particular for the case when the source is located at or close to the free surface. In the far field, the Green function is represented by a single integral along one closed dispersion curve and two open dispersion curves. The single integral along the open dispersion curves is analysed based on the asymptotic expansion of a complex error function. The singular and highly oscillatory behaviour of the Green function is captured, which shows that the Green function oscillates with indefinitely increasing amplitude and indefinitely decreasing wavelength, when a field point approaches the track of the source point at the free surface. This sheds some light on the nature of the difficulties in the numerical methods used for predicting the motion of a ship advancing in waves.

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.

Numerical solution methods for viscoelastic orthotropic materials

NASA Technical Reports Server (NTRS)

Gramoll, K. C.; Dillard, D. A.; Brinson, H. F.

1988-01-01

Numerical solution methods for viscoelastic orthotropic materials, specifically fiber reinforced composite materials, are examined. The methods include classical lamination theory using time increments, direction solution of the Volterra Integral, Zienkiewicz's linear Prony series method, and a new method called Nonlinear Differential Equation Method (NDEM) which uses a nonlinear Prony series. The criteria used for comparison of the various methods include the stability of the solution technique, time step size stability, computer solution time length, and computer memory storage. The Volterra Integral allowed the implementation of higher order solution techniques but had difficulties solving singular and weakly singular compliance function. The Zienkiewicz solution technique, which requires the viscoelastic response to be modeled by a Prony series, works well for linear viscoelastic isotropic materials and small time steps. The new method, NDEM, uses a modified Prony series which allows nonlinear stress effects to be included and can be used with orthotropic nonlinear viscoelastic materials. The NDEM technique is shown to be accurate and stable for both linear and nonlinear conditions with minimal computer time.

Geometric constraints on potentially singular solutions for the 3-D Euler equations

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

Constantin, P.; Fefferman, C.; Majda, A.J.

1996-12-31

We discuss necessary and sufficient conditions for the formation of finite time singularities (blow up) in the incompressible three dimensional Euler equations. The well-known result of Beale, Kato and Majda states that these equations have smooth solutions on the time interval (0,t) if, and only if lim/t{r_arrow}T {integral}{sup t}{sub 0} {parallel}{Omega}({center_dot},s){parallel}{sub L}{sup {infinity}} (dx)dx < {infinity} where {Omega} = {triangledown} X u is the vorticity of the fluid and u is its divergence=free velocity. In this paper we prove criteria in which the direction of vorticity {xi} = {Omega}/{vert_bar}{Omega}{vert_bar} plays an important role.

A rapid local singularity analysis algorithm with applications

NASA Astrophysics Data System (ADS)

Chen, Zhijun; Cheng, Qiuming; Agterberg, Frits

2015-04-01

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

Computational approach to compact Riemann surfaces

NASA Astrophysics Data System (ADS)

Frauendiener, Jörg; Klein, Christian

2017-01-01

A purely numerical approach to compact Riemann surfaces starting from plane algebraic curves is presented. The critical points of the algebraic curve are computed via a two-dimensional Newton iteration. The starting values for this iteration are obtained from the resultants with respect to both coordinates of the algebraic curve and a suitable pairing of their zeros. A set of generators of the fundamental group for the complement of these critical points in the complex plane is constructed from circles around these points and connecting lines obtained from a minimal spanning tree. The monodromies are computed by solving the defining equation of the algebraic curve on collocation points along these contours and by analytically continuing the roots. The collocation points are chosen to correspond to Chebychev collocation points for an ensuing Clenshaw-Curtis integration of the holomorphic differentials which gives the periods of the Riemann surface with spectral accuracy. At the singularities of the algebraic curve, Puiseux expansions computed by contour integration on the circles around the singularities are used to identify the holomorphic differentials. The Abel map is also computed with the Clenshaw-Curtis algorithm and contour integrals. As an application of the code, solutions to the Kadomtsev-Petviashvili equation are computed on non-hyperelliptic Riemann surfaces.

Differential Flatness and Cooperative Tracking in the Lorenz System

NASA Technical Reports Server (NTRS)

Crespo, Luis G.

2002-01-01

In this paper the control of the Lorenz system for both stabilization and tracking problems is studied via feedback linearization and differential flatness. By using the Rayleigh number as the control, only variable physically tunable, a barrier in the controllability of the system is incidentally imposed. This is reflected in the appearance of a singularity in the state transformation. Composite controllers that overcome this difficulty are designed and evaluated. The transition through the manifold defined by such a singularity is achieved by inducing a chaotic response within a boundary layer that contains it. Outside this region, a conventional feedback nonlinear control is applied. In this fashion, the authority of the control is enlarged to the whole. state space and the need for high control efforts is mitigated. In addition, the differential parametrization of the problem is used to track nonlinear functions of one state variable (single tracking) as well as several state variables (cooperative tracking). Control tasks that lead to integrable and non-integrable differential equations for the nominal flat output in steady-state are considered. In particular, a novel numerical strategy to deal with the non-integrable case is proposed. Numerical results validate very well the control design.

Vorticity dipoles and a theoretical model of a finite force at the moving contact line singularity

NASA Astrophysics Data System (ADS)

Zhang, Peter; Devoria, Adam; Mohseni, Kamran

2017-11-01

In the well known works of Moffatt (1964) and Huh & Scriven (1971), an infinite force was reported at the moving contact line (MCL) and attributed to a non-integrable stress along the fluid-solid boundary. In our recent investigation of the boundary driven wedge, a model of the MCL, we find that the classical solution theoretically predicts a finite force at the contact line if the forces applied by the two boundaries that make up the corner are taken into consideration. Mathematically, this force can be obtained by the complex contour integral of the holomorphic vorticity-pressure function given by G = μω + ip . Alternatively, this force can also be found using a carefully defined real integral that incorporates the two boundaries. Motivated by this discovery, we have found that the rate of change in circulation, viscous energy dissipation, and viscous energy flux is also finite per unit contact line length. The analysis presented demonstrates that despite a singular stress and a relatively simple geometry, the no-slip semi-infinite wedge is capable of capturing some physical quantities of interest. Furthermore, this result provides a foundation for other challenging topics such as dynamic contact angle.

Landau singularities from the amplituhedron

DOE PAGES

Dennen, T.; Prlina, I.; Spradlin, M.; ...

2017-06-28

We propose a simple geometric algorithm for determining the complete set of branch points of amplitudes in planar N = 4 super-Yang-Mills theory directly from the amplituhedron, without resorting to any particular representation in terms of local Feynman integrals. This represents a step towards translating integrands directly into integrals. In particular, the algorithm provides information about the symbol alphabets of general amplitudes. We illustrate the algorithm applied to the one- and two-loop MHV amplitudes.

Fuchsia : A tool for reducing differential equations for Feynman master integrals to epsilon form

NASA Astrophysics Data System (ADS)

Gituliar, Oleksandr; Magerya, Vitaly

2017-10-01

We present Fuchsia - an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients ∂x J(x , ɛ) = A(x , ɛ) J(x , ɛ) finds a basis transformation T(x , ɛ) , i.e., J(x , ɛ) = T(x , ɛ) J‧(x , ɛ) , such that the system turns into the epsilon form : ∂xJ‧(x , ɛ) = ɛ S(x) J‧(x , ɛ) , where S(x) is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator ɛ. That makes the construction of the transformation T(x , ɛ) crucial for obtaining solutions of the initial system. In principle, Fuchsia can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals. Program Files doi:http://dx.doi.org/10.17632/zj6zn9vfkh.1 Licensing provisions: MIT Programming language:Python 2.7 Nature of problem: Feynman master integrals may be calculated from solutions of a linear system of differential equations with rational coefficients. Such a system can be easily solved as an ɛ-series when its epsilon form is known. Hence, a tool which is able to find the epsilon form transformations can be used to evaluate Feynman master integrals. Solution method: The solution method is based on the Lee algorithm (Lee, 2015) which consists of three main steps: fuchsification, normalization, and factorization. During the fuchsification step a given system of differential equations is transformed into the Fuchsian form with the help of the Moser method (Moser, 1959). Next, during the normalization step the system is transformed to the form where eigenvalues of all residues are proportional to the dimensional regulator ɛ. Finally, the system is factorized to the epsilon form by finding an unknown transformation which satisfies a system of linear equations. Additional comments including Restrictions and Unusual features: Systems of single-variable differential equations are considered. A system needs to be reducible to Fuchsian form and eigenvalues of its residues must be of the form n + m ɛ, where n is integer. Performance depends upon the input matrix, its size, number of singular points and their degrees. It takes around an hour to reduce an example 74 × 74 matrix with 20 singular points on a PC with a 1.7 GHz Intel Core i5 CPU. An additional slowdown is to be expected for matrices with complex and/or irrational singular point locations, as these are particularly difficult for symbolic algebra software to handle.

Education That Is Multicultural for Urban Schools: Rationale and Recommendation.

ERIC Educational Resources Information Center

Grant, Carl A.

Diverse school populations, desegregation and integration, minority-majority group splits, institutional racism, and the singularity of school norms are significant factors which affect respect for individual differences within urban schools. These facts illustrate the need for adoption of education that is multicultural to effect systematic…

Efficient Solution of Three-Dimensional Problems of Acoustic and Electromagnetic Scattering by Open Surfaces

NASA Technical Reports Server (NTRS)

Turc, Catalin; Anand, Akash; Bruno, Oscar; Chaubell, Julian

2011-01-01

We present a computational methodology (a novel Nystrom approach based on use of a non-overlapping patch technique and Chebyshev discretizations) for efficient solution of problems of acoustic and electromagnetic scattering by open surfaces. Our integral equation formulations (1) Incorporate, as ansatz, the singular nature of open-surface integral-equation solutions, and (2) For the Electric Field Integral Equation (EFIE), use analytical regularizes that effectively reduce the number of iterations required by iterative linear-algebra solution based on Krylov-subspace iterative solvers.

Integrated flight/propulsion control - Subsystem specifications for performance

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

Multi-star processing and gyro filtering for the video inertial pointing system

NASA Technical Reports Server (NTRS)

Murphy, J. P.

1976-01-01

The video inertial pointing (VIP) system is being developed to satisfy the acquisition and pointing requirements of astronomical telescopes. The VIP system uses a single video sensor to provide star position information that can be used to generate three-axis pointing error signals (multi-star processing) and for input to a cathode ray tube (CRT) display of the star field. The pointing error signals are used to update the telescope's gyro stabilization system (gyro filtering). The CRT display facilitates target acquisition and positioning of the telescope by a remote operator. Linearized small angle equations are used for the multistar processing and a consideration of error performance and singularities lead to star pair location restrictions and equation selection criteria. A discrete steady-state Kalman filter which uses the integration of the gyros is developed and analyzed. The filter includes unit time delays representing asynchronous operations of the VIP microprocessor and video sensor. A digital simulation of a typical gyro stabilized gimbal is developed and used to validate the approach to the gyro filtering.

Through the Immune Looking Glass: A Model for Brain Memory Strategies

PubMed Central

Sánchez-Ramón, Silvia; Faure, Florence

2016-01-01

The immune system (IS) and the central nervous system (CNS) are complex cognitive networks involved in defining the identity (self) of the individual through recognition and memory processes that enable one to anticipate responses to stimuli. Brain memory has traditionally been classified as either implicit or explicit on psychological and anatomical grounds, with reminiscences of the evolutionarily-based innate-adaptive IS responses. Beyond the multineuronal networks of the CNS, we propose a theoretical model of brain memory integrating the CNS as a whole. This is achieved by analogical reasoning between the operational rules of recognition and memory processes in both systems, coupled to an evolutionary analysis. In this new model, the hippocampus is no longer specifically ascribed to explicit memory but rather it both becomes part of the innate (implicit) memory system and tightly controls the explicit memory system. Alike the antigen presenting cells for the IS, the hippocampus would integrate transient and pseudo-specific (i.e., danger-fear) memories and would drive the formation of long-term and highly specific or explicit memories (i.e., the taste of the Proust’s madeleine cake) by the more complex and recent, evolutionarily speaking, neocortex. Experimental and clinical evidence is provided to support the model. We believe that the singularity of this model’s approximation could help to gain a better understanding of the mechanisms operating in brain memory strategies from a large-scale network perspective. PMID:26869886

Resolution of singularities for multi-loop integrals

NASA Astrophysics Data System (ADS)

Bogner, Christian; Weinzierl, Stefan

2008-04-01

We report on a program for the numerical evaluation of divergent multi-loop integrals. The program is based on iterated sector decomposition. We improve the original algorithm of Binoth and Heinrich such that the program is guaranteed to terminate. The program can be used to compute numerically the Laurent expansion of divergent multi-loop integrals regulated by dimensional regularisation. The symbolic and the numerical steps of the algorithm are combined into one program. Program summaryProgram title: sector_decomposition Catalogue identifier: AEAG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAG_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 47 506 No. of bytes in distributed program, including test data, etc.: 328 485 Distribution format: tar.gz Programming language: C++ Computer: all Operating system: Unix RAM: Depending on the complexity of the problem Classification: 4.4 External routines: GiNaC, available from http://www.ginac.de, GNU scientific library, available from http://www.gnu.org/software/gsl Nature of problem: Computation of divergent multi-loop integrals. Solution method: Sector decomposition. Restrictions: Only limited by the available memory and CPU time. Running time: Depending on the complexity of the problem.

Development of surgical skill with singular neurectomy using human cadaveric temporal bones.

PubMed

Feigl, Georg; Kos, Izabel; Anderhuber, Friedrich; Guyot, Jean Phillippe; Fasel, Jean

2008-01-01

Profound anatomical knowledge and surgical experience are essential for safe otological surgery. The surgeon's learning curve is evaluated in performing Gacek's singular neurectomy on cadaveric specimens. One otological surgeon performed Gacek's approach on 96 halves of human heads embalmed according to Thiel's method, divided into four groups (24 halves per group) and evaluated them concurrent to the evaluation of an anatomist after a first surgical attempt. Successful operations were subdivided into "direct hits" of the osseous canal of the posterior ampullary nerve also known as the singular nerve and "indirect hits" with access to the posterior ampullary recess. Unsuccessful operations showed "no hit" of the nerve without lesion of the membranous labyrinth. "Indirect" or "no hits" were reinvestigated in a second attempt to evaluate possible reclassifications due to a learning process of the surgeon. The order of dissection, the rate of success and the changes of results in correlation with the numbers of dissected specimens were documented. The success rate significantly increased from 54.2% direct hits after the first group to 87.36% in the fourth group after the first attempt. Successful operations were performed in 86.5% after completion of the first attempt and 97.9% after the second attempt. The number of new allocations decreased from 11 cases in the first group of dissected specimens to zero in the fourth group. This paper strengthens the value of cadaveric training for surgeons and the crucial role of dissection of a large number of specimens in improvement of the surgeon's experience and success rate.

Stochastic theory of log-periodic patterns

NASA Astrophysics Data System (ADS)

Canessa, Enrique

2000-12-01

We introduce an analytical model based on birth-death clustering processes to help in understanding the empirical log-periodic corrections to power law scaling and the finite-time singularity as reported in several domains including rupture, earthquakes, world population and financial systems. In our stochastic theory log-periodicities are a consequence of transient clusters induced by an entropy-like term that may reflect the amount of co-operative information carried by the state of a large system of different species. The clustering completion rates for the system are assumed to be given by a simple linear death process. The singularity at t0 is derived in terms of birth-death clustering coefficients.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

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

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

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

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

Extension of the KLI approximation toward the exact optimized effective potential.

PubMed

Iafrate, G J; Krieger, J B

2013-03-07

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

Extension of the KLI approximation toward the exact optimized effective potential

NASA Astrophysics Data System (ADS)

Iafrate, G. J.; Krieger, J. B.

2013-03-01

The integral equation for the optimized effective potential (OEP) is utilized in a compact form from which an accurate OEP solution for the spin-unrestricted exchange-correlation potential, Vxcσ, is obtained for any assumed orbital-dependent exchange-correlation energy functional. The method extends beyond the Krieger-Li-Iafrate (KLI) approximation toward the exact OEP result. The compact nature of the OEP equation arises by replacing the integrals involving the Green's function terms in the traditional OEP equation by an equivalent first-order perturbation theory wavefunction often referred to as the "orbital shift" function. Significant progress is then obtained by solving the equation for the first order perturbation theory wavefunction by use of Dalgarno functions which are determined from well known methods of partial differential equations. The use of Dalgarno functions circumvents the need to explicitly address the Green's functions and the associated problems with "sum over states" numerics; as well, the Dalgarno functions provide ease in dealing with inherent singularities arising from the origin and the zeros of the occupied orbital wavefunctions. The Dalgarno approach for finding a solution to the OEP equation is described herein, and a detailed illustrative example is presented for the special case of a spherically symmetric exchange-correlation potential. For the case of spherical symmetry, the relevant Dalgarno function is derived by direct integration of the appropriate radial equation while utilizing a user friendly method which explicitly treats the singular behavior at the origin and at the nodal singularities arising from the zeros of the occupied states. The derived Dalgarno function is shown to be an explicit integral functional of the exact OEP Vxcσ, thus allowing for the reduction of the OEP equation to a self-consistent integral equation for the exact exchange-correlation potential; the exact solution to this integral equation can be determined by iteration with the natural zeroth order correction given by the KLI exchange-correlation potential. Explicit analytic results are provided to illustrate the first order iterative correction beyond the KLI approximation. The derived correction term to the KLI potential explicitly involves spatially weighted products of occupied orbital densities in any assumed orbital-dependent exchange-correlation energy functional; as well, the correction term is obtained with no adjustable parameters. Moreover, if the equation for the exact optimized effective potential is further iterated, one can obtain the OEP as accurately as desired.

FastMag: Fast micromagnetic simulator for complex magnetic structures (invited)

NASA Astrophysics Data System (ADS)

Chang, R.; Li, S.; Lubarda, M. V.; Livshitz, B.; Lomakin, V.

2011-04-01

A fast micromagnetic simulator (FastMag) for general problems is presented. FastMag solves the Landau-Lifshitz-Gilbert equation and can handle multiscale problems with a high computational efficiency. The simulator derives its high performance from efficient methods for evaluating the effective field and from implementations on massively parallel graphics processing unit (GPU) architectures. FastMag discretizes the computational domain into tetrahedral elements and therefore is highly flexible for general problems. The magnetostatic field is computed via the superposition principle for both volume and surface parts of the computational domain. This is accomplished by implementing efficient quadrature rules and analytical integration for overlapping elements in which the integral kernel is singular. Thus, discretized superposition integrals are computed using a nonuniform grid interpolation method, which evaluates the field from N sources at N collocated observers in O(N) operations. This approach allows handling objects of arbitrary shape, allows easily calculating of the field outside the magnetized domains, does not require solving a linear system of equations, and requires little memory. FastMag is implemented on GPUs with ?> GPU-central processing unit speed-ups of 2 orders of magnitude. Simulations are shown of a large array of magnetic dots and a recording head fully discretized down to the exchange length, with over a hundred million tetrahedral elements on an inexpensive desktop computer.

Resistive MHD Stability Analysis in Near Real-time

NASA Astrophysics Data System (ADS)

Glasser, Alexander; Kolemen, Egemen

2017-10-01

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

Automatic computer procedure for generating exact and analytical kinetic energy operators based on the polyspherical approach: General formulation and removal of singularities

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

Ndong, Mamadou; Lauvergnat, David; Nauts, André

2013-11-28

We present new techniques for an automatic computation of the kinetic energy operator in analytical form. These techniques are based on the use of the polyspherical approach and are extended to take into account Cartesian coordinates as well. An automatic procedure is developed where analytical expressions are obtained by symbolic calculations. This procedure is a full generalization of the one presented in Ndong et al., [J. Chem. Phys. 136, 034107 (2012)]. The correctness of the new implementation is analyzed by comparison with results obtained from the TNUM program. We give several illustrations that could be useful for users of themore » code. In particular, we discuss some cyclic compounds which are important in photochemistry. Among others, we show that choosing a well-adapted parameterization and decomposition into subsystems can allow one to avoid singularities in the kinetic energy operator. We also discuss a relation between polyspherical and Z-matrix coordinates: this comparison could be helpful for building an interface between the new code and a quantum chemistry package.« less

Tensor calculus in polar coordinates using Jacobi polynomials

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

Computation of NLO processes involving heavy quarks using Loop-Tree Duality

NASA Astrophysics Data System (ADS)

Driencourt-Mangin, Félix

2017-03-01

We present a new method to compute higher-order corrections to physical cross-sections, at Next-to-Leading Order and beyond. This method, based on the Loop Tree Duality, leads to locally integrable expressions in four dimensions. By introducing a physically motivated momentum mapping between the momenta involved in the real and the virtual contributions, infrared singularities naturally cancel at integrand level, without the need to introduce subtraction counter-terms. Ultraviolet singularities are dealt with by using dual representations of suitable counter-terms, with some subtleties regarding the self-energy contributions. As an example, we apply this method to compute the 1 → 2 decay rate in the context of a scalar toy model with massive particles.

Dark optical, singular solitons and conservation laws to the nonlinear Schrödinger’s equation with spatio-temporal dispersion

NASA Astrophysics Data System (ADS)

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

2017-05-01

This paper studies the dynamics of solitons to the nonlinear Schrödinger’s equation (NLSE) with spatio-temporal dispersion (STD). The integration algorithm that is employed in this paper is the Riccati-Bernoulli sub-ODE method. This leads to dark and singular soliton solutions that are important in the field of optoelectronics and fiber optics. The soliton solutions appear with all necessary constraint conditions that are necessary for them to exist. There are four types of nonlinear media studied in this paper. They are Kerr law, power law, parabolic law and dual law. The conservation laws (Cls) for the Kerr law and parabolic law nonlinear media are constructed using the conservation theorem presented by Ibragimov.

PROGRAM VSAERO: A computer program for calculating the non-linear aerodynamic characteristics of arbitrary configurations: User's manual

NASA Technical Reports Server (NTRS)

Maskew, B.

1982-01-01

VSAERO is a computer program used to predict the nonlinear aerodynamic characteristics of arbitrary three-dimensional configurations in subsonic flow. Nonlinear effects of vortex separation and vortex surface interaction are treated in an iterative wake-shape calculation procedure, while the effects of viscosity are treated in an iterative loop coupling potential-flow and integral boundary-layer calculations. The program employs a surface singularity panel method using quadrilateral panels on which doublet and source singularities are distributed in a piecewise constant form. This user's manual provides a brief overview of the mathematical model, instructions for configuration modeling and a description of the input and output data. A listing of a sample case is included.

Dual Vector Spaces and Physical Singularities

NASA Astrophysics Data System (ADS)

Rowlands, Peter

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

Integrability and Linearizability of the Lotka-Volterra System with a Saddle Point with Rational Hyperbolicity Ratio

NASA Astrophysics Data System (ADS)

Gravel, Simon; Thibault, Pierre

In this paper, we consider normalizability, integrability and linearizability properties of the Lotka-Volterra system in the neighborhood of a singular point with eigenvalues 1 and - λ. The results are obtained by generalizing and expanding two methods already known: the power expansion of the first integral or of the linearizing transformation and the transformation of the saddle into a node. With these methods we find conditions that are valid for λ∈ R+ or λ∈ Q. These conditions will allow us to find all the integrable and linearizable systems for λ= {p}/{2} and {2}/{p} with p∈ N+.

A conservative spectral method for the Boltzmann equation with anisotropic scattering and the grazing collisions limit

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

Gamba, Irene M.; ICES, The University of Texas at Austin, 201 E. 24th St., Stop C0200, Austin, TX 78712; Haack, Jeffrey R.

2014-08-01

We present the formulation of a conservative spectral method for the Boltzmann collision operator with anisotropic scattering cross-sections. The method is an extension of the conservative spectral method of Gamba and Tharkabhushanam [17,18], which uses the weak form of the collision operator to represent the collisional term as a weighted convolution in Fourier space. The method is tested by computing the collision operator with a suitably cut-off angular cross section and comparing the results with the solution of the Landau equation. We analytically study the convergence rate of the Fourier transformed Boltzmann collision operator in the grazing collisions limit tomore » the Fourier transformed Landau collision operator under the assumption of some regularity and decay conditions of the solution to the Boltzmann equation. Our results show that the angular singularity which corresponds to the Rutherford scattering cross section is the critical singularity for which a grazing collision limit exists for the Boltzmann operator. Additionally, we numerically study the differences between homogeneous solutions of the Boltzmann equation with the Rutherford scattering cross section and an artificial cross section, which give convergence to solutions of the Landau equation at different asymptotic rates. We numerically show the rate of the approximation as well as the consequences for the rate of entropy decay for homogeneous solutions of the Boltzmann equation and Landau equation.« less

NUMERICAL INTEGRAL OF RESISTANCE COEFFICIENTS IN DIFFUSION

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

Zhang, Q. S., E-mail: zqs@ynao.ac.cn

2017-01-10

The resistance coefficients in the screened Coulomb potential of stellar plasma are evaluated to high accuracy. I have analyzed the possible singularities in the integral of scattering angle. There are possible singularities in the case of an attractive potential. This may result in a problem for the numerical integral. In order to avoid the problem, I have used a proper scheme, e.g., splitting into many subintervals where the width of each subinterval is determined by the variation of the integrand, to calculate the scattering angle. The collision integrals are calculated by using Romberg’s method, therefore the accuracy is high (i.e.,more » ∼10{sup −12}). The results of collision integrals and their derivatives for −7 ≤ ψ ≤ 5 are listed. By using Hermite polynomial interpolation from those data, the collision integrals can be obtained with an accuracy of 10{sup −10}. For very weakly coupled plasma ( ψ ≥ 4.5), analytical fittings for collision integrals are available with an accuracy of 10{sup −11}. I have compared the final results of resistance coefficients with other works and found that, for a repulsive potential, the results are basically the same as others’; for an attractive potential, the results in cases of intermediate and strong coupling show significant differences. The resulting resistance coefficients are tested in the solar model. Comparing with the widely used models of Cox et al. and Thoul et al., the resistance coefficients in the screened Coulomb potential lead to a slightly weaker effect in the solar model, which is contrary to the expectation of attempts to solve the solar abundance problem.« less

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

NASA Astrophysics Data System (ADS)

Xue, Yan

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

Modern Quantum Field Theory II - Proceeeings of the International Colloquium

NASA Astrophysics Data System (ADS)

Das, S. R.; Mandal, G.; Mukhi, S.; Wadia, S. R.

1995-08-01

The Table of Contents for the book is as follows: * Foreword * 1. Black Holes and Quantum Gravity * Quantum Black Holes and the Problem of Time * Black Hole Entropy and the Semiclassical Approximation * Entropy and Information Loss in Two Dimensions * Strings on a Cone and Black Hole Entropy (Abstract) * Boundary Dynamics, Black Holes and Spacetime Fluctuations in Dilation Gravity (Abstract) * Pair Creation of Black Holes (Abstract) * A Brief View of 2-Dim. String Theory and Black Holes (Abstract) * 2. String Theory * Non-Abelian Duality in WZW Models * Operators and Correlation Functions in c ≤ 1 String Theory * New Symmetries in String Theory * A Look at the Discretized Superstring Using Random Matrices * The Nested BRST Structure of Wn-Symmetries * Landau-Ginzburg Model for a Critical Topological String (Abstract) * On the Geometry of Wn Gravity (Abstract) * O(d, d) Tranformations, Marginal Deformations and the Coset Construction in WZNW Models (Abstract) * Nonperturbative Effects and Multicritical Behaviour of c = 1 Matrix Model (Abstract) * Singular Limits and String Solutions (Abstract) * BV Algebra on the Moduli Spaces of Riemann Surfaces and String Field Theory (Abstract) * 3. Condensed Matter and Statistical Mechanics * Stochastic Dynamics in a Deposition-Evaporation Model on a Line * Models with Inverse-Square Interactions: Conjectured Dynamical Correlation Functions of the Calogero-Sutherland Model at Rational Couplings * Turbulence and Generic Scale Invariance * Singular Perturbation Approach to Phase Ordering Dynamics * Kinetics of Diffusion-Controlled and Ballistically-Controlled Reactions * Field Theory of a Frustrated Heisenberg Spin Chain * FQHE Physics in Relativistic Field Theories * Importance of Initial Conditions in Determining the Dynamical Class of Cellular Automata (Abstract) * Do Hard-Core Bosons Exhibit Quantum Hall Effect? (Abstract) * Hysteresis in Ferromagnets * 4. Fundamental Aspects of Quantum Mechanics and Quantum Field Theory * Finite Quantum Physics and Noncommutative Geometry * Higgs as Gauge Field and the Standard Model * Canonical Quantisation of an Off-Conformal Theory * Deterministic Quantum Mechanics in One Dimension * Spin-Statistics Relations for Topological Geons in 2+1 Quantum Gravity * Generalized Fock Spaces * Geometrical Expression for Short Distance Singularities in Field Theory * 5. Mathematics and Quantum Field Theory * Knot Invariants from Quantum Field Theories * Infinite Grassmannians and Moduli Spaces of G-Bundles * A Review of an Algebraic Geometry Approach to a Model Quantum Field Theory on a Curve (Abstract) * 6. Integrable Models * Spectral Representation of Correlation Functions in Two-Dimensional Quantum Field Theories * On Various Avatars of the Pasquier Algebra * Supersymmetric Integrable Field Theories and Eight Vertex Free Fermion Models (Abstract) * 7. Lattice Field Theory * From Kondo Model and Strong Coupling Lattice QCD to the Isgur-Wise Function * Effective Confinement from a Logarithmically Running Coupling (Abstract)

General relaxation schemes in multigrid algorithms for higher order singularity methods

NASA Technical Reports Server (NTRS)

Oskam, B.; Fray, J. M. J.

1981-01-01

Relaxation schemes based on approximate and incomplete factorization technique (AF) are described. The AF schemes allow construction of a fast multigrid method for solving integral equations of the second and first kind. The smoothing factors for integral equations of the first kind, and comparison with similar results from the second kind of equations are a novel item. Application of the MD algorithm shows convergence to the level of truncation error of a second order accurate panel method.

"Hey, I Didn't Say That!": Teaching Textual Integrity through Misrepresented Quotes

ERIC Educational Resources Information Center

Ford, Jessica L.

2015-01-01

Despite specialized areas of expertise, communication instructors are unified, to a large extent, by a singular belief: the meaning people give words produces behavioral ramifications (Mead, 2009). Communication instructors revere language's ability to reflect both meaning and reality. Yet, they also are tasked with the responsibility of conveying…

Analysis of Spanish Policies for the Integration of Immigrant Schoolchildren

ERIC Educational Resources Information Center

Martínez-Usarralde, María Jesús; Yanes-Cabrera, Cristina; Llevot-Calvet, Nuria

2016-01-01

The Organic Law on the Improvement of the National Education Quality ("Ley Orgánica de Reforma de la Calidad Educativa") readdressed one of the most significant educational issues: educational policies related to immigrant students. Therefore, this is an appropriate moment to evaluate these types of policies in three singular Spanish…

Inverse free steering law for small satellite attitude control and power tracking with VSCMGs

NASA Astrophysics Data System (ADS)

Malik, M. S. I.; Asghar, Sajjad

2014-01-01

Recent developments in integrated power and attitude control systems (IPACSs) for small satellite, has opened a new dimension to more complex and demanding space missions. This paper presents a new inverse free steering approach for integrated power and attitude control systems using variable-speed single gimbal control moment gyroscope. The proposed inverse free steering law computes the VSCMG steering commands (gimbal rates and wheel accelerations) such that error signal (difference in command and output) in feedback loop is driven to zero. H∞ norm optimization approach is employed to synthesize the static matrix elements of steering law for a static state of VSCMG. Later these matrix elements are suitably made dynamic in order for the adaptation. In order to improve the performance of proposed steering law while passing through a singular state of CMG cluster (no torque output), the matrix element of steering law is suitably modified. Therefore, this steering law is capable of escaping internal singularities and using the full momentum capacity of CMG cluster. Finally, two numerical examples for a satellite in a low earth orbit are simulated to test the proposed steering law.

Supercritical flow past a symmetrical bicircular arc airfoil

NASA Technical Reports Server (NTRS)

Holt, Maurice; Yew, Khoy Chuah

1989-01-01

A numerical scheme is developed for computing steady supercritical flow about symmetrical airfoils, applying it to an ellipse for zero angle of attack. An algorithmic description of this new scheme is presented. Application to a symmetrical bicircular arc airfoil is also proposed. The flow field before the shock is region 1. For transonic flow, singularity can be avoided by integrating the resulting ordinary differential equations away from the body. Region 2 contains the shock which will be located by shock fitting techniques. The shock divides region 2 into supersonic and subsonic regions and there is no singularity problem in this case. The Method of Lines is used in this region and it is advantageous to integrate the resulting ordinary differential equation along the body for shock fitting. Coaxial coordinates have to be used for the bicircular arc airfoil so that boundary values on the airfoil body can be taken with one direction of the coaxial coordinates fixed. To avoid taking boundary values at + or - infinity in the coaxial co-ordinary system, approximate analytical representation of the flow field near the tips of the airfoil is proposed.

Characterization of Atmospheric Infrasound for Improved Weather Monitoring

NASA Astrophysics Data System (ADS)

Threatt, Arnesha; Elbing, Brian

2016-11-01

Collaboration Leading Operational UAS Development for Meteorology and Atmospheric Physics (CLOUD MAP) is a multi-university collaboration focused on development and implementation of unmanned aircraft systems (UAS) and integration with sensors for atmospheric measurements. A primary objective for this project is to create and demonstrate UAS capabilities needed to support UAS operating in extreme conditions, such as a tornado producing storm system. These storm systems emit infrasound (acoustic signals below human hearing, <20 Hz) up to 2 hours before tornadogenesis. Due to an acoustic ceiling and weak atmospheric absorption, infrasound can be detected from distances in excess of 300 miles. Thus infrasound could be used for long-range, passive monitoring and detection of tornadogenesis as well as directing UAS resources to high-decision-value-information. To achieve this the infrasonic signals with and without severe storms must be understood. This presentation will report findings from the first CLOUD MAP field demonstration, which acquired infrasonic signals while simultaneously sampling the atmosphere with UAS. Infrasonic spectra will be shown from a typical calm day, a continuous source (pulsed gas-combustion torch), singular events, and UAS flights as well as localization results from a controlled source and multiple microphones. This work was supported by NSF Grant 1539070: CLOUD MAP - Collaboration Leading Operational UAS Development for Meteorology and Atmospheric Physics.

Functional renormalization group approach to the Yang-Lee edge singularity

DOE PAGES

An, X.; Mesterházy, D.; Stephanov, M. A.

2016-07-08

Here, we determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂more » 4) truncations of the scale-dependent effective action.« less

Functional renormalization group approach to the Yang-Lee edge singularity

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

An, X.; Mesterházy, D.; Stephanov, M. A.

Here, we determine the scaling properties of the Yang-Lee edge singularity as described by a one-component scalar field theory with imaginary cubic coupling, using the nonperturbative functional renormalization group in 3 ≤ d ≤ 6 Euclidean dimensions. We find very good agreement with high-temperature series data in d = 3 dimensions and compare our results to recent estimates of critical exponents obtained with the four-loop ϵ = 6 - d expansion and the conformal bootstrap. The relevance of operator insertions at the corresponding fixed point of the RG β functions is discussed and we estimate the error associated with O(∂more » 4) truncations of the scale-dependent effective action.« less

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

NASA Astrophysics Data System (ADS)

Kunszt, Z.

1983-11-01

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

Vibrating Systems with Singular Mass-Inertia Matrices

NASA Technical Reports Server (NTRS)

Balakrishnan, A. V.

1996-01-01

Vibrating systems with singular mass-inertia matrices arise in recent continuum models of Smart Structures (beams with PZT strips) in assessing the damping attainable with rate feedback. While they do not quite yield 'distributed' controls, we show that they can provide a fixed nonzero lower bound for the damping coefficient at all mode frequencies. The mathematical machinery for modelling the motion involves the theory of Semigroups of Operators. We consider a Timoshenko model for torsion only, a 'smart string,' where the damping coefficient turns out to be a constant at all frequencies. We also observe that the damping increases initially with the feedback gain but decreases to zero eventually as the gain increases without limit.

Refined Weyl Law for Homogeneous Perturbations of the Harmonic Oscillator

NASA Astrophysics Data System (ADS)

Doll, Moritz; Gannot, Oran; Wunsch, Jared

2018-02-01

Let H denote the harmonic oscillator Hamiltonian on R}^d,} perturbed by an isotropic pseudodifferential operator of order 1. We consider the Schrödinger propagator {U(t)=e^{-itH},} and find that while sing-supp Tr U(t) \\subset 2 π Z as in the unperturbed case, there exists a large class of perturbations in dimensions {d ≥ 2 for which the singularities of {Tr U(t)} at nonzero multiples of {2 π} are weaker than the singularity at t = 0. The remainder term in the Weyl law is of order {o(λ^{d-1})} , improving in these cases the {o(λ^{d-1})} remainder previously established by Helffer-Robert.

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

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

Shen, C; Chen, L; Jia, X

2016-06-15

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

Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control

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

Glasser, Alexander; Kolemen, Egemen; Glasser, Alan H.

To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescalemore » $$\\tau$$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.« less

Fast Numerical Solution of the Plasma Response Matrix for Real-time Ideal MHD Control

DOE PAGES

Glasser, Alexander; Kolemen, Egemen; Glasser, Alan H.

2018-03-26

To help effectuate near real-time feedback control of ideal MHD instabilities in tokamak geometries, a parallelized version of A.H. Glasser’s DCON (Direct Criterion of Newcomb) code is developed. To motivate the numerical implementation, we first solve DCON’s δW formulation with a Hamilton-Jacobi theory, elucidating analytical and numerical features of the ideal MHD stability problem. The plasma response matrix is demonstrated to be the solution of an ideal MHD Riccati equation. We then describe our adaptation of DCON with numerical methods natural to solutions of the Riccati equation, parallelizing it to enable its operation in near real-time. We replace DCON’s serial integration of perturbed modes—which satisfy a singular Euler- Lagrange equation—with a domain-decomposed integration of state transition matrices. Output is shown to match results from DCON with high accuracy, and with computation time < 1s. Such computational speed may enable active feedback ideal MHD stability control, especially in plasmas whose ideal MHD equilibria evolve with inductive timescalemore » $$\\tau$$ ≳ 1s—as in ITER. Further potential applications of this theory are discussed.« less

Design, dynamics and control of an Adaptive Singularity-Free Control Moment Gyroscope actuator for microspacecraft Attitude Determination and Control System

NASA Astrophysics Data System (ADS)

Viswanathan, Sasi Prabhakaran

Design, dynamics, control and implementation of a novel spacecraft attitude control actuator called the "Adaptive Singularity-free Control Moment Gyroscope" (ASCMG) is presented in this dissertation. In order to construct a comprehensive attitude dynamics model of a spacecraft with internal actuators, the dynamics of a spacecraft with an ASCMG, is obtained in the framework of geometric mechanics using the principles of variational mechanics. The resulting dynamics is general and complete model, as it relaxes the simplifying assumptions made in prior literature on Control Moment Gyroscopes (CMGs) and it also addresses the adaptive parameters in the dynamics formulation. The simplifying assumptions include perfect axisymmetry of the rotor and gimbal structures, perfect alignment of the centers of mass of the gimbal and the rotor etc. These set of simplifying assumptions imposed on the design and dynamics of CMGs leads to adverse effects on their performance and results in high manufacturing cost. The dynamics so obtained shows the complex nonlinear coupling between the internal degrees of freedom associated with an ASCMG and the spacecraft bus's attitude motion. By default, the general ASCMG cluster can function as a Variable Speed Control Moment Gyroscope, and reduced to function in CMG mode by spinning the rotor at constant speed, and it is shown that even when operated in CMG mode, the cluster can be free from kinematic singularities. This dynamics model is then extended to include the effects of multiple ASCMGs placed in the spacecraft bus, and sufficient conditions for non-singular ASCMG cluster configurations are obtained to operate the cluster both in VSCMG and CMG modes. The general dynamics model of the ASCMG is then reduced to that of conventional VSCMGs and CMGs by imposing the standard set of simplifying assumptions used in prior literature. The adverse effects of the simplifying assumptions that lead to the complexities in conventional CMG design, and how they lead to CMG singularities, are described. General ideas on control of the angular momentum of the spacecraft using changes in the momentum variables of a finite number of ASCMGs, are provided. Control schemes for agile and precise attitude maneuvers using ASCMG cluster in the absence of external torques and when the total angular momentum of the spacecraft is zero, is presented for both constant speed and variable speed modes. A Geometric Variational Integrator (GVI) that preserves the geometry of the state space and the conserved norm of the total angular momentum is constructed for numerical simulation and microcontroller implementation of the control scheme. The GVI is obtained by discretizing the Lagrangian of the rnultibody systems, in which the rigid body attitude is globally represented on the Lie group of rigid body rotations. Hardware and software architecture of a novel spacecraft Attitude Determination and Control System (ADCS) based on commercial smartphones and a bare minimum hardware prototype of an ASCMG using low cost COTS components is also described. A lightweight, dynamics model-free Variational Attitude Estimator (VAE) suitable for smartphone implementation is employed for attitude determination and the attitude control is performed by ASCMG actuators. The VAE scheme presented here is implemented and validated onboard an Unmanned Aerial Vehicle (UAV) platform and the real time performance is analyzed. On-board sensing, data acquisition, data uplink/downlink, state estimation and real-time feedback control objectives can be performed using this novel spacecraft ADCS. The mechatronics realization of the attitude determination through variational attitude estimation scheme and control implementation using ASCMG actuators are presented here. Experimental results of the attitude estimation (filtering) scheme using smartphone sensors as an Inertial Measurement Unit (IMU) on the Hardware In the Loop (HIL) simulator testbed are given. These results, obtained in the Spacecraft Guidance, Navigation and Control Laboratory at New Mexico State University, demonstrate the performance of this estimation scheme with the noisy raw data from the smartphone sensors. Keywords: Spacecraft, momentum exchange devices, control moment gyroscope, variational mechanics, geometric mechanics, variational integrators, attitude determination, attitude control, ADCS, estimation, ASCMG, VSCMG, cubesat, mechatronics, smartphone, Android, MEMS sensor, embedded programming, microcontroller, brushless DC drives, HIL simulation.

Predicting aerodynamic characteristics of vortical flows on three-dimensional configurations using a surface-singularity panel method

NASA Technical Reports Server (NTRS)

Maskew, B.

1983-01-01

A general low-order surface-singularity panel method is used to predict the aerodynamic characteristics of a problem where a wing-tip vortex from one wing closely interacts with an aft mounted wing in a low Reynolds Number flow; i.e., 125,000. Nonlinear effects due to wake roll-up and the influence of the wings on the vortex path are included in the calculation by using a coupled iterative wake relaxation scheme. The interaction also affects the wing pressures and boundary layer characteristics: these effects are also considered using coupled integral boundary layer codes and preliminary calculations using free vortex sheet separation modelling are included. Calculated results are compared with water tunnel experimental data with generally remarkably good agreement.

Deformations of the Almheiri-Polchinski model

NASA Astrophysics Data System (ADS)

Kyono, Hideki; Okumura, Suguru; Yoshida, Kentaroh

2017-03-01

We study deformations of the Almheiri-Polchinski (AP) model by employing the Yang-Baxter deformation technique. The general deformed AdS2 metric becomes a solution of a deformed AP model. In particular, the dilaton potential is deformed from a simple quadratic form to a hyperbolic function-type potential similarly to integrable deformations. A specific solution is a deformed black hole solution. Because the deformation makes the spacetime structure around the boundary change drastically and a new naked singularity appears, the holographic interpretation is far from trivial. The Hawking temperature is the same as the undeformed case but the Bekenstein-Hawking entropy is modified due to the deformation. This entropy can also be reproduced by evaluating the renormalized stress tensor with an appropriate counter-term on the regularized screen close to the singularity.

Singular perturbations and vanishing passage through a turning point

NASA Astrophysics Data System (ADS)

De Maesschalck, P.; Dumortier, F.

The paper deals with planar slow-fast cycles containing a unique generic turning point. We address the question on how to study canard cycles when the slow dynamics can be singular at the turning point. We more precisely accept a generic saddle-node bifurcation to pass through the turning point. It reveals that in this case the slow divergence integral is no longer the good tool to use, but its derivative with respect to the layer variable still is. We provide general results as well as a number of applications. We show how to treat the open problems presented in Artés et al. (2009) [1] and Dumortier and Rousseau (2009) [13], dealing respectively with the graphics DI2a and DF1a from Dumortier et al. (1994) [14].

Spectral Characteristics of the Unitary Critical Almost-Mathieu Operator

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

Comparison of two SVD-based color image compression schemes.

PubMed

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

2017-01-01

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

Comparison of two SVD-based color image compression schemes

PubMed Central

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

2017-01-01

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

A robust method of computing finite difference coefficients based on Vandermonde matrix

NASA Astrophysics Data System (ADS)

Zhang, Yijie; Gao, Jinghuai; Peng, Jigen; Han, Weimin

2018-05-01

When the finite difference (FD) method is employed to simulate the wave propagation, high-order FD method is preferred in order to achieve better accuracy. However, if the order of FD scheme is high enough, the coefficient matrix of the formula for calculating finite difference coefficients is close to be singular. In this case, when the FD coefficients are computed by matrix inverse operator of MATLAB, inaccuracy can be produced. In order to overcome this problem, we have suggested an algorithm based on Vandermonde matrix in this paper. After specified mathematical transformation, the coefficient matrix is transformed into a Vandermonde matrix. Then the FD coefficients of high-order FD method can be computed by the algorithm of Vandermonde matrix, which prevents the inverse of the singular matrix. The dispersion analysis and numerical results of a homogeneous elastic model and a geophysical model of oil and gas reservoir demonstrate that the algorithm based on Vandermonde matrix has better accuracy compared with matrix inverse operator of MATLAB.

Cold-Flow Testing of a Proposed Integrated Center-Body Diffuser/Steam Blocker Concept for Plum Brook Station's B-2 Test Facility

NASA Technical Reports Server (NTRS)

Edwards, Daryl A.; Weaver, Harold F; Kastner, Carl E., Jr.

2009-01-01

The center-body diffuser (CBD) steam blocker (SB) system is a concept that incorporates a set of secondary drive nozzles into the envelope of a CBD, such that both nozzle systems (i.e., the rocket engine and the steam blocking nozzles) utilize the same supersonic diffuser, and will operate either singularly or concurrently. In this manner, the SB performs as an exhaust system stage when the rocket engine is not operating, and virtually eliminates discharge flow on rocket engine shutdown. A 2.25-percent scale model of a proposed SB integrated into a diffuser for the Plum Brook B-2 facility was constructed and cold-flow tested for the purpose of evaluating performance characteristics of various design options. These specific design options addressed secondary drive nozzle design (method of steam injection), secondary drive nozzle location relative to CBD throat, and center-body throat length to diameter (L/D) ratios. The objective of the test program is to identify the desired configuration to carry forward should the next phase of design proceed. The tested scale model can provide data for various pressure ratios; however, its design is based on a proposed B-2 spray chamber (SC) operating pressure of 4.0 psia and a steam supply pressure of 165 psia. Evaluation of the test data acquired during these tests indicate that either the discrete axial or annular nozzle configuration integrated into a CBD, with an annular throat length of 1.5 L/D at the nominal injection position, would be suitable to carry forward from the SB's perspective. Selection between these two then becomes more a function of constructability and implementation than performance. L/D also has some flexibility, and final L/D selection can be a function of constructability issues within a limited range.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics.

PubMed

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y C

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals.

Boundary regularized integral equation formulation of the Helmholtz equation in acoustics

PubMed Central

Sun, Qiang; Klaseboer, Evert; Khoo, Boo-Cheong; Chan, Derek Y. C.

2015-01-01

A boundary integral formulation for the solution of the Helmholtz equation is developed in which all traditional singular behaviour in the boundary integrals is removed analytically. The numerical precision of this approach is illustrated with calculation of the pressure field owing to radiating bodies in acoustic wave problems. This method facilitates the use of higher order surface elements to represent boundaries, resulting in a significant reduction in the problem size with improved precision. Problems with extreme geometric aspect ratios can also be handled without diminished precision. When combined with the CHIEF method, uniqueness of the solution of the exterior acoustic problem is assured without the need to solve hypersingular integrals. PMID:26064591

Classical and quantum fold catastrophe in the presence of axial symmetry

NASA Astrophysics Data System (ADS)

Dhont, G.; Zhilinskií, B. I.

2008-11-01

We introduce a family of Hamiltonians with two degrees of freedom, axial symmetry and complete integrability. The potential function depends on coordinates and one control parameter. A fold catastrophe typically occurs in such a family of potentials and its consequences on the global dynamics are investigated through the energy-momentum map which defines the singular fibration of the four-dimensional phase space. The two inequivalent local canonical forms of the catastrophe are presented: the first case corresponds to the appearance of a second sheet in the image of the energy-momentum map while the second case is associated with the breaking of an already existing second sheet. A special effort is placed on the description of the singularities. In particular, the existence of cuspidal tori is related to a second-order contact point between the energy level set and the reduced phase space. The quantum mechanical aspects of the changes induced by the fold catastrophe are investigated with the quantum eigenstates computed for an octic potential and are interpreted through the quantum-classical correspondence. We note that the singularity exposed in this paper is not an obstruction to a global definition of action-angle variables.

Action growth of charged black holes with a single horizon

NASA Astrophysics Data System (ADS)

Cai, Rong-Gen; Sasaki, Misao; Wang, Shao-Jiang

2017-06-01

According to the conjecture "complexity equals action," the complexity of a holographic state is equal to the action of a Wheeler-DeWitt (WDW) patch of black holes in anti-de Sitter space. In this paper we calculate the action growth of charged black holes with a single horizon, paying attention to the contribution from a spacelike singularity inside the horizon. We consider two kinds of such charged black holes: one is a charged dilaton black hole, and the other is a Born-Infeld black hole with β2Q2<1 /4 . In both cases, although an electric charge appears in the black hole solutions, the inner horizon is absent; instead a spacelike singularity appears inside the horizon. We find that the action growth of the WDW patch of the charged black hole is finite and satisfies the Lloyd bound. As a check, we also calculate the action growth of a charged black hole with a phantom Maxwell field. In this case, although the contributions from the bulk integral and the spacelike singularity are individually divergent, these two divergences just cancel each other and a finite action growth is obtained. But in this case, the Lloyd bound is violated as expected.

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

PubMed

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

2015-10-14

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

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

NASA Astrophysics Data System (ADS)

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

2015-10-01

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

Raman q-plates for Singular Atom Optics

NASA Astrophysics Data System (ADS)

Schultz, Justin T.; Hansen, Azure; Murphree, Joseph D.; Jayaseelan, Maitreyi; Bigelow, Nicholas P.

2016-05-01

We use a coherent two-photon Raman interaction as the atom-optic equivalent of a birefringent optical q-plate to facilitate spin-to-orbital angular momentum conversion in a pseudo-spin-1/2 BEC. A q-plate is a waveplate with a fixed retardance but a spatially varying fast axis orientation angle. We derive the time evolution operator for the system and compare it to a Jones matrix for an optical waveplate to show that in our Raman q-plate, the equivalent orientation of the fast axis is described by the relative phase of the Raman beams and the retardance is determined by the pulse area. The charge of the Raman q-plate is determined by the orbital angular momentum of the Raman beams, and the beams contain umbilic C-point polarization singularities which are imprinted into the condensate as spin singularities: lemons, stars, spirals, and saddles. By tuning the optical beam parameters, we can create a full-Bloch BEC, which is a coreless vortex that contains every possible superposition of two spin states, that is, it covers the Bloch sphere.

Total variation regularization of the 3-D gravity inverse problem using a randomized generalized singular value decomposition

NASA Astrophysics Data System (ADS)

Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.

2018-04-01

We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.

On nonsingular potentials of Cox-Thompson inversion scheme

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

Palmai, Tamas; Apagyi, Barnabas

2010-02-15

We establish a condition for obtaining nonsingular potentials using the Cox-Thompson inverse scattering method with one phase shift. The anomalous singularities of the potentials are avoided by maintaining unique solutions of the underlying Regge-Newton integral equation for the transformation kernel. As a by-product, new inequality sequences of zeros of Bessel functions are discovered.

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…

Dissociating Interference-Control Processes between Memory and Response

ERIC Educational Resources Information Center

Bissett, Patrick G.; Nee, Derek Evan; Jonides, John

2009-01-01

The ability to mitigate interference is of central importance to cognition. Previous research has provided conflicting accounts about whether operations that resolve interference are singular in character or form a family of functions. Here, the authors examined the relationship between interference-resolution processes acting on working memory…

XRF map identification problems based on a PDE electrodeposition model

NASA Astrophysics Data System (ADS)

Sgura, Ivonne; Bozzini, Benedetto

2017-04-01

In this paper we focus on the following map identification problem (MIP): given a morphochemical reaction-diffusion (RD) PDE system modeling an electrodepostion process, we look for a time t *, belonging to the transient dynamics and a set of parameters \\mathbf{p} , such that the PDE solution, for the morphology h≤ft(x,y,{{t}\\ast};\\mathbf{p}\\right) and for the chemistry θ ≤ft(x,y,{{t}\\ast};\\mathbf{p}\\right) approximates a given experimental map M *. Towards this aim, we introduce a numerical algorithm using singular value decomposition (SVD) and Frobenius norm to give a measure of error distance between experimental maps for h and θ and simulated solutions of the RD-PDE system on a fixed time integration interval. The technique proposed allows quantitative use of microspectroscopy images, such as XRF maps. Specifically, in this work we have modelled the morphology and manganese distributions of nanostructured components of innovative batteries and we have followed their changes resulting from ageing under operating conditions. The availability of quantitative information on space-time evolution of active materials in terms of model parameters will allow dramatic improvements in knowledge-based optimization of battery fabrication and operation.

Conditions for the optical wireless links bit error ratio determination

NASA Astrophysics Data System (ADS)

Kvíčala, Radek

2017-11-01

To determine the quality of the Optical Wireless Links (OWL), there is necessary to establish the availability and the probability of interruption. This quality can be defined by the optical beam bit error rate (BER). Bit error rate BER presents the percentage of successfully transmitted bits. In practice, BER runs into the problem with the integration time (measuring time) determination. For measuring and recording of BER at OWL the bit error ratio tester (BERT) has been developed. The 1 second integration time for the 64 kbps radio links is mentioned in the accessible literature. However, it is impossible to use this integration time for singularity of coherent beam propagation.

The gravitational potential of axially symmetric bodies from a regularized green kernel

NASA Astrophysics Data System (ADS)

Trova, A.; Huré, J.-M.; Hersant, F.

2011-12-01

The determination of the gravitational potential inside celestial bodies (rotating stars, discs, planets, asteroids) is a common challenge in numerical Astrophysics. Under axial symmetry, the potential is classically found from a two-dimensional integral over the body's meridional cross-section. Because it involves an improper integral, high accuracy is generally difficult to reach. We have discovered that, for homogeneous bodies, the singular Green kernel can be converted into a regular kernel by direct analytical integration. This new kernel, easily managed with standard techniques, opens interesting horizons, not only for numerical calculus but also to generate approximations, in particular for geometrically thin discs and rings.

Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

NASA Astrophysics Data System (ADS)

Kamiya, Ryo; Kanki, Masataka; Mase, Takafumi; Tokihiro, Tetsuji

2017-01-01

We introduce a so-called coprimeness-preserving non-integrable extension to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equations defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.

Feedback control for fuel-optimal descents using singular perturbation techniques

NASA Technical Reports Server (NTRS)

Price, D. B.

1984-01-01

In response to rising fuel costs and reduced profit margins for the airline companies, the optimization of the paths flown by transport aircraft has been considered. It was found that application of optimal control theory to the considered problem can result in savings in fuel, time, and direct operating costs. The best solution to the aircraft trajectory problem is an onboard real-time feedback control law. The present paper presents a technique which shows promise of becoming a part of a complete solution. The application of singular perturbation techniques to the problem is discussed, taking into account the benefits and some problems associated with them. A different technique for handling the descent part of a trajectory is also discussed.

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

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

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

2012-12-15

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

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

Singular measures versus nondifferentiability: from the solid earth to the atmosphere and their interface (Invited)

NASA Astrophysics Data System (ADS)

Lovejoy, S.; Schertzer, D. J.

2010-12-01

In the 1980’s, the paradigm of Fractal Geometry popularized the fact that the ubiquitous geostatistical power laws imply nondifferentiabilty of the corresponding fractal sets, fractal functions. The prototypical examples of such scaling have flucutations Δf which change with scale Δx accordng to laws of the form Δf ≈ φΔx**H where H is the scaling exponent and φ is flux. The famous Kolmorogov turbulence law is the special case where Δf = Δv for velocity fluctuations across a distance Δx with H = 1/3 and φ = ɛ**1/3 where ɛ is the turbulent energy flux. Similarly, there is much evidence that topographic altitude fluctuations Δh are of the same form with Δf = Δh , H ≈1/2 and with φ a fundamental flux field governing topography dynamics. In both cases the basic laws are quite classical going back to 1941 (Kolmogorov; Δv) and to 1951 (Venig-Meinsz; Δh) respectively. From the above form we see that Δf/Δx ≈ φΔx**(H-1) which (when H<1) diverges as Δx tends to zero implying the divergence of the first derivative. Indeed, all (fractional) derivatives of order >H diverge. The focus on the geometry / differentiability properties puts the spotlight on the old H parameter. This has unfortunately drawn attention away from the more important consequences of our new understanding of the nonclassical flux φ as a singular multifractal measure. Over the last 25 years it has become clear that nonlinear processes that are scale invariant over wide ranges generically give rise to singular measures with statistics satisfying the relation <φ(λ)**q> ≈ λ**K(q) where λ is the resolution (defined as the ratio of the largest scale of the variability to the averaging scale), q is an arbitrary order of moment “<>” means statistical averaging, and K(q) is a scaling exponent function which characterizes the statistics of the flux at all the scales λ. Since φ(λ) is the ratio of the (Lebesque) integral of φ over a λ-resolution line, square or cube to the corrsponding length, area or volume of the integration set, such fluxes are singular with respect to Lebesgue measures (the scaling exponent K(q) - which is a cumulant generating function - diverges in the small scale limit i.e. as λ -> infinity). We give examples of such singular geomeasures ranging from ore concentrations, geopotential fields, topography, to surface and atmospheric radiances and to the state variables showing the ubiquity of singular measures throughout the geosciences. Classical geostatistics is based on point process random functions; it can easily handle nondifferentiability. However, it implicitly assumes that the relevant geomeasures are on the contrary regular with respect to Lebesgue measures. It would thus seem that real world geodata are outside the domain of application of classical geostatistics. We discuss the consequences.

Gauge fixing and BFV quantization

NASA Astrophysics Data System (ADS)

Rogers, Alice

2000-01-01

Non-singularity conditions are established for the Batalin-Fradkin-Vilkovisky (BFV) gauge-fixing fermion which are sufficient for it to lead to the correct path integral for a theory with constraints canonically quantized in the BFV approach. The conditions ensure that the anticommutator of this fermion with the BRST charge regularizes the path integral by regularizing the trace over non-physical states in each ghost sector. The results are applied to the quantization of a system which has a Gribov problem, using a non-standard form of the gauge-fixing fermion.

On the solution of integral equations with a generalized Cauchy kernel

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

A numerical technique is developed analytically to solve a class of singular integral equations occurring in mixed boundary-value problems for nonhomogeneous elastic media with discontinuities. The approach of Kaya and Erdogan (1987) is extended to treat equations with generalized Cauchy kernels, reformulating the boundary-value problems in terms of potentials as the unknown functions. The numerical implementation of the solution is discussed, and results for an epoxy-Al plate with a crack terminating at the interface and loading normal to the crack are presented in tables.

The spectral function of a singular differential operator of order 2m

NASA Astrophysics Data System (ADS)

Kozko, Artem I.; Pechentsov, Alexander S.

2010-12-01

We study the spectral function of a self-adjoint semibounded below differential operator on a Hilbert space L_2 \\lbrack 0,\\infty) and obtain the formulae for the spectral function of the operator (-1)^{m}y^{(2m)}(x) with general boundary conditions at the zero. In particular, for the boundary conditions y(0)=y'(0)=\\dots=y^{(m-1)}(0)=0 we find the explicit form of the spectral function \\Theta_{mB'}(x,x,\\lambda) on the diagonal x=y for \\lambda \\ge 0.

Capture of fixation by rotational flow; a deterministic hypothesis regarding scaling and stochasticity in fixational eye movements

PubMed Central

Wilkinson, Nicholas M.; Metta, Giorgio

2014-01-01

Visual scan paths exhibit complex, stochastic dynamics. Even during visual fixation, the eye is in constant motion. Fixational drift and tremor are thought to reflect fluctuations in the persistent neural activity of neural integrators in the oculomotor brainstem, which integrate sequences of transient saccadic velocity signals into a short term memory of eye position. Despite intensive research and much progress, the precise mechanisms by which oculomotor posture is maintained remain elusive. Drift exhibits a stochastic statistical profile which has been modeled using random walk formalisms. Tremor is widely dismissed as noise. Here we focus on the dynamical profile of fixational tremor, and argue that tremor may be a signal which usefully reflects the workings of oculomotor postural control. We identify signatures reminiscent of a certain flavor of transient neurodynamics; toric traveling waves which rotate around a central phase singularity. Spiral waves play an organizational role in dynamical systems at many scales throughout nature, though their potential functional role in brain activity remains a matter of educated speculation. Spiral waves have a repertoire of functionally interesting dynamical properties, including persistence, which suggest that they could in theory contribute to persistent neural activity in the oculomotor postural control system. Whilst speculative, the singularity hypothesis of oculomotor postural control implies testable predictions, and could provide the beginnings of an integrated dynamical framework for eye movements across scales. PMID:24616670

Creep crack-growth: A new path-independent integral (T sub c), and computational studies. Ph.D. Thesis Final Report

NASA Technical Reports Server (NTRS)

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

1982-01-01

The development of valid creep fracture criteria is considered. Two path-independent integral parameters which show some degree of promise are the C* and (Delta T)sub c integrals. The mathematical aspects of these parameters are reviewed by deriving generalized vector forms of the parameters using conservation laws which are valid for arbitrary, three dimensional, cracked bodies with crack surface tractions (or applied displacements), body forces, inertial effects, and large deformations. Two principal conclusions are that (Delta T)sub c has an energy rate interpretation whereas C* does not. The development and application of fracture criteria often involves the solution of boundary/initial value problems associated with deformation and stresses. The finite element method is used for this purpose. An efficient, small displacement, infinitesimal strain, displacement based finite element model is specialized to two dimensional plane stress and plane strain and to power law creep constitutive relations. A mesh shifting/remeshing procedure is used for simulating crack growth. The model is implemented with the quartz-point node technique and also with specially developed, conforming, crack-tip singularity elements which provide for the r to the n-(1+n) power strain singularity associated with the HRR crack-tip field. Comparisons are made with a variety of analytical solutions and alternate numerical solutions for a number of problems.

Contact Line Dynamics

NASA Astrophysics Data System (ADS)

Kreiss, Gunilla; Holmgren, Hanna; Kronbichler, Martin; Ge, Anthony; Brant, Luca

2017-11-01

The conventional no-slip boundary condition leads to a non-integrable stress singularity at a moving contact line. This makes numerical simulations of two-phase flow challenging, especially when capillarity of the contact point is essential for the dynamics of the flow. We will describe a modeling methodology, which is suitable for numerical simulations, and present results from numerical computations. The methodology is based on combining a relation between the apparent contact angle and the contact line velocity, with the similarity solution for Stokes flow at a planar interface. The relation between angle and velocity can be determined by theoretical arguments, or from simulations using a more detailed model. In our approach we have used results from phase field simulations in a small domain, but using a molecular dynamics model should also be possible. In both cases more physics is included and the stress singularity is removed.

Lifting-surface theory for calculating the loading induced on a wing by a flap

NASA Technical Reports Server (NTRS)

Johnson, W. A.

1972-01-01

A method is described for using lifting-surface theory to obtain the pressure distribution on a wing with a trailing-edge flap or control surface. The loading has a logarithmic singularity at the flap edges, which may be determined directly by the method of matched asymptotic expansions. Expressions are given for the singular flap loading for various flap hinge line and side edge geometries, both for steady and unsteady flap deflection. The regular part of the flap loading must be obtained by inverting the lifting-surface-theory integral equation relating the pressure and the downwash on the wing: procedures are described to accomplish this for a general wing and flap geometry. The method is applied to several example wings, and the results are compared with experimental data. Theory and test correlate well.

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.

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.

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)].

Chaotic processes using the two-parameter derivative with non-singular and non-local kernel: Basic theory and applications

NASA Astrophysics Data System (ADS)

Doungmo Goufo, Emile Franc

2016-08-01

After having the issues of singularity and locality addressed recently in mathematical modelling, another question regarding the description of natural phenomena was raised: How influent is the second parameter β of the two-parameter Mittag-Leffler function E α , β ( z ) , z ∈ ℂ ? To answer this question, we generalize the newly introduced one-parameter derivative with non-singular and non-local kernel [A. Atangana and I. Koca, Chaos, Solitons Fractals 89, 447 (2016); A. Atangana and D. Bealeanu (e-print)] by developing a similar two-parameter derivative with non-singular and non-local kernel based on Eα,β(z). We exploit the Agarwal/Erdelyi higher transcendental functions together with their Laplace transforms to explicitly establish the Laplace transform's expressions of the two-parameter derivatives, necessary for solving related fractional differential equations. Explicit expression of the associated two-parameter fractional integral is also established. Concrete applications are done on atmospheric convection process by using Lorenz non-linear simple system. Existence result for the model is provided and a numerical scheme established. As expected, solutions exhibit chaotic behaviors for α less than 0.55, and this chaos is not interrupted by the impact of β. Rather, this second parameter seems to indirectly squeeze and rotate the solutions, giving an impression of twisting. The whole graphics seem to have completely changed its orientation to a particular direction. This is a great observation that clearly shows the substantial impact of the second parameter of Eα,β(z), certainly opening new doors to modeling with two-parameter derivatives.

Chaotic processes using the two-parameter derivative with non-singular and non-local kernel: Basic theory and applications.

PubMed

Doungmo Goufo, Emile Franc

2016-08-01

After having the issues of singularity and locality addressed recently in mathematical modelling, another question regarding the description of natural phenomena was raised: How influent is the second parameter β of the two-parameter Mittag-Leffler function Eα,β(z), z∈ℂ? To answer this question, we generalize the newly introduced one-parameter derivative with non-singular and non-local kernel [A. Atangana and I. Koca, Chaos, Solitons Fractals 89, 447 (2016); A. Atangana and D. Bealeanu (e-print)] by developing a similar two-parameter derivative with non-singular and non-local kernel based on Eα , β(z). We exploit the Agarwal/Erdelyi higher transcendental functions together with their Laplace transforms to explicitly establish the Laplace transform's expressions of the two-parameter derivatives, necessary for solving related fractional differential equations. Explicit expression of the associated two-parameter fractional integral is also established. Concrete applications are done on atmospheric convection process by using Lorenz non-linear simple system. Existence result for the model is provided and a numerical scheme established. As expected, solutions exhibit chaotic behaviors for α less than 0.55, and this chaos is not interrupted by the impact of β. Rather, this second parameter seems to indirectly squeeze and rotate the solutions, giving an impression of twisting. The whole graphics seem to have completely changed its orientation to a particular direction. This is a great observation that clearly shows the substantial impact of the second parameter of Eα , β(z), certainly opening new doors to modeling with two-parameter derivatives.

Singular boundary method for global gravity field modelling

NASA Astrophysics Data System (ADS)

Cunderlik, Robert

2014-05-01

The singular boundary method (SBM) and method of fundamental solutions (MFS) are meshless boundary collocation techniques that use the fundamental solution of a governing partial differential equation (e.g. the Laplace equation) as their basis functions. They have been developed to avoid singular numerical integration as well as mesh generation in the traditional boundary element method (BEM). SBM have been proposed to overcome a main drawback of MFS - its controversial fictitious boundary outside the domain. The key idea of SBM is to introduce a concept of the origin intensity factors that isolate singularities of the fundamental solution and its derivatives using some appropriate regularization techniques. Consequently, the source points can be placed directly on the real boundary and coincide with the collocation nodes. In this study we deal with SBM applied for high-resolution global gravity field modelling. The first numerical experiment presents a numerical solution to the fixed gravimetric boundary value problem. The achieved results are compared with the numerical solutions obtained by MFS or the direct BEM indicating efficiency of all methods. In the second numerical experiments, SBM is used to derive the geopotential and its first derivatives from the Tzz components of the gravity disturbing tensor observed by the GOCE satellite mission. A determination of the origin intensity factors allows to evaluate the disturbing potential and gravity disturbances directly on the Earth's surface where the source points are located. To achieve high-resolution numerical solutions, the large-scale parallel computations are performed on the cluster with 1TB of the distributed memory and an iterative elimination of far zones' contributions is applied.

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.

Preschoolers' Use of Morphosyntactic Cues to Identify Generic Sentences: Indefinite Singular Noun Phrases, Tense, and Aspect

ERIC Educational Resources Information Center

Cimpian, Andrei; Meltzer, Trent J.; Markman, Ellen M.

2011-01-01

Generic sentences (e.g., "Birds lay eggs") convey generalizations about entire categories and may thus be an important source of knowledge for children. However, these sentences cannot be identified by a simple rule, requiring instead the integration of multiple cues. The present studies focused on 3- to 5-year-olds' (N = 91) use of…

Sputtered pin amorphous silicon semi-conductor device and method therefor

DOEpatents

Moustakas, Theodore D.; Friedman, Robert A.

1983-11-22

A high efficiency amorphous silicon PIN semi-conductor device is constructed by the sequential sputtering of N, I and P layers of amorphous silicon and at least one semi-transparent ohmic electrode. A method of construction produces a PIN device, exhibiting enhanced physical integrity and facilitates ease of construction in a singular vacuum system and vacuum pump down procedure.

A Human Rights and History Education Model for Teaching about Historical Events of Mass Violence: The 1947 British India Partition

ERIC Educational Resources Information Center

Chhabra, Meenakshi

2017-01-01

This article examines singular historical narratives of the 1947 British India Partition in four history textbooks from India, Pakistan, Bangladesh, and Britain, respectively. Drawing on analysis and work in the field, this study proposes a seven-module "integrated snail model" with a human rights orientation that can be applied to…

Green's functions for dislocations in bonded strips and related crack problems

NASA Technical Reports Server (NTRS)

Ballarini, R.; Luo, H. A.

1990-01-01

Green's functions are derived for the plane elastostatics problem of a dislocation in a bimaterial strip. Using these fundamental solutions as kernels, various problems involving cracks in a bimaterial strip are analyzed using singular integral equations. For each problem considered, stress intensity factors are calculated for several combinations of the parameters which describe loading, geometry and material mismatch.

Kowalevski's analysis of the swinging Atwood's machine

NASA Astrophysics Data System (ADS)

Babelon, O.; Talon, M.; Capdequi Peyranère, M.

2010-02-01

We study the Kowalevski expansions near singularities of the swinging Atwood's machine. We show that there is an infinite number of mass ratios M/m where such expansions exist with the maximal number of arbitrary constants. These expansions are of the so-called weak Painlevé type. However, in view of these expansions, it is not possible to distinguish between integrable and nonintegrable cases.

Renormalization of composite operators in Yang-Mills theories using a general covariant gauge

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

Collins, J.C.; Scalise, R.J.

Essential to QCD applications of the operator product expansion, etc., is a knowledge of those operators that mix with gauge-invariant operators. A standard theorem asserts that the renormalization matrix is triangular: Gauge-invariant operators have alien'' gauge-variant operators among their counterterms, but, with a suitably chosen basis, the necessary alien operators have only themselves as counterterms. Moreover, the alien operators are supposed to vanish in physical matrix elements. A recent calculation by Hamberg and van Neerven apparently contradicts these results. By explicit calculations with the energy-momentum tensor, we show that the problems arise because of subtle infrared singularities that appear whenmore » gluonic matrix elements are taken on shell at zero momentum transfer.« less

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.

Probing the Topology of Density Matrices

NASA Astrophysics Data System (ADS)

Bardyn, Charles-Edouard; Wawer, Lukas; Altland, Alexander; Fleischhauer, Michael; Diehl, Sebastian

2018-01-01

The mixedness of a quantum state is usually seen as an adversary to topological quantization of observables. For example, exact quantization of the charge transported in a so-called Thouless adiabatic pump is lifted at any finite temperature in symmetry-protected topological insulators. Here, we show that certain directly observable many-body correlators preserve the integrity of topological invariants for mixed Gaussian quantum states in one dimension. Our approach relies on the expectation value of the many-body momentum-translation operator and leads to a physical observable—the "ensemble geometric phase" (EGP)—which represents a bona fide geometric phase for mixed quantum states, in the thermodynamic limit. In cyclic protocols, the EGP provides a topologically quantized observable that detects encircled spectral singularities ("purity-gap" closing points) of density matrices. While we identify the many-body nature of the EGP as a key ingredient, we propose a conceptually simple, interferometric setup to directly measure the latter in experiments with mesoscopic ensembles of ultracold atoms.

Matrix quantum mechanics on S1 /Z2

NASA Astrophysics Data System (ADS)

Betzios, P.; Gürsoy, U.; Papadoulaki, O.

2018-03-01

We study Matrix Quantum Mechanics on the Euclidean time orbifold S1 /Z2. Upon Wick rotation to Lorentzian time and taking the double-scaling limit this theory provides a toy model for a big-bang/big crunch universe in two dimensional non-critical string theory where the orbifold fixed points become cosmological singularities. We derive the MQM partition function both in the canonical and grand canonical ensemble in two different formulations and demonstrate agreement between them. We pinpoint the contribution of twisted states in both of these formulations either in terms of bi-local operators acting at the end-points of time or branch-cuts on the complex plane. We calculate, in the matrix model, the contribution of the twisted states to the torus level partition function explicitly and show that it precisely matches the world-sheet result, providing a non-trivial test of the proposed duality. Finally we discuss some interesting features of the partition function and the possibility of realising it as a τ-function of an integrable hierarchy.

Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

NASA Astrophysics Data System (ADS)

Broedel, Johannes; Duhr, Claude; Dulat, Falko; Tancredi, Lorenzo

2018-05-01

We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring that they have at most simple poles, implying that the iterated integrals have at most logarithmic singularities. We study the properties of our iterated integrals and their relationship to the multiple elliptic polylogarithms from the mathematics literature. On the one hand, we find that our iterated integrals span essentially the same space of functions as the multiple elliptic polylogarithms. On the other, our formulation allows for a more direct use to solve a large variety of problems in high-energy physics. We demonstrate the use of our functions in the evaluation of the Laurent expansion of some hypergeometric functions for values of the indices close to half integers.

Numerical integration techniques for curved-element discretizations of molecule-solvent interfaces.

PubMed

Bardhan, Jaydeep P; Altman, Michael D; Willis, David J; Lippow, Shaun M; Tidor, Bruce; White, Jacob K

2007-07-07

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, here methods were developed to model several important surface formulations using exact surface discretizations. Following and refining Zauhar's work [J. Comput.-Aided Mol. Des. 9, 149 (1995)], two classes of curved elements were defined that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. Numerical integration techniques are presented that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, a set of calculations are presented that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planar-triangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute-solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that the methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online as supplemental material.

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

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.

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.

A Proposed System of "Project Management" for Study Items.

ERIC Educational Resources Information Center

Worcester Public Schools, MA.

The purposes of the proposed system are to provide a standard operating procedure for a systematic and effective handling of project-type study items as differentiated from informational-type items; to assign definite singular responsibility for projects; to suggest specific sequential steps to be taken in the preparation of the project report;…

Characterization of an elastic target in a shallow water waveguide by decomposition of the time-reversal operator.

PubMed

Philippe, Franck D; Prada, Claire; de Rosny, Julien; Clorennec, Dominique; Minonzio, Jean-Gabriel; Fink, Mathias

2008-08-01

This paper reports the results of an investigation into extracting of the backscattered frequency signature of a target in a waveguide. Retrieving the target signature is difficult because it is blurred by waveguide reflections and modal interference. It is shown that the decomposition of the time-reversal operator method provides a solution to this problem. Using a modal theory, this paper shows that the first singular value associated with a target is proportional to the backscattering form function. It is linked to the waveguide geometry through a factor that weakly depends on frequency as long as the target is far from the boundaries. Using the same approach, the second singular value is shown to be proportional to the second derivative of the angular form function which is a relevant parameter for target identification. Within this framework the coupling between two targets is considered. Small scale experimental studies are performed in the 3.5 MHz frequency range for 3 mm spheres in a 28 mm deep and 570 mm long waveguide and confirm the theoretical results.

Improved control of the betatron coupling in the Large Hadron Collider

NASA Astrophysics Data System (ADS)

Persson, T.; Tomás, R.

2014-05-01

The control of the betatron coupling is of importance for safe beam operation in the LHC. In this article we show recent advancements in methods and algorithms to measure and correct coupling. The benefit of using a more precise formula relating the resonance driving term f1001 to the ΔQmin is presented. The quality of the coupling measurements is increased, with about a factor 3, by selecting beam position monitor (BPM) pairs with phase advances close to π/2 and through data cleaning using singular value decomposition with an optimal number of singular values. These improvements are beneficial for the implemented automatic coupling correction, which is based on injection oscillations, presented in the article. Furthermore, a proposed coupling feedback for the LHC is presented. The system will rely on the measurements from BPMs equipped with a new type of high resolution electronics, diode orbit and oscillation, which will be operational when the LHC restarts in 2015. The feedback will combine the coupling measurements from the available BPMs in order to calculate the best correction.

Infrared singularities of scattering amplitudes in perturbative QCD

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

Becher, Thomas; Neubert, Matthias

2013-11-01

An exact formula is derived for the infrared singularities of dimensionally regularized scattering amplitudes in massless QCD with an arbitrary number of legs, valid at any number of loops. It is based on the conjecture that the anomalous-dimension matrix of n-jet operators in soft-collinear effective theory contains only a single non-trivial color structure, whose coefficient is the cusp anomalous dimension of Wilson loops with light-like segments. Its color-diagonal part is characterized by two anomalous dimensions, which are extracted to three-loop order from known perturbative results for the quark and gluon form factors. This allows us to predict the three-loop coefficientsmore » of all 1/epsilon^k poles for an arbitrary n-parton scattering amplitudes, generalizing existing two-loop results.« less

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

NASA Astrophysics Data System (ADS)

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

2016-07-01

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

Singular value decomposition for 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.

The compressible aerodynamics of rotating blades based on an acoustic formulation

NASA Technical Reports Server (NTRS)

Long, L. N.

1983-01-01

An acoustic formula derived for the calculation of the noise of moving bodies is applied to aerodynamic problems. The acoustic formulation is a time domain result suitable for slender wings and bodies moving at subsonic speeds. A singular integral equation is derived in terms of the surface pressure which must then be solved numerically for aerodynamic purposes. However, as the 'observer' is moved onto the body surface, the divergent integrals in the acoustic formulation are semiconvergent. The procedure for regularization (or taking principal values of divergent integrals) is explained, and some numerical examples for ellipsoids, wings, and lifting rotors are presented. The numerical results show good agreement with available measured surface pressure data.

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

Engine Operating Conditions and Fuel Properties on Pre-Spark Heat Release and SPI Promotion in SI Engines

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

Splitter, Derek A; Kaul, Brian C; Szybist, James P

This work explores the dependence of fuel ignition delay on stochastic pre-ignition (SPI). Findings are based on bulk gas thermodynamic state, where the effects of kinetically controlled bulk gas pre-spark heat release (PSHR) are correlated to SPI tendency and magnitude. Specifically, residual gas and low temperature PSHR chemistry effects and observations are explored, which are found to be indicative of bulk gas conditions required for strong SPI events. Analyzed events range from non-knocking SPI to knocking SPI and even detonation SPI events in excess of 325 bar peak cylinder pressure. The work illustrates that singular SPI event count and magnitudemore » are found to be proportional to PSHR of the bulk gas mixture and residual gas fraction. Cycle-to-cycle variability in trapped residual mass and temperature are found to impose variability in singular SPI event count and magnitude. However, clusters and short lived bursts of multiple SPI events are found to better correlate with fuel-wall interaction. The results highlight the interplay of bulk gas thermodynamics and SPI ignition source, on SPI event magnitude and cluster tendency. Moreover, the results highlight fundamental fuel reactivity and associated hypersensitivity to operating conditions at SPI prone operating conditions.« less

A singular-value method for reconstruction of nonradial and lossy objects.

PubMed

Jiang, Wei; Astheimer, Jeffrey; Waag, Robert

2012-03-01

Efficient inverse scattering algorithms for nonradial lossy objects are presented using singular-value decomposition to form reduced-rank representations of the scattering operator. These algorithms extend eigenfunction methods that are not applicable to nonradial lossy scattering objects because the scattering operators for these objects do not have orthonormal eigenfunction decompositions. A method of local reconstruction by segregation of scattering contributions from different local regions is also presented. Scattering from each region is isolated by forming a reduced-rank representation of the scattering operator that has domain and range spaces comprised of far-field patterns with retransmitted fields that focus on the local region. Methods for the estimation of the boundary, average sound speed, and average attenuation slope of the scattering object are also given. These methods yielded approximations of scattering objects that were sufficiently accurate to allow residual variations to be reconstructed in a single iteration. Calculated scattering from a lossy elliptical object with a random background, internal features, and white noise is used to evaluate the proposed methods. Local reconstruction yielded images with spatial resolution that is finer than a half wavelength of the center frequency and reproduces sound speed and attenuation slope with relative root-mean-square errors of 1.09% and 11.45%, respectively.

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

PubMed

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

2017-03-27

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

A Proof of Factorization Theorem of Drell-Yan Process at Operator Level

NASA Astrophysics Data System (ADS)

Zhou, Gao-Liang

2016-02-01

An alternative proof of factorization theorem for Drell-Yan process that works at operator level is presented in this paper. Contributions of interactions after the hard collision for such inclusive processes are proved to be canceled at operator level according to the unitarity of time evolution operator. After this cancellation, there are no longer leading pinch singular surface in Glauber region in the time evolution of electromagnetic currents. Effects of soft gluons are absorbed into Wilson lines of scalar-polarized gluons. Cancelation of soft gluons is attribute to unitarity of time evolution operator and such Wilson lines. Supported by the National Natural Science Foundation of China under Grant No. 11275242

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.

On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

NASA Astrophysics Data System (ADS)

Voytishek, Anton V.; Shipilov, Nikolay M.

2017-11-01

In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

Triangle singularities and XYZ quarkonium peaks

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

Szczepaniak, Adam P.

2015-06-01

We discuss analytical properties of partial waves derived from projection of a 4-legged amplitude with crossed-channel exchanges in the kinematic region of the direct channel that corresponds to the XYZ peaks in charmonium and bottomonium. We show that in general partial waves can develop anomalous branch points in the vicinity of the direct channel physical region. In a specific case, when these branch points lie on the opposite side of the unitary cut they pinch the integration contour in a dispersion relation and if the pinch happens close to threshold, the normal threshold cusp is enhanced. We show that this effect only occurs if masses of resonances in the crossed channel are in a specific, narrow range. We estimate the size of threshold enhancements originating from these anomalous singularities in reactions where themore » $$Z_c(3900)$$ and the $$Z_b(10610)$$ peaks have been observed.« less

A new approach to the effect of sound on vortex dynamics

NASA Technical Reports Server (NTRS)

Lund, Fernando; Zabusky, Norman J.

1987-01-01

Analytical results are presented on the effect of acoustic radiation on three-dimensional vortex motions in a homogeneous, slightly compressible, inviscid fluid. The flow is considered as linear and irrotational everywhere except inside a very thin cylindrical core region around the vortex filament. In the outside region, a velocity potential is introduced that must be multivalued, and it is shown how to compute this scalar potential if the motion of the vortex filament is prescribed. To find the motion of this singularity in an external potential flow, a variational principle involving a volume integral that must exclude the singular region is considered. A functional of the external potential and vortex filament position is obtained whose extrema give equations to determine the sought-after evolution. Thus, a generalization of the Biot-Savart law to flows with constant sound speed at low Mach number is obtained.

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

PubMed

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

2017-03-01

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

Alien calculus and a Schwinger-Dyson equation: two-point function with a nonperturbative mass scale

NASA Astrophysics Data System (ADS)

Bellon, Marc P.; Clavier, Pierre J.

2018-02-01

Starting from the Schwinger-Dyson equation and the renormalization group equation for the massless Wess-Zumino model, we compute the dominant nonperturbative contributions to the anomalous dimension of the theory, which are related by alien calculus to singularities of the Borel transform on integer points. The sum of these dominant contributions has an analytic expression. When applied to the two-point function, this analysis gives a tame evolution in the deep euclidean domain at this approximation level, making doubtful the arguments on the triviality of the quantum field theory with positive β -function. On the other side, we have a singularity of the propagator for timelike momenta of the order of the renormalization group invariant scale of the theory, which has a nonperturbative relationship with the renormalization point of the theory. All these results do not seem to have an interpretation in terms of semiclassical analysis of a Feynman path integral.

A novel equivalent definition of Caputo fractional derivative without singular kernel and superconvergent analysis

NASA Astrophysics Data System (ADS)

Liu, Zhengguang; Li, Xiaoli

2018-05-01

In this article, we present a new second-order finite difference discrete scheme for a fractal mobile/immobile transport model based on equivalent transformative Caputo formulation. The new transformative formulation takes the singular kernel away to make the integral calculation more efficient. Furthermore, this definition is also effective where α is a positive integer. Besides, the T-Caputo derivative also helps us to increase the convergence rate of the discretization of the α-order(0 < α < 1) Caputo derivative from O(τ2-α) to O(τ3-α), where τ is the time step. For numerical analysis, a Crank-Nicolson finite difference scheme to solve the fractal mobile/immobile transport model is introduced and analyzed. The unconditional stability and a priori estimates of the scheme are given rigorously. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

Tensor hypercontraction. II. Least-squares renormalization

NASA Astrophysics Data System (ADS)

Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.; Sherrill, C. David

2012-12-01

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)], 10.1063/1.4732310. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1/r12 operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N^5) effort if exact integrals are decomposed, or O(N^4) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N^4) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

Tensor hypercontraction. II. Least-squares renormalization.

PubMed

Parrish, Robert M; Hohenstein, Edward G; Martínez, Todd J; Sherrill, C David

2012-12-14

The least-squares tensor hypercontraction (LS-THC) representation for the electron repulsion integral (ERI) tensor is presented. Recently, we developed the generic tensor hypercontraction (THC) ansatz, which represents the fourth-order ERI tensor as a product of five second-order tensors [E. G. Hohenstein, R. M. Parrish, and T. J. Martínez, J. Chem. Phys. 137, 044103 (2012)]. Our initial algorithm for the generation of the THC factors involved a two-sided invocation of overlap-metric density fitting, followed by a PARAFAC decomposition, and is denoted PARAFAC tensor hypercontraction (PF-THC). LS-THC supersedes PF-THC by producing the THC factors through a least-squares renormalization of a spatial quadrature over the otherwise singular 1∕r(12) operator. Remarkably, an analytical and simple formula for the LS-THC factors exists. Using this formula, the factors may be generated with O(N(5)) effort if exact integrals are decomposed, or O(N(4)) effort if the decomposition is applied to density-fitted integrals, using any choice of density fitting metric. The accuracy of LS-THC is explored for a range of systems using both conventional and density-fitted integrals in the context of MP2. The grid fitting error is found to be negligible even for extremely sparse spatial quadrature grids. For the case of density-fitted integrals, the additional error incurred by the grid fitting step is generally markedly smaller than the underlying Coulomb-metric density fitting error. The present results, coupled with our previously published factorizations of MP2 and MP3, provide an efficient, robust O(N(4)) approach to both methods. Moreover, LS-THC is generally applicable to many other methods in quantum chemistry.

Calogero-Sutherland system with two types interacting spins

NASA Astrophysics Data System (ADS)

Kharchev, S.; Levin, A.; Olshanetsky, M.; Zotov, A.

2017-08-01

We consider the classical Calogero-Sutherland system with two types of interacting spin variables. It can be reduced to the standard Calogero-Sutherland system, when one of the spin variables vanishes. We describe the model in the Hitchin approach and prove complete integrability of the system by constructing the Lax pair and the classical r-matrix with the spectral parameter on a singular curve.

The resolvent of singular integral equations. [of kernel functions in mixed boundary value problems

NASA Technical Reports Server (NTRS)

Williams, M. H.

1977-01-01

The investigation reported is concerned with the construction of the resolvent for any given kernel function. In problems with ill-behaved inhomogeneous terms as, for instance, in the aerodynamic problem of flow over a flapped airfoil, direct numerical methods become very difficult. A description is presented of a solution method by resolvent which can be employed in such problems.

Astronaut activity in weightlessness and unsupported space

NASA Technical Reports Server (NTRS)

Ivanov, Y. A.; Popov, V. A.; Kachaturyants, L. S.

1975-01-01

For the purpose of study of the performance ability of a human operator in prolonged weightless conditions was studied by the following methods: (1) psychophysiological analysis of certain operations; (2) the dynamic characteristics of a man, included in a model control system, with direct and delayed feedback; (3) evaluation of the singularities of analysis and quality of the working memory, in working with outlines of patterned and random lines; and (4) biomechanical analysis of spatial orientation and motor activity in unsupported space.

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.

Quantum walks with an anisotropic coin I: spectral theory

NASA Astrophysics Data System (ADS)

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

2018-02-01

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

High speed propeller acoustics and aerodynamics - A boundary element approach

NASA Technical Reports Server (NTRS)

Farassat, F.; Myers, M. K.; Dunn, M. H.

1989-01-01

The Boundary Element Method (BEM) is applied in this paper to the problems of acoustics and aerodynamics of high speed propellers. The underlying theory is described based on the linearized Ffowcs Williams-Hawkings equation. The surface pressure on the blade is assumed unknown in the aerodynamic problem. It is obtained by solving a singular integral equation. The acoustic problem is then solved by moving the field point inside the fluid medium and evaluating some surface and line integrals. Thus the BEM provides a powerful technique in calculation of high speed propeller aerodynamics and acoustics.

Analysis of a Generally Oriented Crack in a Functionally Graded Strip Sandwiched Between Two Homogeneous Half Planes

NASA Technical Reports Server (NTRS)

Shbeeb, N.; Binienda, W. K.; Kreider, K.

1999-01-01

The driving forces for a generally oriented crack embedded in a Functionally Graded strip sandwiched between two half planes are analyzed using singular integral equations with Cauchy kernels, and integrated using Lobatto-Chebyshev collocation. Mixed-mode Stress Intensity Factors (SIF) and Strain Energy Release Rates (SERR) are calculated. The Stress Intensity Factors are compared for accuracy with previously published results. Parametric studies are conducted for various nonhomogeneity ratios, crack lengths. crack orientation and thickness of the strip. It is shown that the SERR is more complete and should be used for crack propagation analysis.

Analysis of an Interface Crack for a Functionally Graded Strip Sandwiched between Two Homogeneous Layers of Finite Thickness

NASA Technical Reports Server (NTRS)

Shbeeh, N. I.; Binienda, W. K.

1999-01-01

The interface crack problem for a composite layer that consists of a homogeneous substrate, coating and a non-homogeneous interface was formulated for singular integral equations with Cauchy kernels and integrated using the Lobatto-Chebyshev collocation technique. Mixed-mode Stress Intensity Factors and Strain Energy Release Rates were calculated. The Stress Intensity Factors were compared for accuracy with relevant results previously published. The parametric studies were conducted for the various thickness of each layer and for various non-homogeneity ratios. Particular application to the Zirconia thermal barrier on steel substrate is demonstrated.

A new aerodynamic integral equation based on an acoustic formula in the time domain

NASA Technical Reports Server (NTRS)

Farassat, F.

1984-01-01

An aerodynamic integral equation for bodies moving at transonic and supersonic speeds is presented. Based on a time-dependent acoustic formula for calculating the noise emanating from the outer portion of a propeller blade travelling at high speed (the Ffowcs Williams-Hawking formulation), the loading terms and a conventional thickness source terms are retained. Two surface and three line integrals are employed to solve an equation for the loading noise. The near-field term is regularized using the collapsing sphere approach to obtain semiconvergence on the blade surface. A singular integral equation is thereby derived for the unknown surface pressure, and is amenable to numerical solutions using Galerkin or collocation methods. The technique is useful for studying the nonuniform inflow to the propeller.

Stability conditions for exact-exchange Kohn-Sham methods and their relation to correlation energies from the adiabatic-connection fluctuation-dissipation theorem.

PubMed

Bleiziffer, Patrick; Schmidtel, Daniel; Görling, Andreas

2014-11-28

The occurrence of instabilities, in particular singlet-triplet and singlet-singlet instabilities, in the exact-exchange (EXX) Kohn-Sham method is investigated. Hessian matrices of the EXX electronic energy with respect to the expansion coefficients of the EXX effective Kohn-Sham potential in an auxiliary basis set are derived. The eigenvalues of these Hessian matrices determine whether or not instabilities are present. Similar as in the corresponding Hartree-Fock case instabilities in the EXX method are related to symmetry breaking of the Hamiltonian operator for the EXX orbitals. In the EXX methods symmetry breaking can easily be visualized by displaying the local multiplicative exchange potential. Examples (N2, O2, and the polyyne C10H2) for instabilities and symmetry breaking are discussed. The relation of the stability conditions for EXX methods to approaches calculating the Kohn-Sham correlation energy via the adiabatic-connection fluctuation-dissipation (ACFD) theorem is discussed. The existence or nonexistence of singlet-singlet instabilities in an EXX calculation is shown to indicate whether or not the frequency-integration in the evaluation of the correlation energy is singular in the EXX-ACFD method. This method calculates the Kohn-Sham correlation energy through the ACFD theorem theorem employing besides the Coulomb kernel also the full frequency-dependent exchange kernel and yields highly accurate electronic energies. For the case of singular frequency-integrands in the EXX-ACFD method a regularization is suggested. Finally, we present examples of molecular systems for which the self-consistent field procedure of the EXX as well as the Hartree-Fock method can converge to more than one local minimum depending on the initial conditions.

An Industrial Perspective of CAM/ROB Fuzzy Integrated Postprocessing Implementation for Redundant Robotic Workcells Applicability for Big Volume Prototyping

NASA Astrophysics Data System (ADS)

Andrés, J.; Gracia, L.; Tornero, J.; García, J. A.; González, F.

2009-11-01

The implementation of a postprocessor for the NX™ platform (Siemens Corp.) is described in this paper. It is focused on a milling redundant robotic milling workcell consisting of one KUKA KR 15/2 manipulator (6 rotary joints, KRC2 controller) mounted on a linear axis and synchronized with a rotary table (i.e., two additional joints). For carrying out a milling task, a choice among a set of possible configurations is required, taking into account the ability to avoid singular configurations by using both additional joints. Usually, experience and knowledge of the workman allow an efficient control in these cases, but being it a tedious job. Similarly to this expert knowledge, a stand-alone fuzzy controller has been programmed with Matlab's Fuzzy Logic Toolbox (The MathWorks, Inc.). Two C++ programs complement the translation of the toolpath tracking (expressed in the Cartesian space) from the NX™-CAM module into KRL (KUKA Robot Language). In order to avoid singularities or joint limits, the location of the robot and the workpiece during the execution of the task is fit after an inverse kinematics position analysis and a fuzzy inference (i.e., fuzzy criterion in the Joint Space). Additionally, the applicability of robot arms for the manufacture of big volume prototypes with this technique is proven by means of one case studied. It consists of a big orographic model to simulate floodways, return flows and retention storage of a reservoir in the Mijares river (Puebla de Arenoso, Spain). This article deals with the problem for a constant tool orientation milling process and sets the technological basis for future research at five axis milling operations.

FEWZ 2.0: A code for hadronic Z production at next-to-next-to-leading order

NASA Astrophysics Data System (ADS)

Gavin, Ryan; Li, Ye; Petriello, Frank; Quackenbush, Seth

2011-11-01

We introduce an improved version of the simulation code FEWZ ( Fully Exclusive W and Z Production) for hadron collider production of lepton pairs through the Drell-Yan process at next-to-next-to-leading order (NNLO) in the strong coupling constant. The program is fully differential in the phase space of leptons and additional hadronic radiation. The new version offers users significantly more options for customization. FEWZ now bins multiple, user-selectable histograms during a single run, and produces parton distribution function (PDF) errors automatically. It also features a significantly improved integration routine, and can take advantage of multiple processor cores locally or on the Condor distributed computing system. We illustrate the new features of FEWZ by presenting numerous phenomenological results for LHC physics. We compare NNLO QCD with initial ATLAS and CMS results, and discuss in detail the effects of detector acceptance on the measurement of angular quantities associated with Z-boson production. We address the issue of technical precision in the presence of severe phase-space cuts. Program summaryProgram title: FEWZ Catalogue identifier: AEJP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEJP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 6 280 771 No. of bytes in distributed program, including test data, etc.: 173 027 645 Distribution format: tar.gz Programming language: Fortran 77, C++, Python Computer: Mac, PC Operating system: Mac OSX, Unix/Linux Has the code been vectorized or parallelized?: Yes. User-selectable, 1 to 219 RAM: 200 Mbytes for common parton distribution functions Classification: 11.1 External routines: CUBA numerical integration library, numerous parton distribution sets (see text); these are provided with the code. Nature of problem: Determination of the Drell-Yan Z/photon production cross section and decay into leptons, with kinematic distributions of leptons and jets including full spin correlations, at next-to-next-to-leading order in the strong coupling constant. Solution method: Virtual loop integrals are decomposed into master integrals using automated techniques. Singularities are extracted from real radiation terms via sector decomposition, which separates singularities and maps onto suitable phase space variables. Result is convoluted with parton distribution functions. Each piece is numerically integrated over phase space, which allows arbitrary cuts on the observed particles. Each sample point may be binned during numerical integration, providing histograms, and reweighted by parton distribution function error eigenvectors, which provides PDF errors. Restrictions: Output does not correspond to unweighted events, and cannot be interfaced with a shower Monte Carlo. Additional comments: !!!!! The distribution file for this program is over 170 Mbytes and therefore is not delivered directly when download or E-mail is requested. Instead a html file giving details of how the program can be obtained is sent. Running time: One day for total cross sections with 0.1% integration errors assuming typical cuts, up to 1 week for smooth kinematic distributions with sub-percent integration errors for each bin.

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…

Implicit-shifted Symmetric QR Singular Value Decomposition of 3x3 Matrices

DTIC Science & Technology

2016-04-01

Graph 33, 4, 138:1– 138:11. TREFETHEN, L. N., AND BAU III, D. 1997. Numerical linear algebra , vol. 50. Siam. XU, H., SIN, F., ZHU, Y., AND BARBIČ, J...matrices with minimal branching and elementary floating point operations. Tech. rep., University of Wisconsin- Madison. SAITO, S., ZHOU, Z.-Y., AND

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

A tele-operated mobile ultrasound scanner using a light-weight robot.

PubMed

Delgorge, Cécile; Courrèges, Fabien; Al Bassit, Lama; Novales, Cyril; Rosenberger, Christophe; Smith-Guerin, Natalie; Brù, Concepció; Gilabert, Rosa; Vannoni, Maurizio; Poisson, Gérard; Vieyres, Pierre

2005-03-01

This paper presents a new tele-operated robotic chain for real-time ultrasound image acquisition and medical diagnosis. This system has been developed in the frame of the Mobile Tele-Echography Using an Ultralight Robot European Project. A light-weight six degrees-of-freedom serial robot, with a remote center of motion, has been specially designed for this application. It holds and moves a real probe on a distant patient according to the expert gesture and permits an image acquisition using a standard ultrasound device. The combination of mechanical structure choice for the robot and dedicated control law, particularly nearby the singular configuration allows a good path following and a robotized gesture accuracy. The choice of compression techniques for image transmission enables a compromise between flow and quality. These combined approaches, for robotics and image processing, enable the medical specialist to better control the remote ultrasound probe holder system and to receive stable and good quality ultrasound images to make a diagnosis via any type of communication link from terrestrial to satellite. Clinical tests have been performed since April 2003. They used both satellite or Integrated Services Digital Network lines with a theoretical bandwidth of 384 Kb/s. They showed the tele-echography system helped to identify 66% of lesions and 83% of symptomatic pathologies.

Genomic signal processing: from matrix algebra to genetic networks.

PubMed

Alter, Orly

2007-01-01

DNA microarrays make it possible, for the first time, to record the complete genomic signals that guide the progression of cellular processes. Future discovery in biology and medicine will come from the mathematical modeling of these data, which hold the key to fundamental understanding of life on the molecular level, as well as answers to questions regarding diagnosis, treatment, and drug development. This chapter reviews the first data-driven models that were created from these genome-scale data, through adaptations and generalizations of mathematical frameworks from matrix algebra that have proven successful in describing the physical world, in such diverse areas as mechanics and perception: the singular value decomposition model, the generalized singular value decomposition model comparative model, and the pseudoinverse projection integrative model. These models provide mathematical descriptions of the genetic networks that generate and sense the measured data, where the mathematical variables and operations represent biological reality. The variables, patterns uncovered in the data, correlate with activities of cellular elements such as regulators or transcription factors that drive the measured signals and cellular states where these elements are active. The operations, such as data reconstruction, rotation, and classification in subspaces of selected patterns, simulate experimental observation of only the cellular programs that these patterns represent. These models are illustrated in the analyses of RNA expression data from yeast and human during their cell cycle programs and DNA-binding data from yeast cell cycle transcription factors and replication initiation proteins. Two alternative pictures of RNA expression oscillations during the cell cycle that emerge from these analyses, which parallel well-known designs of physical oscillators, convey the capacity of the models to elucidate the design principles of cellular systems, as well as guide the design of synthetic ones. In these analyses, the power of the models to predict previously unknown biological principles is demonstrated with a prediction of a novel mechanism of regulation that correlates DNA replication initiation with cell cycle-regulated RNA transcription in yeast. These models may become the foundation of a future in which biological systems are modeled as physical systems are today.

Wave-function functionals

NASA Astrophysics Data System (ADS)

Pan, Xiao-Yin; Slamet, Marlina; Sahni, Viraht

2010-04-01

We extend our prior work on the construction of variational wave functions ψ that are functionals of functions χ:ψ=ψ[χ] rather than simply being functions. In this manner, the space of variations is expanded over those of traditional variational wave functions. In this article we perform the constrained search over the functions χ chosen such that the functional ψ[χ] satisfies simultaneously the constraints of normalization and the exact expectation value of an arbitrary single- or two-particle Hermitian operator, while also leading to a rigorous upper bound to the energy. As such the wave function functional is accurate not only in the region of space in which the principal contributions to the energy arise but also in the other region of the space represented by the Hermitian operator. To demonstrate the efficacy of these ideas, we apply such a constrained search to the ground state of the negative ion of atomic hydrogen H-, the helium atom He, and its positive ions Li+ and Be2+. The operators W whose expectations are obtained exactly are the sum of the single-particle operators W=∑irin,n=-2,-1,1,2, W=∑iδ(ri), W=-(1)/(2)∑i∇i2, and the two-particle operators W=∑nun,n=-2,-1,1,2, where u=|ri-rj|. Comparisons with the method of Lagrangian multipliers and of other constructions of wave-function functionals are made. Finally, we present further insights into the construction of wave-function functionals by studying a previously proposed construction of functionals ψ[χ] that lead to the exact expectation of arbitrary Hermitian operators. We discover that analogous to the solutions of the Schrödinger equation, there exist ψ[χ] that are unphysical in that they lead to singular values for the expectations. We also explain the origin of the singularity.

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.

Quantum chaos inside black holes

NASA Astrophysics Data System (ADS)

Addazi, Andrea

2017-06-01

We show how semiclassical black holes can be reinterpreted as an effective geometry, composed of a large ensemble of horizonless naked singularities (eventually smoothed at the Planck scale). We call these new items frizzy-balls, which can be rigorously defined by Euclidean path integral approach. This leads to interesting implications about information paradoxes. We demonstrate that infalling information will chaotically propagate inside this system before going to the full quantum gravity regime (Planck scale).

Similarity solutions of time-dependent relativistic radiation-hydrodynamical plane-parallel flows

NASA Astrophysics Data System (ADS)

Fukue, Jun

2018-04-01

Similarity solutions are examined for the frequency-integrated relativistic radiation-hydrodynamical flows, which are described by the comoving quantities. The flows are vertical plane-parallel time-dependent ones with a gray opacity coefficient. For adequate boundary conditions, the flows are accelerated in a somewhat homologous manner, but terminate at some singular locus, which originates from the pathological behavior in relativistic radiation moment equations truncated in finite orders.

Similarity solutions of time-dependent relativistic radiation-hydrodynamical plane-parallel flows

NASA Astrophysics Data System (ADS)

Fukue, Jun

2018-06-01

Similarity solutions are examined for the frequency-integrated relativistic radiation-hydrodynamical flows, which are described by the comoving quantities. The flows are vertical plane-parallel time-dependent ones with a gray opacity coefficient. For adequate boundary conditions, the flows are accelerated in a somewhat homologous manner, but terminate at some singular locus, which originates from the pathological behavior in relativistic radiation moment equations truncated in finite orders.

A study of the generation of linear energy transfer spectra for space radiations

NASA Technical Reports Server (NTRS)

Wilson, John W.; Badavi, Francis F.

1992-01-01

The conversion of particle-energy spectra into a linear energy transfer (LET) distribution is a guide in assessing biologically significant components. The mapping of LET to energy is triple valued and can be defined only on open subintervals. A well-defined numerical procedure is found to allow generation of LET spectra on the open subintervals that are integrable in spite of their singular nature.

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

NASA Technical Reports Server (NTRS)

Shin, Jong-Yeob; Belcastro, Christine

2008-01-01

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

Integrating international responses to complex emergencies, unconventional war, and terrorism.

PubMed

Burkle, Frederick M

2005-01-01

The world is experiencing unprecedented violence and threats of violence, taking the form of complex internal nation-state conflicts, unconventional or guerrilla warfare against established governments, and stateless threats of terrorism by potential biologic, chemical, and nuclear weapons. What happens locally has immediate ramifications internationally. Real and potential health consequences of these events have evoked global concerns and realization that capacities and capabilities to respond to such events require unparalleled integration, coordination, and cooperation of the international community. However, politics and the institutions singular governments form are inherently limited in their objectives and capability to effectively respond. Public health, broadly defined, must be recognized as a security and strategic requirement, one that serves to build a foundation for an international integrated response capacity.

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.

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.

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

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

NASA Astrophysics Data System (ADS)

Wang, Linhong; He, Yiwen

2011-12-01

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

Continuations of the nonlinear Schrödinger equation beyond the singularity

NASA Astrophysics Data System (ADS)

Fibich, G.; Klein, M.

2011-07-01

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

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.

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

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

Woolgar, Eric, E-mail: ewoolgar@ualberta.ca; Wylie, William, E-mail: wwylie@syr.edu

We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the “pure Bakry-Émery” N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able tomore » extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (−∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (−∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.« less

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

NASA Astrophysics Data System (ADS)

Passarino, Giampiero

2001-12-01

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

Singular lensing from the scattering on special space-time defects

NASA Astrophysics Data System (ADS)

Mavromatos, Nick E.; Papavassiliou, Joannis

2018-01-01

It is well known that certain special classes of self-gravitating point-like defects, such as global (non gauged) monopoles, give rise to non-asymptotically flat space-times characterized by solid angle deficits, whose size depends on the details of the underlying microscopic models. The scattering of electrically neutral particles on such space-times is described by amplitudes that exhibit resonant behaviour when thescattering and deficit angles coincide. This, in turn, leads to ring-like structures where the cross sections are formally divergent ("singular lensing"). In this work, we revisit this particular phenomenon, with the twofold purpose of placing it in a contemporary and more general context, in view of renewed interest in the theory and general phenomenology of such defects, and, more importantly, of addressing certain subtleties that appear in the particular computation that leads to the aforementioned effect. In particular, by adopting a specific regularization procedure for the formally infinite Legendre series encountered, we manage to ensure the recovery of the Minkowski space-time, and thus the disappearance of the lensing phenomenon, in the no-defect limit, and the validity of the optical theorem for the elastic total cross section. In addition, the singular nature of the phenomenon is confirmed by means of an alternative calculation, which, unlike the original approach, makes no use of the generating function of the Legendre polynomials, but rather exploits the asymptotic properties of the Fresnel integrals.

Cosmological singularity theorems and splitting theorems for N-Bakry-Émery spacetimes

NASA Astrophysics Data System (ADS)

Woolgar, Eric; Wylie, William

2016-02-01

We study Lorentzian manifolds with a weight function such that the N-Bakry-Émery tensor is bounded below. Such spacetimes arise in the physics of scalar-tensor gravitation theories, including Brans-Dicke theory, theories with Kaluza-Klein dimensional reduction, and low-energy approximations to string theory. In the "pure Bakry-Émery" N = ∞ case with f uniformly bounded above and initial data suitably bounded, cosmological-type singularity theorems are known, as are splitting theorems which determine the geometry of timelike geodesically complete spacetimes for which the bound on the initial data is borderline violated. We extend these results in a number of ways. We are able to extend the singularity theorems to finite N-values N ∈ (n, ∞) and N ∈ (-∞, 1]. In the N ∈ (n, ∞) case, no bound on f is required, while for N ∈ (-∞, 1] and N = ∞, we are able to replace the boundedness of f by a weaker condition on the integral of f along future-inextendible timelike geodesics. The splitting theorems extend similarly, but when N = 1, the splitting is only that of a warped product for all cases considered. A similar limited loss of rigidity has been observed in a prior work on the N-Bakry-Émery curvature in Riemannian signature when N = 1 and appears to be a general feature.

Orbit Maintenance and Navigation of Human Spacecraft at Cislunar Near Rectilinear Halo Orbits

NASA Technical Reports Server (NTRS)

Davis, Diane; Bhatt, Sagar; Howell, Kathleen; Jang, Jiann-Woei; Whitley, Ryan; Clark, Fred; Guzzetti, Davide; Zimovan, Emily; Barton, Gregg

2017-01-01

Multiple studies have concluded that Earth-Moon libration point orbits are attractive candidates for staging operations. The Near Rectilinear Halo Orbit (NRHO), a member of the Earth-Moon halo orbit family, has been singularly demonstrated to meet multi-mission architectural constraints. In this paper, the challenges associated with operating human spacecraft in the NRHO are evaluated. Navigation accuracies and human vehicle process noise effects are applied to various station keeping strategies in order to obtain a reliable orbit maintenance algorithm. Additionally, the ability to absorb missed burns, construct phasing maneuvers to avoid eclipses and conduct rendezvous and proximity operations are examined.

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

PubMed Central

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

2017-01-01

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

7 CFR 46.1 - Words in singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 2 2010-01-01 2010-01-01 false Words in singular form. 46.1 Section 46.1 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... Words in singular form. Words in this part in the singular form shall be deemed to import the plural...

7 CFR 61.1 - Words in singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 3 2010-01-01 2010-01-01 false Words in singular form. 61.1 Section 61.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Standards... Words in singular form. Words used in the regulations in this subpart in the singular form shall be...

The singular values of the imbedding operators of some classes of analytic functions of several variables

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

Parfenov, O.G.

1994-12-25

We discuss three results. The first exhibits the order of decrease of the s-values as a function of the CR-dimension of a compact set on which we approximate the class of analytic functions being studied. The second is an asymptotic formula for the case when the domain of analyticity and the compact set are Reinhart domains. The third is the computation of the s-values of a special operator that is of interest for approximation theory on one-dimensional manifolds.

Refinement of Methods for Evaluation of Near-Hypersingular Integrals in BEM Formulations

NASA Technical Reports Server (NTRS)

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

2006-01-01

In this paper, we present advances in singularity cancellation techniques applied to integrals in BEM formulations that are nearly hypersingular. Significant advances have been made recently in singularity cancellation techniques applied to 1 R type kernels [M. Khayat, D. Wilton, IEEE Trans. Antennas and Prop., 53, pp. 3180-3190, 2005], as well as to the gradients of these kernels [P. Fink, D. Wilton, and M. Khayat, Proc. ICEAA, pp. 861-864, Torino, Italy, 2005] on curved subdomains. In these approaches, the source triangle is divided into three tangent subtriangles with a common vertex at the normal projection of the observation point onto the source element or the extended surface containing it. The geometry of a typical tangent subtriangle and its local rectangular coordinate system with origin at the projected observation point is shown in Fig. 1. Whereas singularity cancellation techniques for 1 R type kernels are now nearing maturity, the efficient handling of near-hypersingular kernels still needs attention. For example, in the gradient reference above, techniques are presented for computing the normal component of the gradient relative to the plane containing the tangent subtriangle. These techniques, summarized in the transformations in Table 1, are applied at the sub-triangle level and correspond particularly to the case in which the normal projection of the observation point lies within the boundary of the source element. They are found to be highly efficient as z approaches zero. Here, we extend the approach to cover two instances not previously addressed. First, we consider the case in which the normal projection of the observation point lies external to the source element. For such cases, we find that simple modifications to the transformations of Table 1 permit significant savings in computational cost. Second, we present techniques that permit accurate computation of the tangential components of the gradient; i.e., tangent to the plane containing the source element.

Maass Forms and Quantum Modular Forms

NASA Astrophysics Data System (ADS)

Rolen, Larry

This thesis describes several new results in the theory of harmonic Maass forms and related objects. Maass forms have recently led to a flood of applications throughout number theory and combinatorics in recent years, especially following their development by the work of Bruinier and Funke the modern understanding Ramanujan's mock theta functions due to Zwegers. The first of three main theorems discussed in this thesis concerns the integrality properties of singular moduli. These are well-known to be algebraic integers, and they play a beautiful role in complex multiplication and explicit class field theory for imaginary quadratic fields. One can also study "singular moduli" for special non-holomorphic functions, which are algebraic but are not necessarily algebraic integers. Here we will explain the phenomenon of integrality properties and provide a sharp bound on denominators of symmetric functions in singular moduli. The second main theme of the thesis concerns Zagier's recent definition of a quantum modular form. Since their definition in 2010 by Zagier, quantum modular forms have been connected to numerous different topics such as strongly unimodal sequences, ranks, cranks, and asymptotics for mock theta functions. Motivated by Zagier's example of the quantum modularity of Kontsevich's "strange" function F(q), we revisit work of Andrews, Jimenez-Urroz, and Ono to construct a natural vector-valued quantum modular form whose components. The final chapter of this thesis is devoted to a study of asymptotics of mock theta functions near roots of unity. In his famous deathbed letter, Ramanujan introduced the notion of a mock theta function, and he offered some alleged examples. The theory of mock theta functions has been brought to fruition using the framework of harmonic Maass forms, thanks to Zwegers. Despite this understanding, little attention has been given to Ramanujan's original definition. Here we prove that Ramanujan's examples do indeed satisfy his original definition.

Expressions for tidal conversion at seafloor topography using physical space integrals

NASA Astrophysics Data System (ADS)

Schorghofer, Norbert

2010-12-01

The barotropic tide interacts with seafloor topography to generate internal gravity waves. Equations for streamfunction and power conversion are derived in terms of integrals over the topography in spatial coordinates. The slope of the topography does not need to be small. Explicit equations are derived up to second order in slope for general topography, and conversion by a bell-shaped topography is calculated analytically to this order. A concise formalism using Hilbert transforms is developed, the minimally converting topographic shape is discussed, and a numerical scheme for the evaluation of power conversion is designed that robustly deals with the singular integrand.

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.

Numerical Integration Techniques for Curved-Element Discretizations of Molecule–Solvent Interfaces

PubMed Central

Bardhan, Jaydeep P.; Altman, Michael D.; Willis, David J.; Lippow, Shaun M.; Tidor, Bruce; White, Jacob K.

2012-01-01

Surface formulations of biophysical modeling problems offer attractive theoretical and computational properties. Numerical simulations based on these formulations usually begin with discretization of the surface under consideration; often, the surface is curved, possessing complicated structure and possibly singularities. Numerical simulations commonly are based on approximate, rather than exact, discretizations of these surfaces. To assess the strength of the dependence of simulation accuracy on the fidelity of surface representation, we have developed methods to model several important surface formulations using exact surface discretizations. Following and refining Zauhar’s work (J. Comp.-Aid. Mol. Des. 9:149-159, 1995), we define two classes of curved elements that can exactly discretize the van der Waals, solvent-accessible, and solvent-excluded (molecular) surfaces. We then present numerical integration techniques that can accurately evaluate nonsingular and singular integrals over these curved surfaces. After validating the exactness of the surface discretizations and demonstrating the correctness of the presented integration methods, we present a set of calculations that compare the accuracy of approximate, planar-triangle-based discretizations and exact, curved-element-based simulations of surface-generalized-Born (sGB), surface-continuum van der Waals (scvdW), and boundary-element method (BEM) electrostatics problems. Results demonstrate that continuum electrostatic calculations with BEM using curved elements, piecewise-constant basis functions, and centroid collocation are nearly ten times more accurate than planartriangle BEM for basis sets of comparable size. The sGB and scvdW calculations give exceptional accuracy even for the coarsest obtainable discretized surfaces. The extra accuracy is attributed to the exact representation of the solute–solvent interface; in contrast, commonly used planar-triangle discretizations can only offer improved approximations with increasing discretization and associated increases in computational resources. The results clearly demonstrate that our methods for approximate integration on an exact geometry are far more accurate than exact integration on an approximate geometry. A MATLAB implementation of the presented integration methods and sample data files containing curved-element discretizations of several small molecules are available online at http://web.mit.edu/tidor. PMID:17627358

Integrative omics analysis. A study based on Plasmodium falciparum mRNA and protein data.

PubMed

Tomescu, Oana A; Mattanovich, Diethard; Thallinger, Gerhard G

2014-01-01

Technological improvements have shifted the focus from data generation to data analysis. The availability of large amounts of data from transcriptomics, protemics and metabolomics experiments raise new questions concerning suitable integrative analysis methods. We compare three integrative analysis techniques (co-inertia analysis, generalized singular value decomposition and integrative biclustering) by applying them to gene and protein abundance data from the six life cycle stages of Plasmodium falciparum. Co-inertia analysis is an analysis method used to visualize and explore gene and protein data. The generalized singular value decomposition has shown its potential in the analysis of two transcriptome data sets. Integrative Biclustering applies biclustering to gene and protein data. Using CIA, we visualize the six life cycle stages of Plasmodium falciparum, as well as GO terms in a 2D plane and interpret the spatial configuration. With GSVD, we decompose the transcriptomic and proteomic data sets into matrices with biologically meaningful interpretations and explore the processes captured by the data sets. IBC identifies groups of genes, proteins, GO Terms and life cycle stages of Plasmodium falciparum. We show method-specific results as well as a network view of the life cycle stages based on the results common to all three methods. Additionally, by combining the results of the three methods, we create a three-fold validated network of life cycle stage specific GO terms: Sporozoites are associated with transcription and transport; merozoites with entry into host cell as well as biosynthetic and metabolic processes; rings with oxidation-reduction processes; trophozoites with glycolysis and energy production; schizonts with antigenic variation and immune response; gametocyctes with DNA packaging and mitochondrial transport. Furthermore, the network connectivity underlines the separation of the intraerythrocytic cycle from the gametocyte and sporozoite stages. Using integrative analysis techniques, we can integrate knowledge from different levels and obtain a wider view of the system under study. The overlap between method-specific and common results is considerable, even if the basic mathematical assumptions are very different. The three-fold validated network of life cycle stage characteristics of Plasmodium falciparum could identify a large amount of the known associations from literature in only one study.

Integrative omics analysis. A study based on Plasmodium falciparum mRNA and protein data

PubMed Central

2014-01-01

Background Technological improvements have shifted the focus from data generation to data analysis. The availability of large amounts of data from transcriptomics, protemics and metabolomics experiments raise new questions concerning suitable integrative analysis methods. We compare three integrative analysis techniques (co-inertia analysis, generalized singular value decomposition and integrative biclustering) by applying them to gene and protein abundance data from the six life cycle stages of Plasmodium falciparum. Co-inertia analysis is an analysis method used to visualize and explore gene and protein data. The generalized singular value decomposition has shown its potential in the analysis of two transcriptome data sets. Integrative Biclustering applies biclustering to gene and protein data. Results Using CIA, we visualize the six life cycle stages of Plasmodium falciparum, as well as GO terms in a 2D plane and interpret the spatial configuration. With GSVD, we decompose the transcriptomic and proteomic data sets into matrices with biologically meaningful interpretations and explore the processes captured by the data sets. IBC identifies groups of genes, proteins, GO Terms and life cycle stages of Plasmodium falciparum. We show method-specific results as well as a network view of the life cycle stages based on the results common to all three methods. Additionally, by combining the results of the three methods, we create a three-fold validated network of life cycle stage specific GO terms: Sporozoites are associated with transcription and transport; merozoites with entry into host cell as well as biosynthetic and metabolic processes; rings with oxidation-reduction processes; trophozoites with glycolysis and energy production; schizonts with antigenic variation and immune response; gametocyctes with DNA packaging and mitochondrial transport. Furthermore, the network connectivity underlines the separation of the intraerythrocytic cycle from the gametocyte and sporozoite stages. Conclusion Using integrative analysis techniques, we can integrate knowledge from different levels and obtain a wider view of the system under study. The overlap between method-specific and common results is considerable, even if the basic mathematical assumptions are very different. The three-fold validated network of life cycle stage characteristics of Plasmodium falciparum could identify a large amount of the known associations from literature in only one study. PMID:25033389

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.