Do sewn up singularities falsify the Palatini cosmology?

NASA Astrophysics Data System (ADS)

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

2016-10-01

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

Zero Dimensional Field Theory of Tachyon Matter

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

Dimitrijevic, D. D.; Djordjevic, G. S.

2007-04-23

The first issue about the object (now) called tachyons was published almost one century ago. Even though there is no experimental evidence of tachyons there are several reasons why tachyons are still of interest today, in fact interest in tachyons is increasing. Many string theories have tachyons occurring as some of the particles in the theory. In this paper we consider the zero dimensional version of the field theory of tachyon matter proposed by A. Sen. Using perturbation theory and ideas of S. Kar, we demonstrate how this tachyon field theory can be connected with a classical mechanical system, suchmore » as a massive particle moving in a constant field with quadratic friction. The corresponding Feynman path integral form is proposed using a perturbative method. A few promising lines for further applications and investigations are noted.« less

Tachyon dynamics — for neutrinos?

NASA Astrophysics Data System (ADS)

Schwartz, Charles

2018-04-01

Following earlier studies that provided a consistent theory of kinematics for tachyons (faster-than-light particles), we here embark on a study of tachyon dynamics, both in classical physics and in the quantum theory. Examining a general scattering process, we come to recognize that the labels given to “in” and “out” states are not Lorentz invariant for tachyons; and this lets us find a sensible interpretation of negative energy states. For statistical mechanics, as well as for scattering problems, we study what should be the proper expression for density of states for tachyons. We review the previous work on quantization of a Dirac field for tachyons and go on to expand earlier considerations of neutrinos as tachyons in the context of cosmology. We stumble into the realization that tachyon neutrinos would contribute to gravitation with the opposite sign compared to tachyon antineutrinos. This leads to the gobsmacking prediction that the Cosmic Neutrino Background, if they are indeed tachyons, might explain both phenomena of Dark Matter and Dark Energy. This theoretical study also makes contact with the anticipated results from the experiments KATRIN and PTOLEMY, which focus on beta decay and neutrino absorption by Tritium.

Tachyon cosmology with non-vanishing minimum potential: a unified model

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

Li, Huiquan, E-mail: hqli@ustc.edu.cn

2012-07-01

We investigate the tachyon condensation process in the effective theory with non-vanishing minimum potential and its implications to cosmology. It is shown that the tachyon condensation on an unstable three-brane described by this modified tachyon field theory leads to lower-dimensional branes (defects) forming within a stable three-brane. Thus, in the cosmological background, we can get well-behaved tachyon matter after tachyon inflation, (partially) avoiding difficulties encountered in the original tachyon cosmological models. This feature also implies that the tachyon inflated and reheated universe is followed by a Chaplygin gas dark matter and dark energy universe. Hence, such an unstable three-brane behavesmore » quite like our universe, reproducing the key features of the whole evolutionary history of the universe and providing a unified description of inflaton, dark matter and dark energy in a very simple single-scalar field model.« less

Acoustics of tachyon Fermi gas

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

Trojan, Ernst; Vlasov, George V.

2011-06-15

We consider a Fermi gas of free tachyons as a continuous medium and find whether it satisfies the causality condition. There is no stable tachyon matter with the particle density below critical value n{sub T} and the Fermi momentum k{sub F}<{radical}((3/2))m that depends on the tachyon mass m. The pressure P and energy density E cannot be arbitrary small, but the situation P>E is not forbidden. Existence of shock waves in tachyon gas is also discussed. At low density n{sub T}

Lorentz-invariant formulation of Cherenkov radiation by tachyons

NASA Technical Reports Server (NTRS)

Jones, F. C.

1972-01-01

Previous treatments of Cherenkov radiation, electromagnetic and gravitational, by tachyons were in error because the prescription employed to cut off the divergent integral over frequency is not a Lorentz invariant procedure. The resulting equation of motion for the tachyon is therefore not covariant. The proper procedure requires an extended, deformable distribution of charge or mass and yields a particularly simple form for the tachyon's world line, one that could be deduced from simple invariance considerations. It is shown that Cherenkov radiation by tachyons implys their ultimate annihilation with an antitachyon and demonstrates a disturbing property of tachyons, namely the impossibility of specifying arbitrary Cauchy data even in a purely classical theory.

Cosmological perturbations and noncommutative tachyon inflation

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

Liu Daojun; Li Xinzhou

2004-12-15

The motivation for studying the rolling tachyon and noncommutative inflation comes from string theory. In the tachyon inflation scenario, metric perturbations are created by tachyon field fluctuations during inflation. We drive the exact mode equation for scalar perturbations of the metric and investigate the cosmological perturbations in the commutative and noncommutative inflationary spacetime driven by the tachyon field which have a Born-Infeld Lagrangian. Although at lowest order the predictions of tachyon inflation are no different than those from standard slow-roll inflation, due to the modified inflationary dynamics there exists modifications to the power spectra of fluctuations generated during inflation. Inmore » the noncommutative tachyon inflation scenario, the stringy noncommutativity of spacetime results in corrections to the primordial power spectrum that lead to a spectral index that is greater than 1 on large scales and less than 1 on small scales as the first-year results of the Wilkinson Microwave Anisotropy Probe indicate.« less

Next Generation Instrumentation Bus Test Plan for Fibre Channel

DTIC Science & Technology

1999-09-30

sample for port testing. The heart of the Fibre Xpress network cards is the tachyon chip from Hewlett Packard. The tachyon chip is basically a single...be to test the protocols. 1.5.1.1 Tachyon chip The user’s manual for the Tachyon controller chip identifies the following FC-AL specification

Integration of Optimal Scheduling with Case-Based Planning.

DTIC Science & Technology

1995-08-01

integrates Case-Based Reasoning (CBR) and Rule-Based Reasoning (RBR) systems. ’ Tachyon : A Constraint-Based Temporal Reasoning Model and Its...Implementation’ provides an overview of the Tachyon temporal’s reasoning system and discusses its possible applications. ’Dual-Use Applications of Tachyon : From...Force Structure Modeling to Manufacturing Scheduling’ discusses the application of Tachyon to real world problems, specifically military force deployment and manufacturing scheduling.

Tachyon field in loop quantum cosmology: Inflation and evolution picture

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

Xiong Huaui; Zhu Jianyang

2007-04-15

Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universne through a bounce in the high energy region. We show that this is always true in tachyon matter LQC. Differing from the classical Friedman-Robertson-Walker (FRW) cosmology, the super inflation can appear in the tachyon matter LQC; furthermore, the inflation can be extended to the region where classical inflation stops. Using the numerical method, we give an evolution picture of the tachyon field with an exponential potential in the context of LQC. It indicates that the quantum dynamical solutions have the same attractive behavior as the classical solutions do. Themore » whole evolution of the tachyon field is that in the distant past, the tachyon field--being in the contracting cosmology--accelerates to climb up the potential hill with a negative velocity; then at the boundary the tachyon field is bounced into an expanding universe with positive velocity rolling down to the bottom of the potential. In the slow roll limit, we compare the quantum inflation with the classical case in both an analytic and a numerical way.« less

Don't Panic! Closed String Tachyons in ALE Spacetimes

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

Silverstein, Eva M

2001-08-20

We consider closed string tachyons localized at the fixed points of noncompact nonsupersymmetric orbifolds. We argue that tachyon condensation drives these orbifolds to flat space or supersymmetric ALE spaces. The decay proceeds via an expanding shell of dilaton gradients and curvature which interpolates between two regions of distinct angular geometry. The string coupling remains weak throughout. For small tachyon VEVs, evidence comes from quiver theories on D-branes probes, in which deformations by twisted couplings smoothly connect non-supersymmetric orbifolds to supersymmetric orbifolds of reduced order. For large tachyon VEVs, evidence comes from worldsheet RG flow and spacetime gravity. For C{sup 2}/Z{submore » n}, we exhibit infinite sequences of transitions producing SUSY ALE spaces via twisted closed string condensation from non-supersymmetric ALE spaces. In a T-dual description this provides a mechanism for creating NS5-branes via closed string tachyon condensation similar to the creation of D-branes via open string tachyon condensation. We also apply our results to recent duality conjectures involving fluxbranes and the type 0 string.« less

Cosmology in the laboratory: An analogy between hyperbolic metamaterials and the Milne universe

NASA Astrophysics Data System (ADS)

Figueiredo, David; Moraes, Fernando; Fumeron, Sébastien; Berche, Bertrand

2017-11-01

This article shows that the compactified Milne universe geometry, a toy model for the big crunch/big bang transition, can be realized in hyperbolic metamaterials, a new class of nanoengineered systems which have recently found its way as an experimental playground for cosmological ideas. On one side, Klein-Gordon particles, as well as tachyons, are used as probes of the Milne geometry. On the other side, the propagation of light in two versions of a liquid crystal-based metamaterial provides the analogy. It is shown that ray and wave optics in the metamaterial mimic, respectively, the classical trajectories and wave function propagation, of the Milne probes, leading to the exciting perspective of realizing experimental tests of particle tunneling through the cosmic singularity, for instance.

Evolution of spherical over-densities in tachyon scalar field model

NASA Astrophysics Data System (ADS)

Setare, M. R.; Felegary, F.; Darabi, F.

2017-09-01

We study the tachyon scalar field model in flat FRW cosmology with the particular potential ϕ-2 and the scale factor behavior a (t) =tn. We consider the spherical collapse model and investigate the effects of the tachyon scalar field on the structure formation in flat FRW universe. We calculate δc (zc), λ (zc), ξ (zc), ΔV (zc), log ⁡ [ νf (ν) ] and log ⁡ [ n (k) ] for the tachyon scalar field model and compare the results with the results of EdS model and ΛCDM model. It is shown that in the tachyon scalar field model the structure formation may occur earlier, in comparison to the other models.

Energy-momentum tensor of perturbed tachyon matter

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

Jokela, Niko; Department of Mathematics and Physics, University of Haifa at Oranim, Tivon 36006; Jaervinen, Matti

2009-05-15

We add an initial nonhomogeneous perturbation to an otherwise homogeneous condensing tachyon background and compute its spacetime energy-momentum tensor from world-sheet string theory. We show that in the far future the energy-momentum tensor corresponds to nonhomogeneous pressureless tachyon matter.

Faster-than-light particles: A review of tachyon characteristics

NASA Astrophysics Data System (ADS)

Puscher, E. A.

1980-10-01

This report documents an analytical prediction of some of the characteristics which presently undiscovered faster-than-light sub-atomic particles (called tachyons) must possess if they are to exist without violating the Theory of Special Relativity. A brief review of necessary concepts from the Special Theory is included so that the reader might more readily understand the reasoning as it is developed. Necessary, but not all characteristics of tachyons are then identified and presented. Finally, an interesting potential relationship between tachyons and anti-gravity is discussed.

Tachyon warm-intermediate inflationary universe model in high dissipative regime

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

Setare, M.R.; Kamali, V., E-mail: rezakord@ipm.ir, E-mail: vkamali1362@gmail.com

2012-08-01

We consider tachyonic warm-inflationary models in the context of intermediate inflation. We derive the characteristics of this model in slow-roll approximation and develop our model in two cases, 1- For a constant dissipative parameter Γ. 2- Γ as a function of tachyon field φ. We also describe scalar and tensor perturbations for this scenario. The parameters appearing in our model are constrained by recent observational data. We find that the level of non-Gaussianity for this model is comparable with non-tachyonic model.

Dark energy cosmology with tachyon field in teleparallel gravity

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

Motavalli, H., E-mail: Motavalli@Tabrizu.ac.ir; Akbarieh, A. Rezaei; Nasiry, M.

2016-07-15

We construct a tachyon teleparallel dark energy model for a homogeneous and isotropic flat universe in which a tachyon as a non-canonical scalar field is non-minimally coupled to gravity in the framework of teleparallel gravity. The explicit form of potential and coupling functions are obtained under the assumption that the Lagrangian admits the Noether symmetry approach. The dynamical behavior of the basic cosmological observables is compared to recent observational data, which implies that the tachyon field may serve as a candidate for dark energy.

Exciting gauge field and gravitons in brane-antibrane annihilation.

PubMed

Mazumdar, Anupam; Stoica, Horace

2009-03-06

In this Letter we point out the inevitability of an explosive production of gauge field and gravity wave during an open string tachyon condensation in a cosmological setting, in an effective field theory model. We will be particularly studying a toy model of brane-antibrane inflation in a warped throat where inflation ends via tachyon condensation. We point out that a tachyonic instability helps fragmenting the homogeneous tachyon and excites gauge field and contributes to the stress-energy tensor which also feeds into the gravity waves.

Consistency of the tachyon warm inflationary universe models

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

Zhang, Xiao-Min; Zhu, Jian-Yang, E-mail: zhangxm@mail.bnu.edu.cn, E-mail: zhujy@bnu.edu.cn

2014-02-01

This study concerns the consistency of the tachyon warm inflationary models. A linear stability analysis is performed to find the slow-roll conditions, characterized by the potential slow-roll (PSR) parameters, for the existence of a tachyon warm inflationary attractor in the system. The PSR parameters in the tachyon warm inflationary models are redefined. Two cases, an exponential potential and an inverse power-law potential, are studied, when the dissipative coefficient Γ = Γ{sub 0} and Γ = Γ(φ), respectively. A crucial condition is obtained for a tachyon warm inflationary model characterized by the Hubble slow-roll (HSR) parameter ε{sub H}, and the conditionmore » is extendable to some other inflationary models as well. A proper number of e-folds is obtained in both cases of the tachyon warm inflation, in contrast to existing works. It is also found that a constant dissipative coefficient (Γ = Γ{sub 0}) is usually not a suitable assumption for a warm inflationary model.« less

Faster-than-light particles: a review of tachyon characteristics. Interim report

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

Puscher, E.A.

1980-10-01

This report documents an analytical prediction of some of the characteristics which presently undiscovered faster-than-light sub-atomic particles (called tachyons) must possess if they are to exist without violating the Theory of Special Relativity. A brief review of necessary concepts from the Special Theory is included so that the reader might more readily understand the reasoning as it is developed. Necessary, but not all, characteristics of tachyons are then identified and presented. Finally, an interesting potential relationship between tachyons and anti-gravity is discussed.

Faster-than-Light Particles: A Review of Tachyon Characteristics.

DTIC Science & Technology

1980-10-01

A-DlAO9(4 529 RAND CORP SANTA MNtICA CA F/6 20/S FASTER-THAN-LIBI4T PARTICLES: A REVIEW OF TACHYON CHARACTERISTIC--ETCWU) OCT B0 E A PUSCHER F49620...77-C-0023 UNCLASSIFIED RAI0IN-1530-AF N. I nmui ininmuuuI LEVEL A RAND NOTE FASTER-THAN-LIGHT PARTICLES: A REVIEW OF ) ( TACHYON CHARACTERISTICS Edward...RECIPIENT’S CATALOG NUMBER 4TIT LE ( d Subtitle) TYPE OF REPORT & PERIOD COVERED ( Faster-than-Light Particles: A Review of /Interim -i Tachyon

Thermodynamics of hairy black holes in Lovelock gravity

NASA Astrophysics Data System (ADS)

Hennigar, Robie A.; Tjoa, Erickson; Mann, Robert B.

2017-02-01

We perform a thorough study of the thermodynamic properties of a class of Lovelock black holes with conformal scalar hair arising from coupling of a real scalar field to the dimensionally extended Euler densities. We study the linearized equations of motion of the theory and describe constraints under which the theory is free from ghosts/tachyons. We then consider, within the context of black hole chemistry, the thermodynamics of the hairy black holes in the Gauss-Bonnet and cubic Lovelock theories. We clarify the connection between isolated critical points and thermodynamic singularities, finding a one parameter family of these critical points which occur for well-defined thermodynamic parameters. We also report on a number of novel results, including `virtual triple points' and the first example of a `λ-line' — a line of second order phase transitions — in black hole thermodynamics.

Developing a Fly-Away-Kit (FLAK) to Support Hastily Formed Networks (HFN) for Humanitarian Assistance and Disaster Relief (HA/DR)

DTIC Science & Technology

2005-06-01

HFN Components: Reach-Back, Last-Mile, and FLAK .............19 Figure 5. Example of a VSAT solution (from Tachyon , 2004...and IDU (From Tachyon Networks, 2004) ............................................31 Figure 16. IDU...44 Figure 22. Tachyon Auto Deploy ODU and IDU .............................................................44 Figure

O-Plan2 VS Sipe-2 - A General Comparison

DTIC Science & Technology

1994-07-01

on them that are satisfied by the planner. SIPE-2 has been extended to interface with General Electric’s Tachyon system for temporal reasoning...Temporal constraints in SIPE-2 are written to a file that is read by Tachyon . Tachyon processes these constraints and writes a file of narrowed time

Late time behaviors of an inhomogeneous rolling tachyon

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

Kwon, O-Kab; Lee, Chong Oh; Basic Science Research Institute, Chonbuk National University, Chonju 561-756

2006-06-15

We study an inhomogeneous decay of an unstable D-brane in the context of Dirac-Born-Infeld (DBI)-type effective action. We consider tachyon and electromagnetic fields with dependence of time and one spatial coordinate, and an exact solution is found under an exponentially decreasing tachyon potential, e{sup -|T|/{radical}}{sup (2)}, which is valid for the description of the late time behavior of an unstable D-brane. Though the obtained solution contains both time and spatial dependence, the corresponding momentum density vanishes over the entire spacetime region. The solution is governed by two parameters. One adjusts the distribution of energy density in the inhomogeneous direction, andmore » the other interpolates between the homogeneous rolling tachyon and static configuration. As time evolves, the energy of the unstable D-brane is converted into the electric flux and tachyon matter.« less

Collapsing radiating stars with various equations of state

NASA Astrophysics Data System (ADS)

Brassel, Byron P.; Goswami, Rituparno; Maharaj, Sunil D.

2017-06-01

We study the gravitational collapse of radiating stars in the context of the cosmic censorship conjecture. We consider a generalized Vaidya spacetime with three concentric regions. The local internal atmosphere is a two-component system consisting of standard pressure-free, null radiation and an additional string fluid with energy density and nonzero pressure obeying all physically realistic energy conditions. The middle region is purely radiative which matches to a third region which is the Schwarzschild exterior. We outline the general mathematical framework to study the conditions on the mass function so that future-directed nonspacelike geodesics can terminate at the singularity in the past. Mass functions for several equations of state are analyzed using this framework and it is shown that the collapse in each case terminates at a locally naked central singularity. We calculate the strength of these singularities to show that they are strong curvature singularities which implies that no extension of spacetime through them is possible.

Transient and late time attractor tachyon dark energy: Can we distinguish it from quintessence?

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

Ali, Amna; Sami, M.; Sen, A. A.

2009-06-15

The string inspired tachyon field can serve as a candidate of dark energy. Its equation of state parameter w varies from 0 to -1. In the case of tachyon field potential V({phi}){yields}0 slower (faster) than 1/{phi}{sup 2} at infinity, dark energy (dark matter) is a late time attractor. We investigate the tachyon dark energy models under the assumption that w is close to -1. We find that all the models exhibit unique behavior around the present epoch which is exactly the same as that of the thawing quintessence.

Observational constraints on tachyonic chameleon dark energy model

NASA Astrophysics Data System (ADS)

Banijamali, A.; Bellucci, S.; Fazlpour, B.; Solbi, M.

2018-03-01

It has been recently shown that tachyonic chameleon model of dark energy in which tachyon scalar field non-minimally coupled to the matter admits stable scaling attractor solution that could give rise to the late-time accelerated expansion of the universe and hence alleviate the coincidence problem. In the present work, we use data from Type Ia supernova (SN Ia) and Baryon Acoustic oscillations to place constraints on the model parameters. In our analysis we consider in general exponential and non-exponential forms for the non-minimal coupling function and tachyonic potential and show that the scenario is compatible with observations.

Cosmological evolution of a tachyon-quintom model of dark energy

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

Shi, Shang-Gang; Piao, Yun-Song; Qiao, Cong-Feng, E-mail: shishanggang06@mails.gucas.ac.cn, E-mail: yspiao@gucas.ac.cn, E-mail: qiaocf@gucas.ac.cn

2009-04-15

In this work we study the cosmological evolution of a dark energy model with two scalar fields, i.e. the tachyon and the phantom tachyon. This model enables the equation of state w to change from w > -1 to w < -1 in the evolution of the universe. The phase-space analysis for such a system with inverse square potentials shows that there exists a unique stable critical point, which has power-law solution. In this paper, we also study another form of tachyon-quintom model with two fields, which involves the interactions between both fields.

Are partons confined tachyons?

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

Noyes, H.P.

1996-03-01

The author notes that if hadrons are gravitationally stabilized ``black holes``, as discrete physics suggests, it is possible that partons, and in particular quarks, could be modeled as tachyons, i.e. particles having v{sup 2} > c{sup 2}, without conflict with the observational fact that neither quarks nor tachyons have appeared as ``free particles``. Some consequences of this model are explored.

Note on tachyon actions in string theory

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

Headrick, Matthew

2009-02-15

A number of spacetime fields in string theory (notably the metric, dilaton, bosonic and type 0 bulk closed-string tachyon, and bosonic open-string tachyon) have the following property: whenever the spacetime field configuration factorizes in an appropriate sense, the matter sector of the world-sheet theory factorizes into a tensor product of two decoupled theories. Since the beta functions for such a product theory necessarily also factorize, this property strongly constrains the form of the spacetime action encoding those beta functions. We show that this constraint alone--without needing actually to compute any of the beta functions--is sufficient to fix the form ofmore » the two-derivative action for the metric-dilaton system, as well as the potential for the bosonic open-string tachyon. We also show that no action consistent with this constraint exists for the closed-string tachyon coupled to the metric and dilaton.« less

Remarks on non-BPS string amplitudes and their all order α' contact interactions in IIB, IIA

NASA Astrophysics Data System (ADS)

Hatefi, Ehsan

2017-03-01

We explore the entire form of S-Matrix elements of a potential C n-1 Ramond-Ramond (RR) form field, a tachyon and two transverse scalar fields on both world volume and transverse directions of type IIB and IIA superstring theories. Apart from < {V}_{C^{-2}}{V}_{φ^0}{V}_{φ^0}{V}_{T^0}\\rangle the other scattering amplitude, namely < {V}_{C^{-1}}{V}_{φ^{-1}}{V}_{φ^0}{V}_{T^0}\\rangle is also revealed. We then start to compare all singularity structures of symmetric and asymmetric analysis, generating all infinite singularity structures as well as all order α' contact interactions on the whole directions. This leads to deriving various new contact terms and several new restricted Bianchi identities in both type IIB and IIA. It is also shown that just some of the new couplings of type IIB (IIA) string theory can be re-verified in an Effective Field Theory (EFT) by pull-back of branes. To construct the rest of S-matrix elements one needs to first derive restricted world volume (or bulk) Bianchi identities and then discover new EFT couplings in both type IIB and IIA. Finally the presence of commutator of scalar fields inside the exponential of Wess-Zumino action for non-BPS branes has been confirmed as well.

On the break down of reality at superluminal velocities, Quantum entanglement and Singularities (Complex Universe)

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2017-09-01

In the real world nothing can move faster than the speed of light. But what convinces you that our world is all real? I realized that reality break down at superluminal velocities (By studying the physics of tachyonic neutrinos), Quantum entanglement and Singularities of Black Holes, I realized that infact our world is complex and has two parts, one part of the world is real (the part that nothing can move faster than the speed of light) but the other part of the world is imaginary. z = a + ib Einstein was wrong because he thought our world is completely real (Of course he was not alone in this belief almost all physicists believe that our world is completely real) Eventually his false interpretation of reality censored imaginary part of the universe. Einstein's Second Postulate of special theory of relativity was a misleading guide to the true nature of reality. He `expected' the true nature of reality will follow to his (false) postulate, But the true nature of reality is unlike what anyone ever `expected'!. Einstein twist facts to suit his theory of relativity instead of theories to suit facts!. This is a dramatic revisions to our conception of the theory of relativity, Reality is complex but We always perceive its real part.

Crossing of the phantom divide using tachyon-Gauss-Bonnet gravity

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

Sadeghi, J.; Banijamali, A.; Milani, F.

2009-06-15

In this paper we consider two models. First, we study tachyon-Gauss-Bonnet gravity and obtain the condition of the equation of state crossing -1. Second, we discuss the modified Gauss-Bonnet gravity with the tachyon field and show the condition of {omega} crossing -1. Also, we plot figures for {omega} numerically in special potential and coupling function.

Tachyon and quintessence in brane worlds

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

Chimento, Luis P.; Forte, Monica; Richarte, Martin G.

2009-04-15

Using tachyon or quintessence fields along with a barotropic fluid on the brane we examine the different cosmological stages in a Friedmann-Robertson-Walker universe, from the first radiation scenario to the later era dominated by cosmic string networks. We introduce a new algorithm to generalize previous works on exact solutions and apply it to study tachyon and quintessence fields localized on the brane. We also explore the low and high energy regimes of the solutions. Besides, we show that the tachyon and quintessence fields are driven by an inverse power law potential. Finally, we find several simple exacts solutions for tachyonmore » and/or quintessence fields.« less

Exploiting Data Similarity to Reduce Memory Footprints

DTIC Science & Technology

2011-01-01

leslie3d Fortran Computational Fluid Dynamics (CFD) application 122. tachyon C Parallel Ray Tracing application 128.GAPgeofem C and Fortran Simulates...benefits most from SBLLmalloc; LAMMPS, which shows moderate similarity from primarily zero pages; and 122. tachyon , a parallel ray- tracing application...similarity across MPI tasks. They primarily are zero- pages although a small fraction (≈10%) are non-zero pages. 122. tachyon is an image rendering

IMPGSS - International Medical Program Global Satellite System

DTIC Science & Technology

2004-02-01

additional comments regarding the significance of working with Tachyon and NASK under this Contract). 5.2.5 Requirements - Country/Region Assessments...services on a tentative exploratory basis by Tachyon ]. 5.2.7 Program Development Deliverable A 007 This is currently summarized in the Program Content...based satellite transmissions and transmission pricing based on segmented, limited use data volumes via Tachyon . " A more involved use of evaluation

Tachyon driven quantum cosmology in string theory

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

Garcia-Compean, H.; Garcia-Jimenez, G.; Obregon, O.

2005-03-15

Recently an effective action of the SDp-brane decaying process in string theory has been proposed. This effective description involves the Tachyon driven matter coupled to bosonic ten-dimensional Type II supergravity. Here the Hamiltonian formulation of this system is given. Exact solutions for the corresponding quantum theory by solving the Wheeler-deWitt equation in the late-time limit of the rolling tachyon are found. The energy spectrum and the probability densities for several values of p are shown and their possible interpretation is discussed. In the process the effects of electromagnetic fields are also incorporated and it is shown that in this casemore » the interpretation of tachyon regarded as 'matter clock' is modified.« less

Duality linking standard and tachyon scalar field cosmologies

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

Avelino, P. P.; Bazeia, D.; Losano, L.

2010-09-15

In this work we investigate the duality linking standard and tachyon scalar field homogeneous and isotropic cosmologies in N+1 dimensions. We determine the transformation between standard and tachyon scalar fields and between their associated potentials, corresponding to the same background evolution. We show that, in general, the duality is broken at a perturbative level, when deviations from a homogeneous and isotropic background are taken into account. However, we find that for slow-rolling fields the duality is still preserved at a linear level. We illustrate our results with specific examples of cosmological relevance, where the correspondence between scalar and tachyon scalarmore » field models can be calculated explicitly.« less

Calculation of the decay rate of tachyonic neutrinos against charged-lepton-pair and neutrino-pair Cerenkov radiation

NASA Astrophysics Data System (ADS)

Jentschura, Ulrich D.; Nándori, István; Ehrlich, Robert

2017-10-01

We consider in detail the calculation of the decay rate of high-energy superluminal neutrinos against (charged) lepton pair Cerenkov radiation, and neutrino pair Cerenkov radiation, i.e., against the decay channels ν \\to ν {e}+ {e}- and ν \\to ν \\overline{ν } ν . Under the hypothesis of a tachyonic nature of neutrinos, these decay channels put constraints on the lifetime of high-energy neutrinos for terrestrial experiments as well as on cosmic scales. For the oncoming neutrino, we use the Lorentz-covariant tachyonic relation {E}ν =\\sqrt{{p}2-{m}ν 2}, where m ν is the tachyonic mass parameter. We derive both threshold conditions as well as on decay and energy loss rates, using the plane-wave fundamental bispinor solutions of the tachyonic Dirac equation. Various intricacies of rest frame versus lab frame calculations are highlighted. The results are compared to the observations of high-energy IceCube neutrinos of cosmological origin.

Tachyon inflation in the large-N formalism

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

Barbosa-Cendejas, Nandinii; De-Santiago, Josue; German, Gabriel

2015-11-01

We study tachyon inflation within the large-N formalism, which takes a prescription for the small Hubble flow slow-roll parameter ε{sub 1} as a function of the large number of e-folds N. This leads to a classification of models through their behaviour at large N. In addition to the perturbative N class, we introduce the polynomial and exponential classes for the ε{sub 1} parameter. With this formalism we reconstruct a large number of potentials used previously in the literature for tachyon inflation. We also obtain new families of potentials from the polynomial class. We characterize the realizations of tachyon inflation bymore » computing the usual cosmological observables up to second order in the Hubble flow slow-roll parameters. This allows us to look at observable differences between tachyon and canonical single field inflation. The analysis of observables in light of the Planck 2015 data shows the viability of some of these models, mostly for certain realization of the polynomial and exponential classes.« less

Perturbations and moduli space dynamics of tachyon kinks

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

Hindmarsh, Mark; Li Huiquan

2008-03-15

The dynamic process of unstable D-branes decaying into stable ones with one dimension lower can be described by a tachyon field with a Dirac-Born-Infeld effective action. In this paper we investigate the fluctuation modes of the tachyon field around a two-parameter family of static solutions representing an array of brane-antibrane pairs. Besides a pair of zero modes associated with the parameters of the solution, and instabilities associated with annihilation of the brane-antibrane pairs, we find states corresponding to excitations of the tachyon field around the brane and in the bulk. In the limit that the brane thickness tends to zero,more » the support of the eigenmodes is limited to the brane, consistent with the idea that propagating tachyon modes drop out of the spectrum as the tachyon field approaches its ground state. The zero modes, and other low-lying excited states, show a fourfold degeneracy in this limit, which can be identified with some of the massless superstring modes in the brane-antibrane system. Finally, we also discuss the slow motion of the solution corresponding to the decay process in the moduli space, finding a trajectory which oscillates periodically between the unstable D-brane and the brane-antibrane pairs of one dimension lower.« less

Interacting tachyon: Cosmological evolution for a tachyon and a scalar field

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

Macorra, A. de la; Filobello, U.

2008-01-15

We study the cosmological evolution of a tachyon scalar field T with a Dirac-Born-Infeld type Lagrangian and potential V(T) coupled to a canonically normalized scalar field {phi} with an interaction term B(T,{phi}) in the presence of a barotropic fluid {rho}{sub b}, which can be matter or radiation. The force between the barotropic fluid and the scalar fields is only gravitational. We show that the dynamics is completely determined by only three parameters {lambda}{sub 1}=-V{sub T}/V{sup 3/2}, {lambda}{sub 2}=-B{sub T}/B{sup 3/2}, and {lambda}{sub 3}=-B{sub {phi}}/B. We determine analytically the conditions for {lambda}{sub i} under which the energy density of T, {phi},more » and {rho}{sub b} have the same redshift. We study the behavior of T and {phi} in the asymptotic limits for {lambda} and we show the numerical solution for different interesting cases. The effective equation of state for the tachyon field changes due to the interaction with the scalar field and we show that it is possible for a tachyon field to redshift as matter in the absence of an interaction term B and as radiation when B is turned on. This result solves then the tachyonic matter problem.« less

Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems.

PubMed

Chen, Mou; Wu, Qing-Xian; Cui, Rong-Xin

2013-03-01

In this paper, the terminal sliding mode tracking control is proposed for the uncertain single-input and single-output (SISO) nonlinear system with unknown external disturbance. For the unmeasured disturbance of nonlinear systems, terminal sliding mode disturbance observer is presented. The developed disturbance observer can guarantee the disturbance approximation error to converge to zero in the finite time. Based on the output of designed disturbance observer, the terminal sliding mode tracking control is presented for uncertain SISO nonlinear systems. Subsequently, terminal sliding mode tracking control is developed using disturbance observer technique for the uncertain SISO nonlinear system with control singularity and unknown non-symmetric input saturation. The effects of the control singularity and unknown input saturation are combined with the external disturbance which is approximated using the disturbance observer. Under the proposed terminal sliding mode tracking control techniques, the finite time convergence of all closed-loop signals are guaranteed via Lyapunov analysis. Numerical simulation results are given to illustrate the effectiveness of the proposed terminal sliding mode tracking control. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Planning in Dynamic and Uncertain Environments

DTIC Science & Technology

1994-05-01

particular, General Electric’s (GE) Tachyon system [2]), and uses the communication software provided in the CPE (in particular, the Cronus and Knet...and gets back information about the world and replanning requests. "* We extended SIPE-2 to interact with GE’s Tachyon system in a loosely coupled...manner. Tachyon is able to process extended temporal constraints for SIPE-2 during planning. They communicate by using the Cronus system in the CPE

Tachyon search speeds up retrieval of similar sequences by several orders of magnitude.

PubMed

Tan, Joshua; Kuchibhatla, Durga; Sirota, Fernanda L; Sherman, Westley A; Gattermayer, Tobias; Kwoh, Chia Yee; Eisenhaber, Frank; Schneider, Georg; Maurer-Stroh, Sebastian

2012-06-15

The usage of current sequence search tools becomes increasingly slower as databases of protein sequences continue to grow exponentially. Tachyon, a new algorithm that identifies closely related protein sequences ~200 times faster than standard BLAST, circumvents this limitation with a reduced database and oligopeptide matching heuristic. The tool is publicly accessible as a webserver at http://tachyon.bii.a-star.edu.sg and can also be accessed programmatically through SOAP.

Observational constraints on holographic tachyonic dark energy in interaction with dark matter

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

Micheletti, Sandro M. R., E-mail: smrm@fma.if.usp.br

2010-05-01

We discuss an interacting tachyonic dark energy model in the context of the holographic principle. The potential of the holographic tachyon field in interaction with dark matter is constructed. The model results are compared with CMB shift parameter, baryonic acoustic oscilations, lookback time and the Constitution supernovae sample. The coupling constant of the model is compatible with zero, but dark energy is not given by a cosmological constant.

Causality-Preserving Timestamps in Distributed Programs

DTIC Science & Technology

1993-06-01

monitoring,deh!bigging. tac-hvon,catisaIi tvý Abstract A tachyon is an improperly ordered event in a distributed program. Tachvonis are most often...that tachyons do in fact. occur commonly in distributed pro- grams on our Ethernet at Carnegie Mellon University. and we disc’ss some ways of...before it is sent) is called a tach yon. (’learly it is very disconcerting to try to debug a parallel program that contains tachyons . Of course, in "real

Closed-string tachyon condensation and the worldsheet super-higgs effect.

PubMed

Horava, Petr; Keeler, Cynthia A

2008-02-08

Alternative gauge choices for worldsheet supersymmetry can elucidate dynamical phenomena obscured in the usual superconformal gauge. In the particular example of the tachyonic E8 heterotic string, we use a judicious gauge choice to show that the process of closed-string tachyon condensation can be understood in terms of a worldsheet super-Higgs effect. The worldsheet gravitino assimilates the goldstino and becomes a dynamical propagating field. Conformal, but not superconformal, invariance is maintained throughout.

Moving branes in the presence of background tachyon fields

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

Rezaei, Z., E-mail: z.rezaei@aut.ac.ir; Kamani, D., E-mail: kamani@aut.ac.ir

2011-12-15

We compute the boundary state associated with a moving Dp-brane in the presence of the open string tachyon field as a background field. The effect of the tachyon condensation on the boundary state is discussed. It leads to a boundary state associated with a lower-dimensional moving D-brane or a stationary instantonic D-brane. The former originates from condensation along the spatial directions and the latter comes from the temporal direction of the D-brane worldvolume. Using the boundary state, we also study the interaction amplitude between two arbitrary Dp{sub 1}- and Dp{sub 2}-branes. The long-range behavior of the amplitude is investigated, demonstratingmore » an obvious deviation from the conventional form, due to the presence of the background tachyon field.« less

Catalog of Resources for Education in Ada (Trade Name) and Software Engineering (CREASE). Version 4.0.

DTIC Science & Technology

1986-05-01

offering the course is a company. Name and Address of offeror: Tachyon Corporation 2725 Congress Street Suite 2H San Diego, CA 92110 Offeror’s...Background: Tachyon Corporation specializes in Ada software quality assurance, computer hosted instruction and information retrieval systems, authoring tools...easy to use (on-line help) and can look up or search for terms. Tachyon Corporation 20 CDURSE OFFERINGS 2.2. Lecture/Seminar Courses 2.2.1. Company

Dynamical analysis of tachyonic chameleon

NASA Astrophysics Data System (ADS)

Banijamali, Ali; Solbi, Milad

2017-08-01

In the present paper we investigate tachyonic chameleon scalar field and present the phase space analysis for four different combinations of the tachyonic potential V(φ ) and the coupling function f(φ ) of the chameleon field with matter. We find some stable solution in which accelerated expansion of the universe is satisfied. In one case where both f(φ ) and V(φ ) are exponential a scaling attractor was found that can give rise to the late-time acceleration of the universe and alleviate the coincidence problem.

Remarks on non-BPS string amplitudes and their all order α' contact interactions in IIB, IIA

DOE PAGES

Hatefi, Ehsan

2017-03-06

Here, we explore the entire form of S-Matrix elements of a potential C n–1 Ramond-Ramond (RR) form field, a tachyon and two transverse scalar fields on both world volume and transverse directions of type IIB and IIA superstring theories. Apart from V C–2V Φ0V Φ0V T0 the other scattering amplitude, namely V C–1V Φ–1V Φ0V T0 is also revealed. We then start to compare all singularity structures of symmetric and asymmetric analysis, generating all infinite singularity structures as well as all order α' contact interactions on the whole directions. This leads to deriving various new contact terms and several newmore » restricted Bianchi identities in both type IIB and IIA. It is also shown that just some of the new couplings of type IIB (IIA) string theory can be re-verified in an Effective Field Theory (EFT) by pull-back of branes. To construct the rest of S-matrix elements one needs to first derive restricted world volume (or bulk) Bianchi identities and then discover new EFT couplings in both type IIB and IIA. Finally the presence of commutator of scalar fields inside the exponential of Wess-Zumino action for non-BPS branes has been confirmed as well.« less

Spherical D-brane by tachyon condensation

NASA Astrophysics Data System (ADS)

Asakawa, Tsuguhiko; Matsuura, So

2018-03-01

We find a novel tachyon condensation which provides a D-brane system with spherical worldvolume in the flat spacetime. The tachyon profile is a deformation of a known D0-brane solution on non-BPS D3-branes in type IIA superstring theory, which realizes a bound state of a spherical D2-brane and a D0-brane. The D0-brane is resolved into the sphere as a U(1) monopole flux of the unit magnetic charge. We show that the system has the correct tension and the RR-coupling. Although the low-energy effective action of the system is the same as that of the dual description of the fuzzy sphere solution of multiple D0-branes, our system cannot be equivalent to the fuzzy sphere. The use of projective modules in describing the tachyon condensation is emphasized.

Performance of the Tachyon Time-of-Flight PET Camera

NASA Astrophysics Data System (ADS)

Peng, Q.; Choong, W.-S.; Vu, C.; Huber, J. S.; Janecek, M.; Wilson, D.; Huesman, R. H.; Qi, Jinyi; Zhou, Jian; Moses, W. W.

2015-02-01

We have constructed and characterized a time-of-flight Positron Emission Tomography (TOF PET) camera called the Tachyon. The Tachyon is a single-ring Lutetium Oxyorthosilicate (LSO) based camera designed to obtain significantly better timing resolution than the 550 ps found in present commercial TOF cameras, in order to quantify the benefit of improved TOF resolution for clinically relevant tasks. The Tachyon's detector module is optimized for timing by coupling the 6.15 ×25 mm2 side of 6.15 ×6.15 ×25 mm3 LSO scintillator crystals onto a 1-inch diameter Hamamatsu R-9800 PMT with a super-bialkali photocathode. We characterized the camera according to the NEMA NU 2-2012 standard, measuring the energy resolution, timing resolution, spatial resolution, noise equivalent count rates and sensitivity. The Tachyon achieved a coincidence timing resolution of 314 ps +/- 20 ps FWHM over all crystal-crystal combinations. Experiments were performed with the NEMA body phantom to assess the imaging performance improvement over non-TOF PET. The results show that at a matched contrast, incorporating 314 ps TOF reduces the standard deviation of the contrast by a factor of about 2.3.

M-theory through the looking glass: Tachyon condensation in the E8 heterotic string

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

Horava, Petr; Horava, Petr; Keeler, Cynthia A.

2007-09-20

We study the spacetime decay to nothing in string theory and M-theory. First we recall a nonsupersymmetric version of heterotic M-theory, in which bubbles of nothing -- connecting the two E_8 boundaries by a throat -- are expected to be nucleated. We argue that the fate of this system should be addressed at weak string coupling, where the nonperturbative instanton instability is expected to turn into a perturbative tachyonic one. We identify the unique string theory that could describe this process: The heterotic model with one E_8 gauge group and a singlet tachyon. We then use worldsheet methods to studymore » the tachyon condensation in the NSR formulation of this model, and show that it induces a worldsheet super-Higgs effect. The main theme of our analysis is the possibility of making meaningful alternative gauge choices for worldsheet supersymmetry, in place of the conventional superconformal gauge. We show in a version of unitary gauge how the worldsheet gravitino assimilates the goldstino and becomes dynamical. This picture clarifies recent results of Hellerman and Swanson. We also present analogs of R_\\xi gauges, and note the importance of logarithmic CFT in the context of tachyon condensation.« less

Performance of the Tachyon Time-of-Flight PET Camera.

PubMed

Peng, Q; Choong, W-S; Vu, C; Huber, J S; Janecek, M; Wilson, D; Huesman, R H; Qi, Jinyi; Zhou, Jian; Moses, W W

2015-02-01

We have constructed and characterized a time-of-flight Positron Emission Tomography (TOF PET) camera called the Tachyon. The Tachyon is a single-ring Lutetium Oxyorthosilicate (LSO) based camera designed to obtain significantly better timing resolution than the ~ 550 ps found in present commercial TOF cameras, in order to quantify the benefit of improved TOF resolution for clinically relevant tasks. The Tachyon's detector module is optimized for timing by coupling the 6.15 × 25 mm 2 side of 6.15 × 6.15 × 25 mm 3 LSO scintillator crystals onto a 1-inch diameter Hamamatsu R-9800 PMT with a super-bialkali photocathode. We characterized the camera according to the NEMA NU 2-2012 standard, measuring the energy resolution, timing resolution, spatial resolution, noise equivalent count rates and sensitivity. The Tachyon achieved a coincidence timing resolution of 314 ps +/- ps FWHM over all crystal-crystal combinations. Experiments were performed with the NEMA body phantom to assess the imaging performance improvement over non-TOF PET. The results show that at a matched contrast, incorporating 314 ps TOF reduces the standard deviation of the contrast by a factor of about 2.3.

Performance of the Tachyon Time-of-Flight PET Camera

DOE PAGES

Peng, Q.; Choong, W. -S.; Vu, C.; ...

2015-01-23

We have constructed and characterized a time-of-flight Positron Emission Tomography (TOF PET) camera called the Tachyon. The Tachyon is a single-ring Lutetium Oxyorthosilicate (LSO) based camera designed to obtain significantly better timing resolution than the ~ 550 ps found in present commercial TOF cameras, in order to quantify the benefit of improved TOF resolution for clinically relevant tasks. The Tachyon's detector module is optimized for timing by coupling the 6.15 ×25 mm 2 side of 6.15 ×6.15 ×25 mm 3 LSO scintillator crystals onto a 1-inch diameter Hamamatsu R-9800 PMT with a super-bialkali photocathode. We characterized the camera according tomore » the NEMA NU 2-2012 standard, measuring the energy resolution, timing resolution, spatial resolution, noise equivalent count rates and sensitivity. The Tachyon achieved a coincidence timing resolution of 314 ps +/- 20 ps FWHM over all crystal-crystal combinations. Experiments were performed with the NEMA body phantom to assess the imaging performance improvement over non-TOF PET. We find that the results show that at a matched contrast, incorporating 314 ps TOF reduces the standard deviation of the contrast by a factor of about 2.3.« less

Exploring Data Sharing Between Geographically Distributed Mobile and Fixed Nodes Supporting Extended Maritime Interdiction Operations (EMIO)

DTIC Science & Technology

2008-06-01

Diablo and LLNL o ITT Mesh, OPAREA TWO: between BP RHIB and BV, and between Sea Fox (USV) and BV o Sky Pilot, OPAREA THREE: between Tachyon ...between Sea Fox (USV) and BV o Sky Pilot, OPAREA THREE: between Tachyon Satellite and Sky Pilot Relay and between Sky Pilot Relay and BV o Wave Relay...between Tachyon Satellite and Sky Pilot Relay and between Sky Pilot Relay and BV o Wave Relay, OPAREA THREE: between BV and Balloon and between

Results of a search for monopoles and tachyons in horizontal cosmic ray flux

NASA Technical Reports Server (NTRS)

Ashitkov, V. D.; Kirina, T. M.; Klimakov, A. P.; Kokoulin, R. P.; Petrukhin, A. A.

1985-01-01

A search for monopoles and tachyons at ground level was carried out using an arrangement consisting of an ionization calorimeter and two hodoscope detectors. No clear evidence for these particles was obtained. The flux of monopoles with velocities beta approximately 0.01 is found to be less than 5.1 x 10 to the minus 13th power square centimeters s(-1) sr(-1) (95% cl.). The upper limit on the tachyon flux density is set as a 6 x 10 the minus 9th power particle/square centimeter event.

Prediction of Supersonic Store Separation Characteristics Including Fuselage and Stores of Noncircular Cross Section. Volume II. Users Manual for the Computer Program.

DTIC Science & Technology

1980-11-01

CMACH $ FMACH) 132 TRJTRY STOP normal termination (test: TIME > TIMEF-0.00001 or NDIFEQ = 1) BDCOEF message warning - NAFLD exceeds blank common...BDCOEF**, NTAP7- , IUB= , NAFLD = . (Test: NAFLD > NADIM) CRFWBD STOP 001 (Test: NER > 1; equation solution singular) INVER2 STOP **Matrix is singular

Revised theory of tachyons in general relativity

NASA Astrophysics Data System (ADS)

Schwartz, Charles

2017-08-01

A minus sign is inserted, for good reason, into the formula for the energy-momentum tensor for tachyons. This leads to remarkable theoretical consequences and a plausible explanation for the phenomenon called dark energy in the cosmos.

Gravitational waves from non-Abelian gauge fields at a tachyonic transition

NASA Astrophysics Data System (ADS)

Tranberg, Anders; Tähtinen, Sara; Weir, David J.

2018-04-01

We compute the gravitational wave spectrum from a tachyonic preheating transition of a Standard Model-like SU(2)-Higgs system. Tachyonic preheating involves exponentially growing IR modes, at scales as large as the horizon. Such a transition at the electroweak scale could be detectable by LISA, if these non-perturbatively large modes translate into non-linear dynamics sourcing gravitational waves. Through large-scale numerical simulations, we find that the spectrum of gravitational waves does not exhibit such IR features. Instead, we find two peaks corresponding to the Higgs and gauge field mass, respectively. We find that the gravitational wave production is reduced when adding non-Abelian gauge fields to a scalar-only theory, but increases when adding Abelian gauge fields. In particular, gauge fields suppress the gravitational wave spectrum in the IR. A tachyonic transition in the early Universe will therefore not be detectable by LISA, even if it involves non-Abelian gauge fields.

Finite temperature corrections to tachyon mass in intersecting D-branes

NASA Astrophysics Data System (ADS)

Sethi, Varun; Chowdhury, Sudipto Paul; Sarkar, Swarnendu

2017-04-01

We continue with the analysis of finite temperature corrections to the Tachyon mass in intersecting branes which was initiated in [1]. In this paper we extend the computation to the case of intersecting D3 branes by considering a setup of two intersecting branes in flat-space background. A holographic model dual to BCS superconductor consisting of intersecting D8 branes in D4 brane background was proposed in [2]. The background considered here is a simplified configuration of this dual model. We compute the one-loop Tachyon amplitude in the Yang-Mills approximation and show that the result is finite. Analyzing the amplitudes further we numerically compute the transition temperature at which the Tachyon becomes massless. The analytic expressions for the one-loop amplitudes obtained here reduce to those for intersecting D1 branes obtained in [1] as well as those for intersecting D2 branes.

Quantum tachyons

NASA Astrophysics Data System (ADS)

Tomaschitz, R.

2005-02-01

The interaction of superluminal radiation with matter in atomic bound-bound and bound-free transitions is investigated. We study transitions in the relativistic hydrogen atom effected by superluminal quanta. The superluminal radiation field is coupled by minimal substitution to the Dirac equation in a Coulomb potential. We quantize the interaction to obtain the transition matrix for induced and spontaneous superluminal radiation in hydrogen-like ions. The tachyonic photoelectric effect is scrutinized, the cross-sections for ground state ionization by transversal and longitudinal tachyons are derived. We examine the relativistic regime, high electronic ejection energies, as well as the first order correction to the non-relativistic cross-sections. In the ultra-relativistic limit, both the longitudinal and transversal cross-sections are peaked at small but noticeably different scattering angles. In the non-relativistic limit, the longitudinal cross-section has two maxima, and its minimum is located at the transversal maximum. Ionization cross-sections can thus be used to discriminate longitudinal radiation from transversal tachyons and photons.

Dynamical tachyons on fuzzy spheres

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

Berenstein, David; Institute for Advanced Study, School of Natural Science, Princeton, New Jersey 08540; Trancanelli, Diego

2011-05-15

We study the spectrum of off-diagonal fluctuations between displaced fuzzy spheres in the Berenstein-Maldacena-Nastase plane wave matrix model. The displacement is along the plane of the fuzzy spheres. We find that when two fuzzy spheres intersect at angles, classical tachyons develop and that the spectrum of these modes can be computed analytically. These tachyons can be related to the familiar Nielsen-Olesen instabilities in Yang-Mills theory on a constant magnetic background. Many features of the problem become more apparent when we compare with maximally supersymmetric Yang-Mills theory on a sphere, of which this system is a truncation. We also set upmore » a simple oscillatory trajectory on the displacement between the fuzzy spheres and study the dynamics of the modes as they become tachyonic for part of the oscillations. We speculate on their role regarding the possible thermalization of the system.« less

A novel adaptive finite time controller for bilateral teleoperation system

NASA Astrophysics Data System (ADS)

Wang, Ziwei; Chen, Zhang; Liang, Bin; Zhang, Bo

2018-03-01

Most bilateral teleoperation researches focus on the system stability within time-delays. However, practical teleoperation tasks require high performances besides system stability, such as convergence rate and accuracy. This paper investigates bilateral teleoperation controller design with transient performances. To ensure the transient performances and system stability simultaneously, an adaptive non-singular fast terminal mode controller is proposed to achieve practical finite-time stability considering system uncertainties and time delays. In addition, a novel switching scheme is introduced, in which way the singularity problem of conventional terminal sliding manifold is avoided. Finally, numerical simulations demonstrate the effectiveness and validity of the proposed method.

Empirical Protocol for Measuring Virtual Tachyon / Tardon Interactions in a Dirac Vacuum

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

Amoroso, Richard L.; Rauscher, Elizabeth A.

2010-12-22

Here we present discussion for the utility of resonant interference in Calabi-Yau mirror symmetry as a putative empirical test of the existence of virtual tachyon / tardon interactions in a covariant Dirac polarized vacuum.

Tachyon search speeds up retrieval of similar sequences by several orders of magnitude

PubMed Central

Tan, Joshua; Kuchibhatla, Durga; Sirota, Fernanda L.; Sherman, Westley A.; Gattermayer, Tobias; Kwoh, Chia Yee; Eisenhaber, Frank; Schneider, Georg; Maurer-Stroh, Sebastian

2012-01-01

Summary: The usage of current sequence search tools becomes increasingly slower as databases of protein sequences continue to grow exponentially. Tachyon, a new algorithm that identifies closely related protein sequences ~200 times faster than standard BLAST, circumvents this limitation with a reduced database and oligopeptide matching heuristic. Availability and implementation: The tool is publicly accessible as a webserver at http://tachyon.bii.a-star.edu.sg and can also be accessed programmatically through SOAP. Contact: sebastianms@bii.a-star.edu.sg Supplementary information: Supplementary data are available at the Bioinformatics online. PMID:22531216

Spacelike brane actions.

PubMed

Hashimoto, Koji; Ho, Pei-Ming; Wang, John E

2003-04-11

We derive effective actions for "spacelike branes" (S-branes) and find a solution describing the formation of fundamental strings in the rolling tachyon background. The S-brane action is a Dirac-Born-Infeld action for Euclidean world volumes defined in the context of time-dependent tachyon condensation of non-BPS (Bogomol'nyi-Prasad-Sommerfield) branes. It includes gauge fields and, in particular, a scalar field associated with translation along the time direction. We show that the BIon spike solutions constructed in this system correspond to the production of a confined electric flux tube (a fundamental string) at late time of the rolling tachyon.

Constant-roll tachyon inflation and observational constraints

NASA Astrophysics Data System (ADS)

Gao, Qing; Gong, Yungui; Fei, Qin

2018-05-01

For the constant-roll tachyon inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts and the tensor to scalar ratio to the first order of epsilon1 by using the method of Bessel function approximation. The derived ns-r results are compared with the observations, we find that only the constant-roll inflation with ηH being a constant is consistent with the observations and observations constrain the constant-roll inflation to be slow-roll inflation. The tachyon potential is also reconstructed for the constant-roll inflation which is consistent with the observations.

M theory through the looking glass: Tachyon condensation in the E{sub 8} heterotic string

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

Horava, Petr; Keeler, Cynthia A.

2008-03-15

We study the spacetime decay to nothing in string theory and M-theory. First we recall a nonsupersymmetric version of heterotic M-theory, in which bubbles of nothing--connecting the two E{sub 8} boundaries by a throat--are expected to be nucleated. We argue that the fate of this system should be addressed at weak string coupling, where the nonperturbative instanton instability is expected to turn into a perturbative tachyonic one. We identify the unique string theory that could describe this process: The heterotic model with one E{sub 8} gauge group and a singlet tachyon. We then use world sheet methods to study themore » tachyon condensation in the Neveu-Schwarz-Ramond formulation of this model, and show that it induces a world sheet super-Higgs effect. The main theme of our analysis is the possibility of making meaningful alternative gauge choices for world sheet supersymmetry, in place of the conventional superconformal gauge. We show in a version of unitary gauge how the world sheet gravitino assimilates the Goldstino and becomes dynamical. This picture clarifies recent results of Hellerman and Swanson. We also present analogs of R{sub {xi}} gauges, and note the importance of logarithmic conformal field theories in the context of tachyon condensation.« less

The solutions and thermodynamic dark energy in the accelerating universe

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

Demirel, E. C. Günay

Recently, Tachyonic matter expressed in terms of scalar field is suggested to be the reason of acceleration of the universe as dark energy [1]-[3]. In this study, dynamic solutions and thermodynamic properties of matters such as Tachyonic matters were investigated.

Tachyon condensation and quark mass in the modified Sakai-Sugimoto model

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

Dhar, Avinash; High Energy Accelerator Research Organization; Nag, Partha

2008-09-15

This paper continues the investigation of the modified Sakai-Sugimoto model proposed previously [J. High Energy Phys. 01 (2008) 055]. Here we discuss in detail numerical solutions to the classical equations for the brane profile and the tachyon condensate. An ultraviolet cutoff turns out to be essential because the numerical solutions tend to rapidly diverge from the desired asymptotic solutions, beyond a sufficiently large value of the holographic coordinate. The required cutoff is determined by the non-normalizable part of the tachyon and is parametrically far smaller than that dictated by consistency of a description in terms of ten-dimensional bulk gravity. Wemore » had argued [J. High Energy Phys. 01 (2008) 055] that the solution in which the tachyon field goes to infinity at the point where the brane and antibrane meet has only one free parameter, which may be taken to be the asymptotic brane-antibrane separation. Here we present numerical evidence in favor of this observation. We also present evidence that the non-normalizable part of the asymptotic tachyon solution, which is identified with quark mass in the QCD-like boundary theory, is determined by this parameter. We show that the normalizable part of the asymptotic tachyon solution determines the quark condensate, but this requires holographic renormalization of the on-shell boundary brane action because of the presence of infinite cutoff-dependent terms. Our renormalization scheme gives an exponential dependence on the cutoff to the quark mass. We also discuss meson spectra in detail and show that the pion mass is nonzero and satisfies the Gell-Mann-Oakes-Renner relation when a small quark mass is switched on.« less

Tachyons in the Galilean limit

NASA Astrophysics Data System (ADS)

Batlle, Carles; Gomis, Joaquim; Mezincescu, Luca; Townsend, Paul K.

2017-04-01

The Souriau massless Galilean particle of "colour" k and spin s is shown to be the Galilean limit of the Souriau tachyon of mass m = ik and spin s. We compare and contrast this result with the Galilean limit of the Nambu-Goto string and Green-Schwarz superstring.

In search of superluminal quantum communications: recent experiments and possible improvements

NASA Astrophysics Data System (ADS)

Cocciaro, B.; Faetti, S.; Fronzoni, L.

2013-06-01

As shown in the famous EPR paper (Einstein, Podolsky e Rosen, 1935), Quantum Mechanics is non-local. The Bell theorem and the experiments by Aspect and many others, ruled out the possibility of explaining quantum correlations between entangled particles using local hidden variables models (except for implausible combinations of loopholes). Some authors (Bell, Eberhard, Bohm and Hiley) suggested that quantum correlations could be due to superluminal communications (tachyons) that propagate isotropically with velocity vt > c in a preferred reference frame. For finite values of vt, Quantum Mechanics and superluminal models lead to different predictions. Some years ago a Geneva group and our group did experiments on entangled photons to evidence possible discrepancies between experimental results and quantum predictions. Since no discrepancy was found, these experiments established only lower bounds for the possible tachyon velocities vt. Here we propose an improved experiment that should lead us to explore a much larger range of possible tachyon velocities Vt for any possible direction of velocity vec V of the tachyons preferred frame.

Tachyonic instabilities in 2  +  1 dimensional Yang-Mills theory and its connection to number theory

NASA Astrophysics Data System (ADS)

Chamizo, Fernando; González-Arroyo, Antonio

2017-06-01

We consider the 2  +  1 dimensional Yang-Mills theory with gauge group {{SU}}(N) on a flat 2-torus under twisted boundary conditions. We study the possibility of phase transitions (tachyonic instabilities) when N and the volume vary and certain chromomagnetic flux associated to the topology of the bundle can be adjusted. Under natural assumptions about how to match the perturbative regime and the expected confinement, we prove that the absence of tachyonic instabilities is related to some problems in number theory, namely the Diophantine approximation of irreducible fractions by other fractions of smaller denominator.

Tachyon warm inflation with the effects of loop quantum cosmology in the light of Planck 2015

NASA Astrophysics Data System (ADS)

Kamali, Vahid; Basilakos, Spyros; Mehrabi, Ahmad; Motaharfar, Meysam; Massaeli, Erfan

We investigate the observational signatures of quantum cosmology in the Cosmic Microwave Background data provided by Planck collaboration. We apply the warm inflationary paradigm with a tachyon scalar field to the loop quantum cosmology. In this context, we first provide the basic cosmological functions in terms of the tachyon field. We then obtain the slow-roll parameters and the power spectrum of scalar and tensor fluctuations, respectively. Finally, we study the performance of various warm inflationary scenarios against the latest Planck data and we find a family of models which are in agreement with the observations.

Particle creation and reheating in a braneworld inflationary scenario

NASA Astrophysics Data System (ADS)

Bilić, Neven; Domazet, Silvije; Djordjevic, Goran S.

2017-10-01

We study the cosmological particle creation in the tachyon inflation based on the D-brane dynamics in the Randall-Sundrum (RSII) model extended to include matter in the bulk. The presence of matter modifies the warp factor which results in two effects: a modification of the RSII cosmology and a modification of the tachyon potential. Besides, a string theory D-brane supports among other fields a U(1) gauge field reflecting open strings attached to the brane. We demonstrate how the interaction of the tachyon with the U(1) gauge field drives cosmological creation of massless particles and estimate the resulting reheating at the end of inflation.

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

NASA Technical Reports Server (NTRS)

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

1979-01-01

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

Analytical Tools for Investigating and Modeling Agent-Based Systems

DTIC Science & Technology

2005-06-01

of Black Holes Cluster 10 : Juan M. Maldacena (1924), Journal of High Energy Physics Field theory models for tachyon and gauge field string dy...namics; Super-Poincare Invariant Superstring Field The- ory; Level Four Approximation to the Tachyon Potential in Superstring Field Theory; SO(32) Spinors

Terminal attractors for addressable memory in neural networks

NASA Technical Reports Server (NTRS)

Zak, Michail

1988-01-01

A new type of attractors - terminal attractors - for an addressable memory in neural networks operating in continuous time is introduced. These attractors represent singular solutions of the dynamical system. They intersect (or envelope) the families of regular solutions while each regular solution approaches the terminal attractor in a finite time period. It is shown that terminal attractors can be incorporated into neural networks such that any desired set of these attractors with prescribed basins is provided by an appropriate selection of the weight matrix.

Particles That Travel Faster than Light?

ERIC Educational Resources Information Center

Newton, Roger G.

1970-01-01

A discussion of the possible existence of tachyons, particles that travel faster than light, and their theoretical properties. Suggests that if tachyons were found, the consequences for relativity theory, quantum mechanics and the concept of casuality would be far-reaching. Concludes that the final answer rests with the experimentalist.…

N-point functions in rolling tachyon background

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

Jokela, Niko; Keski-Vakkuri, Esko; Department of Physics, P.O. Box 64, FIN-00014, University of Helsinki

2009-04-15

We study n-point boundary correlation functions in timelike boundary Liouville theory, relevant for open string multiproduction by a decaying unstable D brane. We give an exact result for the one-point function of the tachyon vertex operator and show that it is consistent with a previously proposed relation to a conserved charge in string theory. We also discuss when the one-point amplitude vanishes. Using a straightforward perturbative expansion, we find an explicit expression for a tachyon n-point amplitude for all n, however the result is still a toy model. The calculation uses a new asymptotic approximation for Toeplitz determinants, derived bymore » relating the system to a Dyson gas at finite temperature.« less

NCPA Research Program, FY94.

DTIC Science & Technology

1995-10-31

sound, which is beyond the range of the perturbation theory. They would thus be " tachyons " in sound. Our proposed physical system could be a probe of the...v/c > 1. Hence, there is the possibility of an acoustic " tachyon " here. Lack of smallness of v/c violates the assumptions of the perturbation

Tachyon condensation and black hole entropy.

PubMed

Dabholkar, Atish

2002-03-04

String propagation on a cone with deficit angle 2pi(1-1 / N) is considered for the purpose of computing the entropy of a large mass black hole. The entropy computed using the recent results on condensation of twisted-sector tachyons in this theory is found to be in precise agreement with the Bekenstein-Hawking entropy.

Description and Analysis of Military Planning Systems

DTIC Science & Technology

2005-07-01

layer placed on top of SIPE-2 so as to keep track of the temporal constraints within a plan. The added module is Tachyon , a general-purpose...constraint-based subsystem developed by GE’s R&D Centre to provide temporal reasoning. The interface to Tachyon is a 34 DRDC Valcartier TR 2004-320

Intersecting flavor branes

NASA Astrophysics Data System (ADS)

Pomoni, Elli; Rastelli, Leonardo

2012-10-01

We consider an instance of the AdS/CFT duality where the bulk theory contains an open string tachyon, and study the instability from the viewpoint of the boundary field theory. We focus on the specific example of the AdS5 × S 5 background with two probe D7 branes intersecting at general angles. For generic angles supersymmetry is completely broken and there is an open string tachyon between the branes. The field theory action for this system is obtained by coupling to {N}=4 super Yang-Mills two {N}=2 hyper multiplets in the fundamental representation of the SU( N) gauge group, but with different choices of embedding of the two {N}=2 subalgebras into {N}=4 . On the field theory side we find a one-loop Coleman-Weinberg instability in the effective potential for the fundamental scalars. We identify a mesonic operator as the dual of the open string tachyon. By AdS/CFT, we predict the tachyon mass for small 't Hooft coupling (large bulk curvature) and confirm that it violates the AdS stability bound.

Observational status of Tachyon Natural Inflation and reheating

NASA Astrophysics Data System (ADS)

Rashidi, Narges; Nozari, Kourosh; Grøn, Øyvind

2018-05-01

We study observational viability of Natural Inflation with a tachyon field as inflaton. By obtaining the main perturbation parameters in this model, we perform a numerical analysis on the parameter space of the model and in confrontation with 68% and 95% CL regions of Planck2015 data. By adopting a warped background geometry, we find some new constraints on the width of the potential in terms of its height and the warp factor. We show that the Tachyon Natural Inflation in the large width limit recovers the tachyon model with a phi2 potential which is consistent with Planck2015 observational data. Then we focus on the reheating era after inflation by treating the number of e-folds, temperature and the effective equation of state parameter in this era. Since it is likely that the value of the effective equation of state parameter during the reheating era to be in the range 0<= ωeff<= 1/3, we obtain some new constraints on the tensor to scalar ratio, r, as well as the e-folds number and reheating temperature in this Tachyon Natural Inflation model. In particular, we show that a prediction of this model is r<=8/3 δns, where δns is the scalar spectral tilt, δns=1‑ns. In this regard, given that from the Planck2015 data we have δns=0.032 (corresponding to ns=0.968), we get r<= 0.085.

Lesion detection and quantification performance of the Tachyon-I time-of-flight PET scanner: phantom and human studies.

PubMed

Zhang, Xuezhu; Peng, Qiyu; Zhou, Jian; Huber, Jennifer S; Moses, William W; Qi, Jinyi

2018-03-16

The first generation Tachyon PET (Tachyon-I) is a demonstration single-ring PET scanner that reaches a coincidence timing resolution of 314 ps using LSO scintillator crystals coupled to conventional photomultiplier tubes. The objective of this study was to quantify the improvement in both lesion detection and quantification performance resulting from the improved time-of-flight (TOF) capability of the Tachyon-I scanner. We developed a quantitative TOF image reconstruction method for the Tachyon-I and evaluated its TOF gain for lesion detection and quantification. Scans of either a standard NEMA torso phantom or healthy volunteers were used as the normal background data. Separately scanned point source and sphere data were superimposed onto the phantom or human data after accounting for the object attenuation. We used the bootstrap method to generate multiple independent noisy datasets with and without a lesion present. The signal-to-noise ratio (SNR) of a channelized hotelling observer (CHO) was calculated for each lesion size and location combination to evaluate the lesion detection performance. The bias versus standard deviation trade-off of each lesion uptake was also calculated to evaluate the quantification performance. The resulting CHO-SNR measurements showed improved performance in lesion detection with better timing resolution. The detection performance was also dependent on the lesion size and location, in addition to the background object size and shape. The results of bias versus noise trade-off showed that the noise (standard deviation) reduction ratio was about 1.1-1.3 over the TOF 500 ps and 1.5-1.9 over the non-TOF modes, similar to the SNR gains for lesion detection. In conclusion, this Tachyon-I PET study demonstrated the benefit of improved time-of-flight capability on lesion detection and ROI quantification for both phantom and human subjects.

Lesion detection and quantification performance of the Tachyon-I time-of-flight PET scanner: phantom and human studies

NASA Astrophysics Data System (ADS)

Zhang, Xuezhu; Peng, Qiyu; Zhou, Jian; Huber, Jennifer S.; Moses, William W.; Qi, Jinyi

2018-03-01

The first generation Tachyon PET (Tachyon-I) is a demonstration single-ring PET scanner that reaches a coincidence timing resolution of 314 ps using LSO scintillator crystals coupled to conventional photomultiplier tubes. The objective of this study was to quantify the improvement in both lesion detection and quantification performance resulting from the improved time-of-flight (TOF) capability of the Tachyon-I scanner. We developed a quantitative TOF image reconstruction method for the Tachyon-I and evaluated its TOF gain for lesion detection and quantification. Scans of either a standard NEMA torso phantom or healthy volunteers were used as the normal background data. Separately scanned point source and sphere data were superimposed onto the phantom or human data after accounting for the object attenuation. We used the bootstrap method to generate multiple independent noisy datasets with and without a lesion present. The signal-to-noise ratio (SNR) of a channelized hotelling observer (CHO) was calculated for each lesion size and location combination to evaluate the lesion detection performance. The bias versus standard deviation trade-off of each lesion uptake was also calculated to evaluate the quantification performance. The resulting CHO-SNR measurements showed improved performance in lesion detection with better timing resolution. The detection performance was also dependent on the lesion size and location, in addition to the background object size and shape. The results of bias versus noise trade-off showed that the noise (standard deviation) reduction ratio was about 1.1–1.3 over the TOF 500 ps and 1.5–1.9 over the non-TOF modes, similar to the SNR gains for lesion detection. In conclusion, this Tachyon-I PET study demonstrated the benefit of improved time-of-flight capability on lesion detection and ROI quantification for both phantom and human subjects.

Tachyon with an inverse power-law potential in a braneworld cosmology

NASA Astrophysics Data System (ADS)

Bilić, Neven; Domazet, Silvije; Djordjevic, Goran S.

2017-08-01

We study a tachyon cosmological model based on the dynamics of a 3-brane in the bulk of the second Randall-Sundrum model extended to more general warp functions. A well known prototype of such a generalization is the bulk with a selfinteracting scalar field. As a consequence of a generalized bulk geometry the cosmology on the observer brane is modified by the scale dependent four-dimensional gravitational constant. In particular, we study a power law warp factor which generates an inverse power-law potential V\\propto \\varphi-n of the tachyon field φ. We find a critical power n cr that divides two subclasses with distinct asymptotic behaviors: a dust universe for n>n_cr and a quasi de Sitter universe for 0.

Pre-inflationary clues from String Theory?

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

Kitazawa, N.; Sagnotti, A., E-mail: kitazawa@phys.se.tmu.ac.jp, E-mail: sagnotti@sns.it

2014-04-01

''Brane supersymmetry breaking'' occurs in String Theory when the only available combinations of D-branes and orientifolds are not mutually BPS and yet do not introduce tree-level tachyon instabilities. It is characterized by the emergence of a steep exponential potential, and thus by the absence of maximally symmetric vacua. The corresponding low-energy supergravity admits intriguing spatially-flat cosmological solutions where a scalar field is forced to climb up toward the steep potential after an initial singularity, and additional milder terms can inject an inflationary phase during the ensuing descent. We show that, in the resulting power spectra of scalar perturbations, an infraredmore » suppression is typically followed by a pre-inflationary peak that reflects the end of the climbing phase and can lie well apart from the approximately scale invariant profile. A first look at WMAP9 raw data shows that, while the χ{sup 2} fits for the low-ℓ CMB angular power spectrum are clearly compatible with an almost scale invariant behavior, they display nonetheless an eye-catching preference for this type of setting within a perturbative string regime.« less

Implications of tachyon-like matter for superdense stars.

NASA Technical Reports Server (NTRS)

Bhatia, M. S.; Pande, L. K.

1972-01-01

Derivation of a new equation of state of superdense matter by treating superdense matter as a perfect, degenerate tachyon gas. Model calculations for superdense stars based on this equation of state are presented. By appropriately choosing a certain parameter, dynamical stability can be achieved for arbitrarily large central densities. Also, a somewhat larger than usual value for the maximum mass is obtained.

Performance of the Tachyon Time-of-Flight PET Camera

PubMed Central

Peng, Q.; Choong, W.-S.; Vu, C.; Huber, J. S.; Janecek, M.; Wilson, D.; Huesman, R. H.; Qi, Jinyi; Zhou, Jian; Moses, W. W.

2015-01-01

We have constructed and characterized a time-of-flight Positron Emission Tomography (TOF PET) camera called the Tachyon. The Tachyon is a single-ring Lutetium Oxyorthosilicate (LSO) based camera designed to obtain significantly better timing resolution than the ~ 550 ps found in present commercial TOF cameras, in order to quantify the benefit of improved TOF resolution for clinically relevant tasks. The Tachyon’s detector module is optimized for timing by coupling the 6.15 × 25 mm2 side of 6.15 × 6.15 × 25 mm3 LSO scintillator crystals onto a 1-inch diameter Hamamatsu R-9800 PMT with a super-bialkali photocathode. We characterized the camera according to the NEMA NU 2-2012 standard, measuring the energy resolution, timing resolution, spatial resolution, noise equivalent count rates and sensitivity. The Tachyon achieved a coincidence timing resolution of 314 ps +/− ps FWHM over all crystal-crystal combinations. Experiments were performed with the NEMA body phantom to assess the imaging performance improvement over non-TOF PET. The results show that at a matched contrast, incorporating 314 ps TOF reduces the standard deviation of the contrast by a factor of about 2.3. PMID:26594057

Quantum descriptions of singularities leading to pair creation. [of gravitons

NASA Technical Reports Server (NTRS)

Misner, C. W.

1974-01-01

A class of cosmological models is analyzed which provide a mathematically convenient (but idealized) description of a cosmological singularity that develops into a pair creation epoch and terminates in an adiabatic expansion with redshifting particle energies. This class of models was obtained by Gowdy (1971, 1974) as a set of exact solutions of the classical empty space Einstein equations describing inhomogeneous universes populated only by gravitational waves. It is shown that these models can be used to exhibit simplified models of quantized gravitational fields, and that a quantum description can be given arbitrarily near a cosmological singularity. Graviton pair creation occurs, and can be seen to convert anisotropic expansion rates into the energy of graviton pairs.

Non-minimally coupled tachyon field in teleparallel gravity

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

Fazlpour, Behnaz; Banijamali, Ali, E-mail: b.fazlpour@umz.ac.ir, E-mail: a.banijamali@nit.ac.ir

2015-04-01

We perform a full investigation on dynamics of a new dark energy model in which the four-derivative of a non-canonical scalar field (tachyon) is non-minimally coupled to the vector torsion. Our analysis is done in the framework of teleparallel equivalent of general relativity which is based on torsion instead of curvature. We show that in our model there exists a late-time scaling attractor (point P{sub 4}), corresponding to an accelerating universe with the property that dark energy and dark matter densities are of the same order. Such a point can help to alleviate the cosmological coincidence problem. Existence of thismore » point is the most significant difference between our model and another model in which a canonical scalar field (quintessence) is used instead of tachyon field.« less

On classical and quantum dynamics of tachyon-like fields and their cosmological implications

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

Dimitrijević, Dragoljub D., E-mail: ddrag@pmf.ni.ac.rs; Djordjević, Goran S., E-mail: ddrag@pmf.ni.ac.rs; Milošević, Milan, E-mail: ddrag@pmf.ni.ac.rs

2014-11-24

We consider a class of tachyon-like potentials, motivated by string theory, D-brane dynamics and inflation theory in the context of classical and quantum mechanics. A formalism for describing dynamics of tachyon fields in spatially homogenous and one-dimensional - classical and quantum mechanical limit is proposed. A few models with concrete potentials are considered. Additionally, possibilities for p-adic and adelic generalization of these models are discussed. Classical actions and corresponding quantum propagators, in the Feynman path integral approach, are calculated in a form invariant on a change of the background number fields, i.e. on both archimedean and nonarchimedean spaces. Looking formore » a quantum origin of inflation, relevance of p-adic and adelic generalizations are briefly discussed.« less

Interaction of moving branes with background massless and tachyon fields in superstring theory

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

Rezaei, Z., E-mail: z.rezaei@aut.ac.ir; Kamani, D., E-mail: kamani@aut.ac.ir

2012-02-15

Using the boundary state formalism, we study a moving Dp-brane in a partially compact space-time in the presence of background fields: the Kalb-Ramond field B{sub {mu}{nu}}, a U(1) gauge field A{sub {alpha}}, and the tachyon field. The boundary state enables us to obtain the interaction amplitude of two branes with the above back-ground fields. The branes are parallel or perpendicular to each other. Because of the presence of background fields, compactification of some space-time directions, motion of the branes, and the arbitrariness of the dimensions of the branes, the system is rather general. Due to the tachyon fields and velocitiesmore » of the branes, the behavior of the interaction amplitude reveals obvious differences from the conventional behavior.« less

The crack problem in bonded nonhomogeneous materials

NASA Technical Reports Server (NTRS)

Erdogan, Fazil; Kaya, A. C.; Joseph, P. F.

1988-01-01

The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip terminating at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors.

The crack problem in bonded nonhomogeneous materials

NASA Technical Reports Server (NTRS)

Erdogan, F.; Joseph, P. F.; Kaya, A. C.

1991-01-01

The plane elasticity problem for two bonded half planes containing a crack perpendicular to the interface was considered. The effect of very steep variations in the material properties near the diffusion plane on the singular behavior of the stresses and stress intensity factors were studied. The two materials were thus, assumed to have the shear moduli mu(o) and mu(o) exp (Beta x), x=0 being the diffusion plane. Of particular interest was the examination of the nature of stress singularity near a crack tip termination at the interface where the shear modulus has a discontinuous derivative. The results show that, unlike the crack problem in piecewise homogeneous materials for which the singularity is of the form r/alpha, 0 less than alpha less than 1, in this problem the stresses have a standard square-root singularity regardless of the location of the crack tip. The nonhomogeneity constant Beta has, however, considerable influence on the stress intensity factors.

The scale invariant power spectrum of the primordial curvature perturbations from the coupled scalar tachyon bounce cosmos

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

Li, Changhong; Cheung, Yeuk-Kwan E., E-mail: chellifegood@gmail.com, E-mail: cheung@nju.edu.cn

2014-07-01

We investigate the spectrum of cosmological perturbations in a bounce cosmos modeled by a scalar field coupled to the string tachyon field (CSTB cosmos). By explicit computation of its primordial spectral index we show the power spectrum of curvature perturbations, generated during the tachyon matter dominated contraction phase, to be nearly scale invariant. We propose a unified parameter space for a systematic study of inflationary and bounce cosmologies. The CSTB cosmos is dual-in Wands's sense-to slow-roll inflation as can be visualized with the aid of this parameter space. Guaranteed by the dynamical attractor behavior of the CSTB Cosmos, the scalemore » invariance of its power spectrum is free of the fine-tuning problem, in contrast to the slow-roll inflation model.« less

Behavior of boundary string field theory associated with integrable massless flow.

PubMed

Fujii, A; Itoyama, H

2001-06-04

We put forward an idea that the boundary entropy associated with integrable massless flow of thermodynamic Bethe ansatz (TBA) is identified with tachyon action of boundary string field theory. We show that the temperature parametrizing a massless flow in the TBA formalism can be identified with tachyon energy for the classical action at least near the ultraviolet fixed point, i.e., the open string vacuum.

Comments on real tachyon vacuum solution without square roots

NASA Astrophysics Data System (ADS)

Arroyo, E. Aldo

2018-01-01

We analyze the consistency of a recently proposed real tachyon vacuum solution without square roots in open bosonic string field theory. We show that the equation of motion contracted with the solution itself is satisfied. Additionally, by expanding the solution in the basis of the curly ℒ0 and the traditional L 0 eigenstates, we evaluate numerically the vacuum energy and obtain a result in agreement with Sen's conjecture.

Tachyon Condensation and Brane Annihilation in Bose-Einstein Condensates: Spontaneous Symmetry Breaking in Restricted Lower-Dimensional Subspace

NASA Astrophysics Data System (ADS)

Takeuchi, Hiromitsu; Kasamatsu, Kenichi; Tsubota, Makoto; Nitta, Muneto

2013-05-01

In brane cosmology, the Big Bang is hypothesized to occur by the annihilation of the brane-anti-brane pair in a collision, where the branes are three-dimensional objects in a higher-dimensional Universe. Spontaneous symmetry breaking accompanied by the formation of lower-dimensional topological defects, e.g. cosmic strings, is triggered by the so-called `tachyon condensation', where the existence of tachyons is attributable to the instability of the brane-anti-brane system. Here, we discuss the closest analogue of the tachyon condensation in atomic Bose-Einstein condensates. We consider annihilation of domain walls, namely branes, in strongly segregated two-component condensates, where one component is sandwiched by two domains of the other component. In this system, the process of the brane annihilation can be projected effectively as ferromagnetic ordering dynamics onto a two-dimensional space. Based on this correspondence, three-dimensional formation of vortices from a domain-wall annihilation is considered to be a kink formation due to spontaneous symmetry breaking in the two-dimensional space. We also discuss a mechanism to create a `vorton' when the sandwiched component has a vortex string bridged between the branes. We hope that this study motivates experimental researches to realize this exotic phenomenon of spontaneous symmetry breaking in superfluid systems.

Search for tachyons associated with extensive air showers in the ground level cosmic radiation

NASA Technical Reports Server (NTRS)

Masjed, H. F.; Ashton, F.

1985-01-01

Events detected in a shielded plastic scintillation counter occurring in the 26 microsec preceding the arrival of an extensive air shower at ground level with local electron density or = 20 m to the -2 power and the 240 microsec after its arrival have been studied. No significant excess of events (tachyons) arriving in the early time domain have been observed in a sample of 11,585 air shower triggers.

Noncommutative Field Theories and (super)string Field Theories

NASA Astrophysics Data System (ADS)

Aref'eva, I. Ya.; Belov, D. M.; Giryavets, A. A.; Koshelev, A. S.; Medvedev, P. B.

2002-11-01

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, "comma" and matrix representations of vertices.

Numerical solution of open string field theory in Schnabl gauge

NASA Astrophysics Data System (ADS)

Arroyo, E. Aldo; Fernandes-Silva, A.; Szitas, R.

2018-01-01

Using traditional Virasoro L 0 level-truncation computations, we evaluate the open bosonic string field theory action up to level (10 , 30). Extremizing this level-truncated potential, we construct a numerical solution for tachyon condensation in Schnabl gauge. We find that the energy associated to the numerical solution overshoots the expected value -1 at level L = 6. Extrapolating the level-truncation data for L ≤ 10 to estimate the vacuum energies for L > 10, we predict that the energy reaches a minimum value at L ˜ 12, and then turns back to approach -1 asymptotically as L → ∞. Furthermore, we analyze the tachyon vacuum expectation value (vev), for which by extrapolating its corresponding level-truncation data, we predict that the tachyon vev reaches a minimum value at L ˜ 26, and then turns back to approach the expected analytical result as L → ∞.

Theoretical and observational constraints on Tachyon Inflation

NASA Astrophysics Data System (ADS)

Barbosa-Cendejas, Nandinii; De-Santiago, Josue; German, Gabriel; Hidalgo, Juan Carlos; Rigel Mora-Luna, Refugio

2018-03-01

We constrain several models in Tachyonic Inflation derived from the large-N formalism by considering theoretical aspects as well as the latest observational data. On the theoretical side, we assess the field range of our models by means of the excursion of the equivalent canonical field. On the observational side, we employ BK14+PLANCK+BAO data to perform a parameter estimation analysis as well as a Bayesian model selection to distinguish the most favoured models among all four classes here presented. We observe that the original potential V propto sech(T) is strongly disfavoured by observations with respect to a reference model with flat priors on inflationary observables. This realisation of Tachyon inflation also presents a large field range which may demand further quantum corrections. We also provide examples of potentials derived from the polynomial and the perturbative classes which are both statistically favoured and theoretically acceptable.

The reconstruction of tachyon inflationary potentials

NASA Astrophysics Data System (ADS)

Fei, Qin; Gong, Yungui; Lin, Jiong; Yi, Zhu

2017-08-01

We derive a lower bound on the field excursion for the tachyon inflation, which is determined by the amplitude of the scalar perturbation and the number of e-folds before the end of inflation. Using the relation between the observables like ns and r with the slow-roll parameters, we reconstruct three classes of tachyon potentials. The model parameters are determined from the observations before the potentials are reconstructed, and the observations prefer the concave potential. We also discuss the constraints from the reheating phase preceding the radiation domination for the three classes of models by assuming the equation of state parameter wre during reheating is a constant. Depending on the model parameters and the value of wre, the constraints on Nre and Tre are different. As ns increases, the allowed reheating epoch becomes longer for wre=-1/3, 0 and 1/6 while the allowed reheating epoch becomes shorter for wre=2/3.

Terminal attractors in neural networks

NASA Technical Reports Server (NTRS)

Zak, Michail

1989-01-01

A new type of attractor (terminal attractors) for content-addressable memory, associative memory, and pattern recognition in artificial neural networks operating in continuous time is introduced. The idea of a terminal attractor is based upon a violation of the Lipschitz condition at a fixed point. As a result, the fixed point becomes a singular solution which envelopes the family of regular solutions, while each regular solution approaches such an attractor in finite time. It will be shown that terminal attractors can be incorporated into neural networks such that any desired set of these attractors with prescribed basins is provided by an appropriate selection of the synaptic weights. The applications of terminal attractors for content-addressable and associative memories, pattern recognition, self-organization, and for dynamical training are illustrated.

Stability analysis in tachyonic potential chameleon cosmology

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

Farajollahi, H.; Salehi, A.; Tayebi, F.

2011-05-01

We study general properties of attractors for tachyonic potential chameleon scalar-field model which possess cosmological scaling solutions. An analytic formulation is given to obtain fixed points with a discussion on their stability. The model predicts a dynamical equation of state parameter with phantom crossing behavior for an accelerating universe. We constrain the parameters of the model by best fitting with the recent data-sets from supernovae and simulated data points for redshift drift experiment generated by Monte Carlo simulations.

Tachyon logamediate inflation on the brane

NASA Astrophysics Data System (ADS)

Kamali, Vahid; Nik, Elahe Navaee

2017-07-01

According to a Barrow solution for the scale factor of the universe, the main properties of the tachyon inflation model in the framework of the RSII braneworld are studied. Within this framework the basic slow-roll parameters are calculated analytically. We compare this inflationary scenario to the latest observational data. The predicted spectral index and the tensor-to-scalar fluctuation ratio are in excellent agreement with those of Planck 2015. The current predictions are consistent with those of viable inflationary models.

Stability of a tachyon braneworld

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

Germán, Gabriel; Kuerten, André Martorano; Malagón-Morejón, Dagoberto

2016-01-01

Within the braneworld paradigm the tachyonic scalar field has been used to generate models that attempt to solve some of the open problems that physics faces nowadays, both in cosmology and high energy physics as well. When these field configurations are produced by the interplay of higher dimensional warped gravity with some matter content, braneworld models must prove to be stable under the whole set of small fluctuations of the gravitational and matter fields background, among other consistency tests. Here we present a complete proof of the stability under scalar perturbations of tachyonic thick braneworlds with an embedded maximally symmetricmore » 4D space-time, revealing its physical consistency. This family of models contains a recently reported tachyonic de Sitter thick braneworld which possesses a series of appealing properties. These features encompass complete regularity, asymptotic flatness (instead of being asymptotically dS or AdS) even when it contains a negative bulk cosmological constant, a relevant 3-brane with dS metric which naturally arises from the full set of field equations of the 5D background (it is not imposed), qualitatively describing the inflationary epochs of our Universe, and a graviton spectrum with a single zero mode bound state that accounts for the 4D graviton localised on the brane and is separated from the continuum of Kaluza-Klein massive graviton excitations by a mass gap. The presence of this mass gap in the graviton spectrum makes the extra-dimensional corrections to Newton's law decay exponentially. Gauge vector fields with a single massless bound state in its mass spectrum are also localised on this braneworld model a fact that allows us to recover the Coulomb's law of our 4D world. All these properties of the above referred tachyonic braneworld together with the positive stability analysis provided in this work, constitute a firm step towards the construction of realistic cosmological models within the braneworld paradigm.« less

A de Sitter tachyon thick braneworld

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

Germán, Gabriel; Herrera-Aguilar, Alfredo; Malagón-Morejón, Dagoberto

2013-02-01

Among the multiple 5D thick braneworld models that have been proposed in the last years, in order to address several open problems in modern physics, there is a specific one involving a tachyonic bulk scalar field. Delving into this framework, a thick braneworld with a cosmological background induced on the brane is here investigated. The respective field equations — derived from the model with a warped 5D geometry — are highly non-linear equations, admitting a non-trivial solution for the warp factor and the tachyon scalar field as well, in a de Sitter 4D cosmological background. Moreover, the non-linear tachyonic scalarmore » field, that generates the brane in complicity with warped gravity, has the form of a kink-like configuration. Notwithstanding, the non-linear field equations restricting character does not allow one to easily find thick brane solutions with a decaying warp factor which leads to the localization of 4D gravity and other matter fields. We derive such a thick brane configuration altogether in this tachyon-gravity setup. When analyzing the spectrum of gravity fluctuations in the transverse traceless sector, the 4D gravity is shown to be localized due to the presence of a single zero mode bound state, separated by a continuum of massive Kaluza-Klein (KK) modes by a mass gap. It contrasts with previous results, where there is a KK massive bound excitation providing no clear physical interpretation. The mass gap is determined by the scale of the metric parameter H. Finally, the corrections to Newton's law in this model are computed and shown to decay exponentially. It is in full compliance to corrections reported in previous results (up to a constant factor) within similar braneworlds with induced 4D de Sitter metric, despite the fact that the warp factor and the massive modes have a different form.« less

Stability of a tachyon braneworld

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

Germán, Gabriel; Herrera-Aguilar, Alfredo; Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo,Ciudad Universitaria, CP 58040, Morelia, Michoacán

2016-01-26

Within the braneworld paradigm the tachyonic scalar field has been used to generate models that attempt to solve some of the open problems that physics faces nowadays, both in cosmology and high energy physics as well. When these field configurations are produced by the interplay of higher dimensional warped gravity with some matter content, braneworld models must prove to be stable under the whole set of small fluctuations of the gravitational and matter fields background, among other consistency tests. Here we present a complete proof of the stability under scalar perturbations of tachyonic thick braneworlds with an embedded maximally symmetricmore » 4D space-time, revealing its physical consistency. This family of models contains a recently reported tachyonic de Sitter thick braneworld which possesses a series of appealing properties. These features encompass complete regularity, asymptotic flatness (instead of being asymptotically dS or AdS) even when it contains a negative bulk cosmological constant, a relevant 3-brane with dS metric which naturally arises from the full set of field equations of the 5D background (it is not imposed), qualitatively describing the inflationary epochs of our Universe, and a graviton spectrum with a single zero mode bound state that accounts for the 4D graviton localised on the brane and is separated from the continuum of Kaluza-Klein massive graviton excitations by a mass gap. The presence of this mass gap in the graviton spectrum makes the extra-dimensional corrections to Newton’s law decay exponentially. Gauge vector fields with a single massless bound state in its mass spectrum are also localised on this braneworld model a fact that allows us to recover the Coulomb’s law of our 4D world. All these properties of the above referred tachyonic braneworld together with the positive stability analysis provided in this work, constitute a firm step towards the construction of realistic cosmological models within the braneworld paradigm.« less

Stability of a tachyon braneworld

NASA Astrophysics Data System (ADS)

Germán, Gabriel; Herrera-Aguilar, Alfredo; Martorano Kuerten, André; Malagón-Morejón, Dagoberto; da Rocha, Roldão

2016-01-01

Within the braneworld paradigm the tachyonic scalar field has been used to generate models that attempt to solve some of the open problems that physics faces nowadays, both in cosmology and high energy physics as well. When these field configurations are produced by the interplay of higher dimensional warped gravity with some matter content, braneworld models must prove to be stable under the whole set of small fluctuations of the gravitational and matter fields background, among other consistency tests. Here we present a complete proof of the stability under scalar perturbations of tachyonic thick braneworlds with an embedded maximally symmetric 4D space-time, revealing its physical consistency. This family of models contains a recently reported tachyonic de Sitter thick braneworld which possesses a series of appealing properties. These features encompass complete regularity, asymptotic flatness (instead of being asymptotically dS or AdS) even when it contains a negative bulk cosmological constant, a relevant 3-brane with dS metric which naturally arises from the full set of field equations of the 5D background (it is not imposed), qualitatively describing the inflationary epochs of our Universe, and a graviton spectrum with a single zero mode bound state that accounts for the 4D graviton localised on the brane and is separated from the continuum of Kaluza-Klein massive graviton excitations by a mass gap. The presence of this mass gap in the graviton spectrum makes the extra-dimensional corrections to Newton's law decay exponentially. Gauge vector fields with a single massless bound state in its mass spectrum are also localised on this braneworld model a fact that allows us to recover the Coulomb's law of our 4D world. All these properties of the above referred tachyonic braneworld together with the positive stability analysis provided in this work, constitute a firm step towards the construction of realistic cosmological models within the braneworld paradigm.

Universal statistics of terminal dynamics before collapse

NASA Astrophysics Data System (ADS)

Lenner, Nicolas; Eule, Stephan; Wolf, Fred

Recent biological developments have both drastically increased the precision as well as amount of generated data, allowing for a switching from pure mean value characterization of the process under consideration to an analysis of the whole ensemble, exploiting the stochastic nature of biology. We focus on the general class of non-equilibrium processes with distinguished terminal points as can be found in cell fate decision, check points or cognitive neuroscience. Aligning the data to a terminal point (e.g. represented as an absorbing boundary) allows to device a general methodology to characterize and reverse engineer the terminating history. Using a small noise approximation we derive mean variance and covariance of the aligned data for general finite time singularities.

Tachyon condensation due to domain-wall annihilation in Bose-Einstein condensates.

PubMed

Takeuchi, Hiromitsu; Kasamatsu, Kenichi; Tsubota, Makoto; Nitta, Muneto

2012-12-14

We show theoretically that a domain-wall annihilation in two-component Bose-Einstein condensates causes tachyon condensation accompanied by spontaneous symmetry breaking in a two-dimensional subspace. Three-dimensional vortex formation from domain-wall annihilations is considered a kink formation in subspace. Numerical experiments reveal that the subspatial dynamics obey the dynamic scaling law of phase-ordering kinetics. This model is experimentally feasible and provides insights into how the extra dimensions influence subspatial phase transition in higher-dimensional space.

Tachyon field non-minimally coupled to massive neutrino matter

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

Ahmad, Safia; Myrzakulov, Nurgissa; Myrzakulov, R., E-mail: safia@ctp-jamia.res.in, E-mail: nmyrzakulov@gmail.com, E-mail: rmyrzakulov@gmail.com

2016-07-01

In this paper, we consider rolling tachyon, with steep run-away type of potentials non-minimally coupled to massive neutrino matter. The coupling dynamically builds up at late times as neutrino matter turns non-relativistic. In case of scaling and string inspired potentials, we have shown that non-minimal coupling leads to minimum in the field potential. Given a suitable choice of model parameters, it is shown to give rise to late-time acceleration with the desired equation of state.

Goldstone Gauginos.

PubMed

Alves, Daniele S M; Galloway, Jamison; McCullough, Matthew; Weiner, Neal

2015-10-16

Models of supersymmetry with Dirac gauginos provide an attractive scenario for physics beyond the standard model. The "supersoft" radiative corrections and suppressed supersymmetry production at colliders provide for more natural theories and an understanding of why no new states have been seen. Unfortunately, these models are handicapped by a tachyon which is naturally present in existing models of Dirac gauginos. We argue that this tachyon is absent, with the phenomenological successes of the model preserved, if the right-handed gaugino is a (pseudo-)Goldstone field of a spontaneously broken anomalous flavor symmetry.

About non standard Lagrangians in cosmology

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

Dimitrijevic, Dragoljub D.; Milosevic, Milan

A review of non standard Lagrangians present in modern cosmological models will be considered. Well known example of non standard Lagrangian is Dirac-Born-Infeld (DBI) type Lagrangian for tachyon field. Another type of non standard Lagrangian under consideration contains scalar field which describes open p-adic string tachyon and is called p-adic string theory Lagrangian. We will investigate homogenous cases of both DBI and p-adic fields and obtain Lagrangians of the standard type which have the same equations of motions as aforementioned non standard one.

Chaotic inflation in Jordan frame supergravity

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

Lee, Hyun Min, E-mail: hyun.min.lee@cern.ch

2010-08-01

We consider the inflationary scenario with non-minimal coupling in 4D Jordan frame supergravity. We find that there occurs a tachyonic instability along the direction of the accompanying non-inflaton field in generic Jordan frame supergravity models. We propose a higher order correction to the Jordan frame function for solving the tachyonic mass problem and show that the necessary correction can be naturally generated by the heavy thresholds without spoiling the slow-roll conditions. We discuss the implication of the result on the Higgs inflation in NMSSM.

The reconstruction of tachyon inflationary potentials

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

Fei, Qin; Gong, Yungui; Lin, Jiong

We derive a lower bound on the field excursion for the tachyon inflation, which is determined by the amplitude of the scalar perturbation and the number of e -folds before the end of inflation. Using the relation between the observables like n {sub s} and r with the slow-roll parameters, we reconstruct three classes of tachyon potentials. The model parameters are determined from the observations before the potentials are reconstructed, and the observations prefer the concave potential. We also discuss the constraints from the reheating phase preceding the radiation domination for the three classes of models by assuming the equationmore » of state parameter w {sub re} during reheating is a constant. Depending on the model parameters and the value of w {sub re} , the constraints on N {sub re} and T {sub re} are different. As n {sub s} increases, the allowed reheating epoch becomes longer for w {sub re} =−1/3, 0 and 1/6 while the allowed reheating epoch becomes shorter for w {sub re} =2/3.« less

Solving Lauricella string scattering amplitudes through recurrence relations

NASA Astrophysics Data System (ADS)

Lai, Sheng-Hong; Lee, Jen-Chi; Lee, Taejin; Yang, Yi

2017-09-01

We show that there exist infinite number of recurrence relations valid for all energies among the open bosonic string scattering amplitudes (SSA) of three tachyons and one arbitrary string state, or the Lauricella SSA. Moreover, these infinite number of recurrence relations can be used to solve all the Lauricella SSA and express them in terms of one single four tachyon amplitude. These results extend the solvability of SSA at the high energy, fixed angle scattering limit and those at the Regge scattering limit discovered previously to all kinematic regimes.

Observational constraints on Tachyon and DBI inflation

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

Li, Sheng; Liddle, Andrew R., E-mail: sl277@sussex.ac.uk, E-mail: arl@roe.ac.uk

2014-03-01

We present a systematic method for evaluation of perturbation observables in non-canonical single-field inflation models within the slow-roll approximation, which allied with field redefinitions enables predictions to be established for a wide range of models. We use this to investigate various non-canonical inflation models, including Tachyon inflation and DBI inflation. The Lambert W function will be used extensively in our method for the evaluation of observables. In the Tachyon case, in the slow-roll approximation the model can be approximated by a canonical field with a redefined potential, which yields predictions in better agreement with observations than the canonical equivalents. Formore » DBI inflation models we consider contributions from both the scalar potential and the warp geometry. In the case of a quartic potential, we find a formula for the observables under both non-relativistic (sound speed c{sub s}{sup 2} ∼ 1) and relativistic behaviour (c{sub s}{sup 2} || 1) of the scalar DBI inflaton. For a quadratic potential we find two branches in the non-relativistic c{sub s}{sup 2} ∼ 1 case, determined by the competition of model parameters, while for the relativistic case c{sub s}{sup 2} → 0, we find consistency with results already in the literature. We present a comparison to the latest Planck satellite observations. Most of the non-canonical models we investigate, including the Tachyon, are better fits to data than canonical models with the same potential, but we find that DBI models in the slow-roll regime have difficulty in matching the data.« less

Tachyonic quench in a free bosonic field theory

NASA Astrophysics Data System (ADS)

Montes, Sebastián; Sierra, Germán; Rodríguez-Laguna, Javier

2018-02-01

We present a characterization of a bosonic field theory driven by a free (Gaussian) tachyonic Hamiltonian. This regime is obtained from a theory describing two coupled bosonic fields after a regular quench. Relevant physical quantities such as simple correlators, entanglement entropies, and the mutual information of disconnected subregions are computed. We show that the causal structure resembles a critical (massless) quench. For short times, physical quantities also resemble critical quenches. However, exponential divergences end up dominating the dynamics in a very characteristic way. This is related to the fact that the low-frequency modes do not equilibrate. Some applications and extensions are outlined.

Note on tachyon moduli and closed strings

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

Carneiro da Cunha, Bruno

2008-07-15

The collective behavior of the SL(2,R) covariant brane states of noncritical c=1 string theory, found in a previous work, is studied in the Fermi liquid approximation. It is found that such states mimic the coset WZW model, whereas only by further restrictions one recovers the double-scaling limit which was purported to be equivalent to closed string models. Another limit is proposed, inspired by the tachyon condensation ideas, where the spectrum is the same of two-dimensional string theory. We close by noting some strange connections between vacuum states of the theory in their different interpretations.

Dark solitons, D-branes and noncommutative tachyon field theory

NASA Astrophysics Data System (ADS)

Giaccari, Stefano; Nian, Jun

2017-11-01

In this paper we discuss the boson/vortex duality by mapping the (3+1)D Gross-Pitaevskii theory into an effective string theory in the presence of boundaries. Via the effective string theory, we find the Seiberg-Witten map between the commutative and the noncommutative tachyon field theories, and consequently identify their soliton solutions with D-branes in the effective string theory. We perform various checks of the duality map and the identification of soliton solutions. This new insight between the Gross-Pitaevskii theory and the effective string theory explains the similarity of these two systems at quantitative level.

Cosmological tachyon condensation

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

Bilic, Neven; Tupper, Gary B.; Viollier, Raoul D.

2009-07-15

We consider the prospects for dark matter/energy unification in k-essence type cosmologies. General mappings are established between the k-essence scalar field, the hydrodynamic and braneworld descriptions. We develop an extension of the general relativistic dust model that incorporates the effects of both pressure and the associated acoustic horizon. Applying this to a tachyon model, we show that this inhomogeneous 'variable Chaplygin gas' does evolve into a mixed system containing cold dark matter like gravitational condensate in significant quantities. Our methods can be applied to any dark energy model, as well as to mixtures of dark energy and traditional dark matter.

Recent Results on Singularity Strengths

NASA Astrophysics Data System (ADS)

Nolan, Brien

2002-12-01

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

Terminal Forecast Reference Notebook for Hanau AAF, Germany.

DTIC Science & Technology

1983-04-22

Vogelsberg, just west of Fulda, rises to a prominence of 2359 feet. This is a singular feature of volcanic origin with the land rising up from small...near 2000 feet 50 miles south of Hanau. Farther to the southwest, on the west side of the Rhein River valley, are the Eifel Mountains. EFFECTS OF

A premier analysis of supersymmetric closed string tachyon cosmology

NASA Astrophysics Data System (ADS)

Vázquez-Báez, V.; Ramírez, C.

2018-04-01

From a previously found worldline supersymmetric formulation for the effective action of the closed string tachyon in a FRW background, the Hamiltonian of the theory is constructed, by means of the Dirac procedure, and written in a quantum version. Using the supersymmetry algebra we are able to find solutions to the Wheeler-DeWitt equation via a more simple set of first order differential equations. Finally, for the k = 0 case, we compute the expectation value of the scale factor with a suitably potential also favored in the present literature. We give some interpretations of the results and state future work lines on this matter.

Renormalizable, asymptotically free gravity without ghosts or tachyons

NASA Astrophysics Data System (ADS)

Einhorn, Martin B.; Jones, D. R. Timothy

2017-12-01

We analyze scale invariant quadratic quantum gravity incorporating nonminimal coupling to a multiplet of scalar fields in a gauge theory, with particular emphasis on the consequences for its interpretation resulting from a transformation from the Jordan frame to the Einstein frame. The result is the natural emergence of a de Sitter space solution which, depending the gauge theory and region of parameter space chosen, can be free of ghosts and tachyons, and completely asymptotically free. In the case of an SO(10) model, we present a detailed account of the spontaneous symmetry breaking, and we calculate the leading (two-loop) contribution to the dilaton mass.

Simulations of cold electroweak baryogenesis: dependence on the source of CP-violation

NASA Astrophysics Data System (ADS)

Mou, Zong-Gang; Saffin, Paul M.; Tranberg, Anders

2018-05-01

We compute the baryon asymmetry created in a tachyonic electroweak symmetry breaking transition, focusing on the dependence on the source of effective CP-violation. Earlier simulations of Cold Electroweak Baryogenesis have almost exclusively considered a very specific CP-violating term explicitly biasing Chern-Simons number. We compare four different dimension six, scalar-gauge CP-violating terms, involving both the Higgs field and another dynamical scalar coupled to SU(2) or U(1) gauge fields. We find that for sensible values of parameters, all implementations can generate a baryon asymmetry consistent with observations, showing that baryogenesis is a generic outcome of a fast tachyonic electroweak transition.

Topological view of quantum tunneling coherent destruction

NASA Astrophysics Data System (ADS)

Bernardini, Alex E.; Chinaglia, Mariana

2017-08-01

Quantum tunneling of the ground and first excited states in a quantum superposition driven by a novel analytical configuration of a double-well (DW) potential is investigated. Symmetric and asymmetric potentials are considered as to support quantum mechanical zero mode and first excited state analytical solutions. Reporting about a symmetry breaking that supports the quantum conversion of a zero-mode stable vacuum into an unstable tachyonic quantum state, two inequivalent topological scenarios are supposed to drive stable tunneling and coherent tunneling destruction respectively. A complete prospect of the Wigner function dynamics, vector field fluxes and the time dependence of stagnation points is obtained for the analytical potentials that support stable and tachyonic modes.

Dynamics and stability of light-like tachyon condensation

NASA Astrophysics Data System (ADS)

Barnaby, Neil; Mulryne, David J.; Nunes, Nelson J.; Robinson, Patrick

2009-03-01

Recently, Hellerman and Schnabl considered the dynamics of unstable D-branes in the background of a linear dilaton. Remarkably, they were able to construct light-like tachyon solutions which interpolate smoothly between the perturbative and nonperturbative vacua, without undergoing the wild oscillations that plague time-like solutions. In their analysis, however, the full structure of the initial value problem for the nonlocal dynamical equations was not considered. In this paper, therefore, we reexamine the nonlinear dynamics of light-like tachyon condensation using a combination of numerical and analytical techniques. We find that for the p-adic string the monotonic behaviour obtained previously relied on a special choice of initial conditions near the unstable maximum. For generic initial conditions the wild oscillations come back to haunt us. Interestingly, we find an ``island of stability'' in initial condition space that leads to sensible evolution at late times. For the string field theory case, on the other hand, we find that the evolution is completely stable for generic choices of initial data. This provides an explicit example of a string theoretic system that admits infinitely many initial data but is nevertheless nonperturbatively stable. Qualitatively similar dynamics are obtained in nonlocal cosmologies where the Hubble damping plays a role very analogous to the dilaton gradient.

The development of a mixing layer under the action of weak streamwise vortices

NASA Technical Reports Server (NTRS)

Goldstein, Marvin E.; Mathew, Joseph

1993-01-01

The action of weak, streamwise vortices on a plane, incompressible, steady mixing layer is examined in the large Reynolds-number limit. The outer, inviscid region is bounded by a vortex sheet to which the viscous region is confined. It is shown that the local linear analysis becomes invalid at streamwise distances O(epsilon(sup -1)), where epsilon is much less than 1 is the cross flow amplitude, and a new nonlinear analysis is constructed for this region. Numerical solutions of the nonlinear problem show that the vortex sheet undergoes an O(1) change in position and that the solution is ultimately terminated by the appearance of a singularity. The corresponding viscous layer shows downstream thickening, but appears to remain well behaved up to the singular location.

Past incompleteness of a bouncing multiverse

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

Vilenkin, Alexander; Zhang, Jun, E-mail: vilenkin@cosmos.phy.tufts.edu, E-mail: jun.zhang@tufts.edu

2014-06-01

According to classical GR, Anti-de Sitter (AdS) bubbles in the multiverse terminate in big crunch singularities. It has been conjectured, however, that the fundamental theory may resolve these singularities and replace them by nonsingular bounces. This may have important implications for the beginning of the multiverse. Geodesics in cosmological spacetimes are known to be past-incomplete, as long as the average expansion rate along the geodesic is positive, but it is not clear that the latter condition is satisfied if the geodesic repeatedly passes through crunching AdS bubbles. We investigate this issue in a simple multiverse model, where the spacetime consistsmore » of a patchwork of FRW regions. The conclusion is that the spacetime is still past-incomplete, even in the presence of AdS bounces.« less

α-Attractor and reheating in a model with noncanonical scalar fields

NASA Astrophysics Data System (ADS)

Rashidi, Narges; Nozari, Kourosh

We consider two noncanonical scalar fields [tachyon and Dirac-Born-Infeld (DBI)] with E-model type of the potential. We study cosmological inflation in these models to find possible α-attractors. We show that similar to the canonical scalar field case, in both tachyon and DBI models there is a value of the scalar spectral index in small α limit which is just a function of the e-folds number. However, the value of ns in DBI model is somewhat different from the other ones. We also compare the results with Planck2015 TT, TE, EE+lowP data. The reheating phase after inflation is studied in these models which gives some more constraints on the model parameters.

Gott time machines in anti-de Sitter space

NASA Astrophysics Data System (ADS)

Holst, Sören

1996-04-01

In 1991 Gott presented a solution of Einstein's field equations in 2+1 dimensions with λ=0 that contained closed timelike curves ( ctc's). This solution was remarkable because at first it did not seem to be unphysical in any other respect. Later, however, it was shown that Gott's solution is tachyonic in a certain sense. Here the case λ<0 is discussed. We show that it is also possible to construct ctc's in this case, in a way analogous to that used by Gott. We also show a special case of this construction to be tachyonic. λ<0 means that we are dealing with anti-de Sitter space, and since the CTC-construction necessitates some understanding of its structure, a few pages are devoted to this subject.

Classical evolution and quantum generation in generalized gravity theories including string corrections and tachyons: Unified analyses

NASA Astrophysics Data System (ADS)

Hwang, Jai-Chan; Noh, Hyerim

2005-03-01

We present cosmological perturbation theory based on generalized gravity theories including string theory correction terms and a tachyonic complication. The classical evolution as well as the quantum generation processes in these varieties of gravity theories are presented in unified forms. These apply both to the scalar- and tensor-type perturbations. Analyses are made based on the curvature variable in two different gauge conditions often used in the literature in Einstein’s gravity; these are the curvature variables in the comoving (or uniform-field) gauge and the zero-shear gauge. Applications to generalized slow-roll inflation and its consequent power spectra are derived in unified forms which include a wide range of inflationary scenarios based on Einstein’s gravity and others.

Spin connection as Lorentz gauge field in Fairchild’s action

NASA Astrophysics Data System (ADS)

Cianfrani, Francesco; Montani, Giovanni; Scopelliti, Vincenzo

2016-06-01

We propose a modified gravitational action containing besides the Einstein-Cartan term some quadratic contributions resembling the Yang-Mills Lagrangian for the Lorentz spin connections. We outline how a propagating torsion arises and we solve explicitly the linearized equations of motion on a Minkowski background. We identify among torsion components six degrees of freedom: one is carried by a pseudo-scalar particle, five by a tachyon field. By adding spinor fields and neglecting backreaction on the geometry, we point out how only the pseudo-scalar particle couples directly with fermions, but the resulting coupling constant is suppressed by the ratio between fermion and Planck masses. Including backreaction, we demonstrate how the tachyon field provides causality violation in the matter sector, via an interaction mediated by gravitational waves.

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.

Swinging Atwood's Machine

NASA Astrophysics Data System (ADS)

Tufillaro, Nicholas B.; Abbott, Tyler A.; Griffiths, David J.

1984-10-01

We examine the motion of an Atwood's Machine in which one of the masses is allowed to swing in a plane. Computer studies reveal a rich variety of trajectories. The orbits are classified (bounded, periodic, singular, and terminating), and formulas for the critical mass ratios are developed. Perturbative techniques yield good approximations to the computer-generated trajectories. The model constitutes a simple example of a nonlinear dynamical system with two degrees of freedom.

Evading the Lyth bound in hybrid natural inflation

NASA Astrophysics Data System (ADS)

Hebecker, A.; Kraus, S. C.; Westphal, A.

2013-12-01

Generically, the gravitational-wave or tensor-mode contribution to the primordial curvature spectrum of inflation is tiny if the field range of the inflaton is much smaller than the Planck scale. We show that this pessimistic conclusion is naturally avoided in a rather broad class of small-field models. More specifically, we consider models where an axionlike shift symmetry keeps the inflaton potential flat (up to nonperturbative cosine-shaped modulations), but inflation nevertheless ends in a waterfall regime, as is typical for hybrid inflation. In such hybrid natural inflation scenarios (examples are provided by Wilson line inflation and fluxbrane inflation), the slow-roll parameter ɛ can be sizable during an early period (relevant for the cosmic microwave background spectrum). Subsequently, ɛ quickly becomes very small before the tachyonic instability eventually terminates the slow-roll regime. In this scenario, one naturally generates a considerable tensor-mode contribution in the curvature spectrum, collecting nevertheless the required amount of e-foldings during the final period of inflation. While nonobservation of tensors by Planck is certainly not a problem, a discovery in the medium- to long-term future is realistic.

AdS/CFT beyond the N = 4 SYM paradigm

NASA Astrophysics Data System (ADS)

Pomoni, Elli

In this thesis we present studies in the AdS/CFT correspondence that intend to push the present knowledge beyond the N = 4 super Yang-Mills (SYM) paradigm. The first part is concerned with the study of non-supersymmetric deformations of N = 4 SYM (which still are in the N = 4 universality class). For non-supersymmetric CFT's at Large N we explore the correspondence between string theory tachyons in the bulk and instabilities on the boundary effective action. The operators dual to AdS tachyons have anomalous dimensions that are purely complex numbers. We give a prescription for calculating the mass of the tachyon from the field theory side. Moreover, we apply this general dictionary to the case of intersecting D7 flavor branes in AdS 5 x S5 and obtain the mass of the open string tachyon that is dual to the instability in the mesonic sector of the theory. In the second part we present work aiming at finding string theory duals for gauge theories beyond the N = 4 universality class, i.e. theories that have genuinely less supersymmetry and unquenched flavor. Arguably the next simplest example after N = 4 SYM is N = 2 SU(Nc) SYM coupled to Nf = 2Nc fundamental hypermultiplets. The theory admits a Veneziano expansion of large Nc and large Nf, with Nf/Nc and lambda = g2Nc kept fixed. The topological structure of large N diagrams invites a general conjecture: the flavor-singlet sector of a gauge theory in the Veneziano limit is dual to a closed string theory. We present the one-loop Hamiltonian for the scalar sector of N = 2 superconformal QCD and study this integrability of the theory. Furthermore, we explore the chiral spectrum of the protected operators of the theory using the one-loop anomalous dimensions and, additionally, by studying the index of the theory. We finally search for possible AdS dual trying to match the chiral spectrum. We conclude that the string dual is a sub-critical background containing both an AdS 5 and an S1 factor.

Cosmological signatures of ultralight dark matter with an axionlike potential

NASA Astrophysics Data System (ADS)

Cedeño, Francisco X. Linares; González-Morales, Alma X.; Ureña-López, L. Arturo

2017-09-01

Nonlinearities in a realistic axion field potential may play an important role in the cosmological dynamics. In this paper we use the Boltzmann code class to solve the background and linear perturbations evolution of an axion field and contrast our results with those of CDM and the free axion case. We conclude that there is a slight delay in the onset of the axion field oscillations when nonlinearities in the axion potential are taken into account. Besides, we identify a tachyonic instability of linear modes resulting in the presence of a bump in the power spectrum at small scales. Some comments are in turn about the true source of the tachyonic instability, how the parameters of the axionlike potential can be constrained by Ly-α observations, and the consequences in the stability of self-gravitating objects made of axions.

On non-homogeneous tachyon condensation in closed string theory

NASA Astrophysics Data System (ADS)

Giribet, Gaston; Rado, Laura

2017-08-01

Lorentzian continuation of the Sine-Liouville model describes non-homogeneous rolling closed string tachyon. Via T-duality, this relates to the gauged H + 3 Wess-Zumino-Witten model at subcritical level. This model is exactly solvable. We give a closed formula for the 3-point correlation functions for the model at level k within the range 0 < k < 2, which relates to the analogous quantity for k > 2 in a similar way as how the Harlow-Maltz-Witten 3-point function of timelike Liouville field theory relates to the analytic continuation of the Dorn-Otto-Zamolodchikov-Zamolodchikov structure constants: we find that the ratio between both 3-point functions can be written in terms of quotients of Jacobi's θ-functions, while their product exhibits remarkable cancellations and eventually factorizes. Our formula is consistent with previous proposals made in the literature.

Tachyon solutions in boundary and open string field theory

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

Calcagni, Gianluca; Nardelli, Giuseppe; Dipartimento di Matematica e Fisica, Universita Cattolica, via Musei 41, 25121 Brescia

2008-12-15

We construct rolling tachyon solutions of open and boundary string field theory (OSFT and BSFT, respectively), in the bosonic and supersymmetric (susy) case. The wildly oscillating solution of susy OSFT is recovered, together with a family of time-dependent BSFT solutions, for the bosonic and susy string. These are parametrized by an arbitrary constant r involved in solving the Green equation of the target fields. When r=0 we recover previous results in BSFT, whereas for r attaining the value predicted by OSFT it is shown that the bosonic OSFT solution is the derivative of the boundary one; in the supersymmetric casemore » the relation between the two solutions is more complicated. This technical correspondence sheds some light on the nature of wild oscillations, which appear in both theories whenever r>0.« less

Factorization of chiral string amplitudes

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

Huang, Yu-tin; Siegel, Warren; Yuan, Ellis Ye

We re-examine a closed-string model defined by altering the boundary conditions for one handedness of two-dimensional propagators in otherwise-standard string theory. We evaluate the amplitudes using Kawai-Lewellen-Tye factorization into open-string amplitudes. The only modification to standard string theory is effectively that the spacetime Minkowski metric changes overall sign in one open-string factor. This cancels all but a finite number of states: as found in earlier approaches, with enough supersymmetry (e.g., type II) the tree amplitudes reproduce those of the massless truncation of ordinary string theory. However, we now find for the other cases that additional fields, formerly thought to bemore » auxiliary, describe new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic). The tachyon is always a ghost, but can be avoided in the heterotic case.« less

Factorization of chiral string amplitudes

DOE PAGES

Huang, Yu-tin; Siegel, Warren; Yuan, Ellis Ye

2016-09-16

We re-examine a closed-string model defined by altering the boundary conditions for one handedness of two-dimensional propagators in otherwise-standard string theory. We evaluate the amplitudes using Kawai-Lewellen-Tye factorization into open-string amplitudes. The only modification to standard string theory is effectively that the spacetime Minkowski metric changes overall sign in one open-string factor. This cancels all but a finite number of states: as found in earlier approaches, with enough supersymmetry (e.g., type II) the tree amplitudes reproduce those of the massless truncation of ordinary string theory. However, we now find for the other cases that additional fields, formerly thought to bemore » auxiliary, describe new spin-2 states at the two adjacent mass levels (tachyonic and tardyonic). The tachyon is always a ghost, but can be avoided in the heterotic case.« less

A de Sitter tachyonic braneworld revisited

NASA Astrophysics Data System (ADS)

Barbosa-Cendejas, Nandinii; Cartas-Fuentevilla, Roberto; Herrera-Aguilar, Alfredo; Rigel Mora-Luna, Refugio; da Rocha, Roldão

2018-01-01

Within the framework of braneworlds, several interesting physical effects can be described in a wide range of energy scales, starting from high-energy physics to cosmology and low-energy physics. An usual way to generate a thick braneworld model relies in coupling a bulk scalar field to higher dimensional warped gravity. Quite recently, a novel braneworld was generated with the aid of a tachyonic bulk scalar field, having several remarkable properties. It comprises a regular and stable solution that contains a relevant 3-brane with de Sitter induced metric, arising as an exact solution to the 5D field equations, describing the inflationary eras of our Universe. Besides, it is asymptotically flat, despite of the presence of a negative 5D cosmological constant, which is an interesting feature that contrasts with most of the known, asymptotically either dS or AdS models. Moreover, it encompasses a graviton spectrum with a single massless bound state, accounting for 4D gravity localized on the brane, separated from the continuum of Kaluza-Klein massive graviton modes by a mass gap that makes the 5D corrections to Newton's law to decay exponentially. Finally, gauge, scalar and fermion fields are also shown to be localized on this braneworld. In this work, we show that this tachyonic braneworld allows for a nontrivial solution with a vanishing 5D cosmological constant that preserves all the above mentioned remarkable properties with a less amount of parameters, constituting an important contribution to the construction of a realistic cosmological braneworld model.

Giant wormholes in ghost-free bigravity theory

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

Sushkov, Sergey V.; Volkov, Mikhail S., E-mail: sergey_sushkov@mail.ru, E-mail: volkov@lmpt.univ-tours.fr

2015-06-01

We study Lorentzian wormholes in the ghost-free bigravity theory described by two metrics, g and f. Wormholes can exist if only the null energy condition is violated, which happens naturally in the bigravity theory since the graviton energy-momentum tensors do not apriori fulfill any energy conditions. As a result, the field equations admit solutions describing wormholes whose throat size is typically of the order of the inverse graviton mass. Hence, they are as large as the universe, so that in principle we might all live in a giant wormhole. The wormholes can be of two different types that we callmore » W1 and W2. The W1 wormholes interpolate between the AdS spaces and have Killing horizons shielding the throat. The Fierz-Pauli graviton mass for these solutions becomes imaginary in the AdS zone, hence the gravitons behave as tachyons, but since the Breitenlohner-Freedman bound is fulfilled, there should be no tachyon instability. For the W2 wormholes the g-geometry is globally regular and in the far field zone it becomes the AdS up to subleading terms, its throat can be traversed by timelike geodesics, while the f-geometry has a completely different structure and is not geodesically complete. There is no evidence of tachyons for these solutions, although a detailed stability analysis remains an open issue. It is possible that the solutions may admit a holographic interpretation.« less

Giant wormholes in ghost-free bigravity theory

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

Sushkov, Sergey V.; Volkov, Mikhail S.; Laboratoire de Mathématiques et Physique Théorique CNRS-UMR 7350, Université de Tours, Parc de Grandmont, 37200 Tours

2015-06-09

We study Lorentzian wormholes in the ghost-free bigravity theory described by two metrics, g and f. Wormholes can exist if only the null energy condition is violated, which happens naturally in the bigravity theory since the graviton energy-momentum tensors do not apriori fulfill any energy conditions. As a result, the field equations admit solutions describing wormholes whose throat size is typically of the order of the inverse graviton mass. Hence, they are as large as the universe, so that in principle we might all live in a giant wormhole. The wormholes can be of two different types that we callmore » W1 and W2. The W1 wormholes interpolate between the AdS spaces and have Killing horizons shielding the throat. The Fierz-Pauli graviton mass for these solutions becomes imaginary in the AdS zone, hence the gravitons behave as tachyons, but since the Breitenlohner-Freedman bound is fulfilled, there should be no tachyon instability. For the W2 wormholes the g-geometry is globally regular and in the far field zone it becomes the AdS up to subleading terms, its throat can be traversed by timelike geodesics, while the f-geometry has a completely different structure and is not geodesically complete. There is no evidence of tachyons for these solutions, although a detailed stability analysis remains an open issue. It is possible that the solutions may admit a holographic interpretation.« less

Singular Isothermal Disks and the Formation of Multiple Stars

NASA Technical Reports Server (NTRS)

Galli, Daniele; Shu, Frank H.; Laughlin, Gregory; Lizano, Susana; DeVincenzi, Donald (Technical Monitor)

2000-01-01

A crucial missing ingredient in previous theoretical studies of fragmentation is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore consider the equilibrium configuration of isopedically magnetized, scale-free, singular isothermal disks, without the assumption of axial symmetry. We find that lopsided (M = 1) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...) configurations bifurcate from an underlying axisymmetric sequence at progressively higher dimensionless rates of rotation, but such nonaxisymmetric sequences always terminate in shockwaves before they have a chance to fission into separate bodies. We advance the hypothesis that binary and multiple star-formation from smooth (i.e., not highly turbulent) starting states that are supercritical but in unstable mechanical balance requires the rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing gravitational collapse.

Behavioral Context of Call Production by Eastern North Pacific Blue Whales

DTIC Science & Technology

2007-01-25

pairs occurring in a repeated song sequence; B calls from a different blue whale are also evident; spectrogram parameters: fast Fourier transform (FFT...Acoustic data were viewed in spectrogram form ( fast Fourier transform [FFT] length 1 s, 80% overlap, Hanning window) to de- termine the presence of calls...dura- tion to song A and B units (Table 2), but the intermit - tent timing clearly distinguishes them from song. Whales producing singular calls were

Hamiltonian analysis of non-relativistic non-BPS Dp-brane

NASA Astrophysics Data System (ADS)

Klusoň, J.

2017-07-01

We perform Hamiltonian analysis of non-relativistic non-BPS Dp-brane. We find the constraint structure of this theory and determine corresponding equations of motion. We further discuss property of this theory at the tachyon vacuum.

High-energy zero-norm states and symmetries of string theory.

PubMed

Chan, Chuan-Tsung; Ho, Pei-Ming; Lee, Jen-Chi; Teraguchi, Shunsuke; Yang, Yi

2006-05-05

High-energy limit of zero-norm states in the old covariant first quantized spectrum of the 26D open bosonic string, together with the assumption of a smooth behavior of string theory in this limit, are used to derive infinitely many linear relations among the leading high-energy, fixed-angle behavior of four-point functions of different string states. As a result, ratios among all high-energy scattering amplitudes of four arbitrary string states can be calculated algebraically and the leading order amplitudes can be expressed in terms of that of four tachyons as conjectured by Gross in 1988. A dual calculation can also be performed and equivalent results are obtained by taking the high-energy limit of Virasoro constraints. Finally, we compute all high-energy scattering amplitudes of three tachyons and one massive state at the leading order by saddle-point approximation to verify our results.

Holographic cosmology from a system of M2–M5 branes

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

Sepehri, Alireza, E-mail: alireza.sepehri@uk.ac.ir; Research Institute for Astronomy and Astrophysics of Maragha; Faizal, Mir, E-mail: f2mir@uwaterloo.ca

In this paper, we analyze the holographic cosmology using a M2–M5 brane configuration. In this configuration, a M2-brane will be placed in between a M5-brane and an anti-M5-brane. The M2-brane will act as a channel for energy to flow from an anti-M5-brane to a M5-brane, and this will increase the degrees of freedom on the M5-brane causing inflation. The inflation will end when the M5-brane and anti-M5-brane get separated. However, at a later stage the distance between the M5-brane and the anti-M5-bran can reduce and this will cause the formation of tachyonic states. These tachyonic states will again open amore » bridge between the M5-branes and the anti-M5-branes, which will cause further acceleration of the universe.« less

General gauge mediation at the weak scale

DOE PAGES

Knapen, Simon; Redigolo, Diego; Shih, David

2016-03-09

We completely characterize General Gauge Mediation (GGM) at the weak scale by solving all IR constraints over the full parameter space. This is made possible through a combination of numerical and analytical methods, based on a set of algebraic relations among the IR soft masses derived from the GGM boundary conditions in the UV. We show how tensions between just a few constraints determine the boundaries of the parameter space: electroweak symmetry breaking (EWSB), the Higgs mass, slepton tachyons, and left-handed stop/sbottom tachyons. While these constraints allow the left-handed squarks to be arbitrarily light, they place strong lower bounds onmore » all of the right-handed squarks. Meanwhile, light EW superpartners are generic throughout much of the parameter space. This is especially the case at lower messenger scales, where a positive threshold correction to m h coming from light Higgsinos and winos is essential in order to satisfy the Higgs mass constraint.« less

Singular perturbation analysis of AOTV-related trajectory optimization problems

NASA Technical Reports Server (NTRS)

Calise, Anthony J.; Bae, Gyoung H.

1990-01-01

The problem of real time guidance and optimal control of Aeroassisted Orbit Transfer Vehicles (AOTV's) was addressed using singular perturbation theory as an underlying method of analysis. Trajectories were optimized with the objective of minimum energy expenditure in the atmospheric phase of the maneuver. Two major problem areas were addressed: optimal reentry, and synergetic plane change with aeroglide. For the reentry problem, several reduced order models were analyzed with the objective of optimal changes in heading with minimum energy loss. It was demonstrated that a further model order reduction to a single state model is possible through the application of singular perturbation theory. The optimal solution for the reduced problem defines an optimal altitude profile dependent on the current energy level of the vehicle. A separate boundary layer analysis is used to account for altitude and flight path angle dynamics, and to obtain lift and bank angle control solutions. By considering alternative approximations to solve the boundary layer problem, three guidance laws were derived, each having an analytic feedback form. The guidance laws were evaluated using a Maneuvering Reentry Research Vehicle model and all three laws were found to be near optimal. For the problem of synergetic plane change with aeroglide, a difficult terminal boundary layer control problem arises which to date is found to be analytically intractable. Thus a predictive/corrective solution was developed to satisfy the terminal constraints on altitude and flight path angle. A composite guidance solution was obtained by combining the optimal reentry solution with the predictive/corrective guidance method. Numerical comparisons with the corresponding optimal trajectory solutions show that the resulting performance is very close to optimal. An attempt was made to obtain numerically optimized trajectories for the case where heating rate is constrained. A first order state variable inequality constraint was imposed on the full order AOTV point mass equations of motion, using a simple aerodynamic heating rate model.

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

Cartas-Fuentevilla, Roberto; Escalante, Alberto; Germán, Gabriel

Following recent studies which show that it is possible to localize gravity as well as scalar and gauge vector fields in a tachyonic de Sitter thick braneworld, we investigate the solution of the gauge hierarchy problem, the localization of fermion fields in this model, the recovering of the Coulomb law on the non-relativistic limit of the Yukawa interaction between bulk fermions and gauge bosons localized in the brane, and confront the predicted 5D corrections to the photon mass with its upper experimental/observational bounds, finding the model physically viable since it passes these tests. In order to achieve the latter aimsmore » we first consider the Yukawa interaction term between the fermionic and the tachyonic scalar fields MF(T)ΨΨ-bar in the action and analyze four distinct tachyonic functions F(T) that lead to four different structures of the respective fermionic mass spectra with different physics. In particular, localization of the massless left-chiral fermion zero mode is possible for three of these cases. We further analyze the phenomenology of these Yukawa interactions among fermion fields and gauge bosons localized on the brane and obtain the crucial and necessary information to compute the corrections to Coulomb’s law coming from massive KK vector modes in the non-relativistic limit. These corrections are exponentially suppressed due to the presence of the mass gap in the mass spectrum of the bulk gauge vector field. From our results we conclude that corrections to Coulomb’s law in the thin brane limit have the same form (up to a numerical factor) as far as the left-chiral massless fermion field is localized on the brane. Finally we compute the corrections to the Coulomb’s law for an arbitrarily thick brane scenario which can be interpreted as 5D corrections to the photon mass. By performing consistent estimations with brane phenomenology, we found that the predicted corrections to the photon mass, which are well bounded by the experimentally observed or astrophysically inferred photon mass, are far beyond its upper bound, positively testing the viability of our tachyonic braneworld. Moreover, the 5D parameters that define these corrections possess the same order, providing naturalness to our model, however, a fine-tuning between them is needed in order to fit the corresponding upper bound on the photon mass.« less

Altitude transitions in energy climbs

NASA Technical Reports Server (NTRS)

Weston, A. R.; Cliff, E. M.; Kelley, H. J.

1982-01-01

The aircraft energy-climb trajectory for configurations with a sharp transonic drag rise is well known to possess two branches in the altitude/Mach-number plane. Transition in altitude between the two branches occurs instantaneously, a 'corner' in the minimum-time solution obtained with the energy-state model. If the initial and final values of altitude do not lie on the energy-climb trajectory, then additional jumps (crude approximations to dives and zooms) are required at the initial and terminal points. With a singular-perturbation approach, a 'boundary-layer' correction is obtained for each altitude jump, the transonic jump being a so-called 'internal' boundary layer, different in character from the initial and terminal layers. The determination of this internal boundary layer is examined and some computational results for an example presented.

Cosmology from quantum potential in a system of oscillating branes

NASA Astrophysics Data System (ADS)

Sepehri, Alireza

2016-11-01

Recently, some authors proposed a new mechanism which gets rid of the Big Bang singularity and shows that the age of the universe is infinite. In this paper, we will confirm their results and predict that the universe may expand and contract many N fundamental strings decay to N M0-anti-M0-branes. Then, M0-branes join each other and build a M8-anti-M8 system. This system is unstable, broken and two anti-M4-branes, a compactified M4-brane, a M3-brane in addition to one M0-brane are produced. The M3-brane wraps around the compactified M4-brane and both of them oscillate between two anti-M4-branes. Our universe is located on the M3-brane and interacts with other branes by exchanging the M0-brane and some scalars in transverse directions. By wrapping of M3-brane, the contraction epoch of universe starts and some higher order of derivatives of scalar fields in the relevant action of branes are produced which are responsible for generating the generalized uncertainty principle (GUP). By oscillating the compactified M4-M3-brane and approaching one of anti-M4-branes, one end of M3-brane glues to the anti-M4-brane and other end remains sticking and wrapping around M4-brane. Then, by getting away of the M4-M3 system, M4 rolls, wrapped M3 opens and expansion epoch of universe begins. By closing the M4 to anti-M4, the mass of some scalars become negative and they make a transition to tachyonic phase. To remove these states, M4 rebounds, rolls and M3 wraps around it again. At this stage, expansion branch ends and universe enters a contraction epoch again. This process is repeated many times and universe expands and contracts due to oscillation of branes. We obtain the scale factor of universe in this system and find that its values only at t →-∞ shrinks to zero. Thus, in our method, the Big Bang is replaced by the fundamental string and the age of universe is predicted to be infinite. Also, when tachyonic states disappear at the beginning of expansion branch, some extra energy is produced and leads to an increase in the velocity of opening of M3. In these conditions, our universe, which is located on this brane, expands very fast and experiences an inflation epoch. Finally, by reducing the fields in 11-dimensional M-theory to the fields in four-dimensional universe, we show that our theory matches with quantum field theory prescriptions.

Carroll limit of non-BPS Dp-brane

NASA Astrophysics Data System (ADS)

Klusoň, J.

2017-05-01

We find Carroll non-BPS Dp-brane action by performing Carroll limit of a canonical form of unstable Dp-brane action. We analyze different Carroll limits and discuss solutions of the equations of motion of Carroll non-BPS Dp-brane at the tachyon vacuum.

Are There Faster Than Light Particles?

ERIC Educational Resources Information Center

Kreisler, Michael N.

1969-01-01

Based upon recent relativistic theory, the researcher describes the search for tachyons, particles having velocities greater than that of a light. The properties of these particles are speculated upon. The author delineates the difficulties anticipated in their detection and the assumptions underlying their methodology. (RR)

Tachyonic instability of the scalar mode prior to the QCD critical point based on the functional renormalization-group method in the two-flavor case

NASA Astrophysics Data System (ADS)

Yokota, Takeru; Kunihiro, Teiji; Morita, Kenji

2017-10-01

We establish and elucidate the physical meaning of the appearance of an acausal mode in the sigma mesonic channel, found in the previous work by the present authors, when the system approaches the Z2 critical point. The functional renormalization-group method is applied to the two-flavor quark-meson model with varying current quark mass mq even away from the physical value at which the pion mass is reproduced. We first determine the whole phase structure in the three-dimensional space (T ,μ ,mq) consisting of temperature T , quark chemical potential μ and mq, with the tricritical point, O(4) and Z2 critical lines being located; they altogether make a winglike shape quite reminiscent of those known in the condensed matters with a tricritical point. We then calculate the spectral functions ρσ ,π(ω ,p ) in the scalar and pseudoscalar channel around the critical points. We find that the sigma mesonic mode becomes tachyonic with a superluminal velocity at finite momenta before the system reaches the Z2 point from the lower density, even for mq smaller than the physical value. One of the possible implications of the appearance of such a tachyonic mode at finite momenta is that the assumed equilibrium state with a uniform chiral condensate is unstable toward a state with an inhomogeneous σ condensate. No such anomalous behavior is found in the pseudoscalar channel. We find that the σ -to-2 σ coupling due to finite mq plays an essential role for the drastic modification of the spectral function.

Physics Courses--Some Suggested Case Studies

ERIC Educational Resources Information Center

Swetman, T. P.

1972-01-01

To communicate the relevance and excitement of science activity to students, the use of more imaginative, and even openly speculative, case studies in physics courses is suggested. Some useful examples are Magnetic Monopoles, Constants, Black Holes, Antimatter, Zero Mass Particles, Tachyons, and the Bootstrap Hypothesis. (DF)

Holographic cosmology from BIonic solutions

NASA Astrophysics Data System (ADS)

Sepehri, Alireza; Faizal, Mir; Setare, Mohammad Reza; Ali, Ahmed Farag

2017-02-01

In this paper, we will use a BIonic solution for analyzing the holographic cosmology. A BIonic solution is a configuration of a D3-brane and an anti-D3-brane connected by a wormhole, and holographic cosmology is a recent proposal to explain cosmic expansion by using the holographic principle. In our model, a BIonic configuration will be produced by the transition of fundamental black strings. The formation of a BIonic configuration will cause inflation. As the D3-brane moves away from the anti-D3-brane, the wormhole will get annihilated, and the inflation will end with the annihilation of this wormhole. However, it is possible for a D3-brane to collide with an anti-D3-brane. Such a collision will occur if the distance between the D3-brane and the anti-D3-brane reduces, and this will create tachyonic states. We will demonstrate that these tachyonic states will lead to the formation of a new wormhole, and this will cause acceleration of the universe before such a collision.

Tachyon constant-roll inflation

NASA Astrophysics Data System (ADS)

Mohammadi, A.; Saaidi, Kh.; Golanbari, T.

2018-04-01

The constant-roll inflation is studied where the inflaton is taken as a tachyon field. Based on this approach, the second slow-roll parameter is taken as a constant which leads to a differential equation for the Hubble parameter. Finding an exact solution for the Hubble parameter is difficult and leads us to a numerical solution for the Hubble parameter. On the other hand, since in this formalism the slow-roll parameter η is constant and could not be assumed to be necessarily small, the perturbation parameters should be reconsidered again which, in turn, results in new terms appearing in the amplitude of scalar perturbations and the scalar spectral index. Utilizing the numerical solution for the Hubble parameter, we estimate the perturbation parameter at the horizon exit time and compare it with observational data. The results show that, for specific values of the constant parameter η , we could have an almost scale-invariant amplitude of scalar perturbations. Finally, the attractor behavior for the solution of the model is presented, and we determine that the feature could be properly satisfied.

Cascading gauge theory on dS4 and String Theory landscape

NASA Astrophysics Data System (ADS)

Buchel, Alex; Galante, Damián A.

2014-06-01

Placing anti-D3 branes at the tip of the conifold in Klebanov-Strassler geometry provides a generic way of constructing meta-stable de Sitter (dS) vacua in String Theory. A local geometry of such vacua exhibit gravitational solutions with a D3 charge measured at the tip opposite to the asymptotic charge. We discuss a restrictive set of such geometries, where anti-D3 branes are smeared at the tip. Such geometries represent holographic dual of cascading gauge theory in dS4 with or without chiral symmetry breaking. We find that in the phase with unbroken chiral symmetry the D3 charge at the tip is always positive. Furthermore, this charge is zero in the phase with spontaneously broken chiral symmetry. We show that the effective potential of the chirally symmetric phase is lower than that in the symmetry broken phase, i.e., there is no spontaneous chiral symmetry breaking for cascading gauge theory in dS4. The positivity of the D3 brane charge in smooth de-Sitter deformed conifold geometries with fluxes presents difficulties in uplifting AdS vacua to dS ones in String Theory via smeared anti-D3 branes. First, turning on fluxes on Calabi-Yau compactifications of type IIB string theory produces highly warped geometry with stabilized complex structure (but not Kähler) moduli of the compactification [3]; Next, including non-perturbative effects (which are under control given the unbroken supersymmetry), one obtains anti-de Sitter (AdS4) vacua with all moduli fixed; Finally, one uses anti-D3 branes of type IIB string theory to uplift AdS4 to de Sitter (dS4) vacua. As the last step of the construction completely breaks supersymmetry, it is much less controlled. In fact, in [4-7] it was argued that putting anti-D3 branes at the tip of the Klebanov-Strassler (KS) [8] geometry (as done in KKLT construction) leads to a naked singularity. Whether or not the resulting singularity is physical is subject to debates. When M4=dS4 and the chiral symmetry is unbroken, the D3 brane charge at the tip of the conifold is always positive, as long as ln H2Λ2/P2g0 ⩾-0.4. When M4=dS4 and the chiral symmetry is broken, the D3 brane charge at the tip of the conifold is always zero; we managed to construct geometries of this type for ln H2Λ2/P2g0⩾-0.03. Comparing effective potential of the gauge theory in broken Veffb and unbroken Veffs phases we establish that in all cases, when we can construct the phase with spontaneously broken chiral symmetry, Veffb>Veffs, when ln H2Λ2/P2g0⩾-0.03, i.e., spontaneous symmetry breaking does not happen for given values of the gauge theory parameters. To put these parameters in perspective, note that the (first-order) confinement/deconfinement and chiral symmetry breaking phase transition in cascading gauge theory plasma occurs at temperature T such that [16] ln Tdeconfinement,χSB2Λ2/P2g0=0.2571(2), and the (first-order) chiral symmetry breaking in cascading gauge theory on S3 occurs for compactification scale μ3≡ℓ3-1 such that [21] ln μ3,χSB2Λ2/P2g0=0.4309(8). When M4=R×S3 and the chiral symmetry is unbroken, the D3 brane charge at the tip of the conifold is negative when ln μ32Λ2/P2g0 μ, and the D3 brane charge at the tip of the conifold in broken phase is zero, the charge in the ground state is in fact zero whenever μ3⩽μ. Furthermore, chirally symmetric states of cascading gauge theory on S3 develop symmetry breaking tachyonic instabilities at μ (below the first order chiral symmetry breaking scale μ) ln μ3,tachyon2Λ2/P2g0=0.3297(3) which is again above μ.Our results represented here, together with those reported in [10], point that the singularity of smeared anti-D3 branes at the tip of the conifold is unphysical: had it been otherwise, we should have been able to implement an infrared cutoff in the geometry with a D3 brane charge measured at the cutoff being negative. The role of the cutoff is played by the temperature (as discussed in [10]), by the compactification scale (when M4=R×S3), or by the Hubble scale (when M4=dS4). Interesting, we find that the D3 brane charge can become negative when the KT throat geometry is S3 deformed; however this occurs in the regime where this phase is unstable both via the first order phase transition and the tachyon condensation to S3 deformed KS throat geometry - the latter geometry has zero D3 brane charge at the tip. All this raises questions about construction of generic de Sitter vacua in String Theory [2].We stress, however, that our analysis does not definitely exclude local non-singular supergravity description of de Sitter vacua in String Theory. The issue stems from the anti-D3 brane “smearing approximation” used. Early discussion of the relevant smearing approximation appeared in [6,9]. There, the authors carefully analyzed non-supersymmetric deformations of KS geometry, invariant under the SU(2)×SU(2) global symmetry of the latter. They further identified a class of perturbations that is being sources by anti-D3 branes, placed at the tip of the conifold, and then computed the leading-order backreaction of those perturbations on KS geometry. Insistence on preserving the SU(2)×SU(2) global symmetry is a smearing approximation - from the brane perspective it implies that anti-D3 branes are uniformly distributed (uniformly smeared) over the transverse compact five-dimensional manifold. Our discussion here shares the same smearing approximation as in [6,9], but extends the analysis to the full (rather than leading-order) backreaction. Smearing approximation is a practical tool enabling the analysis of the complicated cascading geometries involved. However, it must be questioned: it is not clear that non-supersymmetric uniform distribution along T directions of anti-D3 branes is stable against ‘clumping’. While it is highly desirable to lift this approximation, it is very difficult to do this in practice: one is forced to analyze a coupled nonlinear system of partial differential equations, rather than ordinary differential equations. We feel that until fully localized anti-D3 brane analysis in cascading geometries are performed, the singularity question of local supergravity description of de Sitter vacua in String Theory will remain open.

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.

Robust synchronization of master-slave chaotic systems using approximate model: An experimental study.

PubMed

Ahmed, Hafiz; Salgado, Ivan; Ríos, Héctor

2018-02-01

Robust synchronization of master slave chaotic systems are considered in this work. First an approximate model of the error system is obtained using the ultra-local model concept. Then a Continuous Singular Terminal Sliding-Mode (CSTSM) Controller is designed for the purpose of synchronization. The proposed approach is output feedback-based and uses fixed-time higher order sliding-mode (HOSM) differentiator for state estimation. Numerical simulation and experimental results are given to show the effectiveness of the proposed technique. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Quenching of the Quantum Hall Effect in Graphene with Scrolled Edges

NASA Astrophysics Data System (ADS)

Cresti, Alessandro; Fogler, Michael M.; Guinea, Francisco; Castro Neto, A. H.; Roche, Stephan

2012-04-01

Edge nanoscrolls are shown to strongly influence transport properties of suspended graphene in the quantum Hall regime. The relatively long arclength of the scrolls in combination with their compact transverse size results in formation of many nonchiral transport channels in the scrolls. They short circuit the bulk current paths and inhibit the observation of the quantized two-terminal resistance. Unlike competing theoretical proposals, this mechanism of disrupting the Hall quantization in suspended graphene is not caused by ill-chosen placement of the contacts, singular elastic strains, or a small sample size.

Hybrid Inflation: Multi-field Dynamics and Cosmological Constraints

NASA Astrophysics Data System (ADS)

Clesse, Sébastien

2011-09-01

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

Kinematically Optimal Robust Control of Redundant Manipulators

NASA Astrophysics Data System (ADS)

Galicki, M.

2017-12-01

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

Robust Task Space Trajectory Tracking Control of Robotic Manipulators

NASA Astrophysics Data System (ADS)

Galicki, M.

2016-08-01

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

Infrared dim-small target tracking via singular value decomposition and improved Kernelized correlation filter

NASA Astrophysics Data System (ADS)

Qian, Kun; Zhou, Huixin; Rong, Shenghui; Wang, Bingjian; Cheng, Kuanhong

2017-05-01

Infrared small target tracking plays an important role in applications including military reconnaissance, early warning and terminal guidance. In this paper, an effective algorithm based on the Singular Value Decomposition (SVD) and the improved Kernelized Correlation Filter (KCF) is presented for infrared small target tracking. Firstly, the super performance of the SVD-based algorithm is that it takes advantage of the target's global information and obtains a background estimation of an infrared image. A dim target is enhanced by subtracting the corresponding estimated background with update from the original image. Secondly, the KCF algorithm is combined with Gaussian Curvature Filter (GCF) to eliminate the excursion problem. The GCF technology is adopted to preserve the edge and eliminate the noise of the base sample in the KCF algorithm, helping to calculate the classifier parameter for a small target. At last, the target position is estimated with a response map, which is obtained via the kernelized classifier. Experimental results demonstrate that the presented algorithm performs favorably in terms of efficiency and accuracy, compared with several state-of-the-art algorithms.

Lucky Luke--The Man Who Shoots Faster than His Shadow

ERIC Educational Resources Information Center

Bokor, Nándor

2015-01-01

The famous motto of the Lucky Luke comics series and its accompanying drawing are analyzed from a physicist's viewpoint. They provide useful pedagogical tools to discuss such aspects of relativity as causality, the equivalence principle, gravitational blue shift, and the tachyonic antitelephone. [This article was first published in Hungarian in…

Compact 2D OPC modeling of a metal oxide EUV resist for a 7nm node BEOL layer

NASA Astrophysics Data System (ADS)

Lyons, Adam; Rio, David; Lee, Sook; Wallow, Thomas; Delorme, Maxence; Fumar-Pici, Anita; Kocsis, Michael; de Schepper, Peter; Greer, Michael; Stowers, Jason K.; Gillijns, Werner; De Simone, Danilo; Bekaert, Joost

2017-03-01

Inpria has developed a directly patternable metal oxide hard-mask as a high-resolution photoresist for EUV lithography1. In this contribution, we describe a Tachyon 2D OPC full-chip model for an Inpria resist as applied to an N7 BEOL block mask application.

Electrophysiological Rotor Ablation in In-Silico Modeling of Atrial Fibrillation: Comparisons with Dominant Frequency, Shannon Entropy, and Phase Singularity.

PubMed

Hwang, Minki; Song, Jun-Seop; Lee, Young-Seon; Li, Changyong; Shim, Eun Bo; Pak, Hui-Nam

2016-01-01

Although rotors have been considered among the drivers of atrial fibrillation (AF), the rotor definition is inconsistent. We evaluated the nature of rotors in 2D and 3D in- silico models of persistent AF (PeAF) by analyzing phase singularity (PS), dominant frequency (DF), Shannon entropy (ShEn), and complex fractionated atrial electrogram cycle length (CFAE-CL) and their ablation. Mother rotor was spatiotemporally defined as stationary reentries with a meandering tip remaining within half the wavelength and lasting longer than 5 s. We generated 2D- and 3D-maps of the PS, DF, ShEn, and CFAE-CL during AF. The spatial correlations and ablation outcomes targeting each parameter were analyzed. 1. In the 2D PeAF model, we observed a mother rotor that matched relatively well with DF (>9 Hz, 71.0%, p<0.001), ShEn (upper 2.5%, 33.2%, p<0.001), and CFAE-CL (lower 2.5%, 23.7%, p<0.001). 2. The 3D-PeAF model also showed mother rotors that had spatial correlations with DF (>5.5 Hz, 39.7%, p<0.001), ShEn (upper 8.5%, 15.1%, p <0.001), and CFAE (lower 8.5%, 8.0%, p = 0.002). 3. In both the 2D and 3D models, virtual ablation targeting the upper 5% of the DF terminated AF within 20 s, but not the ablations based on long-lasting PS, high ShEn area, or lower CFAE-CL area. Mother rotors were observed in both 2D and 3D human AF models. Rotor locations were well represented by DF, and their virtual ablation altered wave dynamics and terminated AF.

Electrophysiological Rotor Ablation in In-Silico Modeling of Atrial Fibrillation: Comparisons with Dominant Frequency, Shannon Entropy, and Phase Singularity

PubMed Central

Hwang, Minki; Song, Jun-Seop; Lee, Young-Seon; Li, Changyong; Shim, Eun Bo; Pak, Hui-Nam

2016-01-01

Background Although rotors have been considered among the drivers of atrial fibrillation (AF), the rotor definition is inconsistent. We evaluated the nature of rotors in 2D and 3D in- silico models of persistent AF (PeAF) by analyzing phase singularity (PS), dominant frequency (DF), Shannon entropy (ShEn), and complex fractionated atrial electrogram cycle length (CFAE-CL) and their ablation. Methods Mother rotor was spatiotemporally defined as stationary reentries with a meandering tip remaining within half the wavelength and lasting longer than 5 s. We generated 2D- and 3D-maps of the PS, DF, ShEn, and CFAE-CL during AF. The spatial correlations and ablation outcomes targeting each parameter were analyzed. Results 1. In the 2D PeAF model, we observed a mother rotor that matched relatively well with DF (>9 Hz, 71.0%, p<0.001), ShEn (upper 2.5%, 33.2%, p<0.001), and CFAE-CL (lower 2.5%, 23.7%, p<0.001). 2. The 3D-PeAF model also showed mother rotors that had spatial correlations with DF (>5.5 Hz, 39.7%, p<0.001), ShEn (upper 8.5%, 15.1%, p <0.001), and CFAE (lower 8.5%, 8.0%, p = 0.002). 3. In both the 2D and 3D models, virtual ablation targeting the upper 5% of the DF terminated AF within 20 s, but not the ablations based on long-lasting PS, high ShEn area, or lower CFAE-CL area. Conclusion Mother rotors were observed in both 2D and 3D human AF models. Rotor locations were well represented by DF, and their virtual ablation altered wave dynamics and terminated AF. PMID:26909492

The surface and through crack problems in layered orthotropic plates

NASA Technical Reports Server (NTRS)

Erdogan, Fazil; Wu, Binghua

1991-01-01

An analytical method is developed for a relatively accurate calculation of Stress Intensity Factors in a laminated orthotropic plate containing a through or part-through crack. The laminated plate is assumed to be under bending or membrane loading and the mode 1 problem is considered. First three transverse shear deformation plate theories (Mindlin's displacement based first-order theory, Reissner's stress-based first-order theory, and a simple-higher order theory due to Reddy) are reviewed and examined for homogeneous, laminated and heterogeneous orthotropic plates. Based on a general linear laminated plate theory, a method by which the stress intensity factors can be obtained in orthotropic laminated and heterogeneous plates with a through crack is developed. Examples are given for both symmetrically and unsymmetrically laminated plates and the effects of various material properties on the stress intensity factors are studied. In order to implement the line-spring model which is used later to study the surface crack problem, the corresponding plane elasticity problem of a two-bonded orthotropic plated containing a crack perpendicular to the interface is also considered. Three different crack profiles: an internal crack, an edge crack, and a crack terminating at the interface are considered. The effect of the different material combinations, geometries, and material orthotropy on the stress intensity factors and on the power of stress singularity for a crack terminating at the interface is fully examined. The Line Spring model of Rice and Levy is used for the part-through crack problem. The surface crack is assumed to lie in one of the two-layered laminated orthotropic plates due to the limitation of the available plane strain results. All problems considered are of the mixed boundary value type and are reduced to Cauchy type of singular integral equations which are then solved numerically.

Field Performance versus Standard Test Condition Efficiency of Tandem Solar Cells and the Singular Case of Perovskites/Silicon Devices.

PubMed

Dupré, Olivier; Niesen, Bjoern; De Wolf, Stefaan; Ballif, Christophe

2018-01-18

Multijunction cells may offer a cost-effective route to boost the efficiency of industrial photovoltaics. For any technology to be deployed in the field, its performance under actual operating conditions is extremely important. In this perspective, we evaluate the impact of spectrum, light intensity, and module temperature variations on the efficiency of tandem devices with crystalline silicon bottom cells with a particular focus on perovskite top cells. We consider devices with different efficiencies and calculate their energy yields using field data from Denver. We find that annual losses due to differences between operating conditions and standard test conditions are similar for single-junction and four-terminal tandem devices. The additional loss for the two-terminal tandem configuration caused by current mismatch reduces its performance ratio by only 1.7% when an optimal top cell bandgap is used. Additionally, the unusual bandgap temperature dependence of perovskites is shown to have a positive, compensating effect on current mismatch.

Variable generalized Chaplygin gas in a 5D cosmology

NASA Astrophysics Data System (ADS)

Salti, Mustafa; Aydogdu, Oktay; Yanar, Hilmi; Sogut, Kenan

2018-03-01

We construct the variable generalized Chaplygin gas (VGCG) defining a unified dark matter-energy scenario and investigate its essential cosmological properties in a universe governed by the Kaluza-Klein (KK) theory. A possible theoretical basis for the VGCG in the KK cosmology is argued. Also, we check the validity of thermodynamical laws and reimplement dynamics of tachyons in the KK universe.

Positivity of Curvature-Squared Corrections in Gravity

NASA Astrophysics Data System (ADS)

Cheung, Clifford; Remmen, Grant N.

2017-02-01

We study the Gauss-Bonnet (GB) term as the leading higher-curvature correction to pure Einstein gravity. Assuming a tree-level ultraviolet completion free of ghosts or tachyons, we prove that the GB term has a nonnegative coefficient in dimensions greater than 4. Our result follows from unitarity of the spectral representation for a general ultraviolet completion of the GB term.

Regularization of instabilities in gravity theories

NASA Astrophysics Data System (ADS)

Ramazanoǧlu, Fethi M.

2018-01-01

We investigate instabilities and their regularization in theories of gravitation. Instabilities can be beneficial since their growth often leads to prominent observable signatures, which makes them especially relevant to relatively low signal-to-noise ratio measurements such as gravitational wave detections. An indefinitely growing instability usually renders a theory unphysical; hence, a desirable instability should also come with underlying physical machinery that stops the growth at finite values, i.e., regularization mechanisms. The prototypical gravity theory that presents such an instability is the spontaneous scalarization phenomena of scalar-tensor theories, which feature a tachyonic instability. We identify the regularization mechanisms in this theory and show that they can be utilized to regularize other instabilities as well. Namely, we present theories in which spontaneous growth is triggered by a ghost rather than a tachyon and numerically calculate stationary solutions of scalarized neutron stars in these theories. We speculate on the possibility of regularizing known divergent instabilities in certain gravity theories using our findings and discuss alternative theories of gravitation in which regularized instabilities may be present. Even though we study many specific examples, our main point is the recognition of regularized instabilities as a common theme and unifying mechanism in a vast array of gravity theories.

Probing the effects of Lorentz-symmetry violating Chern-Simons and Ricci-Cotton terms in higher derivative gravity

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

Pereira-Dias, B.; Hernaski, C. A.; Helayeel-Neto, J. A.

The combined effects of the Lorentz-symmetry violating Chern-Simons and Ricci-Cotton actions are investigated for the Einstein-Hilbert gravity in the second-order formalism modified by higher derivative terms, and their consequences on the spectrum of excitations are analyzed. We follow the lines of previous works and build up an orthonormal basis of projector-like operators for the degrees of freedom, rather than for the spin modes of the fields. With this new basis, the attainment of the propagators is remarkably simplified and the identification of the physical and unphysical modes becomes more immediate. Our conclusion is that the only tachyon- and ghost-free modelmore » is the Einstein-Hilbert action added up by the Chern-Simons term with a timelike vector of the type v{sup {mu}=}({mu},0-vector). Spectral consistency imposes that the Ricci-Cotton term must be switched off. We then infer that gravity with Lorentz-symmetry violation imposes a drastically different constraint on the background if compared to ordinary gauge theories whenever conditions for the suppression of tachyons and ghosts are imposed.« less

Rules based process window OPC

NASA Astrophysics Data System (ADS)

O'Brien, Sean; Soper, Robert; Best, Shane; Mason, Mark

2008-03-01

As a preliminary step towards Model-Based Process Window OPC we have analyzed the impact of correcting post-OPC layouts using rules based methods. Image processing on the Brion Tachyon was used to identify sites where the OPC model/recipe failed to generate an acceptable solution. A set of rules for 65nm active and poly were generated by classifying these failure sites. The rules were based upon segment runlengths, figure spaces, and adjacent figure widths. 2.1 million sites for active were corrected in a small chip (comparing the pre and post rules based operations), and 59 million were found at poly. Tachyon analysis of the final reticle layout found weak margin sites distinct from those sites repaired by rules-based corrections. For the active layer more than 75% of the sites corrected by rules would have printed without a defect indicating that most rulesbased cleanups degrade the lithographic pattern. Some sites were missed by the rules based cleanups due to either bugs in the DRC software or gaps in the rules table. In the end dramatic changes to the reticle prevented catastrophic lithography errors, but this method is far too blunt. A more subtle model-based procedure is needed changing only those sites which have unsatisfactory lithographic margin.

Minimum-fuel, 3-dimensional flightpath guidance of transfer jets

NASA Technical Reports Server (NTRS)

Neuman, F.; Kreindler, E.

1984-01-01

Minimum fuel, three dimensional flightpaths for commercial jet aircraft are discussed. The theoretical development is divided into two sections. In both sections, the necessary conditions of optimal control, including singular arcs and state constraints, are used. One section treats the initial and final portions (below 10,000 ft) of long optimal flightpaths. Here all possible paths can be derived by generating fields of extremals. Another section treats the complete intermediate length, three dimensional terminal area flightpaths. Here only representative sample flightpaths can be computed. Sufficient detail is provided to give the student of optimal control a complex example of a useful application of optimal control theory.

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

Vázquez-Báez, V.; Ramírez, C.

We present calculations towards obtaining a wave functions of the universe for the supersymmetric closed string tachyon cosmology. Supersymmetrization, in the superfield formalism, is performed by taking advantage of the time reparametrization invariance of the cosmological action and generalizing the transformations to include grassmannian variables. We calculate the corresponding Hamiltonian, by means of the Dirac formalism, and make use of the superalgebra to find solutions to the Wheeler-DeWitt equations indirectly.

Superluminal transformations in complex Minkowski spaces

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

Ramon, C.; Rauscher, E.A.

1980-08-01

We calculate the mixing of real and imaginary components of space and time under the influence of superluminal boots in the x direction. A unique mixing is determined for this superluminal Lorentz transformation when we consider the symmetry properties afforded by the inclusion of three temporal directions. Superluminal transformations in complex six-dimensional space exhibit unique tachyonic connections which have both remote and local space--time event connections.

An Adaptive B-Spline Neural Network and Its Application in Terminal Sliding Mode Control for a Mobile Satcom Antenna Inertially Stabilized Platform.

PubMed

Zhang, Xiaolei; Zhao, Yan; Guo, Kai; Li, Gaoliang; Deng, Nianmao

2017-04-28

The mobile satcom antenna (MSA) enables a moving vehicle to communicate with a geostationary Earth orbit satellite. To realize continuous communication, the MSA should be aligned with the satellite in both sight and polarization all the time. Because of coupling effects, unknown disturbances, sensor noises and unmodeled dynamics existing in the system, the control system should have a strong adaptability. The significant features of terminal sliding mode control method are robustness and finite time convergence, but the robustness is related to the large switching control gain which is determined by uncertain issues and can lead to chattering phenomena. Neural networks can reduce the chattering and approximate nonlinear issues. In this work, a novel B-spline curve-based B-spline neural network (BSNN) is developed. The improved BSNN has the capability of shape changing and self-adaption. In addition, the output of the proposed BSNN is applied to approximate the nonlinear function in the system. The results of simulations and experiments are also compared with those of PID method, non-singularity fast terminal sliding mode (NFTSM) control and radial basis function (RBF) neural network-based NFTSM. It is shown that the proposed method has the best performance, with reliable control precision.

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

NASA Astrophysics Data System (ADS)

Sayevand, K.; Pichaghchi, K.

2018-04-01

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

Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon

NASA Astrophysics Data System (ADS)

Kay, Bernard S.; Radzikowski, Marek J.; Wald, Robert M.

1997-02-01

We prove two theorems which concern difficulties in the formulation of the quantum theory of a linear scalar field on a spacetime, (M,g_{ab}), with a compactly generated Cauchy horizon. These theorems demonstrate the breakdown of the theory at certain base points of the Cauchy horizon, which are defined as 'past terminal accumulation points' of the horizon generators. Thus, the theorems may be interpreted as giving support to Hawking's 'Chronology Protection Conjecture', according to which the laws of physics prevent one from manufacturing a 'time machine'. Specifically, we prove: Theorem 1. There is no extension to (M,g_{ab}) of the usual field algebra on the initial globally hyperbolic region which satisfies the condition of F-locality at any base point. In other words, any extension of the field algebra must, in any globally hyperbolic neighbourhood of any base point, differ from the algebra one would define on that neighbourhood according to the rules for globally hyperbolic spacetimes. Theorem 2. The two-point distribution for any Hadamard state defined on the initial globally hyperbolic region must (when extended to a distributional bisolution of the covariant Klein-Gordon equation on the full spacetime) be singular at every base point x in the sense that the difference between this two point distribution and a local Hadamard distribution cannot be given by a bounded function in any neighbourhood (in M 2 M) of (x,x). In consequence of Theorem 2, quantities such as the renormalized expectation value of J2 or of the stress-energy tensor are necessarily ill-defined or singular at any base point. The proof of these theorems relies on the 'Propagation of Singularities' theorems of Duistermaat and Hörmander.

Partial IK1 blockade destabilizes spiral wave rotation center without inducing wave breakup and facilitates termination of reentrant arrhythmias in ventricles.

PubMed

Kushiyama, Yasunori; Honjo, Haruo; Niwa, Ryoko; Takanari, Hiroki; Yamazaki, Masatoshi; Takemoto, Yoshio; Sakuma, Ichiro; Kodama, Itsuo; Kamiya, Kaichiro

2016-09-01

It has been reported that blockade of the inward rectifier K(+) current (IK1) facilitates termination of ventricular fibrillation. We hypothesized that partial IK1 blockade destabilizes spiral wave (SW) re-entry, leading to its termination. Optical action potential (AP) signals were recorded from left ventricles of Langendorff-perfused rabbit hearts with endocardial cryoablation. The dynamics of SW re-entry were analyzed during ventricular tachycardia (VT), induced by cross-field stimulation. Intercellular electrical coupling in the myocardial tissue was evaluated by the space constant. In separate experiments, AP recordings were made using the microelectrode technique from right ventricular papillary muscles of rabbit hearts. Ba(2+) (10-50 μM) caused a dose-dependent prolongation of VT cycle length and facilitated termination of VT in perfused hearts. Baseline VT was maintained by a stable rotor, where an SW rotated around an I-shaped functional block line (FBL). Ba(2+) at 10 μM prolonged I-shaped FBL and phase-singularity trajectory, whereas Ba(2+) at 50 μM transformed the SW rotation dynamics from a stable linear pattern to unstable circular/cycloidal meandering. The SW destabilization was not accompanied by SW breakup. Under constant pacing, Ba(2+) caused a dose-dependent prolongation of APs, and Ba(2+) at 50 μM decreased conduction velocity. In papillary muscles, Ba(2+) at 50 μM depolarized the resting membrane potential. The space constant was increased by 50 μM Ba(2+) Partial IK1 blockade destabilizes SW rotation dynamics through a combination of prolongation of the wave length, reduction of excitability, and enhancement of electrotonic interactions, which facilitates termination of ventricular tachyarrhythmias. Copyright © 2016 the American Physiological Society.

Optimal symmetric flight with an intermediate vehicle model

NASA Technical Reports Server (NTRS)

Menon, P. K. A.; Kelley, H. J.; Cliff, E. M.

1983-01-01

Optimal flight in the vertical plane with a vehicle model intermediate in complexity between the point-mass and energy models is studied. Flight-path angle takes on the role of a control variable. Range-open problems feature subarcs of vertical flight and singular subarcs. The class of altitude-speed-range-time optimization problems with fuel expenditure unspecified is investigated and some interesting phenomena uncovered. The maximum-lift-to-drag glide appears as part of the family, final-time-open, with appropriate initial and terminal transient exceeding level-flight drag, some members exhibiting oscillations. Oscillatory paths generally fail the Jacobi test for durations exceeding a period and furnish a minimum only for short-duration problems.

Elementary Kaluza-Klein towers revisited

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

Grard, Fernand; Nuyts, Jean

2006-12-15

Considering that the momentum squared in the extra dimensions is the physically relevant quantity for the generation of the Kaluza-Klein mass states, we have reanalyzed mathematically the procedure for five dimensional scalar fields within the Arkhani-Ahmed, Dimopoulos and Dvali scenario. We find new sets of physically allowed boundary conditions. Beside the usual results, they lead to new towers with non regular mass spacing, to lonely mass states and to tachyons.

p-adic string theories provide lattice Discretization to the ordinary string worldsheet.

PubMed

Ghoshal, Debashis

2006-10-13

A class of models called p-adic strings is useful in understanding the tachyonic instability of string theory. These are found to be empirically related to the ordinary strings in the p-->1 limit. We propose that these models provide discretization for the string worldsheet and argue that the limit is naturally thought of as a continuum limit in the sense of the renormalization group.

p-adic String Theories Provide Lattice Discretization to the Ordinary String Worldsheet

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

Ghoshal, Debashis

2006-10-13

A class of models called p-adic strings is useful in understanding the tachyonic instability of string theory. These are found to be empirically related to the ordinary strings in the p{yields}1 limit. We propose that these models provide discretization for the string worldsheet and argue that the limit is naturally thought of as a continuum limit in the sense of the renormalization group.

On the stability conditions for theories of modified gravity in the presence of matter fields

NASA Astrophysics Data System (ADS)

De Felice, Antonio; Frusciante, Noemi; Papadomanolakis, Georgios

2017-03-01

We present a thorough stability analysis of modified gravity theories in the presence of matter fields. We use the Effective Field Theory framework for Dark Energy and Modified Gravity to retain a general approach for the gravity sector and a Sorkin-Schutz action for the matter one. Then, we work out the proper viability conditions to guarantee in the scalar sector the absence of ghosts, gradient and tachyonic instabilities. The absence of ghosts can be achieved by demanding a positive kinetic matrix, while the lack of a gradient instability is ensured by imposing a positive speed of propagation for all the scalar modes. In case of tachyonic instability, the mass eigenvalues have been studied and we work out the appropriate expressions. For the latter, an instability occurs only when the negative mass eigenvalue is much larger, in absolute value, than the Hubble parameter. We discuss the results for the minimally coupled quintessence model showing for a particular set of parameters two typical behaviours which in turn lead to a stable and an unstable configuration. Moreover, we find that the speeds of propagation of the scalar modes strongly depend on matter densities, for the beyond Horndeski theories. Our findings can be directly employed when testing modified gravity theories as they allow to identify the correct viability space.

Comments on Musha's theorem that an evanescent photon in the microtubule is a superluminal particle.

PubMed

Hari, Syamala D

2014-07-01

Takaaki Musha's research of high performance quantum computation in living systems is motivated by the theories of Penrose and Hameroff that microtubules in the brain function as quantum computers, and by those of Jibu and Yasue that the quantum states of microtubules depend upon boson condensates of evanescent photons. His work is based on the assumption that the evanescent photons described by Jibu et al. are superluminal and that they are tachyons defined and discussed by well-known physicists such as Sudarshan, Feinberg and Recami. Musha gives a brief justification for the assumption and sometimes calls it a theorem. However, the assumption is not valid because Jibu et al. stated that the evanescent photons have transmission speed smaller than that of light and that their mass is real and momentum is imaginary whereas a tachyon's mass is imaginary and momentum is real. We show here that Musha's proof of the "theorem" has errors and hence his theorem/assumption is not valid. This article is not meant to further discuss any biological aspects of the brain but only to comment on the consistency of the quantum-physical aspects of earlier work by Musha et al. Copyright © 2014 Elsevier Ireland Ltd. All rights reserved.

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…

Singularities in Optimal Structural Design

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Singularities in optimal structural design

NASA Technical Reports Server (NTRS)

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

1992-01-01

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

Naked singularity resolution in cylindrical collapse

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

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

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

A simple, analytic 3-dimensional downburst model based on boundary layer stagnation flow

NASA Technical Reports Server (NTRS)

Oseguera, Rosa M.; Bowles, Roland L.

1988-01-01

A simple downburst model is developed for use in batch and real-time piloted simulation studies of guidance strategies for terminal area transport aircraft operations in wind shear conditions. The model represents an axisymmetric stagnation point flow, based on velocity profiles from the Terminal Area Simulation System (TASS) model developed by Proctor and satisfies the mass continuity equation in cylindrical coordinates. Altitude dependence, including boundary layer effects near the ground, closely matches real-world measurements, as do the increase, peak, and decay of outflow and downflow with increasing distance from the downburst center. Equations for horizontal and vertical winds were derived, and found to be infinitely differentiable, with no singular points existent in the flow field. In addition, a simple relationship exists among the ratio of maximum horizontal to vertical velocities, the downdraft radius, depth of outflow, and altitude of maximum outflow. In use, a microburst can be modeled by specifying four characteristic parameters, velocity components in the x, y and z directions, and the corresponding nine partial derivatives are obtained easily from the velocity equations.

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)].

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.

Finite-Time Attitude Tracking Control for Spacecraft Using Terminal Sliding Mode and Chebyshev Neural Network.

PubMed

An-Min Zou; Kumar, K D; Zeng-Guang Hou; Xi Liu

2011-08-01

A finite-time attitude tracking control scheme is proposed for spacecraft using terminal sliding mode and Chebyshev neural network (NN) (CNN). The four-parameter representations (quaternion) are used to describe the spacecraft attitude for global representation without singularities. The attitude state (i.e., attitude and velocity) error dynamics is transformed to a double integrator dynamics with a constraint on the spacecraft attitude. With consideration of this constraint, a novel terminal sliding manifold is proposed for the spacecraft. In order to guarantee that the output of the NN used in the controller is bounded by the corresponding bound of the approximated unknown function, a switch function is applied to generate a switching between the adaptive NN control and the robust controller. Meanwhile, a CNN, whose basis functions are implemented using only desired signals, is introduced to approximate the desired nonlinear function and bounded external disturbances online, and the robust term based on the hyperbolic tangent function is applied to counteract NN approximation errors in the adaptive neural control scheme. Most importantly, the finite-time stability in both the reaching phase and the sliding phase can be guaranteed by a Lyapunov-based approach. Finally, numerical simulations on the attitude tracking control of spacecraft in the presence of an unknown mass moment of inertia matrix, bounded external disturbances, and control input constraints are presented to demonstrate the performance of the proposed controller.

Naked singularity, firewall, and Hawking radiation.

PubMed

Zhang, Hongsheng

2017-06-21

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

On the Weyl curvature hypothesis

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

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

2013-11-15

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

Resolution of quantum singularities

NASA Astrophysics Data System (ADS)

Konkowski, Deborah; Helliwell, Thomas

2017-01-01

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

The geometry of singularities and the black hole information paradox

NASA Astrophysics Data System (ADS)

Stoica, O. C.

2015-07-01

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

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

PubMed

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

2017-01-01

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

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

PubMed Central

Prybol, Cameron J.; Kurtzer, Gregory M.

2017-01-01

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

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

NASA Astrophysics Data System (ADS)

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

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

Stress intensity factors in a reinforced thick-walled cylinder

NASA Technical Reports Server (NTRS)

Tang, R.; Erdogan, F.

1984-01-01

An elastic thick-walled cylinder containing a radial crack is considered. It is assumed that the cylinder is reinforced by an elastic membrane on its inner surface. The model is intended to simulate pressure vessels with cladding. The formulation of the problem is reduced to a singular integral equation. Various special cases including that of a crack terminating at the cylinder-reinforcement interface are investigated and numerical examples are given. Results indicate that in the case of the crack touching the interface the crack surface displacement derivative is finite and consequently the stress state around the corresponding crack tip is bounded; and generally, for realistic values of the stiffness parameter, the effect of the reinforcement is not very significant.

Singularity in structural optimization

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2007-01-01

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

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

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

Vasil'ev, Vasilii I; Soskin, M S

2013-02-28

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

Holographic reconstruction of scalar fields in extended Kaluza-Klein cosmology

NASA Astrophysics Data System (ADS)

Korunur, Murat

2018-01-01

In recent years, many studies have been conducted to reconstruct the physical properties of scalar fields by establishing a connection between some energy densities and a scalar field of dark energies. In this paper, using the extended five-dimensional (5D) Kaluza-Klein model, we establish a correspondence among modified holographic dark energy and the tachyon, K-essence and dilaton scalar-field models. We also graphically illustrate the evolution of the equation-of-state parameter versus time.

Signs and stability in higher-derivative gravity

NASA Astrophysics Data System (ADS)

Narain, Gaurav

2018-02-01

Perturbatively renormalizable higher-derivative gravity in four space-time dimensions with arbitrary signs of couplings has been considered. Systematic analysis of the action with arbitrary signs of couplings in Lorentzian flat space-time for no-tachyons, fixes the signs. Feynman + i𝜖 prescription for these signs further grants necessary convergence in path-integral, suppressing the field modes with large action. This also leads to a sensible wick rotation where quantum computation can be performed. Running couplings for these sign of parameters make the massive tensor ghost innocuous leading to a stable and ghost-free renormalizable theory in four space-time dimensions. The theory has a transition point arising from renormalization group (RG) equations, where the coefficient of R2 diverges without affecting the perturbative quantum field theory (QFT). Redefining this coefficient gives a better handle over the theory around the transition point. The flow equations push the flow of parameters across the transition point. The flow beyond the transition point is analyzed using the one-loop RG equations which shows that the regime beyond the transition point has unphysical properties: there are tachyons, the path-integral loses positive definiteness, Newton’s constant G becomes negative and large, and perturbative parameters become large. These shortcomings indicate a lack of completeness beyond the transition point and need of a nonperturbative treatment of the theory beyond the transition point.

On the stability conditions for theories of modified gravity in the presence of matter fields

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

De Felice, Antonio; Frusciante, Noemi; Papadomanolakis, Georgios, E-mail: antonio.defelice@yukawa.kyoto-u.ac.jp, E-mail: fruscian@iap.fr, E-mail: papadomanolakis@lorentz.leidenuniv.nl

We present a thorough stability analysis of modified gravity theories in the presence of matter fields. We use the Effective Field Theory framework for Dark Energy and Modified Gravity to retain a general approach for the gravity sector and a Sorkin-Schutz action for the matter one. Then, we work out the proper viability conditions to guarantee in the scalar sector the absence of ghosts, gradient and tachyonic instabilities. The absence of ghosts can be achieved by demanding a positive kinetic matrix, while the lack of a gradient instability is ensured by imposing a positive speed of propagation for all themore » scalar modes. In case of tachyonic instability, the mass eigenvalues have been studied and we work out the appropriate expressions. For the latter, an instability occurs only when the negative mass eigenvalue is much larger, in absolute value, than the Hubble parameter. We discuss the results for the minimally coupled quintessence model showing for a particular set of parameters two typical behaviours which in turn lead to a stable and an unstable configuration. Moreover, we find that the speeds of propagation of the scalar modes strongly depend on matter densities, for the beyond Horndeski theories. Our findings can be directly employed when testing modified gravity theories as they allow to identify the correct viability space.« less

Can accretion disk properties observationally distinguish black holes from naked singularities?

NASA Astrophysics Data System (ADS)

Kovács, Z.; Harko, T.

2010-12-01

Naked singularities are hypothetical astrophysical objects, characterized by a gravitational singularity without an event horizon. Penrose has proposed a conjecture, according to which there exists a cosmic censor who forbids the occurrence of naked singularities. Distinguishing between astrophysical black holes and naked singularities is a major challenge for present day observational astronomy. In the context of stationary and axially symmetrical geometries, a possibility of differentiating naked singularities from black holes is through the comparative study of thin accretion disks properties around rotating naked singularities and Kerr-type black holes, respectively. In the present paper, we consider accretion disks around axially-symmetric rotating naked singularities, obtained as solutions of the field equations in the Einstein-massless scalar field theory. A first major difference between rotating naked singularities and Kerr black holes is in the frame dragging effect, the angular velocity of a rotating naked singularity being inversely proportional to its spin parameter. Because of the differences in the exterior geometry, the thermodynamic and electromagnetic properties of the disks (energy flux, temperature distribution and equilibrium radiation spectrum) are different for these two classes of compact objects, consequently giving clear observational signatures that could discriminate between black holes and naked singularities. For specific values of the spin parameter and of the scalar charge, the energy flux from the disk around a rotating naked singularity can exceed by several orders of magnitude the flux from the disk of a Kerr black hole. In addition to this, it is also shown that the conversion efficiency of the accreting mass into radiation by rotating naked singularities is always higher than the conversion efficiency for black holes, i.e., naked singularities provide a much more efficient mechanism for converting mass into radiation than black holes. Thus, these observational signatures may provide the necessary tools from clearly distinguishing rotating naked singularities from Kerr-type black holes.

Are Singularities Integral to General Theory of Relativity?

NASA Astrophysics Data System (ADS)

Krori, K.; Dutta, S.

2011-11-01

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

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

NASA Technical Reports Server (NTRS)

Papadopoulos, E.; Dubowsky, S.

1989-01-01

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

Finite element techniques applied to cracks interacting with selected singularities

NASA Technical Reports Server (NTRS)

Conway, J. C.

1975-01-01

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

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

PubMed

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

2015-05-04

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

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

NASA Astrophysics Data System (ADS)

Luo, Yamei; Lü, Baida

2009-06-01

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

Unidirectional spectral singularities.

PubMed

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

2014-12-31

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

Understanding Singular Vectors

ERIC Educational Resources Information Center

James, David; Botteron, Cynthia

2013-01-01

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

Singular Isothermal Disks. Paper 2; Nonaxiymmetric Bifurcations and Equilibria

NASA Technical Reports Server (NTRS)

Galli, Danielle; Shu, Frank H.; Laughlin, Gregory; Lizano, Susana

2000-01-01

We review the difficulties of the classical fission and fragmentation hypotheses for the formation of binary and multiple stars. A crucial missing ingredient in previous theoretical studies is the inclusion of dynamically important levels of magnetic fields. As a minimal model for a candidate presursor to the formation of binary and multiple stars, we therefore formulate and solve the problem of the equilibria of isopedically magnetized, singular isothermal disks, without the assumption of axial symmetry. Considerable analytical progress can be made if we restrict our attention to models that are scale-free, i.e., that have surface densities that vary inversely with distance omega from the rotation axis of the system. In agreement with earlier analysis by Syer and Tremaine, we find that lopsided (M = 1) configurations exist at any dimensionless rotation rate, including zero. Multiple-lobed (M = 2, 3, 4, ...) configurations bifurcate from an underlying axisymmetric sequence at progressively higher dimensionless rates of rotation, but such nonaxisymmetric sequences always terminate in shockwaves before they have a chance to fission into M = 2, 3, 4, ... separate bodies. On the basis of our experience in this paper, we advance the hypothesis that binary and multiple star-formation from smooth (i.e., not highly turbulent) starting states that are supercritical but in unstable mechanical balance requires the rapid (i.e., dynamical) loss of magnetic flux at some stage of the ensuing gravitational collapse.

Yang-Mills gauge conditions from Witten's open string field theory

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

Feng Haidong; Siegel, Warren

2007-02-15

We construct the Zinn-Justin-Batalin-Vilkovisky action for tachyons and gauge bosons from Witten's 3-string vertex of the bosonic open string without gauge fixing. Through canonical transformations, we find the off-shell, local, gauge-covariant action up to 3-point terms, satisfying the usual field theory gauge transformations. Perturbatively, it can be extended to higher-point terms. It also gives a new gauge condition in field theory which corresponds to the Feynman-Siegel gauge on the world-sheet.

A Note on Equivalence Among Various Scalar Field Models of Dark Energies

NASA Astrophysics Data System (ADS)

Mandal, Jyotirmay Das; Debnath, Ujjal

2017-08-01

In this work, we have tried to find out similarities between various available models of scalar field dark energies (e.g., quintessence, k-essence, tachyon, phantom, quintom, dilatonic dark energy, etc). We have defined an equivalence relation from elementary set theory between scalar field models of dark energies and used fundamental ideas from linear algebra to set up our model. Consequently, we have obtained mutually disjoint subsets of scalar field dark energies with similar properties and discussed our observation.

Singularities in loop quantum cosmology.

PubMed

Cailleteau, Thomas; Cardoso, Antonio; Vandersloot, Kevin; Wands, David

2008-12-19

We show that simple scalar field models can give rise to curvature singularities in the effective Friedmann dynamics of loop quantum cosmology (LQC). We find singular solutions for spatially flat Friedmann-Robertson-Walker cosmologies with a canonical scalar field and a negative exponential potential, or with a phantom scalar field and a positive potential. While LQC avoids big bang or big rip type singularities, we find sudden singularities where the Hubble rate is bounded, but the Ricci curvature scalar diverges. We conclude that the effective equations of LQC are not in themselves sufficient to avoid the occurrence of curvature singularities.

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

NASA Technical Reports Server (NTRS)

Sidi, A.; Israeli, M.

1986-01-01

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

Moiré edge states in twisted graphene nanoribbons

NASA Astrophysics Data System (ADS)

Fleischmann, M.; Gupta, R.; Weckbecker, D.; Landgraf, W.; Pankratov, O.; Meded, V.; Shallcross, S.

2018-05-01

The edge physics of graphene based systems is well known to be highly sensitive to the atomic structure at the boundary, with localized zero mode edge states found only on the zigzag-type termination of the lattice. Here we demonstrate that the graphene twist bilayer supports an additional class of edge states, that (i) are found for all edge geometries and thus are robust against edge roughness, (ii) occur at energies coinciding with twist induced Van Hove singularities in the bulk and (iii) possess an electron density strongly modulated by the moiré lattice. Interestingly, these "moiré edge states" exist only for certain lattice commensurations and thus the edge physics of the twist bilayer is, in dramatic contrast to that of the bulk, not uniquely determined by the twist angle.

Singularity analysis: theory and further developments

NASA Astrophysics Data System (ADS)

Cheng, Qiuming

2015-04-01

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

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

ERIC Educational Resources Information Center

Yanai, Haruo; Mukherjee, Bishwa Nath

1987-01-01

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

Field singularities at lossless metal-dielectric arbitrary-angle edges and their ramifications to the numerical modeling of gratings.

PubMed

Li, Lifeng

2012-04-01

I extend a previous work [J. Opt. Soc. Am. A, 738 (2011)] on field singularities at lossless metal-dielectric right-angle edges and their ramifications to the numerical modeling of gratings to the case of arbitrary metallic wedge angles. Simple criteria are given that allow one knowing the lossless permittivities and the arbitrary wedge angles to determine if the electric field at the edges is nonsingular, can be regularly singular, or can be irregularly singular without calculating the singularity exponent. Furthermore, the knowledge of the singularity type enables one to predict immediately if a numerical method that uses Fourier expansions of the transverse electric field components at the edges will converge or not without making any numerical tests. All conclusions of the previous work about the general relationships between field singularities, Fourier representation of singular fields, and convergence of numerical methods for modeling lossless metal-dielectric gratings have been reconfirmed.

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

NASA Technical Reports Server (NTRS)

Wang, S. S.

1983-01-01

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

Future singularity avoidance in phantom dark energy models

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

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

2012-07-01

Different approaches to quantum cosmology are studied in order to deal with the future singularity avoidance problem. Our results show that these future singularities will persist but could take different forms. As an example we have studied the big rip which appear when one considers the state equation P = ωρ with ω < −1, showing that it does not disappear in modified gravity. On the other hand, it is well-known that quantum geometric effects (holonomy corrections) in loop quantum cosmology introduce a quadratic modification, namely proportional to ρ{sup 2}, in Friedmann's equation that replace the big rip by amore » non-singular bounce. However this modified Friedmann equation could have been obtained in an inconsistent way, what means that the obtained results from this equation, in particular singularity avoidance, would be incorrect. In fact, we will show that instead of a non-singular bounce, the big rip singularity would be replaced, in loop quantum cosmology, by other kind of singularity.« less

Loop quantum cosmology and singularities.

PubMed

Struyve, Ward

2017-08-15

Loop quantum gravity is believed to eliminate singularities such as the big bang and big crunch singularity. This belief is based on studies of so-called loop quantum cosmology which concerns symmetry-reduced models of quantum gravity. In this paper, the problem of singularities is analysed in the context of the Bohmian formulation of loop quantum cosmology. In this formulation there is an actual metric in addition to the wave function, which evolves stochastically (rather than deterministically as the case of the particle evolution in non-relativistic Bohmian mechanics). Thus a singularity occurs whenever this actual metric is singular. It is shown that in the loop quantum cosmology for a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker space-time with arbitrary constant spatial curvature and cosmological constant, coupled to a massless homogeneous scalar field, a big bang or big crunch singularity is never obtained. This should be contrasted with the fact that in the Bohmian formulation of the Wheeler-DeWitt theory singularities may exist.

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.

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...

Tachyon inflation with steep potentials

NASA Astrophysics Data System (ADS)

Rezazadeh, K.; Karami, K.; Hashemi, S.

2017-05-01

Within the framework of tachyon inflation, we consider different steep potentials and check their viability in light of the Planck 2015 data. We see that in this scenario, the inverse power-law potential V (ϕ )=V0(ϕ /ϕ0)-n with n =2 leads to the power-law inflation with the scale factor a (t )∝tq where q >1 , while with n <2 , it gives rise to the intermediate inflation with the scale factor a (t )∝exp (A tf) where A >0 and 0 2 can be compatible with the 95% CL region of Planck 2015 TT, TE, EE +lowP data. We further conclude that the exponential potential V (ϕ )=V0e-ϕ /ϕ0, the inverse cosh potential V (ϕ )=V0/cosh (ϕ /ϕ0), and the mutated exponential potential V (ϕ )=V0[1 +(n -1 )-(n -1 )(ϕ /ϕ0)n] e-ϕ /ϕ0 with n =4 , can be consistent with the 95% CL region of Planck 2015 TT, TE, EE +lowP data. Moreover, using the r -ns constraints on the model parameters, we also estimate the running of the scalar spectral index d ns/d ln k and the local non-Gaussianity parameter fNLlocal. We find that the lower and upper bounds evaluated for these observables are compatible with the Planck 2015 results.

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.

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.

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.

Singularities in water waves and Rayleigh-Taylor instability

NASA Technical Reports Server (NTRS)

Tanveer, S.

1991-01-01

Singularities in inviscid two-dimensional finite-amplitude water waves and inviscid Rayleigh-Taylor instability are discussed. For the deep water gravity waves of permanent form, through a combination of analytical and numerical methods, results describing the precise form, number, and location of singularities in the unphysical domain as the wave height is increased are presented. It is shown how the information on the singularity in the unphysical region has the same form as for deep water waves. However, associated with such a singularity is a series of image singularities at increasing distances from the physical plane with possibly different behavior. Furthermore, for the Rayleigh-Taylor problem of motion of fluid over a vacuum and for the unsteady water wave problem, integro-differential equations valid in the unphysical region are derived, and how these equations can give information on the nature of singularities for arbitrary initial conditions is shown.

Topological resolution of gauge theory singularities

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

Saracco, Fabio; Tomasiello, Alessandro; Torroba, Gonzalo

2013-08-21

Some gauge theories with Coulomb branches exhibit singularities in perturbation theory, which are usually resolved by nonperturbative physics. In string theory this corresponds to the resolution of timelike singularities near the core of orientifold planes by effects from F or M theory. We propose a new mechanism for resolving Coulomb branch singularities in three-dimensional gauge theories, based on Chern-Simons interactions. This is illustrated in a supersymmetric S U ( 2 ) Yang-Mills-Chern-Simons theory. We calculate the one-loop corrections to the Coulomb branch of this theory and find a result that interpolates smoothly between the high-energy metric (that would exhibit themore » singularity) and a regular singularity-free low-energy result. We suggest possible applications to singularity resolution in string theory and speculate a relationship to a similar phenomenon for the orientifold six-plane in massive IIA supergravity.« less

Genericity Distinctions and the Interpretation of Determiners in Second Language Acquisition

ERIC Educational Resources Information Center

Ionin, Tania; Montrul, Silvina; Kim, Ji-Hye; Philippov, Vadim

2011-01-01

English uses three types of generic NPs: bare plurals ("Lions are dangerous"), definite singulars ("The lion is dangerous"), and indefinite singulars ("A lion is dangerous"). These three NP types are not interchangeable: definite singulars and bare plurals can have generic reference at the NP-level, while indefinite singulars are compatible only…

7 CFR 900.36 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.36 Section 900.36 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Marketing Orders § 900.36 Words in the singular form. Words in this subpart in the singular form shall be...

7 CFR 900.100 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.100 Section 900.100 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

7 CFR 900.1 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.1 Section 900.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

7 CFR 900.50 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.50 Section 900.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... Words in the singular form. Words in this subpart in the singular form shall be deemed to import the...

7 CFR 900.20 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.20 Section 900.20 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (Marketing... § 900.20 Words in the singular form. Words in this subpart in the singular form shall be deemed to...

7 CFR 1200.50 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Words in the singular form. 1200.50 Section 1200.50 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING....50 Words in the singular form. Words in this subpart in the singular form shall be deemed to import...

Singularities in the classical Rayleigh-Taylor flow - Formation and subsequent motion

NASA Technical Reports Server (NTRS)

Tanveer, S.

1993-01-01

The creation and subsequent motion of singularities of solution to classical Rayleigh-Taylor flow (two dimensional inviscid, incompressible fluid over a vacuum) are discussed. For a specific set of initial conditions, we give analytical evidence to suggest the instantaneous formation of one or more singularities at specific points in the unphysical plane, whose locations depend sensitively on small changes in initial conditions in the physical domain. One-half power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities are also possible. For a specific initial condition, we follow a numerical procedure in the unphysical plane to compute the motion of a one-half singularity. This computation confirms our previous conjecture that the approach of a one-half singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, we present analytical evidence to suggest that a singularity of the one-half type cannot impinge the physical domain in finite time.

Singularities in the classical Rayleigh-Taylor flow: Formation and subsequent motion

NASA Technical Reports Server (NTRS)

Tanveer, S.

1992-01-01

The creation and subsequent motion of singularities of solution to classical Rayleigh-Taylor flow (two dimensional inviscid, incompressible fluid over a vacuum) are discussed. For a specific set of initial conditions, we give analytical evidence to suggest the instantaneous formation of one or more singularities at specific points in the unphysical plane, whose locations depend sensitively on small changes in initial conditions in the physical domain. One-half power singularities are created in accordance with an earlier conjecture; however, depending on initial conditions, other forms of singularities are also possible. For a specific initial condition, we follow a numerical procedure in the unphysical plane to compute the motion of a one-half singularity. This computation confirms our previous conjecture that the approach of a one-half singularity towards the physical domain corresponds to the development of a spike at the physical interface. Under some assumptions that appear to be consistent with numerical calculations, we present analytical evidence to suggest that a singularity of the one-half type cannot impinge the physical domain in finite time.

{lambda} elements for one-dimensional singular problems with known strength of singularity

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

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

1996-10-01

This paper presents a new and general procedure for designing special elements called {lambda} elements for one dimensional singular problems where the strength of the singularity is know. The {lambda} elements presented here are of type C{sup 0}. These elements also provide inter-element C{sup 0} continuity with p-version elements. The {lambda} elements do not require a precise knowledge of the extent of singular zone, i.e., their use may be extended beyond the singular zone. When {lambda} elements are used at the singularity, a singular problem behaves like a smooth problem thereby eliminating the need for h, p-adaptive processes all together.more » One dimensional steady state radial flow of an upper convected Maxwell fluid is considered as a sample problem. Least squares approach (or least squares finite element formulation: LSFEF) is used to construct the integral form (error functional I) from the differential equations. Numerical results presented for radially inward flow with inner radius r{sub i} = 0.1, 0.01, 0.001, 0.0001, 0.00001, and Deborah number of 2 (De = 2) demonstrate the accuracy, faster convergence of the iterative solution procedure, faster convergence rate of the error functional and mesh independent characteristics of the {lambda} elements regardless of the severity of the singularity.« less

Tangled nonlinear driven chain reactions of all optical singularities

NASA Astrophysics Data System (ADS)

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

2012-03-01

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

Metric dimensional reduction at singularities with implications to Quantum Gravity

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

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

2014-08-15

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

Spectral singularities and Bragg scattering in complex crystals

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

Longhi, S.

2010-02-15

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

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

NASA Astrophysics Data System (ADS)

Córdoba, Diego; Pernas-Castaño, Tania

2017-10-01

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

Classical stability of sudden and big rip singularities

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

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

2009-08-15

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

Singularity embedding method in potential flow calculations

NASA Technical Reports Server (NTRS)

Jou, W. H.; Huynh, H.

1982-01-01

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

Naked singularities are not singular in distorted gravity

NASA Astrophysics Data System (ADS)

Garattini, Remo; Majumder, Barun

2014-07-01

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

Contracting singular horseshoe

NASA Astrophysics Data System (ADS)

Morales, C. A.; San Martín, B.

2017-11-01

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

Null cosmological singularities and free strings

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

Narayan, K.

2010-03-15

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

Probing the degenerate states of V-point singularities.

PubMed

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

2017-09-15

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

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

NASA Astrophysics Data System (ADS)

Liu, Pusheng; Lü, Baida

2007-04-01

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

Singularity: Scientific containers for mobility of compute.

PubMed

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

2017-01-01

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

Singularity: Scientific containers for mobility of compute

PubMed Central

Kurtzer, Gregory M.; Bauer, Michael W.

2017-01-01

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

Managing focal fields of vector beams with multiple polarization singularities.

PubMed

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

2016-11-10

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

Can A "Hyperspace" Really Exist?

NASA Technical Reports Server (NTRS)

Zampino, Edward J.

1999-01-01

The idea of "hyperspace" is suggested as a possible approach to faster-than-light (FTL) motion. A brief summary of a 1986 study on the Euclidean representation of space-time by the author is presented. Some new calculations on the relativistic momentum and energy of a free particle in Euclidean "hyperspace" are now added and discussed. The superimposed Energy-Momentum curves for subluminal particles, tachyons, and particles in Euclidean "hyperspace" are presented. It is shown that in Euclidean "hyperspace", instead of a relativistic time dilation there is a time "compression" effect. Some fundamental questions are presented,

Heavy-light mesons in chiral AdS/QCD

NASA Astrophysics Data System (ADS)

Liu, Yizhuang; Zahed, Ismail

2017-06-01

We discuss a minimal holographic model for the description of heavy-light and light mesons with chiral symmetry, defined in a slab of AdS space. The model consists of a pair of chiral Yang-Mills and tachyon fields with specific boundary conditions that break spontaneously chiral symmetry in the infrared. The heavy-light spectrum and decay constants are evaluated explicitly. In the heavy mass limit the model exhibits both heavy-quark and chiral symmetry and allows for the explicit derivation of the one-pion axial couplings to the heavy-light mesons.

Holographic scalar fields in Kaluza-Klein framework

NASA Astrophysics Data System (ADS)

Erkan, Sevda; Pirinccioglu, Nurettin; Salti, Mustafa; Aydogdu, Oktay

2017-12-01

Making use of the Friedmann-Robertson-Walker (FRW) type Kaluza-Klein universe (KKU), we discuss the holographic dark energy density (HDED) in order to develop its correspondence with some scalar field descriptions such as the tachyon, quintessence, DBI-essence, dilaton and the k-essence. It is concluded that the Kaluza-Klein-type HDED proposal becomes stable throughout the history of our universe and is consistent with the current status of the universe. Next, we obtain the exact solutions of self-interacting potential and scalar field function for the selected models.

Non-Abelian gauge preheating

NASA Astrophysics Data System (ADS)

Adshead, Peter; Giblin, John T.; Weiner, Zachary J.

2017-12-01

We study preheating in models where a scalar inflaton is directly coupled to a non-Abelian S U (2 ) gauge field. In particular, we examine m2ϕ2 inflation with a conformal, dilatonlike coupling to the non-Abelian sector. We describe a numerical scheme that combines lattice gauge theory with standard finite difference methods applied to the scalar field. We show that a significant tachyonic instability allows for efficient preheating, which is parametrically suppressed by increasing the non-Abelian self-coupling. Additionally, we comment on the technical implementation of the evolution scheme and setting initial conditions.

Singular perturbation and time scale approaches in discrete control systems

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Overcoming Robot-Arm Joint Singularities

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

7 CFR 900.80 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 8 2010-01-01 2010-01-01 false Words in the singular form. 900.80 Section 900.80....C. 608b(b) and 7 U.S.C. 608e Covering Fruits, Vegetables, and Nuts § 900.80 Words in the singular form. Words in this subpart in the singular form shall be deemed to import the plural, and vice versa...

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

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1983-01-01

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

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

NASA Astrophysics Data System (ADS)

Vasil'ev, Vasiliy; Soskin, Marat S.

2010-02-01

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

New classification methods on singularity of mechanism

NASA Astrophysics Data System (ADS)

Luo, Jianguo; Han, Jianyou

2010-07-01

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

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

NASA Technical Reports Server (NTRS)

Bedrossian, Nazareth Sarkis

1987-01-01

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

Infinite derivative gravity: non-singular cosmology & blackhole solutions

NASA Astrophysics Data System (ADS)

Mazumdar, A.

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

Three dimensional canonical singularity and five dimensional N = 1 SCFT

NASA Astrophysics Data System (ADS)

Xie, Dan; Yau, Shing-Tung

2017-06-01

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

Sharp bounds for singular values of fractional integral operators

NASA Astrophysics Data System (ADS)

Burman, Prabir

2007-03-01

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

A hybrid robust fault tolerant control based on adaptive joint unscented Kalman filter.

PubMed

Shabbouei Hagh, Yashar; Mohammadi Asl, Reza; Cocquempot, Vincent

2017-01-01

In this paper, a new hybrid robust fault tolerant control scheme is proposed. A robust H ∞ control law is used in non-faulty situation, while a Non-Singular Terminal Sliding Mode (NTSM) controller is activated as soon as an actuator fault is detected. Since a linear robust controller is designed, the system is first linearized through the feedback linearization method. To switch from one controller to the other, a fuzzy based switching system is used. An Adaptive Joint Unscented Kalman Filter (AJUKF) is used for fault detection and diagnosis. The proposed method is based on the simultaneous estimation of the system states and parameters. In order to show the efficiency of the proposed scheme, a simulated 3-DOF robotic manipulator is used. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

17,000 years of depicting the junction of two smooth shapes.

PubMed

Biederman, Irving; Kim, Jiye G

2008-01-01

Competent realistic drawings preserve viewpoint-invariant shape characteristics of simple parts, such that a contour in the object that is straight or curved, for example, is depicted that way in the drawing. A more subtle invariant--a V-shaped singularity of the occluding boundary, containing a T-junction and a contour termination--is produced at the junction between articulated smooth surfaces, as with the leg joining the body of a horse. 45% of the drawings made in 2007 by individuals with only minimal art education correctly depicted such junctions, a proportion that is not reliably different from the incidence (42%) of correct depictions in a large sample of cave art made 17000 years ago. Whether a person did or did not include the invariant in their drawing, all agreed that it made for a better depiction.

Black strings, low viscosity fluids, and violation of cosmic censorship.

PubMed

Lehner, Luis; Pretorius, Frans

2010-09-03

We describe the behavior of 5-dimensional black strings, subject to the Gregory-Laflamme instability. Beyond the linear level, the evolving strings exhibit a rich dynamics, where at intermediate stages the horizon can be described as a sequence of 3-dimensional spherical black holes joined by black string segments. These segments are themselves subject to a Gregory-Laflamme instability, resulting in a self-similar cascade, where ever-smaller satellite black holes form connected by ever-thinner string segments. This behavior is akin to satellite formation in low-viscosity fluid streams subject to the Rayleigh-Plateau instability. The simulation results imply that the string segments will reach zero radius in finite asymptotic time, whence the classical space-time terminates in a naked singularity. Since no fine-tuning is required to excite the instability, this constitutes a generic violation of cosmic censorship.

Chirality-Assisted Electronic Cloaking of Confined States in Bilayer Graphene

NASA Astrophysics Data System (ADS)

Gu, Nan; Rudner, Mark; Levitov, Leonid

2011-10-01

We show that the strong coupling of pseudospin orientation and charge carrier motion in bilayer graphene has a drastic effect on transport properties of ballistic p-n-p junctions. Electronic states with zero momentum parallel to the barrier are confined under it for one pseudospin orientation, whereas states with the opposite pseudospin tunnel through the junction totally uninfluenced by the presence of confined states. We demonstrate that the junction acts as a cloak for confined states, making them nearly invisible to electrons in the outer regions over a range of incidence angles. This behavior is manifested in the two-terminal conductance as transmission resonances with non-Lorentzian, singular peak shapes. The response of these phenomena to a weak magnetic field or electric-field-induced interlayer gap can serve as an experimental fingerprint of electronic cloaking.

Diffraction of V-point singularities through triangular apertures.

PubMed

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

2017-05-01

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

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

NASA Technical Reports Server (NTRS)

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

2005-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-09-01

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

Naked shell singularities on the brane

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

Seahra, Sanjeev S.

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

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

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

Adaptive nonsingular fast terminal sliding-mode control for the tracking problem of uncertain dynamical systems.

PubMed

Boukattaya, Mohamed; Mezghani, Neila; Damak, Tarak

2018-06-01

In this paper, robust and adaptive nonsingular fast terminal sliding-mode (NFTSM) control schemes for the trajectory tracking problem are proposed with known or unknown upper bound of the system uncertainty and external disturbances. The developed controllers take the advantage of the NFTSM theory to ensure fast convergence rate, singularity avoidance, and robustness against uncertainties and external disturbances. First, a robust NFTSM controller is proposed which guarantees that sliding surface and equilibrium point can be reached in a short finite-time from any initial state. Then, in order to cope with the unknown upper bound of the system uncertainty which may be occurring in practical applications, a new adaptive NFTSM algorithm is developed. One feature of the proposed control law is their adaptation techniques where the prior knowledge of parameters uncertainty and disturbances is not needed. However, the adaptive tuning law can estimate the upper bound of these uncertainties using only position and velocity measurements. Moreover, the proposed controller eliminates the chattering effect without losing the robustness property and the precision. Stability analysis is performed using the Lyapunov stability theory, and simulation studies are conducted to verify the effectiveness of the developed control schemes. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

New method for detecting singularities in experimental incompressible flows

NASA Astrophysics Data System (ADS)

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

2017-06-01

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

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

NASA Technical Reports Server (NTRS)

Wang, S. S.; Choi, I.

1983-01-01

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

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

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

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

2012-11-15

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

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

NASA Astrophysics Data System (ADS)

Dun, Xiaohong

2018-05-01

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

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

PubMed

Mostafazadeh, Ali

2009-06-05

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

Classification of hyperbolic singularities of rank zero of integrable Hamiltonian systems

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

Oshemkov, Andrey A

2010-10-06

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

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

NASA Technical Reports Server (NTRS)

Wanag, S. S.; Choi, I.

1981-01-01

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

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

PubMed

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

2008-09-01

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

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

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

Mostafazadeh, Ali

2009-06-05

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

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

NASA Technical Reports Server (NTRS)

Karabin, M. E., Jr.

1977-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2003-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Singular spectrum analysis of sleep EEG in insomnia.

PubMed

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

2011-08-01

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

Dynamic Singularity Spectrum Distribution of Sea Clutter

NASA Astrophysics Data System (ADS)

Xiong, Gang; Yu, Wenxian; Zhang, Shuning

2015-12-01

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

Singularity computations. [finite element methods for elastoplastic flow

NASA Technical Reports Server (NTRS)

Swedlow, J. L.

1978-01-01

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

Transmutation of planar media singularities in a conformal cloak.

PubMed

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

2013-11-01

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

Computing singularities of perturbation series

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

Kvaal, Simen; Jarlebring, Elias; Michiels, Wim

2011-03-15

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

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

PubMed

Zhang, Weixuan; Wu, Tong; Zhang, Xiangdong

2017-09-12

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

Stress singularities at the vertex of a cylindrically anisotropic wedge

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

Stanley Corrsin Award Talk: The role of singularities in hydrodynamics

NASA Astrophysics Data System (ADS)

Eggers, Jens

2017-11-01

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

Particle creation by naked singularities in higher dimensions

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

Miyamoto, Umpei; Nemoto, Hiroya; Shimano, Masahiro

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

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.

The Production of FRW Universe and Decay to Particles in Multiverse

NASA Astrophysics Data System (ADS)

Ghaffary, Tooraj

2017-09-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-03-01

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

Membrane-bound human orphan cytochrome P450 2U1: Sequence singularities, construction of a full 3D model, and substrate docking.

PubMed

Ducassou, Lionel; Dhers, Laura; Jonasson, Gabriella; Pietrancosta, Nicolas; Boucher, Jean-Luc; Mansuy, Daniel; André, François

2017-09-01

Human cytochrome P450 2U1 (CYP2U1) is an orphan CYP that exhibits several distinctive characteristics among the 57 human CYPs with a highly conserved sequence in almost all living organisms. We compared its protein sequence with those of the 57 human CYPs and constructed a 3D structure of a full-length CYP2U1 model bound to a POPC membrane. We also performed docking experiments of arachidonic acid (AA) and N-arachidonoylserotonin (AS) in this model. The protein sequence of CYP2U1 displayed two unique characteristics when compared to those of the human CYPs, the presence of a longer N-terminal region upstream of the putative trans-membrane helix (TMH) containing 8 proline residues, and of an insert of about 20 amino acids containing 5 arginine residues between helices A' and A. Its N-terminal part upstream of TMH involved an additional short terminal helix, in a manner similar to what was reported in the crystal structure of Saccharomyces cerevisiae CYP51. Our model also showed a specific interaction between the charged residues of insert AA' and phosphate groups of lipid polar heads, suggesting a possible role of this insert in substrate recruitment. Docking of AA and AS in this model showed these substrates in channel 2ac, with the terminal alkyl chain of AA or the indole ring of AS close to the heme, in agreement with the reported CYP2U1-catalyzed AA and AS hydroxylation regioselectivities. This model should be useful to find new endogenous or exogenous CYP2U1 substrates and to interpret the regioselectivity of their hydroxylation. Copyright © 2017 Elsevier B.V. and Société Française de Biochimie et Biologie Moléculaire (SFBBM). All rights reserved.

Redundant single gimbal control moment gyroscope singularity analysis

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

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

PubMed Central

Brzezicki, Samuel J.

2017-01-01

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

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

PubMed

Crowdy, Darren G; Brzezicki, Samuel J

2017-06-01

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

Looking for a bulk point

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

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

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

Looking for a bulk point

DOE PAGES

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

2017-01-03

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

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

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Observer-dependent sign inversions of polarization singularities.

PubMed

Freund, Isaac

2014-10-15

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

w-cosmological singularities

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

Fernandez-Jambrina, L.

2010-12-15

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

Optical spectral singularities as threshold resonances

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

Mostafazadeh, Ali

2011-04-15

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

Segmentation of singularity maps in the context of soil porosity

NASA Astrophysics Data System (ADS)

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

2016-04-01

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

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.

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

NASA Technical Reports Server (NTRS)

Williams, Robert L., III

1992-01-01

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

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

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

Unver, O.; Gurtug, O.

2010-10-15

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

Multivalued classical mechanics arising from singularity loops in complex time

NASA Astrophysics Data System (ADS)

Koch, Werner; Tannor, David J.

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

Pan, Supriya

2018-01-01

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

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

PubMed

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

2005-05-01

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

Observational constraints on cosmological future singularities

NASA Astrophysics Data System (ADS)

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

2016-11-01

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

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

ERIC Educational Resources Information Center

Hofmann, Richard J.

1978-01-01

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

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

PubMed

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

2017-11-01

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

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

NASA Technical Reports Server (NTRS)

Payton, R. G.

1972-01-01

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

Nonlinear spectral singularities for confined nonlinearities.

PubMed

Mostafazadeh, Ali

2013-06-28

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

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

DTIC Science & Technology

1982-08-01

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

Teleman localization of Hochschild homology in a singular setting

NASA Astrophysics Data System (ADS)

Brasselet, J.-P.; Legrand, A.

2009-09-01

The aim of this paper is to generalize the Hochschild-Kostant-Rosenberg theorem to the case of singular varieties, more precisely, to manifolds with boundary and to varieties with isolated singularities. In these situations, we define suitable algebras of functions and study the localization of the corresponding Hochschild homology. The tool we use is the Teleman localization process. In the case of isolated singularities, the closed Hochschild homology corresponds to the intersection complex which relates the objects defined here to intersection homology.

Naked singularities in higher dimensional Vaidya space-times

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

Ghosh, S. G.; Dadhich, Naresh

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

Acquired toxoplasmosis. A neglected cause of treatable nervous system disease.

PubMed

Townsend, J J; Wolinsky, J S; Baringer, J R; Johnson, P C

1975-05-01

The neurological manifestations of six cases of acquired central nervous system toxoplasmosis are compared with the 39 well-documented cases from the literature. Half of the patients had underlying systemic diseases (18 malignant neoplasms, two renal transplants, three collagen vascular diseases) treated with intensive immunosuppressive therapy. The remainder had primary toxoplasmosis. Three major neurological patterns were seen: (1) diffuse encephalopathy with or without seizures, (2) meningoencephalitis, and (3) singular or multiple progressive mass lesions. Routine neurological diagnostic studies were not helpful. The Sabin-Feldman dye test or IgM indirect fluorescent antibody test or both were effective in confirming the diagnosis. Twenty-seven patients died without a clinical diagnosis of toxoplasmosis. The diagnosis was made terminally in four additional patients. Thirteen of fourteen patients who received a full course of sulfadiazine or pyrimethamine or both did well. Toxoplasmosis should be considered in the immunosuppressed patient who appears with neurological involvement.

Application of Improved 5th-Cubature Kalman Filter in Initial Strapdown Inertial Navigation System Alignment for Large Misalignment Angles.

PubMed

Wang, Wei; Chen, Xiyuan

2018-02-23

In view of the fact the accuracy of the third-degree Cubature Kalman Filter (CKF) used for initial alignment under large misalignment angle conditions is insufficient, an improved fifth-degree CKF algorithm is proposed in this paper. In order to make full use of the innovation on filtering, the innovation covariance matrix is calculated recursively by an innovative sequence with an exponent fading factor. Then a new adaptive error covariance matrix scaling algorithm is proposed. The Singular Value Decomposition (SVD) method is used for improving the numerical stability of the fifth-degree CKF in this paper. In order to avoid the overshoot caused by excessive scaling of error covariance matrix during the convergence stage, the scaling scheme is terminated when the gradient of azimuth reaches the maximum. The experimental results show that the improved algorithm has better alignment accuracy with large misalignment angles than the traditional algorithm.

Evolution model with a cumulative feedback coupling

NASA Astrophysics Data System (ADS)

Trimper, Steffen; Zabrocki, Knud; Schulz, Michael

2002-05-01

The paper is concerned with a toy model that generalizes the standard Lotka-Volterra equation for a certain population by introducing a competition between instantaneous and accumulative, history-dependent nonlinear feedback the origin of which could be a contribution from any kind of mismanagement in the past. The results depend on the sign of that additional cumulative loss or gain term of strength λ. In case of a positive coupling the system offers a maximum gain achieved after a finite time but the population will die out in the long time limit. In this case the instantaneous loss term of strength u is irrelevant and the model exhibits an exact solution. In the opposite case λ<0 the time evolution of the system is terminated in a crash after ts provided u=0. This singularity after a finite time can be avoided if u≠0. The approach may well be of relevance for the qualitative understanding of more realistic descriptions.

Minimum-fuel turning climbout and descent guidance of transport jets

NASA Technical Reports Server (NTRS)

Neuman, F.; Kreindler, E.

1983-01-01

The complete flightpath optimization problem for minimum fuel consumption from takeoff to landing including the initial and final turns from and to the runway heading is solved. However, only the initial and final segments which contain the turns are treated, since the straight-line climbout, cruise, and descent problems have already been solved. The paths are derived by generating fields of extremals, using the necessary conditions of optimal control together with singular arcs and state constraints. Results show that the speed profiles for straight flight and turning flight are essentially identical except for the final horizontal accelerating or decelerating turns. The optimal turns require no abrupt maneuvers, and an approximation of the optimal turns could be easily integrated with present straight-line climb-cruise-descent fuel-optimization algorithms. Climbout at the optimal IAS rather than the 250-knot terminal-area speed limit would save 36 lb of fuel for the 727-100 aircraft.

Interaction of the branes in the presence of the background fields: The dynamical, nonintersecting, perpendicular, wrapped-fractional configuration

NASA Astrophysics Data System (ADS)

Maghsoodi, Elham; Kamani, Davoud

2017-05-01

We shall obtain the interaction of the Dp1- and Dp2-branes in the toroidal-orbifold space-time Tn × ℝ1,d-n-5 × ℂ2/ℤ 2. The configuration of the branes is nonintersecting, perpendicular, moving-rotating, wrapped-fractional with background fields. For this, we calculate the bosonic boundary state corresponding to a dynamical fractional-wrapped Dp-brane in the presence of the Kalb-Ramond field, a U1 gauge potential and an open string tachyon field. The long-range behavior of the interaction amplitude will be extracted.

Localization of U(1) gauge vector field on flat branes with five-dimension (asymptotic) AdS5 spacetime

NASA Astrophysics Data System (ADS)

Zhao, Zhen-Hua; Xie, Qun-Ying

2018-05-01

In order to localize U(1) gauge vector field on Randall-Sundrum-like braneworld model with infinite extra dimension, we propose a new kind of non-minimal coupling between the U(1) gauge field and the gravity. We propose three kinds of coupling methods and they all support the localization of zero mode. In addition, one of them can support the localization of massive modes. Moreover, the massive tachyonic modes can be excluded. And our method can be used not only in the thin braneword models but also in the thick ones.

When can preheating affect the CMB?

NASA Astrophysics Data System (ADS)

Tsujikawa, Shinji; Bassett, Bruce A.

2002-05-01

We discuss the principles governing the selection of inflationary models for which preheating can affect the CMB. This is a (fairly small) subset of those models which have nonnegligible entropy/isocurvature perturbations on large scales during inflation. We study new models which belong to this class-two-field inflation with negative nonminimal coupling and hybrid/double/supernatural inflation models where the tachyonic growth of entropy perturbations can lead to the variation of the curvature perturbation, /R, on super-Hubble scales. Finally, we present evidence against recent claims for the variation of /R in the absence of substantial super-Hubble entropy perturbations.

All orders results for self-crossing Wilson loops mimicking double parton scattering

DOE PAGES

Dixon, Lance J.; Esterlis, Ilya

2016-07-21

Loop-level scattering amplitudes for massless particles have singularities in regions where tree amplitudes are perfectly smooth. For example, a 2 → 4 gluon scattering process has a singularity in which each incoming gluon splits into a pair of gluons, followed by a pair of 2 → 2 collisions between the gluon pairs. This singularity mimics double parton scattering because it occurs when the transverse momentum of a pair of outgoing gluons vanishes. The singularity is logarithmic at fixed order in perturbation theory. We exploit the duality between scattering amplitudes and polygonal Wilson loops to study six-point amplitudes in this limitmore » to high loop order in planar N = 4 super-Yang-Mills theory. The singular configuration corresponds to the limit in which a hexagonal Wilson loop develops a self-crossing. The singular terms are governed by an evolution equation, in which the hexagon mixes into a pair of boxes; the mixing back is suppressed in the planar (large N c) limit. Because the kinematic dependence of the box Wilson loops is dictated by (dual) conformal invariance, the complete kinematic dependence of the singular terms for the self-crossing hexagon on the one nonsingular variable is determined to all loop orders. The complete logarithmic dependence on the singular variable can be obtained through nine loops, up to a couple of constants, using a correspondence with the multi-Regge limit. As a byproduct, we obtain a simple formula for the leading logs to all loop orders. Furthermore, we also show that, although the MHV six-gluon amplitude is singular, remarkably, the transcendental functions entering the non-MHV amplitude are finite in the same limit, at least through four loops.« less

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

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

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

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

All orders results for self-crossing Wilson loops mimicking double parton scattering

NASA Astrophysics Data System (ADS)

Dixon, Lance J.; Esterlis, Ilya

2016-07-01

Loop-level scattering amplitudes for massless particles have singularities in regions where tree amplitudes are perfectly smooth. For example, a 2 → 4 gluon scattering process has a singularity in which each incoming gluon splits into a pair of gluons, followed by a pair of 2 → 2 collisions between the gluon pairs. This singularity mimics double parton scattering because it occurs when the transverse momentum of a pair of outgoing gluons vanishes. The singularity is logarithmic at fixed order in perturbation theory. We exploit the duality between scattering amplitudes and polygonal Wilson loops to study six-point amplitudes in this limit to high loop order in planar {N} = 4 super-Yang-Mills theory. The singular configuration corresponds to the limit in which a hexagonal Wilson loop develops a self-crossing. The singular terms are governed by an evolution equation, in which the hexagon mixes into a pair of boxes; the mixing back is suppressed in the planar (large N c) limit. Because the kinematic dependence of the box Wilson loops is dictated by (dual) conformal invariance, the complete kinematic dependence of the singular terms for the self-crossing hexagon on the one nonsingular variable is determined to all loop orders. The complete logarithmic dependence on the singular variable can be obtained through nine loops, up to a couple of constants, using a correspondence with the multi-Regge limit. As a byproduct, we obtain a simple formula for the leading logs to all loop orders. We also show that, although the MHV six-gluon amplitude is singular, remarkably, the transcendental functions entering the non-MHV amplitude are finite in the same limit, at least through four loops.

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

NASA Astrophysics Data System (ADS)

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

2016-09-01

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

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.

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

NASA Technical Reports Server (NTRS)

Burken, John J.

1992-01-01

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

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

NASA Technical Reports Server (NTRS)

Burken, John J.

1992-01-01

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

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.

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

PubMed

Xin, Yun; Cheng, Zhibo

2017-01-01

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

Locality and Unitarity of Scattering Amplitudes from Singularities and Gauge Invariance

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-04-01

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

Spacetime Singularities in Quantum Gravity

NASA Astrophysics Data System (ADS)

Minassian, Eric A.

2000-04-01

Recent advances in 2+1 dimensional quantum gravity have provided tools to study the effects of quantization of spacetime on black hole and big bang/big crunch type singularities. I investigate effects of quantization of spacetime on singularities of the 2+1 dimensional BTZ black hole and the 2+1 dimensional torus universe. Hosoya has considered the BTZ black hole, and using a "quantum generalized affine parameter" (QGAP), has shown that, for some specific paths, quantum effects "smear" the singularities. Using gaussian wave functions as generic wave functions, I found that, for both BTZ black hole and the torus universe, there are families of paths that still reach the singularities with a finite QGAP, suggesting that singularities persist in quantum gravity. More realistic calculations, using modular invariant wave functions of Carlip and Nelson for the torus universe, offer further support for this conclusion. Currently work is in progress to study more realistic quantum gravity effects for BTZ black holes and other spacetime models.

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.

Generalized teleparallel cosmology and initial singularity crossing

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

Awad, Adel; Nashed, Gamal, E-mail: Adel.Awad@bue.edu.eg, E-mail: gglnashed@sci.asu.edu.eg

We present a class of cosmological solutions for a generalized teleparallel gravity with f ( T )= T +α̃ (− T ) {sup n} , where α̃ is some parameter and n is an integer or half-integer. Choosing α̃ ∼ G {sup n} {sup −1}, where G is the gravitational constant, and working with an equation of state p = w ρ, one obtains a cosmological solution with multiple branches. The dynamics of the solution describes standard cosmology at late times, but the higher-torsion correction changes the nature of the initial singularity from big bang to a sudden singularity. Themore » milder behavior of the sudden singularity enables us to extend timelike or lightlike curves, through joining two disconnected branches of solution at the singularity, leaving the singularity traversable. We show that this extension is consistent with the field equations through checking the known junction conditions for generalized teleparallel gravity. This suggests that these solutions describe a contracting phase a prior to the expanding phase of the universe.« less

Short-time quantum dynamics of sharp boundaries potentials

NASA Astrophysics Data System (ADS)

Granot, Er'el; Marchewka, Avi

2015-02-01

Despite the high prevalence of singular potential in general, and rectangular potentials in particular, in applied scattering models, to date little is known about their short time effects. The reason is that singular potentials cause a mixture of complicated local as well as non-local effects. The object of this work is to derive a generic method to calculate analytically the short-time impact of any singular potential. In this paper it is shown that the scattering of a smooth wavefunction on a singular potential is totally equivalent, in the short-time regime, to the free propagation of a singular wavefunction. However, the latter problem was totally addressed analytically in Ref. [7]. Therefore, this equivalency can be utilized in solving analytically the short time dynamics of any smooth wavefunction at the presence of a singular potentials. In particular, with this method the short-time dynamics of any problem where a sharp boundaries potential (e.g., a rectangular barrier) is turned on instantaneously can easily be solved analytically.

Boundary singularities produced by the motion of soap films.

PubMed

Goldstein, Raymond E; McTavish, James; Moffatt, H Keith; Pesci, Adriana I

2014-06-10

Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a "neck-pinching" boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck's geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures.

Assessing the relationships between phylogenetic and functional singularities in sharks (Chondrichthyes).

PubMed

Cachera, Marie; Le Loc'h, François

2017-08-01

The relationships between diversity and ecosystem functioning have become a major focus of science. A crucial issue is to estimate functional diversity, as it is intended to impact ecosystem dynamics and stability. However, depending on the ecosystem, it may be challenging or even impossible to directly measure ecological functions and thus functional diversity. Phylogenetic diversity was recently under consideration as a proxy for functional diversity. Phylogenetic diversity is indeed supposed to match functional diversity if functions are conservative traits along evolution. However, in case of adaptive radiation and/or evolutive convergence, a mismatch may appear between species phylogenetic and functional singularities. Using highly threatened taxa, sharks, this study aimed to explore the relationships between phylogenetic and functional diversities and singularities. Different statistical computations were used in order to test both methodological issue (phylogenetic reconstruction) and overall a theoretical questioning: the predictive power of phylogeny for function diversity. Despite these several methodological approaches, a mismatch between phylogeny and function was highlighted. This mismatch revealed that (i) functions are apparently nonconservative in shark species, and (ii) phylogenetic singularity is not a proxy for functional singularity. Functions appeared to be not conservative along the evolution of sharks, raising the conservational challenge to identify and protect both phylogenetic and functional singular species. Facing the current rate of species loss, it is indeed of major importance to target phylogenetically singular species to protect genetic diversity and also functionally singular species in order to maintain particular functions within ecosystem.

Time delay and magnification centroid due to gravitational lensing by black holes and naked singularities

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

Virbhadra, K. S.; Keeton, C. R.; Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854

We model the massive dark object at the center of the Galaxy as a Schwarzschild black hole as well as Janis-Newman-Winicour naked singularities, characterized by the mass and scalar charge parameters, and study gravitational lensing (particularly time delay, magnification centroid, and total magnification) by them. We find that the lensing features are qualitatively similar (though quantitatively different) for Schwarzschild black holes, weakly naked, and marginally strongly naked singularities. However, the lensing characteristics of strongly naked singularities are qualitatively very different from those due to Schwarzschild black holes. The images produced by Schwarzschild black hole lenses and weakly naked and marginallymore » strongly naked singularity lenses always have positive time delays. On the other hand, strongly naked singularity lenses can give rise to images with positive, zero, or negative time delays. In particular, for a large angular source position the direct image (the outermost image on the same side as the source) due to strongly naked singularity lensing always has a negative time delay. We also found that the scalar field decreases the time delay and increases the total magnification of images; this result could have important implications for cosmology. As the Janis-Newman-Winicour metric also describes the exterior gravitational field of a scalar star, naked singularities as well as scalar star lenses, if these exist in nature, will serve as more efficient cosmic telescopes than regular gravitational lenses.« 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.

Vibrational spectroscopic study of pH dependent solvation at a Ge(100)-water interface during an electrode potential triggered surface termination transition

NASA Astrophysics Data System (ADS)

Niu, Fang; Rabe, Martin; Nayak, Simantini; Erbe, Andreas

2018-06-01

The charge-dependent structure of interfacial water at the n-Ge(100)-aqueous perchlorate interface was studied by controlling the electrode potential. Specifically, a joint attenuated total reflection infrared spectroscopy and electrochemical experiment was used in 0.1M NaClO4 at pH ≈ 1-10. The germanium surface transformation to an H-terminated surface followed the thermodynamic Nernstian pH dependence and was observed throughout the entire pH range. A singular value decomposition-based spectra deconvolution technique coupled to a sigmoidal transition model for the potential dependence of the main components in the spectra shows the surface transformation to be a two-stage process. The first stage was observed together with the first appearance of Ge-H stretching modes in the spectra and is attributed to the formation of a mixed surface termination. This transition was reversible. The second stage occurs at potentials ≈0.1-0.3 V negative of the first one, shows a hysteresis in potential, and is attributed to the formation of a surface with maximum Ge-H coverage. During the surface transformation, the surface becomes hydrophobic, and an effective desolvation layer, a "hydrophobic gap," developed with a thickness ≈1-3 Å. The largest thickness was observed near neutral pH. Interfacial water IR spectra show a loss of strongly hydrogen-bound water molecules compared to bulk water after the surface transformation, and the appearance of "free," non-hydrogen bound OH groups, throughout the entire pH range. Near neutral pH at negative electrode potentials, large changes at wavenumbers below 1000 cm-1 were observed. Librational modes of water contribute to the observed changes, indicating large changes in the water structure.

Experimental observation of the effect of generic singularities in polychromatic dark hollow beams.

PubMed

Yadav, Bharat Kumar; Joshi, Stuti; Kandpal, Hem Chandra

2014-08-15

This Letter presents the essence of our recent experimental study on generic singularities carrying spatially partially coherent, polychromatic dark hollow beams (PDHBs). To the best of our knowledge, this is the first experimental demonstration of generic singularities-induced wavefront tearing in focused polychromatic beams.

Sign-singular measures - Fast magnetic dynamos, and high-Reynolds-number fluid turbulence

NASA Astrophysics Data System (ADS)

Ott, Edward; Du, Yunson; Sreenivasan, K. R.; Juneja, A.; Suri, A. K.

1992-11-01

It is shown that sign-singular measures with nontrivial cancellation exponents occur in dynamos and fluid turbulence. A cancellation exponent is introduced to characterize such measures quantitatively. Examples from kinematic magnetic dynamos and fluid turbulence are used to illlustrate this kind of singular behavior.

Degenerate SDEs with singular drift and applications to Heisenberg groups

NASA Astrophysics Data System (ADS)

Huang, Xing; Wang, Feng-Yu

2018-09-01

By using the ultracontractivity of a reference diffusion semigroup, Krylov's estimate is established for a class of degenerate SDEs with singular drifts, which leads to existence and pathwise uniqueness by means of Zvonkin's transformation. The main result is applied to singular SDEs on generalized Heisenberg groups.

Dalitz plot distributions in presence of triangle singularities

DOE PAGES

Szczepaniak, Adam P.

2016-03-25

We discuss properties of three-particle Dalitz distributions in coupled channel systems in presence of triangle singularities. The single channel case was discussed long ago where it was found that as a consequence of unitarity, effects of a triangle singularity seen in the Dalitz plot are not seen in Dalitz plot projections. In the coupled channel case we find the same is true for the sum of intensities of all interacting channels. As a result, unlike the single channel case, however, triangle singularities do remain visible in Dalitz plot projections of individual channels.

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.

Dalitz plot distributions in presence of triangle singularities

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

Szczepaniak, Adam P.

We discuss properties of three-particle Dalitz distributions in coupled channel systems in presence of triangle singularities. The single channel case was discussed long ago where it was found that as a consequence of unitarity, effects of a triangle singularity seen in the Dalitz plot are not seen in Dalitz plot projections. In the coupled channel case we find the same is true for the sum of intensities of all interacting channels. As a result, unlike the single channel case, however, triangle singularities do remain visible in Dalitz plot projections of individual channels.

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.

Method of mechanical quadratures for solving singular integral equations of various types

NASA Astrophysics Data System (ADS)

Sahakyan, A. V.; Amirjanyan, H. A.

2018-04-01

The method of mechanical quadratures is proposed as a common approach intended for solving the integral equations defined on finite intervals and containing Cauchy-type singular integrals. This method can be used to solve singular integral equations of the first and second kind, equations with generalized kernel, weakly singular equations, and integro-differential equations. The quadrature rules for several different integrals represented through the same coefficients are presented. This allows one to reduce the integral equations containing integrals of different types to a system of linear algebraic equations.

Boundary Approximation Methods for Sloving Elliptic Problems on Unbounded Domains

NASA Astrophysics Data System (ADS)

Li, Zi-Cai; Mathon, Rudolf

1990-08-01

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

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 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

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

NASA Astrophysics Data System (ADS)

Suramlishvili, Nugzar; Eggers, Jens; Fontelos, Marco

2014-11-01

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

Singular reduction of resonant Hamiltonians

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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.

Nonlinear Spectral Singularity and Laser Output Intensity for the TE and TM Modes

NASA Astrophysics Data System (ADS)

Ghaemidizicheh, Hamed; Mostafazadeh, Ali

The nonlinear spectral singularity arising from a Kerr nonlinearity is explored in. This reference studies the effect of nonlinearity in Lasing condition and shows that Kerr nonlinearity with spectral singularity for a normally incident wave provides an explanation of lasing at gain coefficient g. Lasing occurs when it exceeds threshold gain g0. For oblique waves, Ref. looks at the behavior of threshold gain coefficient g0 which is given by the condition that there is a linear spectral singularity. We investigated imposing the condition of the existence of nonlinear spectral singularity in the TE / TM modes of a mirrorless slab of gain materials and studied the θ-dependence of intensity. Supported by TUBITAK Project No: 114F357 and by the Turkish Academy of Science (TUBA).

Symmetry breaking and singularity structure in Bose-Einstein condensates

NASA Astrophysics Data System (ADS)

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

2012-08-01

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

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

PubMed

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

2018-07-01

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

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

A bridge between unified cosmic history by f( R)-gravity and BIonic system

NASA Astrophysics Data System (ADS)

Sepehri, Alireza; Capozziello, Salvatore; Setare, Mohammad Reza

2016-04-01

Recently, the cosmological deceleration-acceleration transition redshift in f( R) gravity has been considered in order to address consistently the problem of cosmic evolution. It is possible to show that the deceleration parameter changes sign at a given redshift according to observational data. Furthermore, a f( R) gravity cosmological model can be constructed in brane-antibrane system starting from the very early universe and accounting for the cosmological redshift at all phases of cosmic history, from inflation to late time acceleration. Here we propose a f( R) model where transition redshifts correspond to inflation-deceleration and deceleration-late time acceleration transitions starting froma BIon system. At the point where the universe was born, due to the transition of k black fundamental strings to the BIon configuration, the redshift is approximately infinity and decreases with reducing temperature (z˜ T2). The BIon is a configuration in flat space of a universe-brane and a parallel anti-universe-brane connected by a wormhole. This wormhole is a channel for flowing energy from extra dimensions into our universe, occurring at inflation and decreasing with redshift as z˜ T^{4+1/7}. Dynamics consists with the fact that the wormhole misses its energy and vanishes as soon as inflation ends and deceleration begins. Approaching two universe branes together, a tachyon is originated, it grows up and causes the formation of a wormhole. We show that, in the framework of f( R) gravity, the cosmological redshift depends on the tachyonic potential and has a significant decrease at deceleration-late time acceleration transition point (z˜ T^{2/3}). As soon as today acceleration approaches, the redshift tends to zero and the cosmological model reduces to the standard Λ CDM cosmology.

Treatment of charge singularities in implicit solvent models.

PubMed

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-21

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

Treatment of singularities in cracked bodies

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Treatment of singularities in cracked bodies

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

Boundary singularities produced by the motion of soap films

PubMed Central

Goldstein, Raymond E.; McTavish, James; Moffatt, H. Keith; Pesci, Adriana I.

2014-01-01

Recent work has shown that a Möbius strip soap film rendered unstable by deforming its frame changes topology to that of a disk through a “neck-pinching” boundary singularity. This behavior is unlike that of the catenoid, which transitions to two disks through a bulk singularity. It is not yet understood whether the type of singularity is generally a consequence of the surface topology, nor how this dependence could arise from an equation of motion for the surface. To address these questions we investigate experimentally, computationally, and theoretically the route to singularities of soap films with different topologies, including a family of punctured Klein bottles. We show that the location of singularities (bulk or boundary) may depend on the path of the boundary deformation. In the unstable regime the driving force for soap-film motion is the mean curvature. Thus, the narrowest part of the neck, associated with the shortest nontrivial closed geodesic of the surface, has the highest curvature and is the fastest moving. Just before onset of the instability there exists on the stable surface the shortest closed geodesic, which is the initial condition for evolution of the neck’s geodesics, all of which have the same topological relationship to the frame. We make the plausible conjectures that if the initial geodesic is linked to the boundary, then the singularity will occur at the boundary, whereas if the two are unlinked initially, then the singularity will occur in the bulk. Numerical study of mean curvature flows and experiments support these conjectures. PMID:24843162

Treatment of charge singularities in implicit solvent models

NASA Astrophysics Data System (ADS)

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-01

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

Interlaminar stress singularities at a straight free edge in composite laminates

NASA Technical Reports Server (NTRS)

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

1980-01-01

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

Correlation singularities in partially coherent electromagnetic beams.

PubMed

Raghunathan, Shreyas B; Schouten, Hugo F; Visser, Taco D

2012-10-15

We demonstrate that coherence vortices, singularities of the correlation function, generally occur in partially coherent electromagnetic beams. In successive cross sections of Gaussian Schell-model beams, their locus is found to be a closed string. These coherence singularities have implications for both interference experiments and correlation of intensity fluctuation measurements performed with such beams.

Twisting singular solutions of Betheʼs equations

NASA Astrophysics Data System (ADS)

Nepomechie, Rafael I.; Wang, Chunguang

2014-12-01

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 be physical, in which case they correspond to genuine eigenvalues and eigenvectors of the Hamiltonian.

7 CFR 1200.1 - Words in the singular form.

Code of Federal Regulations, 2010 CFR

2010-01-01

... 7 Agriculture 10 2010-01-01 2010-01-01 false Words in the singular form. 1200.1 Section 1200.1 Agriculture Regulations of the Department of Agriculture (Continued) AGRICULTURAL MARKETING SERVICE (MARKETING... Governing Proceedings To Formulate and Amend an Order § 1200.1 Words in the singular form. Words in this...

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.

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

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

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

2014-10-15

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

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

NASA Technical Reports Server (NTRS)

Nguyen, Nhan

2006-01-01

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

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

NASA Astrophysics Data System (ADS)

Lanen, Theo A.; Watt, David W.

1995-10-01

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

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.

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

NASA Technical Reports Server (NTRS)

Ryne, Mark S.; Wang, Tseng-Chan

1991-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

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

2007-08-01

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

Biochemical and MALDI-TOF Mass Spectrometric Characterization of a Novel Native and Recombinant Cystine Knot Miniprotein from Solanum tuberosum subsp. andigenum cv. Churqueña

PubMed Central

Cotabarren, Juliana; Tellechea, Mariana Edith; Tanco, Sebastián Martín; Garcia-Pardo, Javier; Avilés, Francesc Xavier; Obregón, Walter David

2018-01-01

Cystine-knot miniproteins (CKMPs) are an intriguing group of cysteine-rich molecules that combine the characteristics of proteins and peptides. Typically, CKMPs are fewer than 50 residues in length and share a characteristic knotted scaffold characterized by the presence of three intramolecular disulfide bonds that form the singular knotted structure. The knot scaffold confers on these proteins remarkable chemical, thermal, and proteolytic stability. Recently, CKMPs have emerged as a novel class of natural molecules with interesting pharmacological properties. In the present work, a novel cystine-knot metallocarboxypeptidase inhibitor (chuPCI) was isolated from tubers of Solanum tuberosum, subsp. andigenum cv. Churqueña. Our results demonstrated that chuPCI is a member of the A/B-type family of metallocarboxypeptidases inhibitors. chuPCI was expressed and characterized by a combination of biochemical and mass spectrometric techniques. Direct comparison of the MALDI-TOF mass spectra for the native and recombinant molecules allowed us to confirm the presence of four different forms of chuPCI in the tubers. The majority of such forms have a molecular weight of 4309 Da and contain a cyclized Gln in the N-terminus. The other three forms are derived from N-terminal and/or C-terminal proteolytic cleavages. Taken together, our results contribute to increase the current repertoire of natural CKMPs. PMID:29495576

Angular spectra of rainbow scattering at glancing keV He + bombardment of NiAl(1 0 0) surface with transverse energies in the range 1-10 eV

NASA Astrophysics Data System (ADS)

Danailov, Daniel M.

2007-11-01

Previous simulations of glancing incidence ion-surface interaction have demonstrated that classical dynamics using the row-model have successfully reproduced multimodal azimuthal and polar spectra. These studies have also shown considerable sensitivity to the form of the interatomic potential thus making it a strong test of the validity of such potentials and even allow deduction of the ion-surface potentials. In these simulations the individual pairwise interactions between the projectile and the target atoms have been replaced by cylindrical potentials. Comparison to numerous experimental studies have confirmed the existence of rainbow scattering phenomena and successfully tested the validity of the cylindrical potential used in these simulations. The use of cylindrical potentials avoids stochastic effects due to thermal displacements and allows faster computer simulations leading to reliable angular distributions. In the present work we extend the row-model to consider scattering from binary alloys. Using He+ scattered at glancing incidence from NiAl surfaces, Al or Ni terminated, a faster method has been developed to easily and accurately quantize not only the maximum deflection azimuthal angle but all the singular points in the angular distribution. It has been shown that the influence of the surface termination on the rainbow angle and the inelastic losses is small.

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.

Singularities of the Euler equation and hydrodynamic stability

NASA Technical Reports Server (NTRS)

Tanveer, S.; Speziale, Charles G.

1993-01-01

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

Singularities of the Euler equation and hydrodynamic stability

NASA Technical Reports Server (NTRS)

Tanveer, S.; Speziale, Charles G.

1992-01-01

Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.

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 problem of stress singularities in bonded orthotropic materials

NASA Technical Reports Server (NTRS)

Erdogan, F.; Delale, F.

1976-01-01

The problem of stress singularities at the leading edge of a crack lying in the neighborhood of a bimaterial interface in bonded orthotropic materials is considered. The main objective is to study the effect of material orthotropy on the singular behavior of the stress state when the crack touches or intersects the interface. The results indicate that, due to the large number of material constants involved, in orthotropic materials, the power of stress singularity as well as the stress intensity factor can be considerably different than that found in the isotropic materials with the same stiffness ratio perpendicular to the crack.

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.

Integrable mappings and the notion of anticonfinement

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1986-01-01

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

On the solution of integral equations with strong ly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1985-01-01

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

On the solution of integral equations with strongly singular kernels

NASA Technical Reports Server (NTRS)

Kaya, A. C.; Erdogan, F.

1987-01-01

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

Tests of conformal field theory at the Yang-Lee singularity

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

Wydro, Tomasz; McCabe, John F.

2009-12-14

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

Quantum probe of Hořava-Lifshitz gravity

NASA Astrophysics Data System (ADS)

Gurtug, O.; Mangut, M.

2018-04-01

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

Interlaminar stress singularities at a straight free edge in composite laminates

NASA Technical Reports Server (NTRS)

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

1981-01-01

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

Electromechanical vortex filaments during cardiac fibrillation

NASA Astrophysics Data System (ADS)

Christoph, J.; Chebbok, M.; Richter, C.; Schröder-Schetelig, J.; Bittihn, P.; Stein, S.; Uzelac, I.; Fenton, F. H.; Hasenfuß, G.; Gilmour, R. F., Jr.; Luther, S.

2018-03-01

The self-organized dynamics of vortex-like rotating waves, which are also known as scroll waves, are the basis of the formation of complex spatiotemporal patterns in many excitable chemical and biological systems. In the heart, filament-like phase singularities that are associated with three-dimensional scroll waves are considered to be the organizing centres of life-threatening cardiac arrhythmias. The mechanisms that underlie the onset, maintenance and control of electromechanical turbulence in the heart are inherently three-dimensional phenomena. However, it has not previously been possible to visualize the three-dimensional spatiotemporal dynamics of scroll waves inside cardiac tissues. Here we show that three-dimensional mechanical scroll waves and filament-like phase singularities can be observed deep inside the contracting heart wall using high-resolution four-dimensional ultrasound-based strain imaging. We found that mechanical phase singularities co-exist with electrical phase singularities during cardiac fibrillation. We investigated the dynamics of electrical and mechanical phase singularities by simultaneously measuring the membrane potential, intracellular calcium concentration and mechanical contractions of the heart. We show that cardiac fibrillation can be characterized using the three-dimensional spatiotemporal dynamics of mechanical phase singularities, which arise inside the fibrillating contracting ventricular wall. We demonstrate that electrical and mechanical phase singularities show complex interactions and we characterize their dynamics in terms of trajectories, topological charge and lifetime. We anticipate that our findings will provide novel perspectives for non-invasive diagnostic imaging and therapeutic applications.

Singularities of interference of three waves with different polarization states.

PubMed

Kurzynowski, Piotr; Woźniak, Władysław A; Zdunek, Marzena; Borwińska, Monika

2012-11-19

We presented the interference setup which can produce interesting two-dimensional patterns in polarization state of the resulting light wave emerging from the setup. The main element of our setup is the Wollaston prism which gives two plane, linearly polarized waves (eigenwaves of both Wollaston's wedges) with linearly changed phase difference between them (along the x-axis). The third wave coming from the second arm of proposed polarization interferometer is linearly or circularly polarized with linearly changed phase difference along the y-axis. The interference of three plane waves with different polarization states (LLL - linear-linear-linear or LLC - linear-linear-circular) and variable change difference produce two-dimensional light polarization and phase distributions with some characteristic points and lines which can be claimed to constitute singularities of different types. The aim of this article is to find all kind of these phase and polarization singularities as well as their classification. We postulated in our theoretical simulations and verified in our experiments different kinds of polarization singularities, depending on which polarization parameter was considered (the azimuth and ellipticity angles or the diagonal and phase angles). We also observed the phase singularities as well as the isolated zero intensity points which resulted from the polarization singularities when the proper analyzer was used at the end of the setup. The classification of all these singularities as well as their relationships were analyzed and described.

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

NASA Astrophysics Data System (ADS)

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

2016-05-01

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

Singularity in the Laboratory Frame Angular Distribution Derived in Two-Body Scattering Theory

ERIC Educational Resources Information Center

Dick, Frank; Norbury, John W.

2009-01-01

The laboratory (lab) frame angular distribution derived in two-body scattering theory exhibits a singularity at the maximum lab scattering angle. The singularity appears in the kinematic factor that transforms the centre of momentum (cm) angular distribution to the lab angular distribution. We show that it is caused in the transformation by the…

Two Approaches of Studying Singularity of Projective Conics

ERIC Educational Resources Information Center

Broyles, Chris; Muller, Lars; Tikoo, Mohan; Wang, Haohao

2010-01-01

The singularity of a projective conic can be determined via the associated matrix to the implicit equation of the projective conic. In this expository article, we will first derive a known result for determining the singularity of a projective conic via the associated matrix. Then we will introduce the concepts of [mu]-basis of the parametric…

Does the Conceptual Distinction between Singular and Plural Sets Depend on Language?

ERIC Educational Resources Information Center

Li, Peggy; Ogura, Tamiko; Barner, David; Yang, Shu-Ju; Carey, Susan

2009-01-01

Previous studies indicate that English-learning children acquire the distinction between singular and plural nouns between 22 and 24 months of age. Also, their use of the distinction is correlated with the capacity to distinguish nonlinguistically between singular and plural sets in a manual search paradigm (D. Barner, D. Thalwitz, J. Wood, S.…

The Processing of Singular and Plural Nouns in French and English

ERIC Educational Resources Information Center

New, Boris; Brysbaert, Marc; Segui, Juan; Ferrand, Ludovic; Rastle, Kathleen

2004-01-01

Contradictory data have been obtained about the processing of singular and plural nouns in Dutch and English. Whereas the Dutch findings point to an influence of the base frequency of the singular and the plural word forms on lexical decision times (Baayen, Dijkstra, & Schreuder, 1997), the English reaction times depend on the surface frequency of…

Analysis of the Fisher solution

NASA Astrophysics Data System (ADS)

Abdolrahimi, Shohreh; Shoom, Andrey A.

2010-01-01

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

Analysis of the Fisher solution

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

Abdolrahimi, Shohreh; Shoom, Andrey A.

2010-01-15

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

Naked singularities as particle accelerators. II

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

Patil, Mandar; Joshi, Pankaj S.; Malafarina, Daniele

We generalize here our earlier results on particle acceleration by naked singularities. We showed recently [M. Patil and P. S. Joshi, Phys. Rev. D 82, 104049 (2010).] that the naked singularities that form due to the gravitational collapse of massive stars provide a suitable environment where particles could get accelerated and collide at arbitrarily high center-of-mass energies. However, we focused there only on the spherically symmetric gravitational collapse models, which were also assumed to be self-similar. In this paper, we broaden and generalize the result to all gravitational collapse models leading to the formation of a naked singularity as themore » final state of collapse, evolving from a regular initial data, without making any prior restrictive assumptions about the spacetime symmetries such as above. We show that, when the particles interact and collide near the Cauchy horizon, the energy of collision in the center-of-mass frame will be arbitrarily high, thus offering a window to the Planck scale physics. We also consider the issue of various possible physical mechanisms of generation of such very high-energy particles from the vicinity of naked singularity. We then construct a model of gravitational collapse to a timelike naked singularity to demonstrate the working of these ideas, where the pressure is allowed to be negative, but the energy conditions are respected. We show that a finite amount of mass-energy density has to be necessarily radiated away from the vicinity of the naked singularity as the collapse evolves. Therefore, the nature of naked singularities, both at the classical and quantum level, could play an important role in the process of particle acceleration, explaining the occurrence of highly energetic outgoing particles in the vicinity of the Cauchy horizon that participate in extreme high-energy collisions.« less

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

PubMed

Kam, Chon-Fai; Liu, Ren-Bao

2017-08-29

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

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

PubMed Central

Dyachenko, Sergey A.; A. Silantyev, Denis

2017-01-01

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

Predicting financial market crashes using ghost singularities.

PubMed

Smug, Damian; Ashwin, Peter; Sornette, Didier

2018-01-01

We analyse the behaviour of a non-linear model of coupled stock and bond prices exhibiting periodically collapsing bubbles. By using the formalism of dynamical system theory, we explain what drives the bubbles and how foreshocks or aftershocks are generated. A dynamical phase space representation of that system coupled with standard multiplicative noise rationalises the log-periodic power law singularity pattern documented in many historical financial bubbles. The notion of 'ghosts of finite-time singularities' is introduced and used to estimate the end of an evolving bubble, using finite-time singularities of an approximate normal form near the bifurcation point. We test the forecasting skill of this method on different stochastic price realisations and compare with Monte Carlo simulations of the full system. Remarkably, the approximate normal form is significantly more precise and less biased. Moreover, the method of ghosts of singularities is less sensitive to the noise realisation, thus providing more robust forecasts.

Observational constraints on finite scale factor singularities

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

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

2012-07-01

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

Plasmon-Exciton Interactions Probed Using Spatial Coentrapment of Nanoparticles by Topological Singularities.

PubMed

Ackerman, Paul J; Mundoor, Haridas; Smalyukh, Ivan I; van de Lagemaat, Jao

2015-12-22

We study plasmon-exciton interaction by using topological singularities to spatially confine, selectively deliver, cotrap and optically probe colloidal semiconductor and plasmonic nanoparticles. The interaction is monitored in a single quantum system in the bulk of a liquid crystal medium where nanoparticles are manipulated and nanoconfined far from dielectric interfaces using laser tweezers and topological configurations containing singularities. When quantum dot-in-a-rod particles are spatially colocated with a plasmonic gold nanoburst particle in a topological singularity core, its fluorescence increases because blinking is significantly suppressed and the radiative decay rate increases by nearly an order of magnitude owing to the Purcell effect. We argue that the blinking suppression is the result of the radiative rate change that mitigates Auger recombination and quantum dot ionization, consequently reducing nonradiative recombination. Our work demonstrates that topological singularities are an effective platform for studying and controlling plasmon-exciton interactions.

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

PubMed

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

2017-06-01

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

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

PubMed

Herlin, Antoine; Jacquemet, Vincent

2012-05-01

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

Plasmon–Exciton Interactions Probed Using Spatial Coentrapment of Nanoparticles by Topological Singularities

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

Ackerman, Paul J.; Mundoor, Haridas; Smalyukh, Ivan I.

2015-12-22

We study plasmon-exciton interaction by using topological singularities to spatially confine, selectively deliver, cotrap and optically probe colloidal semiconductor and plasmonic nanoparticles. The interaction is monitored in a single quantum system in the bulk of a liquid crystal medium where nanoparticles are manipulated and nanoconfined far from dielectric interfaces using laser tweezers and topological configurations containing singularities. When quantum dot-in-a-rod particles are spatially colocated with a plasmonic gold nanoburst particle in a topological singularity core, its fluorescence increases because blinking is significantly suppressed and the radiative decay rate increases by nearly an order of magnitude owing to the Purcell effect.more » We argue that the blinking suppression is the result of the radiative rate change that mitigates Auger recombination and quantum dot ionization, consequently reducing nonradiative recombination. Our work demonstrates that topological singularities are an effective platform for studying and controlling plasmon-exciton interactions.« less

A novel finite element analysis of three-dimensional circular crack

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

Singularity-free backstepping controller for model helicopters.

PubMed

Zou, Yao; Huo, Wei

2016-11-01

This paper develops a backstepping controller for model helicopters to achieve trajectory tracking without singularity, which occurs in the attitude representation when the roll or pitch reaches ±π2. Based on a simplified model with unmodeled dynamics, backstepping technique is introduced to exploit the controller and hyperbolic tangent functions are utilized to compensate the unmodeled dynamics. Firstly, a position loop controller is designed for the position tracking, where an auxiliary dynamic system with suitable parameters is introduced to warrant the singularity-free requirement for the extracted command attitude. Then, a novel attitude loop controller is proposed to obviate singularity. It is demonstrated that, based on the established criteria for selecting controller parameters and desired trajectories, the proposed controller realizes the singularity-free trajectory tracking of the model helicopter. Simulations confirm the theoretical results. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Statistical analysis of effective singular values in matrix rank determination

NASA Technical Reports Server (NTRS)

Konstantinides, Konstantinos; Yao, Kung

1988-01-01

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

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.

Singular Atom Optics with Spinor BECs

NASA Astrophysics Data System (ADS)

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

2015-05-01

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

Finite conformal quantum gravity and spacetime singularities

NASA Astrophysics Data System (ADS)

Modesto, Leonardo; Rachwał, Lesław

2017-12-01

We show that a class of finite quantum non-local gravitational theories is conformally invariant at classical as well as at quantum level. This is actually a range of conformal anomaly-free theories in the spontaneously broken phase of the Weyl symmetry. At classical level we show how the Weyl conformal invariance is able to tame all the spacetime singularities that plague not only Einstein gravity, but also local and weakly non-local higher derivative theories. The latter statement is proved by a singularity theorem that applies to a large class of weakly non-local theories. Therefore, we are entitled to look for a solution of the spacetime singularity puzzle in a missed symmetry of nature, namely the Weyl conformal symmetry. Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free black hole exact solutions in a class of conformally invariant theories.

Magnetic islands and singular currents at rational surfaces in three-dimensional magnetohydrodynamic equilibria

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

Loizu, J., E-mail: joaquim.loizu@ipp.mpg.de; Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton New Jersey 08543; Hudson, S.

2015-02-15

Using the recently developed multiregion, relaxed MHD (MRxMHD) theory, which bridges the gap between Taylor's relaxation theory and ideal MHD, we provide a thorough analytical and numerical proof of the formation of singular currents at rational surfaces in non-axisymmetric ideal MHD equilibria. These include the force-free singular current density represented by a Dirac δ-function, which presumably prevents the formation of islands, and the Pfirsch-Schlüter 1/x singular current, which arises as a result of finite pressure gradient. An analytical model based on linearized MRxMHD is derived that can accurately (1) describe the formation of magnetic islands at resonant rational surfaces, (2)more » retrieve the ideal MHD limit where magnetic islands are shielded, and (3) compute the subsequent formation of singular currents. The analytical results are benchmarked against numerical simulations carried out with a fully nonlinear implementation of MRxMHD.« less

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

PubMed

Zhang, Xuefeng; Chen, YangQuan

2017-11-01

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

The Big Bang Singularity

NASA Astrophysics Data System (ADS)

Ling, Eric

The big bang theory is a model of the universe which makes the striking prediction that the universe began a finite amount of time in the past at the so called "Big Bang singularity." We explore the physical and mathematical justification of this surprising result. After laying down the framework of the universe as a spacetime manifold, we combine physical observations with global symmetrical assumptions to deduce the FRW cosmological models which predict a big bang singularity. Next we prove a couple theorems due to Stephen Hawking which show that the big bang singularity exists even if one removes the global symmetrical assumptions. Lastly, we investigate the conditions one needs to impose on a spacetime if one wishes to avoid a singularity. The ideas and concepts used here to study spacetimes are similar to those used to study Riemannian manifolds, therefore we compare and contrast the two geometries throughout.

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

PubMed

Vasilev, Vasyl; Soskin, Marat

2016-04-20

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

Entanglement Entropy in Two-Dimensional String Theory.

PubMed

Hartnoll, Sean A; Mazenc, Edward A

2015-09-18

To understand an emergent spacetime is to understand the emergence of locality. Entanglement entropy is a powerful diagnostic of locality, because locality leads to a large amount of short distance entanglement. Two-dimensional string theory is among the very simplest instances of an emergent spatial dimension. We compute the entanglement entropy in the large-N matrix quantum mechanics dual to two-dimensional string theory in the semiclassical limit of weak string coupling. We isolate a logarithmically large, but finite, contribution that corresponds to the short distance entanglement of the tachyon field in the emergent spacetime. From the spacetime point of view, the entanglement is regulated by a nonperturbative "graininess" of space.

Ultra-large distance modification of gravity from Lorentz symmetry breaking at the Planck scale

NASA Astrophysics Data System (ADS)

Gorbunov, Dmitry S.; Sibiryakov, Sergei M.

2005-09-01

We present an extension of the Randall-Sundrum model in which, due to spontaneous Lorentz symmetry breaking, graviton mixes with bulk vector fields and becomes quasilocalized. The masses of KK modes comprising the four-dimensional graviton are naturally exponentially small. This allows to push the Lorentz breaking scale to as high as a few tenth of the Planck mass. The model does not contain ghosts or tachyons and does not exhibit the van Dam-Veltman-Zakharov discontinuity. The gravitational attraction between static point masses becomes gradually weaker with increasing of separation and gets replaced by repulsion (antigravity) at exponentially large distances.

General self-tuning solutions and no-go theorem

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

Förste, Stefan; Kim, Jihn E.; Lee, Hyun Min, E-mail: forste@th.physik.uni-bonn.de, E-mail: jihnekim@gmail.com, E-mail: hyun.min.lee@kias.re.kr

2013-03-01

We consider brane world models with one extra dimension. In the bulk there is in addition to gravity a three form gauge potential or equivalently a scalar (by generalisation of electric magnetic duality). We find classical solutions for which the 4d effective cosmological constant is adjusted by choice of integration constants. No go theorems for such self-tuning mechanism are circumvented by unorthodox Lagrangians for the three form respectively the scalar. It is argued that the corresponding effective 4d theory always includes tachyonic Kaluza-Klein excitations or ghosts. Known no go theorems are extended to a general class of models with unorthodoxmore » Lagrangians.« less

Regularizing cosmological singularities by varying physical constants

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

Dąbrowski, Mariusz P.; Marosek, Konrad, E-mail: mpdabfz@wmf.univ.szczecin.pl, E-mail: k.marosek@wmf.univ.szczecin.pl

2013-02-01

Varying physical constant cosmologies were claimed to solve standard cosmological problems such as the horizon, the flatness and the Λ-problem. In this paper, we suggest yet another possible application of these theories: solving the singularity problem. By specifying some examples we show that various cosmological singularities may be regularized provided the physical constants evolve in time in an appropriate way.

Singularity computations

NASA Technical Reports Server (NTRS)

Swedlow, J. L.

1976-01-01

An approach is described for singularity computations based on a numerical method for elastoplastic flow to delineate radial and angular distribution of field quantities and measure the intensity of the singularity. The method is applicable to problems in solid mechanics and lends itself to certain types of heat flow and fluid motion studies. Its use is not limited to linear, elastic, small strain, or two-dimensional situations.

Art as a Singular Rule

ERIC Educational Resources Information Center

Avital, Doron

2007-01-01

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

The Singular Set of Solutions to Non-Differentiable Elliptic Systems

NASA Astrophysics Data System (ADS)

Mingione, Giuseppe

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

Usage-Based Account of the Acquisition of Liaison: Evidence from Sensitivity to the Singular/Plural Orientation of Nouns

ERIC Educational Resources Information Center

Dugua, Celine; Spinelli, Elsa; Chevrot, Jean-Pierre; Fayol, Michel

2009-01-01

This study investigates whether children's production and recognition of obligatory liaison sequences in French depend on the singular/plural orientation of nouns. Certain nouns occur more frequently in the plural (e.g., "arbre" "tree"), whereas others are found more often in the singular (e.g., "arc-en-ciel" "rainbow"). In the input, children…

Strength of the singularities, equation of state and asymptotic expansion in Kaluza-Klein space time

NASA Astrophysics Data System (ADS)

Samanta, G. C.; Goel, Mayank; Myrzakulov, R.

2018-04-01

In this paper an explicit cosmological model which allows cosmological singularities are discussed in Kaluza-Klein space time. The generalized power-law and asymptotic expansions of the baro-tropic fluid index ω and equivalently the deceleration parameter q, in terms of cosmic time 't' are considered. Finally, the strength of the found singularities is discussed.