Clustering of the human skeletal muscle fibers using linear programming and angular Hilbertian metrics.

PubMed

Neji, Radhouène; Besbes, Ahmed; Komodakis, Nikos; Deux, Jean-François; Maatouk, Mezri; Rahmouni, Alain; Bassez, Guillaume; Fleury, Gilles; Paragios, Nikos

2009-01-01

In this paper, we present a manifold clustering method fo the classification of fibers obtained from diffusion tensor images (DTI) of the human skeletal muscle. Using a linear programming formulation of prototype-based clustering, we propose a novel fiber classification algorithm over manifolds that circumvents the necessity to embed the data in low dimensional spaces and determines automatically the number of clusters. Furthermore, we propose the use of angular Hilbertian metrics between multivariate normal distributions to define a family of distances between tensors that we generalize to fibers. These metrics are used to approximate the geodesic distances over the fiber manifold. We also discuss the case where only geodesic distances to a reduced set of landmark fibers are available. The experimental validation of the method is done using a manually annotated significant dataset of DTI of the calf muscle for healthy and diseased subjects.

A Type D Non-Vacuum Spacetime with Causality Violating Curves, and Its Physical Interpretation

NASA Astrophysics Data System (ADS)

Ahmed, Faizuddin

2017-12-01

We present a topologically trivial, non-vacuum solution of the Einstein’s field equations in four dimensions, which is regular everywhere. The metric admits circular closed timelike curves, which appear beyond the null curve, and these timelike curves are linearly stable under linear perturbations. Additionally, the spacetime admits null geodesics curve, which are not closed, and the metric is of type D in the Petrov classification scheme. The stress-energy tensor anisotropic fluid satisfy the different energy conditions and a generalization of Equation-of-State parameter of perfect fluid p=ω ρ . The metric admits a twisting, shearfree, nonexapnding timelike geodesic congruence. Finally, the physical interpretation of this solution, based on the study of the equation of the geodesics deviation, will be presented.

Complete integrability of geodesics in toric Sasaki-Einstein spaces

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2016-01-01

We describe a method for constructing Killing-Yano tensors on toric Sasaki- Einstein manifolds using their geometrical properties. We take advantage of the fact that the metric cones of these spaces are Calabi-Yau manifolds. The complete list of special Killing forms can be extracted making use of the description of the Calabi-Yau manifolds in terms of toric data. This general procedure for toric Sasaki-Einstein manifolds is exemplified in the case of the 5-dimensional spaces Yp,q and T1,1. Finally we discuss the integrability of geodesic motion in these spaces.

Tensor networks from kinematic space

DOE PAGES

Czech, Bartlomiej; Lamprou, Lampros; McCandlish, Samuel; ...

2016-07-20

We point out that the MERA network for the ground state of a 1+1-dimensional conformal field theory has the same structural features as kinematic space — the geometry of CFT intervals. In holographic theories kinematic space becomes identified with the space of bulk geodesics studied in integral geometry. We argue that in these settings MERA is best viewed as a discretization of the space of bulk geodesics rather than of the bulk geometry itself. As a test of this kinematic proposal, we compare the MERA representation of the thermofield-double state with the space of geodesics in the two-sided BTZ geometry,more » obtaining a detailed agreement which includes the entwinement sector. In conclusion, we discuss how the kinematic proposal can be extended to excited states by generalizing MERA to a broader class of compression networks.« less

Snyder-like modified gravity in Newton's spacetime

NASA Astrophysics Data System (ADS)

Leiva, Carlos

This work is focused on searching a geodesic interpretation of the dynamics of a particle under the effects of a Snyder-like deformation in the background of the Kepler problem. In order to accomplish that task, a Newtonian spacetime is used. Newtonian spacetime is not a metric manifold, but allows to introduce a torsion-free connection in order to interpret the dynamic equations of the deformed Kepler problem as geodesics in a curved spacetime. These geodesics and the curvature terms of the Riemann and Ricci tensors show a mass and a fundamental length dependence as expected, but are velocity-independent that is a feature present in other classical approaches to the problem. In this sense, the effect of introducing a deformed algebra is examined and the corresponding curvature terms calculated, as well as the modifications of the integrals of motion.

Continuous Optimization on Constraint Manifolds

NASA Technical Reports Server (NTRS)

Dean, Edwin B.

1988-01-01

This paper demonstrates continuous optimization on the differentiable manifold formed by continuous constraint functions. The first order tensor geodesic differential equation is solved on the manifold in both numerical and closed analytic form for simple nonlinear programs. Advantages and disadvantages with respect to conventional optimization techniques are discussed.

Comment on the Exterior Solutions and Their Geometry in Scalar-Tensor Theories of Gravity

NASA Astrophysics Data System (ADS)

Tsuchida, T.; Watanabe, K.

1999-01-01

We study series of stationary solutions with asymptotic flatness properties in the Einstein-Maxwell-free scalar system because they are locally equivalent to the exterior solutions in some class of scalar-tensor theories of gravity. First, we classify spherical exterior solutions into two types of solutions, an apparently black hole type solution and an apparently worm hole type solution. The solutions contain three parameters, and we clarify their physical significance. Second, we reduce the field equations for the axisymmetric exterior solutions. We find that the reduced equations are partially the same as the Ernst equations. As simple examples, we derive new series of static, axisymmetric exterior solutions, which correspond to Voorhees's solutions. We then establish a non-trivial relation between the spherical exterior solutions and our new solutions. Finally, since null geodesics have conformally invariant properties, we study the local geometry of the exterior solutions by using the optical scalar equations and find some anomalous behavior of the null geodesics.

Separability of black holes in string theory

NASA Astrophysics Data System (ADS)

Keeler, Cynthia; Larsen, Finn

2012-10-01

We analyze the origin of separability for rotating black holes in string theory, considering both massless and massive geodesic equations as well as the corresponding wave equations. We construct a conformal Killing-Stackel tensor for a general class of black holes with four independent charges, then identify two-charge configurations where enhancement to an exact Killing-Stackel tensor is possible. We show that further enhancement to a conserved Killing-Yano tensor is possible only for the special case of Kerr-Newman black holes. We construct natural null congruences for all these black holes and use the results to show that only the Kerr-Newman black holes are algebraically special in the sense of Petrov. Modifying the asymptotic behavior by the subtraction procedure that induces an exact SL(2)2 also preserves only the conformal Killing-Stackel tensor. Similarly, we find that a rotating Kaluza-Klein black hole possesses a conformal Killing-Stackel tensor but has no further enhancements.

Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green's functions

NASA Technical Reports Server (NTRS)

Chrzanowski, P. L.; Misner, C. W.

1974-01-01

The scalar, electromagnetic, and gravitational geodesic-synchrotron-radiation (GSR) spectra are determined for the case of a test particle moving on a highly relativistic circular orbit about a rotating (Kerr) black hole. It is found that the spectral shape depends only weakly on the value of the angular-momentum parameter (a/M) of the black hole, but the total radiated power drops unexpectedly for a value of at least 0.95 and vanishes as the value approaches unity. A spin-dependent factor (involving the inner product of the polarization of a radiated quantum with the source) is isolated to explain the dependence of the spectral shape on the spin of the radiated field. Although the scalar wave equation is solved by separation of variables, this procedure is avoided for the vector and tensor cases by postulating a sum-over-states expansion for the Green's function similar to that found to hold in the scalar case. The terms in this sum, significant for GSR, can then be evaluated in the geometric-optics approximation without requiring the use of vector or tensor spherical harmonics.

Spacetime encodings. II. Pictures of integrability

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

Brink, Jeandrew

I visually explore the features of geodesic orbits in arbitrary stationary axisymmetric vacuum (SAV) spacetimes that are constructed from a complex Ernst potential. Some of the geometric features of integrable and chaotic orbits are highlighted. The geodesic problem for these SAV spacetimes is rewritten as a 2 degree of freedom problem and the connection between current ideas in dynamical systems and the study of two manifolds sought. The relationship between the Hamilton-Jacobi equations, canonical transformations, constants of motion, and Killing tensors are commented on. Wherever possible I illustrate the concepts by means of examples from general relativity. This investigation ismore » designed to build the readers' intuition about how integrability arises, and to summarize some of the known facts about 2 degree of freedom systems. Evidence is given, in the form of an orbit-crossing structure, that geodesics in SAV spacetimes might admit a fourth constant of motion that is quartic in momentum (by contrast with Kerr spacetime, where Carter's fourth constant is quadratic)« less

On the Landau-de Gennes Elastic Energy of a Q-Tensor Model for Soft Biaxial Nematics

NASA Astrophysics Data System (ADS)

Mucci, Domenico; Nicolodi, Lorenzo

2017-12-01

In the Landau-de Gennes theory of liquid crystals, the propensities for alignments of molecules are represented at each point of the fluid by an element Q of the vector space S_0 of 3× 3 real symmetric traceless matrices, or Q-tensors. According to Longa and Trebin (1989), a biaxial nematic system is called soft biaxial if the tensor order parameter Q satisfies the constraint tr(Q^2) = {const}. After the introduction of a Q-tensor model for soft biaxial nematic systems and the description of its geometric structure, we address the question of coercivity for the most common four-elastic-constant form of the Landau-de Gennes elastic free-energy (Iyer et al. 2015) in this model. For a soft biaxial nematic system, the tensor field Q takes values in a four-dimensional sphere S^4_ρ of radius ρ ≤ √{2/3} in the five-dimensional space S_0 with inner product < Q, P > = tr(QP). The rotation group it{SO}(3) acts orthogonally on S_0 by conjugation and hence induces an action on S^4_ρ \\subset {S}_0. This action has generic orbits of codimension one that are diffeomorphic to an eightfold quotient S^3/H of the unit three-sphere S^3, where H={± 1, ± i, ± j, ± k} is the quaternion group, and has two degenerate orbits of codimension two that are diffeomorphic to the projective plane RP^2. Each generic orbit can be interpreted as the order parameter space of a constrained biaxial nematic system and each singular orbit as the order parameter space of a constrained uniaxial nematic system. It turns out that S^4_ρ is a cohomogeneity one manifold, i.e., a manifold with a group action whose orbit space is one-dimensional. Another important geometric feature of the model is that the set Σ _ρ of diagonal Q-tensors of fixed norm ρ is a (geodesic) great circle in S^4_ρ which meets every orbit of S^4_ρ orthogonally and is then a section for S^4_ρ in the sense of the general theory of canonical forms. We compute necessary and sufficient coercivity conditions for the elastic energy by exploiting the it{SO}(3)-invariance of the elastic energy (frame-indifference), the existence of the section Σ _ρ for S^4_ρ , and the geometry of the model, which allow us to reduce to a suitable invariant problem on (an arc of) Σ _ρ . Our approach can ultimately be seen as an application of the general method of reduction of variables, or cohomogeneity method.

Test-particle motion in the nonsymmetric gravitation theory

NASA Astrophysics Data System (ADS)

Moffat, J. W.

1987-06-01

A derivation of the motion of test particles in the nonsymmetric gravitational theory (NGT) is given using the field equations in the presence of matter. The motion of the particle is governed by the Christoffel symbols, which are formed from the symmetric part of the fundamental tensor gμν, as well as by a tensorial piece determined by the skew part of the contracted curvature tensor Rμν. Given the energy-momentum tensor for a perfect fluid and the definition of a test particle in the NGT, the equations of motion follow from the conservation laws. The tensorial piece in the equations of motion describes a new force in nature that acts on the conserved charge in a body. Particles that carry this new charge do not follow geodesic world lines in the NGT, whereas photons do satisfy geodesic equations of motion and the equivalence principle of general relativity. Astronomical predictions, based on the exact static, spherically symmetric solution of the field equations in a vacuum and the test-particle equations of motion, are derived in detail. The maximally extended coordinates that remove the event-horizon singularities in the static, spherically symmetric solution are presented. It is shown how an inward radially falling test particle can be prevented from forming an event horizon for a value greater than a specified critical value of the source charge. If a test particle does fall through an event horizon, then it must continue to fall until it reaches the singularity at r=0.

Hidden symmetries and supergravity solutions

NASA Astrophysics Data System (ADS)

Santillan, Osvaldo P.

2012-04-01

The role of Killing and Killing-Yano tensors for studying the geodesic motion of the particle and the superparticle in a curved background is reviewed. Additionally, the Papadopoulos list [G. Papadopoulos, Class. Quantum Grav. 25, 105016 (2008)], 10.1088/0264-9381/25/10/105016 for Killing-Yano tensors in G structures is reproduced by studying the torsion types these structures admit. The Papadopoulos list deals with groups G appearing in the Berger classification, and we enlarge the list by considering additional G structures which are not of the Berger type. Possible applications of these results in the study of supersymmetric particle actions and in the AdS/CFT correspondence are outlined.

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

Alani, Ivo; Santillán, Osvaldo P., E-mail: firenzecita@hotmail.com, E-mail: osantil@dm.uba.ar

In the present work some generalizations of the Hawking singularity theorems in the context of f ( R ) theories are presented. The main assumptions are: the matter fields stress energy tensor satisfies the condition ( T {sub ij} −( g {sub ij} /2) T ) k {sup i} k {sup j} ≥ 0 for any generic unit time like field k {sup i} ; the scalaron takes bounded positive values during its evolution and the resulting space time is globally hyperbolic. Then, if there exist a Cauchy hyper-surface Σ for which the expansion parameter θ of the geodesic congruencemore » emanating orthogonally from Σ satisfies some specific bounds, then the resulting space time is geodesically incomplete. Some mathematical results of reference [92] are very important for proving this. The generalized theorems presented here apply directly for some specific models such as the Hu-Sawicki or Starobinsky ones [27,38]. For other scenarios, some extra assumptions should be implemented in order to have a geodesically incomplete space time. The hypothesis considered in this text are sufficient, but not necessary. In other words, their negation does not imply that a singularity is absent.« less

Generalized minimal principle for rotor filaments.

PubMed

Dierckx, Hans; Wellner, Marcel; Bernus, Olivier; Verschelde, Henri

2015-05-01

To a reaction-diffusion medium with an inhomogeneous anisotropic diffusion tensor D, we add a fourth spatial dimension such that the determinant of the diffusion tensor is constant in four dimensions. We propose a generalized minimal principle for rotor filaments, stating that the scroll wave filament strives to minimize its surface area in the higher-dimensional space. As a consequence, stationary scroll wave filaments in the original 3D medium are geodesic curves with respect to the metric tensor G=det(D)D(-1). The theory is confirmed by numerical simulations for positive and negative filament tension and a model with a non-stationary spiral core. We conclude that filaments in cardiac tissue with positive tension preferentially reside or anchor in regions where cardiac cells are less interconnected, such as portions of the cardiac wall with a large number of cleavage planes.

Gaussian mixtures on tensor fields for segmentation: applications to medical imaging.

PubMed

de Luis-García, Rodrigo; Westin, Carl-Fredrik; Alberola-López, Carlos

2011-01-01

In this paper, we introduce a new approach for tensor field segmentation based on the definition of mixtures of Gaussians on tensors as a statistical model. Working over the well-known Geodesic Active Regions segmentation framework, this scheme presents several interesting advantages. First, it yields a more flexible model than the use of a single Gaussian distribution, which enables the method to better adapt to the complexity of the data. Second, it can work directly on tensor-valued images or, through a parallel scheme that processes independently the intensity and the local structure tensor, on scalar textured images. Two different applications have been considered to show the suitability of the proposed method for medical imaging segmentation. First, we address DT-MRI segmentation on a dataset of 32 volumes, showing a successful segmentation of the corpus callosum and favourable comparisons with related approaches in the literature. Second, the segmentation of bones from hand radiographs is studied, and a complete automatic-semiautomatic approach has been developed that makes use of anatomical prior knowledge to produce accurate segmentation results. Copyright © 2010 Elsevier Ltd. All rights reserved.

Quantifying polymer deformation in viscoelastic turbulence: the geometric decomposition and a Riemannian approach to scalar measures

NASA Astrophysics Data System (ADS)

Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer; Gayme, Dennice

2017-11-01

We develop a new framework to quantify the fluctuating behaviour of the conformation tensor in viscoelastic turbulent flows. This framework addresses two shortcomings of the classical approach based on Reynolds decomposition: the fluctuating part of the conformation tensor is not guaranteed to be positive definite and it does not consistently represent polymer expansions and contractions about the mean. Our approach employs a geometric decomposition that yields a positive-definite fluctuating conformation tensor with a clear physical interpretation as a deformation to the mean conformation. We propose three scalar measures of this fluctuating conformation tensor, which respect the non-Euclidean Riemannian geometry of the manifold of positive-definite tensors: fluctuating polymer volume, geodesic distance from the mean, and an anisotropy measure. We use these scalar quantities to investigate drag-reduced viscoelastic turbulent channel flow. Our approach establishes a systematic method to study viscoelastic turbulence. It also uncovers interesting phenomena that are not apparent using traditional analysis tools, including a logarithmic decrease in anisotropy of the mean conformation tensor away from the wall and polymer fluctuations peaking beyond the buffer layer. This work has been partially funded by the following NSF Grants: CBET-1652244, OCE-1633124, CBET-1511937.

White matter degeneration in schizophrenia: a comparative diffusion tensor analysis

NASA Astrophysics Data System (ADS)

Ingalhalikar, Madhura A.; Andreasen, Nancy C.; Kim, Jinsuh; Alexander, Andrew L.; Magnotta, Vincent A.

2010-03-01

Schizophrenia is a serious and disabling mental disorder. Diffusion tensor imaging (DTI) studies performed on schizophrenia have demonstrated white matter degeneration either due to loss of myelination or deterioration of fiber tracts although the areas where the changes occur are variable across studies. Most of the population based studies analyze the changes in schizophrenia using scalar indices computed from the diffusion tensor such as fractional anisotropy (FA) and relative anisotropy (RA). The scalar measures may not capture the complete information from the diffusion tensor. In this paper we have applied the RADTI method on a group of 9 controls and 9 patients with schizophrenia. The RADTI method converts the tensors to log-Euclidean space where a linear regression model is applied and hypothesis testing is performed between the control and patient groups. Results show that there is a significant difference in the anisotropy between patients and controls especially in the parts of forceps minor, superior corona radiata, anterior limb of internal capsule and genu of corpus callosum. To check if the tensor analysis gives a better idea of the changes in anisotropy, we compared the results with voxelwise FA analysis as well as voxelwise geodesic anisotropy (GA) analysis.

Conservation laws and evolution schemes in geodesic, hydrodynamic, and magnetohydrodynamic flows

NASA Astrophysics Data System (ADS)

Markakis, Charalampos; Uryū, Kōji; Gourgoulhon, Eric; Nicolas, Jean-Philippe; Andersson, Nils; Pouri, Athina; Witzany, Vojtěch

2017-09-01

Carter and Lichnerowicz have established that barotropic fluid flows are conformally geodesic and obey Hamilton's principle. This variational approach can accommodate neutral, or charged and poorly conducting, fluids. We show that, unlike what has been previously thought, this approach can also accommodate perfectly conducting magnetofluids, via the Bekenstein-Oron description of ideal magnetohydrodynamics. When Noether symmetries associated with Killing vectors or tensors are present in geodesic flows, they lead to constants of motion polynomial in the momenta. We generalize these concepts to hydrodynamic flows. Moreover, the Hamiltonian descriptions of ideal magnetohydrodynamics allow one to cast the evolution equations into a hyperbolic form useful for evolving rotating or binary compact objects with magnetic fields in numerical general relativity. In this framework, Ertel's potential vorticity theorem for baroclinic fluids arises as a special case of a conservation law valid for any Hamiltonian system. Moreover, conserved circulation laws, such as those of Kelvin, Alfvén and Bekenstein-Oron, emerge simply as special cases of the Poincaré-Cartan integral invariant of Hamiltonian systems. We use this approach to obtain an extension of Kelvin's theorem to baroclinic (nonisentropic) fluids, based on a temperature-dependent time parameter. We further extend this result to perfectly or poorly conducting baroclinic magnetoflows. Finally, in the barotropic case, such magnetoflows are shown to also be geodesic, albeit in a Finsler (rather than Riemann) space.

Planning maximally smooth hand movements constrained to nonplanar workspaces.

PubMed

Liebermann, Dario G; Krasovsky, Tal; Berman, Sigal

2008-11-01

The article characterizes hand paths and speed profiles for movements performed in a nonplanar, 2-dimensional workspace (a hemisphere of constant curvature). The authors assessed endpoint kinematics (i.e., paths and speeds) under the minimum-jerk model assumptions and calculated minimal amplitude paths (geodesics) and the corresponding speed profiles. The authors also calculated hand speeds using the 2/3 power law. They then compared modeled results with the empirical observations. In all, 10 participants moved their hands forward and backward from a common starting position toward 3 targets located within a hemispheric workspace of small or large curvature. Comparisons of modeled observed differences using 2-way RM-ANOVAs showed that movement direction had no clear influence on hand kinetics (p < .05). Workspace curvature affected the hand paths, which seldom followed geodesic lines. Constraining the paths to different curvatures did not affect the hand speed profiles. Minimum-jerk speed profiles closely matched the observations and were superior to those predicted by 2/3 power law (p < .001). The authors conclude that speed and path cannot be unambiguously linked under the minimum-jerk assumption when individuals move the hand in a nonplanar 2-dimensional workspace. In such a case, the hands do not follow geodesic paths, but they preserve the speed profile, regardless of the geometric features of the workspace.

Conformal killing tensors and covariant Hamiltonian dynamics

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

Cariglia, M., E-mail: marco@iceb.ufop.br; Gibbons, G. W., E-mail: G.W.Gibbons@damtp.cam.ac.uk; LE STUDIUM, Loire Valley Institute for Advanced Studies, Tours and Orleans

2014-12-15

A covariant algorithm for deriving the conserved quantities for natural Hamiltonian systems is combined with the non-relativistic framework of Eisenhart, and of Duval, in which the classical trajectories arise as geodesics in a higher dimensional space-time, realized by Brinkmann manifolds. Conserved quantities which are polynomial in the momenta can be built using time-dependent conformal Killing tensors with flux. The latter are associated with terms proportional to the Hamiltonian in the lower dimensional theory and with spectrum generating algebras for higher dimensional quantities of order 1 and 2 in the momenta. Illustrations of the general theory include the Runge-Lenz vector formore » planetary motion with a time-dependent gravitational constant G(t), motion in a time-dependent electromagnetic field of a certain form, quantum dots, the Hénon-Heiles and Holt systems, respectively, providing us with Killing tensors of rank that ranges from one to six.« less

CUDA-Accelerated Geodesic Ray-Tracing for Fiber Tracking

PubMed Central

van Aart, Evert; Sepasian, Neda; Jalba, Andrei; Vilanova, Anna

2011-01-01

Diffusion Tensor Imaging (DTI) allows to noninvasively measure the diffusion of water in fibrous tissue. By reconstructing the fibers from DTI data using a fiber-tracking algorithm, we can deduce the structure of the tissue. In this paper, we outline an approach to accelerating such a fiber-tracking algorithm using a Graphics Processing Unit (GPU). This algorithm, which is based on the calculation of geodesics, has shown promising results for both synthetic and real data, but is limited in its applicability by its high computational requirements. We present a solution which uses the parallelism offered by modern GPUs, in combination with the CUDA platform by NVIDIA, to significantly reduce the execution time of the fiber-tracking algorithm. Compared to a multithreaded CPU implementation of the same algorithm, our GPU mapping achieves a speedup factor of up to 40 times. PMID:21941525

Terrestrial Sagnac delay constraining modified gravity models

NASA Astrophysics Data System (ADS)

Karimov, R. Kh.; Izmailov, R. N.; Potapov, A. A.; Nandi, K. K.

2018-04-01

Modified gravity theories include f(R)-gravity models that are usually constrained by the cosmological evolutionary scenario. However, it has been recently shown that they can also be constrained by the signatures of accretion disk around constant Ricci curvature Kerr-f(R0) stellar sized black holes. Our aim here is to use another experimental fact, viz., the terrestrial Sagnac delay to constrain the parameters of specific f(R)-gravity prescriptions. We shall assume that a Kerr-f(R0) solution asymptotically describes Earth's weak gravity near its surface. In this spacetime, we shall study oppositely directed light beams from source/observer moving on non-geodesic and geodesic circular trajectories and calculate the time gap, when the beams re-unite. We obtain the exact time gap called Sagnac delay in both cases and expand it to show how the flat space value is corrected by the Ricci curvature, the mass and the spin of the gravitating source. Under the assumption that the magnitude of corrections are of the order of residual uncertainties in the delay measurement, we derive the allowed intervals for Ricci curvature. We conclude that the terrestrial Sagnac delay can be used to constrain the parameters of specific f(R) prescriptions. Despite using the weak field gravity near Earth's surface, it turns out that the model parameter ranges still remain the same as those obtained from the strong field accretion disk phenomenon.

Lienard--Wiechert fields and general relativity

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

Newman, E.T.

1974-01-01

An analogy is extablished between the Lienard-Weichart solutions of the Maxwell equations and the Robinson-Trautman solutions of the einstein equations by virtue of the fact that a principal null vector field of either the Maxwell or Weyl tensor in each case satisfies the following four conditions: (1) The field is a geodesic field, (2) it has nonvanishing divergence, (3) it is shear free, and (4) it is twist (or curl) free. (auth)

Hidden symmetries on Kerr-NUT-(A)dS metrics of Einstein-Sasaki type

NASA Astrophysics Data System (ADS)

Visinescu, Mihai

2013-01-01

The hidden symmetries of higher dimensional Euclideanised Kerr-NUT-(A)dS metrics are investigated. In certain scaling limits these metrics are related to the Einstein-Sasaki ones. The complete set of Killing-Yano tensors of the Einstein-Sasaki spaces are presented. For this purpose the Killing forms of the Calabi-Yau cone over the Einstein-Sasaki manifold are constructed. Two new Killing forms on Einstein-Sasaki manifolds are identified associated with the complex volume form of the cone manifolds. As a concrete example we present the complete set of Killing-Yano tensors on the five-dimensional Einstein-Sasaki Y(p, q) spaces. The corresponding hidden symmetries are not anomalous and the geodesic equations are superintegrable.

Robotic Online Path Planning on Point Cloud.

PubMed

Liu, Ming

2016-05-01

This paper deals with the path-planning problem for mobile wheeled- or tracked-robot which drive in 2.5-D environments, where the traversable surface is usually considered as a 2-D-manifold embedded in a 3-D ambient space. Specially, we aim at solving the 2.5-D navigation problem using raw point cloud as input. The proposed method is independent of traditional surface parametrization or reconstruction methods, such as a meshing process, which generally has high-computational complexity. Instead, we utilize the output of 3-D tensor voting framework on the raw point clouds. The computation of tensor voting is accelerated by optimized implementation on graphics computation unit. Based on the tensor voting results, a novel local Riemannian metric is defined using the saliency components, which helps the modeling of the latent traversable surface. Using the proposed metric, we prove that the geodesic in the 3-D tensor space leads to rational path-planning results by experiments. Compared to traditional methods, the results reveal the advantages of the proposed method in terms of smoothing the robot maneuver while considering the minimum travel distance.

Integrability of geodesics in near-horizon extremal geometries: Case of Myers-Perry black holes in arbitrary dimensions

NASA Astrophysics Data System (ADS)

Demirchian, Hovhannes; Nersessian, Armen; Sadeghian, Saeedeh; Sheikh-Jabbari, M. M.

2018-05-01

We investigate dynamics of probe particles moving in the near-horizon limit of extremal Myers-Perry black holes in arbitrary dimensions. Employing ellipsoidal coordinates we show that this problem is integrable and separable, extending the results of the odd dimensional case discussed by Hakobyan et al. [Phys. Lett. B 772, 586 (2017)., 10.1016/j.physletb.2017.07.028]. We find the general solution of the Hamilton-Jacobi equations for these systems and present explicit expressions for the Liouville integrals and discuss Killing tensors and the associated constants of motion. We analyze special cases of the background near-horizon geometry were the system possesses more constants of motion and is hence superintegrable. Finally, we consider a near-horizon extremal vanishing horizon case which happens for Myers-Perry black holes in odd dimensions and show that geodesic equations on this geometry are also separable and work out its integrals of motion.

Controlling effect of geometrically defined local structural changes on chaotic Hamiltonian systems.

PubMed

Ben Zion, Yossi; Horwitz, Lawrence

2010-04-01

An effective characterization of chaotic conservative Hamiltonian systems in terms of the curvature associated with a Riemannian metric tensor derived from the structure of the Hamiltonian has been extended to a wide class of potential models of standard form through definition of a conformal metric. The geodesic equations reproduce the Hamilton equations of the original potential model through an inverse map in the tangent space. The second covariant derivative of the geodesic deviation in this space generates a dynamical curvature, resulting in (energy-dependent) criteria for unstable behavior different from the usual Lyapunov criteria. We show here that this criterion can be constructively used to modify locally the potential of a chaotic Hamiltonian model in such a way that stable motion is achieved. Since our criterion for instability is local in coordinate space, these results provide a minimal method for achieving control of a chaotic system.

Elementary Development of the Gravitational Self-Force

NASA Astrophysics Data System (ADS)

Detweiler, Steven

The gravitational field of a particle of small mass m moving through curved spacetime, with metric g ab , is naturally and easily decomposed into two parts each of which satisfies the perturbed Einstein equations through O(m). One part is an inhomogeneous field h ab S which, near the particle, looks like the Coulomb m / r field with tidal distortion from the local Riemann tensor. This singular field is defined in a neighborhood of the small particle and does not depend upon boundary conditions or upon the behavior of the source in either the past or the future. The other part is a homogeneous field h ab R. In a perturbative analysis, the motion of the particle is then best described as being a geodesic in the metric g ab + h ab R. This geodesic motion includes all of the effects which might be called radiation reaction and conservative effects as well.

Generalised Eisenhart lift of the Toda chain

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

Cariglia, Marco, E-mail: marco@iceb.ufop.br; Gibbons, Gary, E-mail: g.w.gibbons@damtp.cam.ac.uk

The Toda chain of nearest neighbour interacting particles on a line can be described both in terms of geodesic motion on a manifold with one extra dimension, the Eisenhart lift, or in terms of geodesic motion in a symmetric space with several extra dimensions. We examine the relationship between these two realisations and discover that the symmetric space is a generalised, multi-particle Eisenhart lift of the original problem that reduces to the standard Eisenhart lift. Such generalised Eisenhart lift acts as an inverse Kaluza-Klein reduction, promoting coupling constants to momenta in higher dimension. In particular, isometries of the generalised liftmore » metric correspond to energy preserving transformations that mix coordinates and coupling constants. A by-product of the analysis is that the lift of the Toda Lax pair can be used to construct higher rank Killing tensors for both the standard and generalised lift metrics.« less

Upper limit on NUT charge from the observed terrestrial Sagnac effect

NASA Astrophysics Data System (ADS)

Kulbakova, A.; Karimov, R. Kh; Izmailov, R. N.; Nandi, K. K.

2018-06-01

The exact Sagnac delay in the Kerr–Taub–NUT (Newman–Unti–Tamburino) spacetime is derived in the equatorial plane for non-geodesic as well as geodesic circular orbits. The resulting formula, being exact, can be directly applied to motion in the vicinity of any spinning object including black holes but here we are considering only the terrestrial case since observational data are available. The formula reveals that, in the limit of spin , the delay does not vanish. This fact is similar to the non-vanishing of Lense–Thirring precession under even though the two effects originate from different premises. Assuming a reasonable input that the Kerr–Taub–NUT corrections are subsumed in the average residual uncertainty in the measured Sagnac delay, we compute upper limits on the NUT charge n. It is found that the upper limits on n are far larger than the Earth’s gravitational mass, which has not been detected in observations, implying that the Sagnac effect cannot constrain n to smaller values near zero. We find a curious difference between the delays for non-geodesic and geodesic clock orbits and point out its implication for the well known ‘twin paradox’ of special relativity.

Modified gravity (MOG), the speed of gravitational radiation and the event GW170817/GRB170817A

NASA Astrophysics Data System (ADS)

Green, M. A.; Moffat, J. W.; Toth, V. T.

2018-05-01

Modified gravity (MOG) is a covariant, relativistic, alternative gravitational theory whose field equations are derived from an action that supplements the spacetime metric tensor with vector and scalar fields. Both gravitational (spin 2) and electromagnetic waves travel on null geodesics of the theory's one metric. MOG satisfies the weak equivalence principle and is consistent with observations of the neutron star merger and gamma ray burster event GW170817/GRB170817A.

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

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

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

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

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

NASA Astrophysics Data System (ADS)

Woolgar, Eric; Wylie, William

2016-02-01

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

Two-body problem in scalar-tensor theories as a deformation of general relativity: An effective-one-body approach

NASA Astrophysics Data System (ADS)

Julié, Félix-Louis; Deruelle, Nathalie

2017-06-01

In this paper we address the two-body problem in massless scalar-tensor (ST) theories within an effective-one-body (EOB) framework. We focus on the first building block of the EOB approach, that is, mapping the conservative part of the two-body dynamics onto the geodesic motion of a test particle in an effective external metric. To this end, we first deduce the second post-Keplerian (2PK) Hamiltonian of the two-body problem from the known 2PK Lagrangian. We then build, by means of a canonical transformation, a ST deformation of the general relativistic EOB Hamiltonian that allows us to incorporate the scalar-tensor (2PK) corrections to the currently best available general relativity EOB results. This EOB-ST Hamiltonian defines a resummation of the dynamics that may provide information on the strong-field regime, in particular, the ISCO location and associated orbital frequency, and can be compared to, other, e.g., tidal, corrections.

Maximal analytic extension and hidden symmetries of the dipole black ring

NASA Astrophysics Data System (ADS)

Armas, Jay

2011-12-01

We construct analytic extensions across the Killing horizons of non-extremal and extremal dipole black rings in Einstein-Maxwell’s theory using different methods. We show that these extensions are non-globally hyperbolic, have multiple asymptotically flat regions and, in the non-extremal case, are also maximal and timelike complete. Moreover, we find that in both cases, the causal structure of the maximally extended spacetime resembles that of the four-dimensional Reissner-Nordström black hole. Furthermore, motivated by the physical interpretation of one of these extensions, we find a separable solution to the Hamilton-Jacobi equation corresponding to zero energy null geodesics and relate it to the existence of a conformal Killing tensor and a conformal Killing-Yano tensor in a specific dimensionally reduced spacetime.

Classification of Hamilton-Jacobi separation in orthogonal coordinates with diagonal curvature

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

Rajaratnam, Krishan, E-mail: k2rajara@uwaterloo.ca; McLenaghan, Raymond G., E-mail: rgmclenaghan@uwaterloo.ca

2014-08-15

We find all orthogonal metrics where the geodesic Hamilton-Jacobi equation separates and the Riemann curvature tensor satisfies a certain equation (called the diagonal curvature condition). All orthogonal metrics of constant curvature satisfy the diagonal curvature condition. The metrics we find either correspond to a Benenti system or are warped product metrics where the induced metric on the base manifold corresponds to a Benenti system. Furthermore, we show that most metrics we find are characterized by concircular tensors; these metrics, called Kalnins-Eisenhart-Miller metrics, have an intrinsic characterization which can be used to obtain them on a given space. In conjunction withmore » other results, we show that the metrics we found constitute all separable metrics for Riemannian spaces of constant curvature and de Sitter space.« less

Gravitation: Foundations and Frontiers

NASA Astrophysics Data System (ADS)

Padmanabhan, T.

2010-01-01

1. Special relativity; 2. Scalar and electromagnetic fields in special relativity; 3. Gravity and spacetime geometry: the inescapable connection; 4. Metric tensor, geodesics and covariant derivative; 5. Curvature of spacetime; 6. Einstein's field equations and gravitational dynamics; 7. Spherically symmetric geometry; 8. Black holes; 9. Gravitational waves; 10. Relativistic cosmology; 11. Differential forms and exterior calculus; 12. Hamiltonian structure of general relativity; 13. Evolution of cosmological perturbations; 14. Quantum field theory in curved spacetime; 15. Gravity in higher and lower dimensions; 16. Gravity as an emergent phenomenon; Notes; Index.

The exponentiated Hencky energy: anisotropic extension and case studies

NASA Astrophysics Data System (ADS)

Schröder, Jörg; von Hoegen, Markus; Neff, Patrizio

2017-10-01

In this paper we propose an anisotropic extension of the isotropic exponentiated Hencky energy, based on logarithmic strain invariants. Unlike other elastic formulations, the isotropic exponentiated Hencky elastic energy has been derived solely on differential geometric grounds, involving the geodesic distance of the deformation gradient \\varvec{F} to the group of rotations. We formally extend this approach towards anisotropy by defining additional anisotropic logarithmic strain invariants with the help of suitable structural tensors and consider our findings for selected case studies.

Cosmological aspects of the Eisenhart-Duval lift

NASA Astrophysics Data System (ADS)

Cariglia, M.; Galajinsky, A.; Gibbons, G. W.; Horvathy, P. A.

2018-04-01

A cosmological extension of the Eisenhart-Duval metric is constructed by incorporating a cosmic scale factor and the energy-momentum tensor into the scheme. The dynamics of the spacetime is governed by the Ermakov-Milne-Pinney equation. Killing isometries include spatial translations and rotations, Newton-Hooke boosts and translation in the null direction. Geodesic motion in Ermakov-Milne-Pinney cosmoi is analyzed. The derivation of the Ermakov-Lewis invariant, the Friedmann equations and the Dmitriev-Zel'dovich equations within the Eisenhart-Duval framework is presented.

Geodesic least squares regression on information manifolds

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

Verdoolaege, Geert, E-mail: geert.verdoolaege@ugent.be

We present a novel regression method targeted at situations with significant uncertainty on both the dependent and independent variables or with non-Gaussian distribution models. Unlike the classic regression model, the conditional distribution of the response variable suggested by the data need not be the same as the modeled distribution. Instead they are matched by minimizing the Rao geodesic distance between them. This yields a more flexible regression method that is less constrained by the assumptions imposed through the regression model. As an example, we demonstrate the improved resistance of our method against some flawed model assumptions and we apply thismore » to scaling laws in magnetic confinement fusion.« less

Riemann curvature of a boosted spacetime geometry

NASA Astrophysics Data System (ADS)

Battista, Emmanuele; Esposito, Giampiero; Scudellaro, Paolo; Tramontano, Francesco

2016-10-01

The ultrarelativistic boosting procedure had been applied in the literature to map the metric of Schwarzschild-de Sitter spacetime into a metric describing de Sitter spacetime plus a shock-wave singularity located on a null hypersurface. This paper evaluates the Riemann curvature tensor of the boosted Schwarzschild-de Sitter metric by means of numerical calculations, which make it possible to reach the ultrarelativistic regime gradually by letting the boost velocity approach the speed of light. Thus, for the first time in the literature, the singular limit of curvature, through Dirac’s δ distribution and its derivatives, is numerically evaluated for this class of spacetimes. Moreover, the analysis of the Kretschmann invariant and the geodesic equation shows that the spacetime possesses a “scalar curvature singularity” within a 3-sphere and it is possible to define what we here call “boosted horizon”, a sort of elastic wall where all particles are surprisingly pushed away, as numerical analysis demonstrates. This seems to suggest that such “boosted geometries” are ruled by a sort of “antigravity effect” since all geodesics seem to refuse to enter the “boosted horizon” and are “reflected” by it, even though their initial conditions are aimed at driving the particles toward the “boosted horizon” itself. Eventually, the equivalence with the coordinate shift method is invoked in order to demonstrate that all δ2 terms appearing in the Riemann curvature tensor give vanishing contribution in distributional sense.

A Riemannian framework for orientation distribution function computing.

PubMed

Cheng, Jian; Ghosh, Aurobrata; Jiang, Tianzi; Deriche, Rachid

2009-01-01

Compared with Diffusion Tensor Imaging (DTI), High Angular Resolution Imaging (HARDI) can better explore the complex microstructure of white matter. Orientation Distribution Function (ODF) is used to describe the probability of the fiber direction. Fisher information metric has been constructed for probability density family in Information Geometry theory and it has been successfully applied for tensor computing in DTI. In this paper, we present a state of the art Riemannian framework for ODF computing based on Information Geometry and sparse representation of orthonormal bases. In this Riemannian framework, the exponential map, logarithmic map and geodesic have closed forms. And the weighted Frechet mean exists uniquely on this manifold. We also propose a novel scalar measurement, named Geometric Anisotropy (GA), which is the Riemannian geodesic distance between the ODF and the isotropic ODF. The Renyi entropy H1/2 of the ODF can be computed from the GA. Moreover, we present an Affine-Euclidean framework and a Log-Euclidean framework so that we can work in an Euclidean space. As an application, Lagrange interpolation on ODF field is proposed based on weighted Frechet mean. We validate our methods on synthetic and real data experiments. Compared with existing Riemannian frameworks on ODF, our framework is model-free. The estimation of the parameters, i.e. Riemannian coordinates, is robust and linear. Moreover it should be noted that our theoretical results can be used for any probability density function (PDF) under an orthonormal basis representation.

Geodesic-light-cone coordinates and the Bianchi I spacetime

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

Fleury, Pierre; Nugier, Fabien; Fanizza, Giuseppe, E-mail: pierre.fleury@uct.ac.za, E-mail: fnugier@ntu.edu.tw, E-mail: giuseppe.fanizza@ba.infn.it

The geodesic-light-cone (GLC) coordinates are a useful tool to analyse light propagation and observations in cosmological models. In this article, we propose a detailed, pedagogical, and rigorous introduction to this coordinate system, explore its gauge degrees of freedom, and emphasize its interest when geometric optics is at stake. We then apply the GLC formalism to the homogeneous and anisotropic Bianchi I cosmology. More than a simple illustration, this application (i) allows us to show that the Weinberg conjecture according to which gravitational lensing does not affect the proper area of constant-redshift surfaces is significantly violated in a globally anisotropic universe;more » and (ii) offers a glimpse into new ways to constrain cosmic isotropy from the Hubble diagram.« less

Particle localization, spinor two-valuedness, and Fermi quantization of tensor systems

NASA Technical Reports Server (NTRS)

Reifler, Frank; Morris, Randall

1994-01-01

Recent studies of particle localization shows that square-integrable positive energy bispinor fields in a Minkowski space-time cannot be physically distinguished from constrained tensor fields. In this paper we generalize this result by characterizing all classical tensor systems, which admit Fermi quantization, as those having unitary Lie-Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form.

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

Krtous, Pavel; Frolov, Valeri P.; Kubiznak, David

We prove that the most general solution of the Einstein equations with the cosmological constant which admits a principal conformal Killing-Yano tensor is the Kerr-NUT-(A)dS metric. Even when the Einstein equations are not imposed, any spacetime admitting such hidden symmetry can be written in a canonical form which guarantees the following properties: it is of the Petrov type D, it allows the separation of variables for the Hamilton-Jacobi, Klein-Gordon, and Dirac equations, the geodesic motion in such a spacetime is completely integrable. These results naturally generalize the results obtained earlier in four dimensions.

Constraining black holes with light boson hair and boson stars using epicyclic frequencies and quasiperiodic oscillations

NASA Astrophysics Data System (ADS)

Franchini, Nicola; Pani, Paolo; Maselli, Andrea; Gualtieri, Leonardo; Herdeiro, Carlos A. R.; Radu, Eugen; Ferrari, Valeria

2017-06-01

Light bosonic fields are ubiquitous in extensions of the Standard Model. Even when minimally coupled to gravity, these fields might evade the assumptions of the black-hole no-hair theorems and give rise to spinning black holes which can be drastically different from the Kerr metric. Furthermore, they allow for self-gravitating compact solitons, known as (scalar or Proca) boson stars. The quasiperiodic oscillations (QPOs) observed in the x-ray flux emitted by accreting compact objects carry information about the strong-field region, thus providing a powerful tool to constrain deviations from Kerr's geometry and to search for exotic compact objects. By using the relativistic precession model as a proxy to interpret the QPOs in terms of geodesic frequencies, we investigate how the QPO frequencies could be used to test the no-hair theorem and the existence of light bosonic fields near accreting compact objects. We show that a detection of two QPO triplets with current sensitivity can already constrain these models and that the future eXTP mission or a LOFT-like mission can set very stringent constraints on black holes with bosonic hair and on (scalar or Proca) boson stars. The peculiar geodesic structure of compact scalar/Proca boson stars implies that these objects can easily be ruled out as alternative models for x-ray source GRO J1655-40.

Tilted shear-free axially symmetric fluids

NASA Astrophysics Data System (ADS)

Herrera, L.; Di Prisco, A.; Carot, J.

2018-06-01

We carry on a systematic study of the physical properties of axially symmetric fluid distributions, which appear to be geodesic, shearfree, irrotational, nondissipative, and purely electric, for the comoving congruence of observers, from the point of view of the tilted congruence. The vanishing of the magnetic part of the Weyl tensor for the comoving congruence of observers, suggests that no gravitational radiation is produced during the evolution of the system. Instead, the magnetic part of the Weyl tensor as measured by tilted observers is nonvanishing (as well as the shear, the four-acceleration, the vorticity and the dissipation), giving rise to a flux of gravitational radiation that can be characterized through the super-Poynting vector. This result strengthens further the relevance of the role of observers in the description of a physical system. An explanation of this dual interpretation in terms of the information theory, is provided.

Using tensor-based morphometry to detect structural brain abnormalities in rats with adolescent intermittent alcohol exposure

NASA Astrophysics Data System (ADS)

Paniagua, Beatriz; Ehlers, Cindy; Crews, Fulton; Budin, Francois; Larson, Garrett; Styner, Martin; Oguz, Ipek

2011-03-01

Understanding the effects of adolescent binge drinking that persist into adulthood is a crucial public health issue. Adolescent intermittent ethanol exposure (AIE) is an animal model that can be used to investigate these effects in rodents. In this work, we investigate the application of a particular image analysis technique, tensor-based morphometry, for detecting anatomical differences between AIE and control rats using Diffusion Tensor Imaging (DTI). Deformation field analysis is a popular method for detecting volumetric changes analyzing Jacobian determinants calculated on deformation fields. Recent studies showed that computing deformation field metrics on the full deformation tensor, often referred to as tensor-based morphometry (TBM), increases the sensitivity to anatomical differences. In this paper we conduct a comprehensive TBM study for precisely locating differences between control and AIE rats. Using a DTI RARE sequence designed for minimal geometric distortion, 12-directional images were acquired postmortem for control and AIE rats (n=9). After preprocessing, average images for the two groups were constructed using an unbiased atlas building approach. We non-rigidly register the two atlases using Large Deformation Diffeomorphic Metric Mapping, and analyze the resulting deformation field using TBM. In particular, we evaluate the tensor determinant, geodesic anisotropy, and deformation direction vector (DDV) on the deformation field to detect structural differences. This yields data on the local amount of growth, shrinkage and the directionality of deformation between the groups. We show that TBM can thus be used to measure group morphological differences between rat populations, demonstrating the potential of the proposed framework.

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

Klima, Matej; Kucharik, MIlan; Shashkov, Mikhail Jurievich

We analyze several new and existing approaches for limiting tensor quantities in the context of deviatoric stress remapping in an ALE numerical simulation of elastic flow. Remapping and limiting of the tensor component-by-component is shown to violate radial symmetry of derived variables such as elastic energy or force. Therefore, we have extended the symmetry-preserving Vector Image Polygon algorithm, originally designed for limiting vector variables. This limiter constrains the vector (in our case a vector of independent tensor components) within the convex hull formed by the vectors from surrounding cells – an equivalent of the discrete maximum principle in scalar variables.more » We compare this method with a limiter designed specifically for deviatoric stress limiting which aims to constrain the J 2 invariant that is proportional to the specific elastic energy and scale the tensor accordingly. We also propose a method which involves remapping and limiting the J 2 invariant independently using known scalar techniques. The deviatoric stress tensor is then scaled to match this remapped invariant, which guarantees conservation in terms of elastic energy.« less

Tensor non-Gaussianity from axion-gauge-fields dynamics: parameter search

NASA Astrophysics Data System (ADS)

Agrawal, Aniket; Fujita, Tomohiro; Komatsu, Eiichiro

2018-06-01

We calculate the bispectrum of scale-invariant tensor modes sourced by spectator SU(2) gauge fields during inflation in a model containing a scalar inflaton, a pseudoscalar axion and SU(2) gauge fields. A large bispectrum is generated in this model at tree-level as the gauge fields contain a tensor degree of freedom, and its production is dominated by self-coupling of the gauge fields. This is a unique feature of non-Abelian gauge theory. The shape of the tensor bispectrum is approximately an equilateral shape for 3lesssim mQlesssim 4, where mQ is an effective dimensionless mass of the SU(2) field normalised by the Hubble expansion rate during inflation. The amplitude of non-Gaussianity of the tensor modes, characterised by the ratio Bh/P2h, is inversely proportional to the energy density fraction of the gauge field. This ratio can be much greater than unity, whereas the ratio from the vacuum fluctuation of the metric is of order unity. The bispectrum is effective at constraining large mQ regions of the parameter space, whereas the power spectrum constrains small mQ regions.

Using Perturbation Theory to Reduce Noise in Diffusion Tensor Fields

PubMed Central

Bansal, Ravi; Staib, Lawrence H.; Xu, Dongrong; Laine, Andrew F.; Liu, Jun; Peterson, Bradley S.

2009-01-01

We propose the use of Perturbation theory to reduce noise in Diffusion Tensor (DT) fields. Diffusion Tensor Imaging (DTI) encodes the diffusion of water molecules along different spatial directions in a positive-definite, 3 × 3 symmetric tensor. Eigenvectors and eigenvalues of DTs allow the in vivo visualization and quantitative analysis of white matter fiber bundles across the brain. The validity and reliability of these analyses are limited, however, by the low spatial resolution and low Signal-to-Noise Ratio (SNR) in DTI datasets. Our procedures can be applied to improve the validity and reliability of these quantitative analyses by reducing noise in the tensor fields. We model a tensor field as a three-dimensional Markov Random Field and then compute the likelihood and the prior terms of this model using Perturbation theory. The prior term constrains the tensor field to be smooth, whereas the likelihood term constrains the smoothed tensor field to be similar to the original field. Thus, the proposed method generates a smoothed field that is close in structure to the original tensor field. We evaluate the performance of our method both visually and quantitatively using synthetic and real-world datasets. We quantitatively assess the performance of our method by computing the SNR for eigenvalues and the coherence measures for eigenvectors of DTs across tensor fields. In addition, we quantitatively compare the performance of our procedures with the performance of one method that uses a Riemannian distance to compute the similarity between two tensors, and with another method that reduces noise in tensor fields by anisotropically filtering the diffusion weighted images that are used to estimate diffusion tensors. These experiments demonstrate that our method significantly increases the coherence of the eigenvectors and the SNR of the eigenvalues, while simultaneously preserving the fine structure and boundaries between homogeneous regions, in the smoothed tensor field. PMID:19540791

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

Sergyeyev, Artur; Krtous, Pavel; Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holesovickach 2, Prague

We consider the Klein-Gordon equation in generalized higher-dimensional Kerr-NUT-(A)dS spacetime without imposing any restrictions on the functional parameters characterizing the metric. We establish commutativity of the second-order operators constructed from the Killing tensors found in [J. High Energy Phys. 02 (2007) 004] and show that these operators, along with the first-order operators originating from the Killing vectors, form a complete set of commuting symmetry operators (i.e., integrals of motion) for the Klein-Gordon equation. Moreover, we demonstrate that the separated solutions of the Klein-Gordon equation obtained in [J. High Energy Phys. 02 (2007) 005] are joint eigenfunctions for all of thesemore » operators. We also present an explicit form of the zero mode for the Klein-Gordon equation with zero mass. In the semiclassical approximation we find that the separated solutions of the Hamilton-Jacobi equation for geodesic motion are also solutions for a set of Hamilton-Jacobi-type equations which correspond to the quadratic conserved quantities arising from the above Killing tensors.« less

Flat monodromies and a Moduli Space Size Conjecture

NASA Astrophysics Data System (ADS)

Hebecker, Arthur; Henkenjohann, Philipp; Witkowski, Lukas T.

2017-12-01

We investigate how super-Planckian axions can arise when type IIB 3-form flux is used to restrict a two-axion field space to a one-dimensional winding trajectory. If one does not attempt to address notoriously complicated issues like Kähler moduli stabilization, SUSY-breaking and inflation, this can be done very explicitly. We show that the presence of flux generates flat monodromies in the moduli space which we therefore call `Monodromic Moduli Space'. While we do indeed find long axionic trajectories, these are non-geodesic. Moreover, the length of geodesics remains highly constrained, in spite of the (finite) monodromy group introduced by the flux. We attempt to formulate this in terms of a `Moduli Space Size Conjecture'. Interesting mathematical structures arise in that the relevant spaces turn out to be fundamental domains of congruence subgroups of the modular group. In addition, new perspectives on inflation in string theory emerge.

Shaping of arm configuration space by prescription of non-Euclidean metrics with applications to human motor control

NASA Astrophysics Data System (ADS)

Biess, Armin

2013-01-01

The study of the kinematic and dynamic features of human arm movements provides insights into the computational strategies underlying human motor control. In this paper a differential geometric approach to movement control is taken by endowing arm configuration space with different non-Euclidean metric structures to study the predictions of the generalized minimum-jerk (MJ) model in the resulting Riemannian manifold for different types of human arm movements. For each metric space the solution of the generalized MJ model is given by reparametrized geodesic paths. This geodesic model is applied to a variety of motor tasks ranging from three-dimensional unconstrained movements of a four degree of freedom arm between pointlike targets to constrained movements where the hand location is confined to a surface (e.g., a sphere) or a curve (e.g., an ellipse). For the latter speed-curvature relations are derived depending on the boundary conditions imposed (periodic or nonperiodic) and the compatibility with the empirical one-third power law is shown. Based on these theoretical studies and recent experimental findings, I argue that geodesics may be an emergent property of the motor system and that the sensorimotor system may shape arm configuration space by learning metric structures through sensorimotor feedback.

2T Physics, Weyl Symmetry and the Geodesic Completion of Black Hole Backgrounds

NASA Astrophysics Data System (ADS)

Araya Quezada, Ignacio Jesus

In this thesis, we discuss two different contexts where the idea of gauge symmetry and duality is used to solve the dynamics of physical systems. The first of such contexts is 2T-physics in the worldline in d+2 dimensions, where the principle of Sp(2,R) gauge symmetry in phase space is used to relate different 1T systems in (d -- 1) + 1 dimensions, such as a free relativistic particle, and a relativistic particle in an arbitrary V(x2) potential. Because each 1T shadow system corresponds to a particular gauge of the underlying symmetry, there is a web of dualities relating them. The dualities between said systems amount to canonical transformations including time and energy, which allows the different systems to be described by different Hamiltonians, and consequently, to correspond to different dynamics in the (d -- 1)+1 phase space. The second context, corresponds to a Weyl invariant scalar-tensor theory of gravity, obtained as a direct prediction of 2T gravity, where the Weyl symmetry is used to obtain geodesically complete dynamics both in the context of cosmology and black hole (BH) backgrounds. The geodesic incompleteness of usual Einstein gravity, in the presence of singularities in spacetime, is related to the definition of the Einstein gauge, which fixes the sign and magnitude of the gravitational constant GN, and therefore misses the existence of antigravity patches, which are expected to arise generically just beyond gravitational singularities. The definition of the Einstein gauge can be generalized by incorporating a sign flip of the gravitational constant GN at the transitions between gravity and antigravity. This sign is a key aspect that allows us to define geodesically complete dynamics in cosmology and in BH backgrounds, particularly, in the case of the 4D Schwarzschild BH and the 2D stringy BH. The complete nature of particle geodesics in these BH backgrounds is exhibited explicitly at the classical level, and the extension of these results to the behavior of fields, interpreted as the first quantized particle wavefunctions in the backgrounds is discussed for the 2D stringy BH case. It is shown that the geodesic completion also carries through at the quantum level, by examining the effective potential of the corresponding Schwarzschild problem. Also, in the case of the 2D stringy BH, it is explicitly shown that the spacetime has a multi-sheeted structure, which resolves possible issues like the presence of closed timelike curves. This multi-sheeted structure is conjectured to exist also for the 4D Schwarzschild BH (and perhaps for all BH backgrounds). The main new results of this thesis are the extended network of dualities, in the form of canonical transformations including time and energy, between the 1T dynamical systems, presented in Chapter 2 and the construction of the geodesically complete 4D Schwarzschild and 2D stringy black hole backgrounds, presented in Chapter 3.

Constraining the break of spatial diffeomorphism invariance with Planck data

NASA Astrophysics Data System (ADS)

Graef, L. L.; Benetti, M.; Alcaniz, J. S.

2017-07-01

The current most accepted paradigm for the early universe cosmology, the inflationary scenario, shows a good agreement with the recent Cosmic Microwave Background (CMB) and polarization data. However, when the inflation consistency relation is relaxed, these observational data exclude a larger range of red tensor tilt values, prevailing the blue ones which are not predicted by the minimal inflationary models. Recently, it has been shown that the assumption of spatial diffeomorphism invariance breaking (SDB) in the context of an effective field theory of inflation leads to interesting observational consequences. Among them, the possibility of generating a blue tensor spectrum, which can recover the specific consistency relation of the String Gas Cosmology, for a certain choice of parameters. We use the most recent CMB data to constrain the SDB model and test its observational viability through a Bayesian analysis assuming as reference an extended ΛCDM+tensor perturbation model, which considers a power-law tensor spectrum parametrized in terms of the tensor-to-scalar ratio, r, and the tensor spectral index, nt. If the inflation consistency relation is imposed, r=-8 nt, we obtain a strong evidence in favor of the reference model whereas if such relation is relaxed, a weak evidence in favor of the model with diffeomorphism breaking is found. We also use the same CMB data set to make an observational comparison between the SDB model, standard inflation and String Gas Cosmology.

Black Holes, Hidden Symmetry and Complete Integrability: Brief Review

NASA Astrophysics Data System (ADS)

Frolov, Valeri P.

This chapter contains a brief review of the remarkable properties of higher dimensional rotating black holes with the spherical topology of the horizon. We demonstrate that these properties are connected with and generated by a special geometrical object, the Principal Conformal Killing-Yano tensor (PCKYT). The most general solution, describing such black holes, Kerr-NUT-ADS metric, admits this structure. Moreover a solution of the Einstein Equations with (or without) a cosmological constant which possesses PCKYT is the Kerr-NUT-ADS metric. This object (PCKYT) is responsible for such remarkable properties of higher dimensional rotating black holes as: (i) complete integrability of geodesic equations and (ii) complete separation of variables of the important field equations.

The centripetal force law and the equation of motion for a particle on a curved hypersurface

NASA Astrophysics Data System (ADS)

Hu, L. D.; Lian, D. K.; Liu, Q. H.

2016-12-01

It is pointed out that the current form of the extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version; for it is established without regard to the fact that the particle can never depart from the geodesics on the surface. Once this fact is taken into consideration, the equation takes the same form as that for the centripetal force law, provided that the symbols are re-interpreted so that the law is applicable for higher dimensions. The controversial issue of constructing operator forms of these equations is addressed, and our studies show the quantization of constrained system based on the extrinsic equation of motion is preferable.

Initial conditions for cosmological perturbations

NASA Astrophysics Data System (ADS)

Ashtekar, Abhay; Gupt, Brajesh

2017-02-01

Penrose proposed that the big bang singularity should be constrained by requiring that the Weyl curvature vanishes there. The idea behind this past hypothesis is attractive because it constrains the initial conditions for the universe in geometric terms and is not confined to a specific early universe paradigm. However, the precise statement of Penrose’s hypothesis is tied to classical space-times and furthermore restricts only the gravitational degrees of freedom. These are encapsulated only in the tensor modes of the commonly used cosmological perturbation theory. Drawing inspiration from the underlying idea, we propose a quantum generalization of Penrose’s hypothesis using the Planck regime in place of the big bang, and simultaneously incorporating tensor as well as scalar modes. Initial conditions selected by this generalization constrain the universe to be as homogeneous and isotropic in the Planck regime as permitted by the Heisenberg uncertainty relations.

Black holes, hidden symmetries, and complete integrability

NASA Astrophysics Data System (ADS)

Frolov, Valeri P.; Krtouš, Pavel; Kubizňák, David

2017-11-01

The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional Kerr-NUT-(A)dS black hole spacetimes. We start with discussion of the Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a "seed object" which generates all these symmetries. It determines the form of the geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.

Black holes, hidden symmetries, and complete integrability.

PubMed

Frolov, Valeri P; Krtouš, Pavel; Kubizňák, David

2017-01-01

The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of higher-dimensional black holes with the spherical horizon topology and described by the Kerr-NUT-(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional Kerr-NUT-(A)dS black hole spacetimes. We start with discussion of the Killing and Killing-Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a "seed object" which generates all these symmetries. It determines the form of the geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton-Jacobi, Klein-Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.

f( R, L m ) gravity

NASA Astrophysics Data System (ADS)

Harko, Tiberiu; Lobo, Francisco S. N.

2010-11-01

We generalize the f( R) type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R and of the matter Lagrangian L m . We obtain the gravitational field equations in the metric formalism, as well as the equations of motion for test particles, which follow from the covariant divergence of the energy-momentum tensor. The equations of motion for test particles can also be derived from a variational principle in the particular case in which the Lagrangian density of the matter is an arbitrary function of the energy density of the matter only. Generally, the motion is non-geodesic, and it takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equation of motion is also considered, and a procedure for obtaining the energy-momentum tensor of the matter is presented. The gravitational field equations and the equations of motion for a particular model in which the action of the gravitational field has an exponential dependence on the standard general relativistic Hilbert-Einstein Lagrange density are also derived.

C1 finite elements on non-tensor-product 2d and 3d manifolds

PubMed Central

Nguyen, Thien; Karčiauskas, Kęstutis; Peters, Jörg

2015-01-01

Geometrically continuous (Gk) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are Ck also for non-tensor-product layout. This paper describes and analyzes one such concrete C1 geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed G1 surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Remarkably, for Poisson’s equation on the disk using interior vertices of valence 3 and symmetric layout, we observe O(h3) convergence in the L∞ norm for this family of elements. Numerical experiments confirm the elements to be effective for solving the trivariate Poisson equation on the solid cylinder, deformations thereof (a turbine blade), modeling and computing geodesics on smooth free-form surfaces via the heat equation, for solving the biharmonic equation on the disk and for Koiter-type thin-shell analysis. PMID:26594070

C1 finite elements on non-tensor-product 2d and 3d manifolds.

PubMed

Nguyen, Thien; Karčiauskas, Kęstutis; Peters, Jörg

2016-01-01

Geometrically continuous ( G k ) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are C k also for non-tensor-product layout. This paper describes and analyzes one such concrete C 1 geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed G 1 surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Remarkably, for Poisson's equation on the disk using interior vertices of valence 3 and symmetric layout, we observe O ( h 3 ) convergence in the L ∞ norm for this family of elements. Numerical experiments confirm the elements to be effective for solving the trivariate Poisson equation on the solid cylinder, deformations thereof (a turbine blade), modeling and computing geodesics on smooth free-form surfaces via the heat equation, for solving the biharmonic equation on the disk and for Koiter-type thin-shell analysis.

Constraining the break of spatial diffeomorphism invariance with Planck data

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

Graef, L.L.; Benetti, M.; Alcaniz, J.S., E-mail: leilagraef@on.br, E-mail: micolbenetti@on.br, E-mail: alcaniz@on.br

The current most accepted paradigm for the early universe cosmology, the inflationary scenario, shows a good agreement with the recent Cosmic Microwave Background (CMB) and polarization data. However, when the inflation consistency relation is relaxed, these observational data exclude a larger range of red tensor tilt values, prevailing the blue ones which are not predicted by the minimal inflationary models. Recently, it has been shown that the assumption of spatial diffeomorphism invariance breaking (SDB) in the context of an effective field theory of inflation leads to interesting observational consequences. Among them, the possibility of generating a blue tensor spectrum, whichmore » can recover the specific consistency relation of the String Gas Cosmology, for a certain choice of parameters. We use the most recent CMB data to constrain the SDB model and test its observational viability through a Bayesian analysis assuming as reference an extended ΛCDM+tensor perturbation model, which considers a power-law tensor spectrum parametrized in terms of the tensor-to-scalar ratio, r , and the tensor spectral index, n {sub t} . If the inflation consistency relation is imposed, r =−8 n {sub t} , we obtain a strong evidence in favor of the reference model whereas if such relation is relaxed, a weak evidence in favor of the model with diffeomorphism breaking is found. We also use the same CMB data set to make an observational comparison between the SDB model, standard inflation and String Gas Cosmology.« less

Gravitational instantons from minimal surfaces

NASA Astrophysics Data System (ADS)

Aliev, A. N.; Hortaçsu, M.; Kalayci, J.; Nutku, Y.

1999-02-01

Physical properties of gravitational instantons which are derivable from minimal surfaces in three-dimensional Euclidean space are examined using the Newman-Penrose formalism for Euclidean signature. The gravitational instanton that corresponds to the helicoid minimal surface is investigated in detail. This is a metric of Bianchi type 0264-9381/16/2/024/img9, or E(2), which admits a hidden symmetry due to the existence of a quadratic Killing tensor. It leads to a complete separation of variables in the Hamilton-Jacobi equation for geodesics, as well as in Laplace's equation for a massless scalar field. The scalar Green function can be obtained in closed form, which enables us to calculate the vacuum fluctuations of a massless scalar field in the background of this instanton.

New two-metric theory of gravity with prior geometry

NASA Technical Reports Server (NTRS)

Lightman, A. P.; Lee, D. L.

1973-01-01

A Lagrangian-based metric theory of gravity is developed with three adjustable constants and two tensor fields, one of which is a nondynamic 'flat space metric' eta. With a suitable cosmological model and a particular choice of the constants, the 'post-Newtonian limit' of the theory agrees, in the current epoch, with that of general relativity theory (GRT); consequently the theory is consistent with current gravitation experiments. Because of the role of eta, the gravitational 'constant' G is time-dependent and gravitational waves travel null geodesics of eta rather than the physical metric g. Gravitational waves possess six degrees of freedom. The general exact static spherically-symmetric solution is a four-parameter family. Future experimental tests of the theory are discussed.

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

NASA Astrophysics Data System (ADS)

Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian

The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.

A Review of Tensors and Tensor Signal Processing

NASA Astrophysics Data System (ADS)

Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.

Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.

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.

Integrability of spinning particle motion in higher-dimensional rotating black hole spacetimes.

PubMed

Kubizňák, David; Cariglia, Marco

2012-02-03

We study the motion of a classical spinning particle (with spin degrees of freedom described by a vector of Grassmann variables) in higher-dimensional general rotating black hole spacetimes with a cosmological constant. In all dimensions n we exhibit n bosonic functionally independent integrals of spinning particle motion, corresponding to explicit and hidden symmetries generated from the principal conformal Killing-Yano tensor. Moreover, we demonstrate that in 4-, 5-, 6-, and 7-dimensional black hole spacetimes such integrals are in involution, proving the bosonic part of the motion integrable. We conjecture that the same conclusion remains valid in all higher dimensions. Our result generalizes the result of Page et al. [Phys. Rev. Lett. 98, 061102 (2007)] on complete integrability of geodesic motion in these spacetimes.

Diffeomorphometry and geodesic positioning systems for human anatomy.

PubMed

Miller, Michael I; Younes, Laurent; Trouvé, Alain

2014-03-01

The Computational Anatomy project has largely been a study of large deformations within a Riemannian framework as an efficient point of view for generating metrics between anatomical configurations. This approach turns D'Arcy Thompson's comparative morphology of human biological shape and form into a metrizable space. Since the metric is constructed based on the geodesic length of the flows of diffeomorphisms connecting the forms, we call it diffeomorphometry . Just as importantly, since the flows describe algebraic group action on anatomical submanifolds and associated functional measurements, they become the basis for positioning information, which we term geodesic positioning . As well the geodesic connections provide Riemannian coordinates for locating forms in the anatomical orbit, which we call geodesic coordinates . These three components taken together - the metric, geodesic positioning of information, and geodesic coordinates - we term the geodesic positioning system . We illustrate via several examples in human and biological coordinate systems and machine learning of the statistical representation of shape and form.

The concept of geodesic curvature applied to optical surfaces.

PubMed

Barbero, Sergio

2015-07-01

To propose geodesic curvature as a metric to characterise how an optical surface locally differs from axial symmetry. To derive equations to evaluate geodesic curvatures of arbitrary surfaces expressed in polar coordinates. The concept of geodesic curvature is explained in detail as compared to other curvature-based metrics. Starting with the formula representing a surface as function of polar coordinates, an equation for the geodesic curvature is obtained depending only on first and second radial and first order angular derivatives of the surface function. The potential of the geodesic curvature is illustrated using different surface tests. Geodesic curvature reveals local axial asymmetries more sharply than other types of curvatures such as normal curvatures. Geodesic curvature maps could be used to characterise local axial asymmetries for relevant optometry applications such as corneal topography anomalies (keratoconus) or ophthalmic lens metrology. © 2015 The Authors Ophthalmic & Physiological Optics © 2015 The College of Optometrists.

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD

NASA Astrophysics Data System (ADS)

Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Gambhir, Arjun S.; Orginos, Kostas; Savage, Martin J.; Shanahan, Phiala E.; Wagman, Michael L.; Winter, Frank; Nplqcd Collaboration

2018-04-01

Complete flavor decompositions of the matrix elements of the scalar, axial, and tensor currents in the proton, deuteron, diproton, and 3He at SU(3)-symmetric values of the quark masses corresponding to a pion mass mπ˜806 MeV are determined using lattice quantum chromodynamics. At the physical quark masses, the scalar interactions constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor interactions of nuclei constrain their spin content, integrated transversity, and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elements of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. The calculated matrix elements differ from, and are typically smaller than, naive single-nucleon estimates. Given the particularly large, O (10 %), size of nuclear effects in the scalar matrix elements, contributions from correlated multinucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.

An infinite set of Ward identities for adiabatic modes in cosmology

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

Hinterbichler, Kurt; Hui, Lam; Khoury, Justin, E-mail: khinterbichler@perimeterinstitute.ca, E-mail: lh399@columbia.edu, E-mail: jkhoury@sas.upenn.edu

2014-01-01

We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate N+1-point correlation functions with a soft-momentum scalar or tensor mode to a symmetry transformation on N-point correlation functions of hard-momentum modes. We derive these consistency relations from Ward identities for an infinite tower of non-linearly realized global symmetries governing scalar and tensor perturbations. These symmetries can be labeled by an integer n. At each order n, the consistency relations constrain — completely for n = 0,1, and partially for n ≥ 2 — themore » q{sup n} behavior of the soft limits. The identities at n = 0 recover Maldacena's original consistency relations for a soft scalar and tensor mode, n = 1 gives the recently-discovered conformal consistency relations, and the identities for n ≥ 2 are new. As a check, we verify directly that the n = 2 identity is satisfied by known correlation functions in slow-roll inflation.« less

Scalar-tensor theories and modified gravity in the wake of GW170817

NASA Astrophysics Data System (ADS)

Langlois, David; Saito, Ryo; Yamauchi, Daisuke; Noui, Karim

2018-03-01

Theories of dark energy and modified gravity can be strongly constrained by astrophysical or cosmological observations, as illustrated by the recent observation of the gravitational wave event GW170817 and of its electromagnetic counterpart GRB 170817A, which showed that the speed of gravitational waves, cg , is the same as the speed of light, within deviations of order 10-15 . This observation implies severe restrictions on scalar-tensor theories, in particular theories whose action depends on second derivatives of a scalar field. Working in the very general framework of degenerate higher-order scalar-tensor (DHOST) theories, which encompass Horndeski and beyond Horndeski theories, we present the DHOST theories that satisfy cg=c . We then examine, for these theories, the screening mechanism that suppresses scalar interactions on small scales, namely the Vainshtein mechanism, and compute the corresponding gravitational laws for a nonrelativistic spherical body. We show that it can lead to a deviation from standard gravity inside matter, parametrized by three coefficients which satisfy a consistency relation and can be constrained by present and future astrophysical observations.

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD

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

Chang, Emmanuel; Davoudi, Zohreh; Detmold, William

Complete flavor decompositions of the matrix elements of the scalar, axial, and tensor currents in the proton, deuteron, diproton, and 3He at SU(3)-symmetric values of the quark masses corresponding to a pion mass m π~806 MeV are determined using lattice quantum chromodynamics. At the physical quark masses, the scalar interactions constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor interactions of nuclei constrain their spin content, integrated transversity, and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elementsmore » of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. The calculated matrix elements differ from, and are typically smaller than, naive single-nucleon estimates. Given the particularly large, O(10%), size of nuclear effects in the scalar matrix elements, contributions from correlated multinucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.« less

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD

DOE PAGES

Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; ...

2018-04-13

Complete flavor decompositions of the matrix elements of the scalar, axial, and tensor currents in the proton, deuteron, diproton, and 3He at SU(3)-symmetric values of the quark masses corresponding to a pion mass m π~806 MeV are determined using lattice quantum chromodynamics. At the physical quark masses, the scalar interactions constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor interactions of nuclei constrain their spin content, integrated transversity, and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elementsmore » of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. The calculated matrix elements differ from, and are typically smaller than, naive single-nucleon estimates. Given the particularly large, O(10%), size of nuclear effects in the scalar matrix elements, contributions from correlated multinucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.« less

Scalar, Axial, and Tensor Interactions of Light Nuclei from Lattice QCD.

PubMed

Chang, Emmanuel; Davoudi, Zohreh; Detmold, William; Gambhir, Arjun S; Orginos, Kostas; Savage, Martin J; Shanahan, Phiala E; Wagman, Michael L; Winter, Frank

2018-04-13

Complete flavor decompositions of the matrix elements of the scalar, axial, and tensor currents in the proton, deuteron, diproton, and ^{3}He at SU(3)-symmetric values of the quark masses corresponding to a pion mass m_{π}∼806  MeV are determined using lattice quantum chromodynamics. At the physical quark masses, the scalar interactions constrain mean-field models of nuclei and the low-energy interactions of nuclei with potential dark matter candidates. The axial and tensor interactions of nuclei constrain their spin content, integrated transversity, and the quark contributions to their electric dipole moments. External fields are used to directly access the quark-line connected matrix elements of quark bilinear operators, and a combination of stochastic estimation techniques is used to determine the disconnected sea-quark contributions. The calculated matrix elements differ from, and are typically smaller than, naive single-nucleon estimates. Given the particularly large, O(10%), size of nuclear effects in the scalar matrix elements, contributions from correlated multinucleon effects should be quantified in the analysis of dark matter direct-detection experiments using nuclear targets.

Newton-based optimization for Kullback-Leibler nonnegative tensor factorizations

DOE PAGES

Plantenga, Todd; Kolda, Tamara G.; Hansen, Samantha

2015-04-30

Tensor factorizations with nonnegativity constraints have found application in analysing data from cyber traffic, social networks, and other areas. We consider application data best described as being generated by a Poisson process (e.g. count data), which leads to sparse tensors that can be modelled by sparse factor matrices. In this paper, we investigate efficient techniques for computing an appropriate canonical polyadic tensor factorization based on the Kullback–Leibler divergence function. We propose novel subproblem solvers within the standard alternating block variable approach. Our new methods exploit structure and reformulate the optimization problem as small independent subproblems. We employ bound-constrained Newton andmore » quasi-Newton methods. Finally, we compare our algorithms against other codes, demonstrating superior speed for high accuracy results and the ability to quickly find sparse solutions.« less

Hydrogen Burning in Low Mass Stars Constrains Scalar-Tensor Theories of Gravity.

PubMed

Sakstein, Jeremy

2015-11-13

The most general scalar-tensor theories of gravity predict a weakening of the gravitational force inside astrophysical bodies. There is a minimum mass for hydrogen burning in stars that is set by the interplay of plasma physics and the theory of gravity. We calculate this for alternative theories of gravity and find that it is always significantly larger than the general relativity prediction. The observation of several low mass red dwarf stars therefore rules out a large class of scalar-tensor gravity theories and places strong constraints on the cosmological parameters appearing in the effective field theory of dark energy.

Monte Carlo Volcano Seismic Moment Tensors

NASA Astrophysics Data System (ADS)

Waite, G. P.; Brill, K. A.; Lanza, F.

2015-12-01

Inverse modeling of volcano seismic sources can provide insight into the geometry and dynamics of volcanic conduits. But given the logistical challenges of working on an active volcano, seismic networks are typically deficient in spatial and temporal coverage; this potentially leads to large errors in source models. In addition, uncertainties in the centroid location and moment-tensor components, including volumetric components, are difficult to constrain from the linear inversion results, which leads to a poor understanding of the model space. In this study, we employ a nonlinear inversion using a Monte Carlo scheme with the objective of defining robustly resolved elements of model space. The model space is randomized by centroid location and moment tensor eigenvectors. Point sources densely sample the summit area and moment tensors are constrained to a randomly chosen geometry within the inversion; Green's functions for the random moment tensors are all calculated from modeled single forces, making the nonlinear inversion computationally reasonable. We apply this method to very-long-period (VLP) seismic events that accompany minor eruptions at Fuego volcano, Guatemala. The library of single force Green's functions is computed with a 3D finite-difference modeling algorithm through a homogeneous velocity-density model that includes topography, for a 3D grid of nodes, spaced 40 m apart, within the summit region. The homogenous velocity and density model is justified by long wavelength of VLP data. The nonlinear inversion reveals well resolved model features and informs the interpretation through a better understanding of the possible models. This approach can also be used to evaluate possible station geometries in order to optimize networks prior to deployment.

Vaidya spacetime in the diagonal coordinates

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

Berezin, V. A., E-mail: berezin@inr.ac.ru; Dokuchaev, V. I., E-mail: dokuchaev@inr.ac.ru; Eroshenko, Yu. N., E-mail: eroshenko@inr.ac.ru

We have analyzed the transformation from initial coordinates (v, r) of the Vaidya metric with light coordinate v to the most physical diagonal coordinates (t, r). An exact solution has been obtained for the corresponding metric tensor in the case of a linear dependence of the mass function of the Vaidya metric on light coordinate v. In the diagonal coordinates, a narrow region (with a width proportional to the mass growth rate of a black hole) has been detected near the visibility horizon of the Vaidya accreting black hole, in which the metric differs qualitatively from the Schwarzschild metric andmore » cannot be represented as a small perturbation. It has been shown that, in this case, a single set of diagonal coordinates (t, r) is insufficient to cover the entire range of initial coordinates (v, r) outside the visibility horizon; at least three sets of diagonal coordinates are required, the domains of which are separated by singular surfaces on which the metric components have singularities (either g{sub 00} = 0 or g{sub 00} = ∞). The energy–momentum tensor diverges on these surfaces; however, the tidal forces turn out to be finite, which follows from an analysis of the deviation equations for geodesics. Therefore, these singular surfaces are exclusively coordinate singularities that can be referred to as false fire-walls because there are no physical singularities on them. We have also considered the transformation from the initial coordinates to other diagonal coordinates (η, y), in which the solution is obtained in explicit form, and there is no energy–momentum tensor divergence.« less

Integrability of Spinning Particle Motion in Higher-Dimensional Rotating Black Hole Spacetimes

NASA Astrophysics Data System (ADS)

Kubizňák, David; Cariglia, Marco

2012-02-01

We study the motion of a classical spinning particle (with spin degrees of freedom described by a vector of Grassmann variables) in higher-dimensional general rotating black hole spacetimes with a cosmological constant. In all dimensions n we exhibit n bosonic functionally independent integrals of spinning particle motion, corresponding to explicit and hidden symmetries generated from the principal conformal Killing-Yano tensor. Moreover, we demonstrate that in 4-, 5-, 6-, and 7-dimensional black hole spacetimes such integrals are in involution, proving the bosonic part of the motion integrable. We conjecture that the same conclusion remains valid in all higher dimensions. Our result generalizes the result of Page et al. [Phys. Rev. Lett. 98, 061102 (2007)PRLTAO0031-900710.1103/PhysRevLett.98.061102] on complete integrability of geodesic motion in these spacetimes.

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

Connell, Patrick; Frolov, Valeri P.; Kubiznak, David

We obtain and study the equations describing the parallel transport of orthonormal frames along geodesics in a spacetime admitting a nondegenerate, principal, conformal Killing-Yano tensor h. We demonstrate that the operator F, obtained by a projection of h to a subspace orthogonal to the velocity, has in a generic case eigenspaces of dimension not greater than 2. Each of these eigenspaces is independently parallel propagated. This allows one to reduce the parallel transport equations to a set of first order, ordinary, differential equations for the angles of rotation in the 2D eigenspaces. General analysis is illustrated by studying the equationsmore » of the parallel transport in the Kerr-NUT-(A)dS metrics. Examples of three-, four-, and five-dimensional Kerr-NUT-(A)dS are considered, and it is shown that the obtained first order equations can be solved by a separation of variables.« less

Exact geodesic distances in FLRW spacetimes

NASA Astrophysics Data System (ADS)

Cunningham, William J.; Rideout, David; Halverson, James; Krioukov, Dmitri

2017-11-01

Geodesics are used in a wide array of applications in cosmology and astrophysics. However, it is not a trivial task to efficiently calculate exact geodesic distances in an arbitrary spacetime. We show that in spatially flat (3 +1 )-dimensional Friedmann-Lemaître-Robertson-Walker (FLRW) spacetimes, it is possible to integrate the second-order geodesic differential equations, and derive a general method for finding both timelike and spacelike distances given initial-value or boundary-value constraints. In flat spacetimes with either dark energy or matter, whether dust, radiation, or a stiff fluid, we find an exact closed-form solution for geodesic distances. In spacetimes with a mixture of dark energy and matter, including spacetimes used to model our physical universe, there exists no closed-form solution, but we provide a fast numerical method to compute geodesics. A general method is also described for determining the geodesic connectedness of an FLRW manifold, provided only its scale factor.

A regularized approach for geodesic-based semisupervised multimanifold learning.

PubMed

Fan, Mingyu; Zhang, Xiaoqin; Lin, Zhouchen; Zhang, Zhongfei; Bao, Hujun

2014-05-01

Geodesic distance, as an essential measurement for data dissimilarity, has been successfully used in manifold learning. However, most geodesic distance-based manifold learning algorithms have two limitations when applied to classification: 1) class information is rarely used in computing the geodesic distances between data points on manifolds and 2) little attention has been paid to building an explicit dimension reduction mapping for extracting the discriminative information hidden in the geodesic distances. In this paper, we regard geodesic distance as a kind of kernel, which maps data from linearly inseparable space to linear separable distance space. In doing this, a new semisupervised manifold learning algorithm, namely regularized geodesic feature learning algorithm, is proposed. The method consists of three techniques: a semisupervised graph construction method, replacement of original data points with feature vectors which are built by geodesic distances, and a new semisupervised dimension reduction method for feature vectors. Experiments on the MNIST, USPS handwritten digit data sets, MIT CBCL face versus nonface data set, and an intelligent traffic data set show the effectiveness of the proposed algorithm.

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

Source Parameters for Moderate Earthquakes in the Zagros Mountains with Implications for the Depth Extent of Seismicity

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

Adams, A; Brazier, R; Nyblade, A

2009-02-23

Six earthquakes within the Zagros Mountains with magnitudes between 4.9 and 5.7 have been studied to determine their source parameters. These events were selected for study because they were reported in open catalogs to have lower crustal or upper mantle source depths and because they occurred within an area of the Zagros Mountains where crustal velocity structure has been constrained by previous studies. Moment tensor inversion of regional broadband waveforms have been combined with forward modeling of depth phases on short period teleseismic waveforms to constrain source depths and moment tensors. Our results show that all six events nucleated withinmore » the upper crust (<11 km depth) and have thrust mechanisms. This finding supports other studies that call into question the existence of lower crustal or mantle events beneath the Zagros Mountains.« less

Collisional damping of the geodesic acoustic mode with toroidal rotation. I. Viscous damping

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

Gong, Xueyu; Xie, Baoyi; Chen, You

2016-03-15

With the dispersion relation derived for the geodesic acoustic mode in toroidally rotating tokamak plasmas using the fluid model, the effect of the toroidal rotation on the collisional viscous damping of the geodesic acoustic mode is investigated. It is found that the collisional viscous damping of the geodesic acoustic mode has weak increase with respect to the toroidal Mach number.

Constraints on the cosmological parameters from BICEP2, Planck, and WMAP

NASA Astrophysics Data System (ADS)

Cheng, Cheng; Huang, Qing-Guo

2014-11-01

In this paper we constrain the cosmological parameters, in particular the tilt of tensor power spectrum, by adopting Background Imaging of Cosmic Extragalactic Polarization (B2), Planck released in 2013 and Wilkinson Microwaves Anisotropy Probe 9-year Polarization data. We find that a blue tilted tensor power spectrum is preferred at more than confidence level if the data from B2 are assumed to be totally interpreted as the relic gravitational waves, but a scale-invariant tensor power spectrum is consistent with the data once the polarized dust is taken into account. The recent Planck 353 GHz HFI dust polarization data imply that the B2 data are perfectly consistent with there being no gravitational wave signal.

Efficiently computing exact geodesic loops within finite steps.

PubMed

Xin, Shi-Qing; He, Ying; Fu, Chi-Wing

2012-06-01

Closed geodesics, or geodesic loops, are crucial to the study of differential topology and differential geometry. Although the existence and properties of closed geodesics on smooth surfaces have been widely studied in mathematics community, relatively little progress has been made on how to compute them on polygonal surfaces. Most existing algorithms simply consider the mesh as a graph and so the resultant loops are restricted only on mesh edges, which are far from the actual geodesics. This paper is the first to prove the existence and uniqueness of geodesic loop restricted on a closed face sequence; it contributes also with an efficient algorithm to iteratively evolve an initial closed path on a given mesh into an exact geodesic loop within finite steps. Our proposed algorithm takes only an O(k) space complexity and an O(mk) time complexity (experimentally), where m is the number of vertices in the region bounded by the initial loop and the resultant geodesic loop, and k is the average number of edges in the edge sequences that the evolving loop passes through. In contrast to the existing geodesic curvature flow methods which compute an approximate geodesic loop within a predefined threshold, our method is exact and can apply directly to triangular meshes without needing to solve any differential equation with a numerical solver; it can run at interactive speed, e.g., in the order of milliseconds, for a mesh with around 50K vertices, and hence, significantly outperforms existing algorithms. Actually, our algorithm could run at interactive speed even for larger meshes. Besides the complexity of the input mesh, the geometric shape could also affect the number of evolving steps, i.e., the performance. We motivate our algorithm with an interactive shape segmentation example shown later in the paper.

Dark matter as a ghost free conformal extension of Einstein theory

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

Barvinsky, A.O., E-mail: barvin@td.lpi.ru

We discuss ghost free models of the recently suggested mimetic dark matter theory. This theory is shown to be a conformal extension of Einstein general relativity. Dark matter originates from gauging out its local Weyl invariance as an extra degree of freedom which describes a potential flow of the pressureless perfect fluid. For a positive energy density of this fluid the theory is free of ghost instabilities, which gives strong preference to stable configurations with a positive scalar curvature and trace of the matter stress tensor. Instabilities caused by caustics of the geodesic flow, inherent in this model, serve asmore » a motivation for an alternative conformal extension of Einstein theory, based on the generalized Proca vector field. A potential part of this field modifies the inflationary stage in cosmology, whereas its rotational part at the post inflationary epoch might simulate rotating flows of dark matter.« less

Mass effects and internal space geometry in triatomic reaction dynamics

NASA Astrophysics Data System (ADS)

Yanao, Tomohiro; Koon, Wang S.; Marsden, Jerrold E.

2006-05-01

The effect of the distribution of mass in triatomic reaction dynamics is analyzed using the geometry of the associated internal space. Atomic masses are appropriately incorporated into internal coordinates as well as the associated non-Euclidean internal space metric tensor after a separation of the rotational degrees of freedom. Because of the non-Euclidean nature of the metric in the internal space, terms such as connection coefficients arise in the internal equations of motion, which act as velocity-dependent forces in a coordinate chart. By statistically averaging these terms, an effective force field is deduced, which accounts for the statistical tendency of geodesics in the internal space. This force field is shown to play a crucial role in determining mass-related branching ratios of isomerization and dissociation dynamics of a triatomic molecule. The methodology presented can be useful for qualitatively predicting branching ratios in general triatomic reactions, and may be applied to the study of isotope effects.

Study of the Ernst metric

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

Esteban, E.P.

In this thesis some properties of the Ernst metric are studied. This metric could provide a model for a Schwarzschild black hole immersed in a magnetic field. In chapter I, some standard propertiess of the Ernst's metric such as the affine connections, the Riemann, the Ricci, and the Weyl conformal tensor are calculated. In chapter II, the geodesics described by test particles in the Ernst space-time are studied. As an application a formula for the perihelion shift is derived. In the last chapter a null tetrad analysis of the Ernst metric is carried out and the resulting formalism applied tomore » the study of three problems. First, the algebraic classification of the Ernst metric is determined to be of type I in the Petrov scheme. Secondly, an explicit formula for the Gaussian curvature for the event horizon is derived. Finally, the form of the electromagnetic field is evaluated.« less

On the Prediction of Mechanical Behavior of Particulate Composites Using an Improved Mori-Tanaka Method

DTIC Science & Technology

1997-01-01

perturbed strain, [L/ L] P501263.PDF [Page: 12 of 122] UNCLASSIFIED viii €~j constrained strain, [L/ L] €£j eigenstrain , [L/ L] €£J c corrected... eigenstrain of phase-r material, [L/ L] £iJ u uncorrected eigenstrain of phase~r material, [L/ L] fijkl correction matrix of phase-r material... eigenstrains , [2] wher·e St.jkl is known as the Eshelby tensor. The tensor is a function of the matrix Poisson ratio and the shape of the inclusion

An exact solution to the Einstein-Maxwell equations representing a nonspherical, highly charged object

NASA Astrophysics Data System (ADS)

Menon, Govind K.

The Reissner-Nordstrom solution possesses a naked singularity when e2 > m2, where m is the mass and e is the net charge of the system. Also, the singularity at r = 0 is repulsive (i.e., no timelike geodesics (neutral particles) can reach the singularity). These unusual properties of the Reissner-Nordstrom geometry are considered as an accident resulting from the highly symmetric nature of the space-time. Here we wish to generalize the condition of spherical symmetry to axial symmetry and to probe into the issues of naked singularity and gravitational repulsion. To do this, we must construct a nonspherical solution to the Einstein-Maxwell set of equations in the event that e2 > m2. The Erez-Rosen extension of the vacuum Schwarzschild solution to the non-spherical case gave one of the first physically significant solutions of the Einstein field equations. Nonvacuum extensions of the Erez-Rosen solution representing a non-spherical mass containing a very high net charge (i.e., when e2 > m2) will be discussed. The special case of spherical symmetry, as would be expected, results in the Reissner-Nordstrom solution. The search for the physical singularities involves the calculation of a nontrivial scalar constructed from the Riemann curvature tensor. As it turns out, the resulting geometry does indeed possess a naked singularity. In addition, the space-time also entertains gravitational repulsion. However, unlike the Reissner-Nordstrom solution, it has been found that all timelike geodesics are not necessarily repelled from the origin.

Complete set of homogeneous isotropic analytic solutions in scalar-tensor cosmology with radiation and curvature

NASA Astrophysics Data System (ADS)

Bars, Itzhak; Chen, Shih-Hung; Steinhardt, Paul J.; Turok, Neil

2012-10-01

We study a model of a scalar field minimally coupled to gravity, with a specific potential energy for the scalar field, and include curvature and radiation as two additional parameters. Our goal is to obtain analytically the complete set of configurations of a homogeneous and isotropic universe as a function of time. This leads to a geodesically complete description of the Universe, including the passage through the cosmological singularities, at the classical level. We give all the solutions analytically without any restrictions on the parameter space of the model or initial values of the fields. We find that for generic solutions the Universe goes through a singular (zero-size) bounce by entering a period of antigravity at each big crunch and exiting from it at the following big bang. This happens cyclically again and again without violating the null-energy condition. There is a special subset of geodesically complete nongeneric solutions which perform zero-size bounces without ever entering the antigravity regime in all cycles. For these, initial values of the fields are synchronized and quantized but the parameters of the model are not restricted. There is also a subset of spatial curvature-induced solutions that have finite-size bounces in the gravity regime and never enter the antigravity phase. These exist only within a small continuous domain of parameter space without fine-tuning the initial conditions. To obtain these results, we identified 25 regions of a 6-parameter space in which the complete set of analytic solutions are explicitly obtained.

Moment-Tensor Spectra of Source Physics Experiments (SPE) Explosions in Granite

NASA Astrophysics Data System (ADS)

Yang, X.; Cleveland, M.

2016-12-01

We perform frequency-domain moment tensor inversions of Source Physics Experiments (SPE) explosions conducted in granite during Phase I of the experiment. We test the sensitivity of source moment-tensor spectra to factors such as the velocity model, selected dataset and smoothing and damping parameters used in the inversion to constrain the error bound of inverted source spectra. Using source moments and corner frequencies measured from inverted source spectra of these explosions, we develop a new explosion P-wave source model that better describes observed source spectra of these small and over-buried chemical explosions detonated in granite than classical explosion source models derived mainly from nuclear-explosion data. In addition to source moment and corner frequency, we analyze other features in the source spectra to investigate their physical causes.

Source spectra of the first four Source Physics Experiments (SPE) explosions from the frequency-domain moment-tensor inversion

DOE PAGES

Yang, Xiaoning

2016-08-01

In this study, I used seismic waveforms recorded within 2 km from the epicenter of the first four Source Physics Experiments (SPE) explosions to invert for the moment-tensor spectra of these explosions. I employed a one-dimensional (1D) Earth model for Green's function calculations. The model was developed from P- and R g-wave travel times and amplitudes. I selected data for the inversion based on the criterion that they had consistent travel times and amplitude behavior as those predicted by the 1D model. Due to limited azimuthal coverage of the sources and the mostly vertical-component-only nature of the dataset, only long-period,more » volumetric components of the moment-tensor spectra were well constrained.« less

Gauge-invariant formalism of cosmological weak lensing

NASA Astrophysics Data System (ADS)

Yoo, Jaiyul; Grimm, Nastassia; Mitsou, Ermis; Amara, Adam; Refregier, Alexandre

2018-04-01

We present the gauge-invariant formalism of cosmological weak lensing, accounting for all the relativistic effects due to the scalar, vector, and tensor perturbations at the linear order. While the light propagation is fully described by the geodesic equation, the relation of the photon wavevector to the physical quantities requires the specification of the frames, where they are defined. By constructing the local tetrad bases at the observer and the source positions, we clarify the relation of the weak lensing observables such as the convergence, the shear, and the rotation to the physical size and shape defined in the source rest-frame and the observed angle and redshift measured in the observer rest-frame. Compared to the standard lensing formalism, additional relativistic effects contribute to all the lensing observables. We explicitly verify the gauge-invariance of the lensing observables and compare our results to previous work. In particular, we demonstrate that even in the presence of the vector and tensor perturbations, the physical rotation of the lensing observables vanishes at the linear order, while the tetrad basis rotates along the light propagation compared to a FRW coordinate. Though the latter is often used as a probe of primordial gravitational waves, the rotation of the tetrad basis is indeed not a physical observable. We further clarify its relation to the E-B decomposition in weak lensing. Our formalism provides a transparent and comprehensive perspective of cosmological weak lensing.

Synthetic velocity gradient tensors and the identification of statistically significant aspects of the structure of turbulence

NASA Astrophysics Data System (ADS)

Keylock, Christopher J.

2017-08-01

A method is presented for deriving random velocity gradient tensors given a source tensor. These synthetic tensors are constrained to lie within mathematical bounds of the non-normality of the source tensor, but we do not impose direct constraints upon scalar quantities typically derived from the velocity gradient tensor and studied in fluid mechanics. Hence, it becomes possible to ask hypotheses of data at a point regarding the statistical significance of these scalar quantities. Having presented our method and the associated mathematical concepts, we apply it to homogeneous, isotropic turbulence to test the utility of the approach for a case where the behavior of the tensor is understood well. We show that, as well as the concentration of data along the Vieillefosse tail, actual turbulence is also preferentially located in the quadrant where there is both excess enstrophy (Q>0 ) and excess enstrophy production (R<0 ). We also examine the topology implied by the strain eigenvalues and find that for the statistically significant results there is a particularly strong relative preference for the formation of disklike structures in the (Q<0 ,R<0 ) quadrant. With the method shown to be useful for a turbulence that is already understood well, it should be of even greater utility for studying complex flows seen in industry and the environment.

Constraining the Mechanism of D" Anisotropy: Diversity of Observation Types Required

NASA Astrophysics Data System (ADS)

Creasy, N.; Pisconti, A.; Long, M. D.; Thomas, C.

2017-12-01

A variety of different mechanisms have been proposed as explanations for seismic anisotropy at the base of the mantle, including crystallographic preferred orientation of various minerals (bridgmanite, post-perovskite, and ferropericlase) and shape preferred orientation of elastically distinct materials such as partial melt. Investigations of the mechanism for D" anisotropy are usually ambiguous, as seismic observations rarely (if ever) uniquely constrain a mechanism. Observations of shear wave splitting and polarities of SdS and PdP reflections off the D" discontinuity are among our best tools for probing D" anisotropy; however, typical data sets cannot constrain a unique scenario suggested by the mineral physics literature. In this work, we determine what types of body wave observations are required to uniquely constrain a mechanism for D" anisotropy. We test multiple possible models based on both single-crystal and poly-phase elastic tensors provided by mineral physics studies. We predict shear wave splitting parameters for SKS, SKKS, and ScS phases and reflection polarities off the D" interface for a range of possible propagation directions. We run a series of tests that create synthetic data sets by random selection over multiple iterations, controlling the total number of measurements, the azimuthal distribution, and the type of phases. We treat each randomly drawn synthetic dataset with the same methodology as in Ford et al. (2015) to determine the possible mechanism(s), carrying out a grid search over all possible elastic tensors and orientations to determine which are consistent with the synthetic data. We find is it difficult to uniquely constrain the starting model with a realistic number of seismic anisotropy measurements with only one measurement technique or phase type. However, having a mix of SKS, SKKS, and ScS measurements, or a mix of shear wave splitting and reflection polarity measurements, dramatically increases the probability of uniquely constraining the starting model. We also explore what types of datasets are needed to uniquely constrain the orientation(s) of anisotropic symmetry if the mechanism is assumed.

Unveiling the nucleon tensor charge at Jefferson Lab: A study of the SoLID case

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

Ye, Zhihong; Sato, Nobuo; Allada, Kalyan

2017-01-27

Here, future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the transversity quark distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID. Especially, we develop a model-independent method based on the hessian matrix analysis that allows to estimate the uncertainties of the transversity quarkmore » distributions and their tensor charge contributions extracted from the pseudo-data for the SoLID. Both u and d-quark transversity distributions are shown to be very well constrained in the kinematical region of the future experiments with the proton and the effective neutron targets.« less

Every timelike geodesic in Anti-de Sitter spacetime is a circle of the same radius

NASA Astrophysics Data System (ADS)

Sokołowski, Leszek M.; Golda, Zdzisław A.

2016-10-01

In this paper, we refine and analytically prove an old proposition due to Calabi and Markus on the shape of timelike geodesics of anti-de Sitter space in the ambient flat space. We prove that each timelike geodesic forms in the ambient space a circle of the radius determined by Λ, lying on a Euclidean two-plane. Then, we outline an alternative proof for AdS4. We also make a comment on the shape of timelike geodesics in de Sitter space.

Spinning geodesic Witten diagrams

DOE PAGES

Dyer, Ethan; Freedman, Daniel Z.; Sully, James

2017-11-10

We present an expression for the four-point conformal blocks of symmetric traceless operators of arbitrary spin as an integral over a pair of geodesics in Anti-de Sitter space, generalizing the geodesic Witten diagram formalism of Hijano et al. to arbitrary spin. As an intermediate step in the derivation, we identify a convenient basis of bulk threepoint interaction vertices which give rise to all possible boundary three point structures. Lastly, we highlight a direct connection between the representation of the conformal block as geodesic Witten diagram and the shadow operator formalism.

Drift and geodesic effects on the ion sound eigenmode in tokamak plasmas

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

Elfimov, A. G., E-mail: elfimov@if.usp.br; Smolyakov, A. I., E-mail: andrei.smolyakov@usask.ca; Melnikov, A. V.

A kinetic treatment of geodesic acoustic modes (GAMs), taking into account ion parallel dynamics, drift and the second poloidal harmonic effects is presented. It is shown that first and second harmonics of the ion sound modes, which have respectively positive and negative radial dispersion, can be coupled due to the geodesic and drift effects. This coupling results in the drift geodesic ion sound eigenmode with a frequency below the standard GAM continuum frequency. Such eigenmode may be able to explain the split modes observed in some experiments.

Are eikonal quasinormal modes linked to the unstable circular null geodesics?

NASA Astrophysics Data System (ADS)

Konoplya, R. A.; Stuchlík, Z.

2017-08-01

In Cardoso et al. [6] it was claimed that quasinormal modes which any stationary, spherically symmetric and asymptotically flat black hole emits in the eikonal regime are determined by the parameters of the circular null geodesic: the real and imaginary parts of the quasinormal mode are multiples of the frequency and instability timescale of the circular null geodesics respectively. We shall consider asymptotically flat black hole in the Einstein-Lovelock theory, find analytical expressions for gravitational quasinormal modes in the eikonal regime and analyze the null geodesics. Comparison of the both phenomena shows that the expected link between the null geodesics and quasinormal modes is violated in the Einstein-Lovelock theory. Nevertheless, the correspondence exists for a number of other cases and here we formulate its actual limits.

Nonlinear modes of the tensor Dirac equation and CPT violation

NASA Technical Reports Server (NTRS)

Reifler, Frank J.; Morris, Randall D.

1993-01-01

Recently, it has been shown that Dirac's bispinor equation can be expressed, in an equivalent tensor form, as a constrained Yang-Mills equation in the limit of an infinitely large coupling constant. It was also shown that the free tensor Dirac equation is a completely integrable Hamiltonian system with Lie algebra type Poisson brackets, from which Fermi quantization can be derived directly without using bispinors. The Yang-Mills equation for a finite coupling constant is investigated. It is shown that the nonlinear Yang-Mills equation has exact plane wave solutions in one-to-one correspondence with the plane wave solutions of Dirac's bispinor equation. The theory of nonlinear dispersive waves is applied to establish the existence of wave packets. The CPT violation of these nonlinear wave packets, which could lead to new observable effects consistent with current experimental bounds, is investigated.

On the trajectories of null and timelike geodesics in different wormhole geometries

NASA Astrophysics Data System (ADS)

Mishra, Anuj; Chakraborty, Subenoy

2018-05-01

The paper deals with an extensive study of null and timelike geodesics in the background of wormhole geometries. Starting with a spherically symmetric spacetime, null geodesics are analyzed for the Morris-Thorne wormhole (WH) and photon spheres are examined in WH geometries. Both bounded and unbounded orbits are discussed for timelike geodesics. A similar analysis has been done for trajectories in a dynamic spherically symmetric WH and for a rotating WH. Finally, the invariant angle method of Rindler and Ishak has been used to calculate the angle between radial and tangential vectors at any point on the photon's trajectory.

Dome, Sweet Dome--Geodesic Structures Teach Math, Science, and Technology Principles

ERIC Educational Resources Information Center

Shackelford, Ray; Fitzgerald, Michael

2007-01-01

Today, geodesic domes are found on playgrounds, homes, over radar installations, storage facilities, at Disney's Epcot Center, and at World's Fairs. The inventor of the design, Buckminster Fuller, thought that geodesic domes could be used to cover large areas and even designed one to cover all of New York's Manhattan Island. This article details…

Constraining modified gravitational theories by weak lensing with Euclid

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

Martinelli, Matteo; Calabrese, Erminia; De Bernardis, Francesco

2011-01-15

Future proposed satellite missions such as Euclid can offer the opportunity to test general relativity on cosmic scales through mapping of the galaxy weak-lensing signal. In this paper we forecast the ability of these experiments to constrain modified gravity scenarios such as those predicted by scalar-tensor and f(R) theories. We find that Euclid will improve constraints expected from the Planck satellite on these modified theories of gravity by 2 orders of magnitude. We discuss parameter degeneracies and the possible biases introduced by modifications to gravity.

Geodesic Motion of Particles and Quantum Tunneling from Reissner-Nordström Black Holes in Anti-de Sitter Spacetime

NASA Astrophysics Data System (ADS)

Deng, Gao-Ming; Huang, Yong-Chang

2018-03-01

The geodesics of tunneling particles were derived unnaturally and awkwardly in previous works. For one thing, the previous derivation was inconsistent with the variational principle of action. Moreover, the definition of geodesic equations for massive particles was quite different from that of massless case. Even worse, the relativistic and nonrelativistic foundations were mixed with each other during the past derivation of geodesics. As a highlight, remedying the urgent shortcomings, we improve treatment to derive the geodesic equations of massive and massless particles in a unified and self-consistent way. Besides, we extend to investigate the Hawking radiation via tunneling from Reissner-Nordström black holes in the context of AdS spacetime. Of special interest, the trick of utilizing the first law of black hole thermodynamics manifestly simplifies the calculation of tunneling integration.

Full Moment Tensor Analysis Using First Motion Data at The Geysers Geothermal Field

NASA Astrophysics Data System (ADS)

Boyd, O.; Dreger, D. S.; Lai, V. H.; Gritto, R.

2012-12-01

Seismicity associated with geothermal energy production at The Geysers Geothermal Field in northern California has been increasing during the last forty years. We investigate source models of over fifty earthquakes with magnitudes ranging from Mw 3.5 up to Mw 4.5. We invert three-component, complete waveform data from broadband stations of the Berkeley Digital Seismic Network, the Northern California Seismic Network and the USA Array deployment (2005-2007) for the complete, six-element moment tensor. Some solutions are double-couple while others have substantial non-double-couple components. To assess the stability and significance of non-double-couple components, we use a suite of diagnostic tools including the F-test, Jackknife test, bootstrap and network sensitivity solution (NSS). The full moment tensor solutions of the studied events tend to plot in the upper half of the Hudson source type diagram where the fundamental source types include +CLVD, +LVD, tensile-crack, DC and explosion. Using the F-test to compare the goodness-of-fit values between the full and deviatoric moment tensor solutions, most of the full moment tensor solutions do not show a statistically significant improvement in fit over the deviatoric solutions. Because a small isotropic component may not significantly improve the fit, we include first motion polarity data to better constrain the full moment tensor solutions.

Conventional Gymnasium vs. Geodesic Field House. A Comparative Study of High School Physical Education and Assembly Facilities.

ERIC Educational Resources Information Center

Educational Facilities Labs., Inc., New York, NY.

A description is presented of the design features of a high school's geodesic dome field house. Following consideration of various design features and criteria for the physical education facility, a comprehensive analysis is given of comparative costs of a geodesic dome field house and conventional gymnasium. On the basis of the study it would…

A finsler perturbation of the Poincaré metric

NASA Astrophysics Data System (ADS)

Rutz, Solange F.; McCarthy, Patrick J.

1993-02-01

One method of gaining some insight into Finsler geomety is that of studying small Finsler perturbations of Riemannian metrics. We consider here the the standard two-dimensional upper half plane Poincaré metric, for which the geodesics are semi-circles and vertical lines. The effect of a simple Finsler perturbation on these geodesics is given by an explicit computation of the perturbed geodesics.

Geodesics in nonexpanding impulsive gravitational waves with Λ. II

NASA Astrophysics Data System (ADS)

Sämann, Clemens; Steinbauer, Roland

2017-11-01

We investigate all geodesics in the entire class of nonexpanding impulsive gravitational waves propagating in an (anti-)de Sitter universe using the distributional metric. We extend the regularization approach of part I [Sämann, C. et al., Classical Quantum Gravity 33(11), 115002 (2016)] to a full nonlinear distributional analysis within the geometric theory of generalized functions. We prove global existence and uniqueness of geodesics that cross the impulsive wave and hence geodesic completeness in full generality for this class of low regularity spacetimes. This, in particular, prepares the ground for a mathematically rigorous account on the "physical equivalence" of the continuous form with the distributional "form" of the metric.

Principal Curves on Riemannian Manifolds.

PubMed

Hauberg, Soren

2016-09-01

Euclidean statistics are often generalized to Riemannian manifolds by replacing straight-line interpolations with geodesic ones. While these Riemannian models are familiar-looking, they are restricted by the inflexibility of geodesics, and they rely on constructions which are optimal only in Euclidean domains. We consider extensions of Principal Component Analysis (PCA) to Riemannian manifolds. Classic Riemannian approaches seek a geodesic curve passing through the mean that optimizes a criteria of interest. The requirements that the solution both is geodesic and must pass through the mean tend to imply that the methods only work well when the manifold is mostly flat within the support of the generating distribution. We argue that instead of generalizing linear Euclidean models, it is more fruitful to generalize non-linear Euclidean models. Specifically, we extend the classic Principal Curves from Hastie & Stuetzle to data residing on a complete Riemannian manifold. We show that for elliptical distributions in the tangent of spaces of constant curvature, the standard principal geodesic is a principal curve. The proposed model is simple to compute and avoids many of the pitfalls of traditional geodesic approaches. We empirically demonstrate the effectiveness of the Riemannian principal curves on several manifolds and datasets.

Craniofacial reconstruction evaluation by geodesic network.

PubMed

Zhao, Junli; Liu, Cuiting; Wu, Zhongke; Duan, Fuqing; Wang, Kang; Jia, Taorui; Liu, Quansheng

2014-01-01

Craniofacial reconstruction is to estimate an individual's face model from its skull. It has a widespread application in forensic medicine, archeology, medical cosmetic surgery, and so forth. However, little attention is paid to the evaluation of craniofacial reconstruction. This paper proposes an objective method to evaluate globally and locally the reconstructed craniofacial faces based on the geodesic network. Firstly, the geodesic networks of the reconstructed craniofacial face and the original face are built, respectively, by geodesics and isogeodesics, whose intersections are network vertices. Then, the absolute value of the correlation coefficient of the features of all corresponding geodesic network vertices between two models is taken as the holistic similarity, where the weighted average of the shape index values in a neighborhood is defined as the feature of each network vertex. Moreover, the geodesic network vertices of each model are divided into six subareas, that is, forehead, eyes, nose, mouth, cheeks, and chin, and the local similarity is measured for each subarea. Experiments using 100 pairs of reconstructed craniofacial faces and their corresponding original faces show that the evaluation by our method is roughly consistent with the subjective evaluation derived from thirty-five persons in five groups.

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

Berezhiani, Lasha; Khoury, Justin; Wang, Junpu, E-mail: lashaber@gmail.com, E-mail: jkhoury@sas.upenn.edu, E-mail: jwang217@jhu.edu

Single-field perturbations satisfy an infinite number of consistency relations constraining the squeezed limit of correlation functions at each order in the soft momentum. These can be understood as Ward identities for an infinite set of residual global symmetries, or equivalently as Slavnov-Taylor identities for spatial diffeomorphisms. In this paper, we perform a number of novel, non-trivial checks of the identities in the context of single field inflationary models with arbitrary sound speed. We focus for concreteness on identities involving 3-point functions with a soft external mode, and consider all possible scalar and tensor combinations for the hard-momentum modes. In allmore » these cases, we check the consistency relations up to and including cubic order in the soft momentum. For this purpose, we compute for the first time the 3-point functions involving 2 scalars and 1 tensor, as well as 2 tensors and 1 scalar, for arbitrary sound speed.« less

No-Go Theorem for Nonstandard Explanations of the τ →KSπ ντ C P Asymmetry

NASA Astrophysics Data System (ADS)

Cirigliano, Vincenzo; Crivellin, Andreas; Hoferichter, Martin

2018-04-01

The C P asymmetry in τ →KSπ ντ , as measured by the BABAR collaboration, differs from the standard model prediction by 2.8 σ . Most nonstandard interactions do not allow for the required strong phase needed to produce a nonvanishing C P asymmetry, leaving only new tensor interactions as a possible mechanism. We demonstrate that, contrary to previous assumptions in the literature, the crucial interference between vector and tensor phases is suppressed by at least 2 orders of magnitude due to Watson's final-state-interaction theorem. Furthermore, we find that the strength of the relevant C P -violating tensor interaction is strongly constrained by bounds from the neutron electric dipole moment and D - D ¯ mixing. These observations together imply that it is extremely difficult to explain the current τ →KSπ ντ measurement in terms of physics beyond the standard model originating in the ultraviolet.

The observational constraint on constant-roll inflation

NASA Astrophysics Data System (ADS)

Gao, Qing

2018-07-01

We discuss the constant-roll inflation with constant ɛ2 and constant \\bar η . By using the method of Bessel function approximation, the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor to scalar ratio are derived up to the first order of ɛ1. The model with constant ɛ2 is ruled out by the observations at the 3σ confidence level, and the model with constant \\bar η is consistent with the observations at the 1σ confidence level. The potential for the model with constant \\bar η is also obtained from the Hamilton-Jacobi equation. Although the observations constrain the constant-roll inflation to be the slow-roll inflation, the n s- r results from the constant-roll inflation are not the same as those from the slow-roll inflation even when \\bar η 0.01.

Observational constraints on monomial warm inflation

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

Visinelli, Luca, E-mail: Luca.Visinelli@studio.unibo.it

Warm inflation is, as of today, one of the best motivated mechanisms for explaining an early inflationary period. In this paper, we derive and analyze the current bounds on warm inflation with a monomial potential U ∝ φ {sup p} , using the constraints from the PLANCK mission. In particular, we discuss the parameter space of the tensor-to-scalar ratio r and the potential coupling λ of the monomial warm inflation in terms of the number of e-folds. We obtain that the theoretical tensor-to-scalar ratio r ∼ 10{sup −8} is much smaller than the current observational constrain r ∼< 0.12, despitemore » a relatively large value of the field excursion Δ φ ∼ 0.1 M {sub Pl}. Warm inflation thus eludes the Lyth bound set on the tensor-to-scalar ratio by the field excursion.« less

Cosmic strings and chronology protection

NASA Astrophysics Data System (ADS)

Grant, James D. E.

1993-03-01

A space consisting of two rapidly moving cosmic strings has recently been constructed by Gott that contains closed timelike curves. The global structure of this space is analyzed and it is found that, away from the strings, the space is identical to a generalized Misner space. The vacuum expectation value of the energy-momentum tensor for a conformally coupled scalar field is calculated on this generalized Misner space. It is found to diverge very weakly on the chronology horizon, but more strongly on the polarized hypersurfaces. The divergence on the polarized hypersurfaces is strong enough that when the proper geodesic interval around any polarized hypersurface is of the order of the Planck length squared, the perturbation to the metric caused by the back reaction will be of the order one. Thus we expect the structure of the space will be radically altered by the back reaction before quantum gravitational effects become important. This suggests that Hawking's ``chronology protection conjecture'' holds for spaces with a noncompactly generated chronology horizon.

Cosmological perturbations in antigravity

NASA Astrophysics Data System (ADS)

Oltean, Marius; Brandenberger, Robert

2014-10-01

We compute the evolution of cosmological perturbations in a recently proposed Weyl-symmetric theory of two scalar fields with oppositely signed conformal couplings to Einstein gravity. It is motivated from the minimal conformal extension of the standard model, such that one of these scalar fields is the Higgs while the other is a new particle, the dilaton, introduced to make the Higgs mass conformally symmetric. At the background level, the theory admits novel geodesically complete cyclic cosmological solutions characterized by a brief period of repulsive gravity, or "antigravity," during each successive transition from a big crunch to a big bang. For simplicity, we consider scalar perturbations in the absence of anisotropies, with potential set to zero and without any radiation. We show that despite the necessarily wrong-signed kinetic term of the dilaton in the full action, these perturbations are neither ghostlike nor tachyonic in the limit of strongly repulsive gravity. On this basis, we argue—pending a future analysis of vector and tensor perturbations—that, with respect to perturbative stability, the cosmological solutions of this theory are viable.

A semi-automatic method for extracting thin line structures in images as rooted tree network

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

Brazzini, Jacopo; Dillard, Scott; Soille, Pierre

2010-01-01

This paper addresses the problem of semi-automatic extraction of line networks in digital images - e.g., road or hydrographic networks in satellite images, blood vessels in medical images, robust. For that purpose, we improve a generic method derived from morphological and hydrological concepts and consisting in minimum cost path estimation and flow simulation. While this approach fully exploits the local contrast and shape of the network, as well as its arborescent nature, we further incorporate local directional information about the structures in the image. Namely, an appropriate anisotropic metric is designed by using both the characteristic features of the targetmore » network and the eigen-decomposition of the gradient structure tensor of the image. Following, the geodesic propagation from a given seed with this metric is combined with hydrological operators for overland flow simulation to extract the line network. The algorithm is demonstrated for the extraction of blood vessels in a retina image and of a river network in a satellite image.« less

General Relativity Exactly Described by Use of Newton's Laws within a Curved Geometry

NASA Astrophysics Data System (ADS)

Savickas, David

2014-03-01

The connection between general relativity and Newtonian mechanics is shown to be much closer than generally recognized. When Newton's second law is written in a curved geometry by using the physical components of a vector as defined in tensor calculus, and by replacing distance within the momentum's velocity by the vector metric ds in a curved geometry, the second law can then be easily shown to be exactly identical to the geodesic equation of motion occurring in general relativity. By using a time whose vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be separated into two equations one of which is a curved three-dimensional equation of motion and the other is an equation for energy. For the gravitational field of an isolated particle, they yield the Schwarzschild equations. They can be used to describe gravitation for any array of masses for which the Newtonian gravitational potential is known, and is applied here to describe motion in the gravitational field of a thin mass-rod.

Republication of: Contributions to the theory of pure gravitational radiation. Exact solutions of the field equations of the general theory of relativity II

NASA Astrophysics Data System (ADS)

Jordan, Pascual; Ehlers, Jürgen; Sachs, Rainer K.

2013-12-01

This is an English translation of a paper by Pascual Jordan, Juergen Ehlers and Rainer Sachs, first published in 1961 in the proceedings of the Academy of Sciences and Literature in Mainz (Germany). The original paper was part 2 of a five-part series of articles containing the first summary of knowledge about exact solutions of Einstein's equations found until then. (Parts 1 and 4 of the series have already been reprinted, parts 3 and 5 will be printed as Golden Oldies in near future.) This second paper discusses the geometry of geodesic null congruences, the algebraic classification of the Weyl tensor by spinor methods, and applies these to a study of the propagation of gravitational and electromagnetic radiation. It has been selected by the Editors of General Relativity and Gravitation for republication in the Golden Oldies series of the journal. The republication is accompanied by an editorial note written by Malcolm A. H. MacCallum and Wolfgang Kundt.

Moment tensor clustering: a tool to monitor mining induced seismicity

NASA Astrophysics Data System (ADS)

Cesca, Simone; Dahm, Torsten; Tolga Sen, Ali

2013-04-01

Automated moment tensor inversion routines have been setup in the last decades for the analysis of global and regional seismicity. Recent developments could be used to analyse smaller events and larger datasets. In particular, applications to microseismicity, e.g. in mining environments, have then led to the generation of large moment tensor catalogues. Moment tensor catalogues provide a valuable information about the earthquake source and details of rupturing processes taking place in the seismogenic region. Earthquake focal mechanisms can be used to discuss the local stress field, possible orientations of the fault system or to evaluate the presence of shear and/or tensile cracks. Focal mechanism and moment tensor solutions are typically analysed for selected events, and quick and robust tools for the automated analysis of larger catalogues are needed. We propose here a method to perform cluster analysis for large moment tensor catalogues and identify families of events which characterize the studied microseismicity. Clusters include events with similar focal mechanisms, first requiring the definition of distance between focal mechanisms. Different metrics are here proposed, both for the case of pure double couple, constrained moment tensor and full moment tensor catalogues. Different clustering approaches are implemented and discussed. The method is here applied to synthetic and real datasets from mining environments to demonstrate its potential: the proposed cluserting techniques prove to be able to automatically recognise major clusters. An important application for mining monitoring concerns the early identification of anomalous rupture processes, which is relevant for the hazard assessment. This study is funded by the project MINE, which is part of the R&D-Programme GEOTECHNOLOGIEN. The project MINE is funded by the German Ministry of Education and Research (BMBF), Grant of project BMBF03G0737.

A Note on Expansiveness and Hyperbolicity for Generic Geodesic Flows

NASA Astrophysics Data System (ADS)

Bessa, Mário

2018-06-01

In this short note we contribute to the generic dynamics of geodesic flows associated to metrics on compact Riemannian manifolds of dimension ≥ 2. We prove that there exists a C 2-residual subset R of metrics on a given compact Riemannian manifold such that if g\\in R, then its associated geodesic flow φ tg is expansive if and only if the closure of the set of periodic orbits of φtg is a uniformly hyperbolic set. For surfaces, we obtain a stronger statement: there exists a C 2-residual R such that if g\\in R, then its associated geodesic flow φtg is expansive if and only if φtg is an Anosov flow.

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

Sharif, M., E-mail: msharif.math@pu.edu.pk; Manzoor, Rubab, E-mail: rubab.manzoor@umt.edu.pk; Department of Mathematics, University of Management and Technology, Johar Town Campus, Lahore-54782

This paper explores the influences of dark energy on the shear-free axially symmetric evolution by considering self-interacting Brans–Dicke gravity as a dark energy candidate. We describe energy source of the model and derive all the effective dynamical variables as well as effective structure scalars. It is found that scalar field is one of the sources of anisotropy and dissipation. The resulting effective structure scalars help to study the dynamics associated with dark energy in any axial configuration. In order to investigate shear-free evolution, we formulate a set of governing equations along with heat transport equation. We discuss consequences of shear-freemore » condition upon different SBD fluid models like dissipative non-geodesic and geodesic models. For dissipative non-geodesic case, the rotational distribution turns out to be the necessary and sufficient condition for radiating model. The dissipation depends upon inhomogeneous expansion. The geodesic model is found to be irrotational and non-radiating. The non-dissipative geodesic model leads to FRW model for positive values of the expansion parameter.« less

Kinematic space for conical defects

NASA Astrophysics Data System (ADS)

Cresswell, Jesse C.; Peet, Amanda W.

2017-11-01

Kinematic space can be used as an intermediate step in the AdS/CFT dictionary and lends itself naturally to the description of diffeomorphism invariant quantities. From the bulk it has been defined as the space of boundary anchored geodesics, and from the boundary as the space of pairs of CFT points. When the bulk is not globally AdS3 the appearance of non-minimal geodesics leads to ambiguities in these definitions. In this work conical defect spacetimes are considered as an example where non-minimal geodesics are common. From the bulk it is found that the conical defect kinematic space can be obtained from the AdS3 kinematic space by the same quotient under which one obtains the defect from AdS3. The resulting kinematic space is one of many equivalent fundamental regions. From the boundary the conical defect kinematic space can be determined by breaking up OPE blocks into contributions from individual bulk geodesics. A duality is established between partial OPE blocks and bulk fields integrated over individual geodesics, minimal or non-minimal.

Is the permeability of naturally fractured rocks scale dependent?

NASA Astrophysics Data System (ADS)

Azizmohammadi, Siroos; Matthäi, Stephan K.

2017-09-01

The equivalent permeability, keq of stratified fractured porous rocks and its anisotropy is important for hydrocarbon reservoir engineering, groundwater hydrology, and subsurface contaminant transport. However, it is difficult to constrain this tensor property as it is strongly influenced by infrequent large fractures. Boreholes miss them and their directional sampling bias affects the collected geostatistical data. Samples taken at any scale smaller than that of interest truncate distributions and this bias leads to an incorrect characterization and property upscaling. To better understand this sampling problem, we have investigated a collection of outcrop-data-based Discrete Fracture and Matrix (DFM) models with mechanically constrained fracture aperture distributions, trying to establish a useful Representative Elementary Volume (REV). Finite-element analysis and flow-based upscaling have been used to determine keq eigenvalues and anisotropy. While our results indicate a convergence toward a scale-invariant keq REV with increasing sample size, keq magnitude can have multi-modal distributions. REV size relates to the length of dilated fracture segments as opposed to overall fracture length. Tensor orientation and degree of anisotropy also converge with sample size. However, the REV for keq anisotropy is larger than that for keq magnitude. Across scales, tensor orientation varies spatially, reflecting inhomogeneity of the fracture patterns. Inhomogeneity is particularly pronounced where the ambient stress selectively activates late- as opposed to early (through-going) fractures. While we cannot detect any increase of keq with sample size as postulated in some earlier studies, our results highlight a strong keq anisotropy that influences scale dependence.

Spacetime completeness of non-singular black holes in conformal gravity

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

Bambi, Cosimo; Rachwał, Lesław; Modesto, Leonardo, E-mail: bambi@fudan.edu.cn, E-mail: lmodesto@sustc.edu.cn, E-mail: grzerach@gmail.com

We explicitly prove that the Weyl conformal symmetry solves the black hole singularity problem, otherwise unavoidable in a generally covariant local or non-local gravitational theory. Moreover, we yield explicit examples of local and non-local theories enjoying Weyl and diffeomorphism symmetry (in short co-covariant theories). Following the seminal paper by Narlikar and Kembhavi, we provide an explicit construction of singularity-free spherically symmetric and axi-symmetric exact solutions for black hole spacetimes conformally equivalent to the Schwarzschild or the Kerr spacetime. We first check the absence of divergences in the Kretschmann invariant for the rescaled metrics. Afterwords, we show that the new typesmore » of black holes are geodesically complete and linked by a Newman-Janis transformation just as in standard general relativity (based on Einstein-Hilbert action). Furthermore, we argue that no massive or massless particles can reach the former Schwarzschild singularity or touch the former Kerr ring singularity in a finite amount of their proper time or of their affine parameter. Finally, we discuss the Raychaudhuri equation in a co-covariant theory and we show that the expansion parameter for congruences of both types of geodesics (for massless and massive particles) never reaches minus infinity. Actually, the null geodesics become parallel at the r =0 point in the Schwarzschild spacetime (the origin) and the focusing of geodesics is avoided. The arguments of regularity of curvature invariants, geodesic completeness, and finiteness of geodesics' expansion parameter ensure us that we are dealing with singularity-free and geodesically-complete black hole spacetimes.« less

Network sensitivity solutions for regional moment-tensor inversions

DOE PAGES

Ford, Sean R.; Dreger, Douglas S.; Walter, William R.

2010-09-20

Well-resolved moment-tensor solutions reveal information about the sources of seismic waves. In this paper,we introduce a newly of assessing confidence in the regional full moment-tensor inversion via the introduction of the network sensitivity solution (NSS). The NSS takes into account the unique station distribution, frequency band, and signal-to-noise ratio of a given event scenario. The NSS compares both a hypothetical pure source (for example, an explosion or an earthquake) and the actual data with several thousand sets of synthetic data from a uniform distribution of all possible sources. The comparison with a hypothetical pure source provides the theoretically best-constrained source-typemore » distribution for a given set of stations; and with it, one can determine whether further analysis with the data is warranted. The NSS that employs the actual data gives a direct comparison of all other source types with the best fit source. In this way, one can choose a threshold level of fit in which the solution is comfortably constrained. The method is tested for the well-recorded nuclear test, JUNCTION, at the Nevada Test Site. Sources that fit comparably well to a hypothetical pure explosion recorded with no noise at the JUNCTION data stations have a large volumetric component and are not described well by a double-couple (DC) source. The NSS using the real data from JUNCTION is even more tightly constrained to an explosion because the data contain some energy that precludes fitting with any type of deviator source. We also calculate the NSS for the October 2006 North Korea test and a nearby earthquake, where the station coverage is poor and the event magnitude is small. As a result, the earthquake solution is very well fit by a DC source, and the best-fit solution to the nuclear test (M w 4.1) is dominantly explosion.« less

Hidden Symmetries in String Theory

NASA Astrophysics Data System (ADS)

Chervonyi, Iurii

In this thesis we study hidden symmetries within the framework of string theory. Symmetries play a very important role in physics: they lead to drastic simplifications, which allow one to compute various physical quantities without relying on perturbative techniques. There are two kinds of hidden symmetries investigated in this work: the first type is associated with dynamics of quantum fields and the second type is related to integrability of strings on various backgrounds. Integrability is a remarkable property of some theories that allows one to determine all dynamical properties of the system using purely analytical methods. The goals of this thesis are twofold: extension of hidden symmetries known in General Relativity to stringy backgrounds in higher dimensions and construction of new integrable string theories. In the context of the first goal we study hidden symmetries of stringy backgrounds, with and without supersymmetry. For supersymmetric geometries produced by D-branes we identify the backgrounds with solvable equations for geodesics, which can potentially give rise to integrable string theories. Relaxing the requirement of supersymmetry, we also study charged black holes in higher dimensions and identify their hidden symmetries encoded in so-called Killing(-Yano) tensors. We construct the explicit form of the Killing(-Yano) tensors for the charged rotating black hole in arbitrary number of dimensions, study behavior of such tensors under string dualities, and use the analysis of hidden symmetries to explain why exact solutions for black rings (black holes with non-spherical event horizons) in more than five dimensions remain elusive. As a byproduct we identify the standard parameterization of AdSp x Sq backgrounds with elliptic coordinates on a flat base. The second goal of this work is construction of new integrable string theories by applying continuous deformations of known examples. We use the recent developments called (generalized) lambda-deformation to construct new integrable backgrounds depending on several continuous parameters and study analytical properties of the such deformations.

de Sitter geodesics

NASA Astrophysics Data System (ADS)

Cotăescu, Ion I.

2017-12-01

The geodesics on the (1 + 3)-dimensional de Sitter (dS) spacetime are considered studying how their parameters are determined by the conserved quantities in the conformal Euclidean, Friedmann-Lemaître-Robertson-Walker, de Sitter-Painlevé and static local charts with Cartesian space coordinates. Moreover, it is shown that there exists a special static chart in which the geodesics are genuine hyperbolas whose asymptotes are given by the conserved momentum and the associated dual momentum.

An Integrated Tensorial Approach for Quantifying Porous, Fractured Rocks

NASA Astrophysics Data System (ADS)

Healy, David; Rizzo, Roberto; Harland, Sophie; Farrell, Natalie; Browning, John; Meredith, Phil; Mitchell, Tom; Bubeck, Alodie; Walker, Richard

2017-04-01

The patterns of fractures in deformed rocks are rarely uniform or random. Fracture orientations, sizes, shapes and spatial distributions often exhibit some kind of order. In detail, there may be relationships among the different fracture attributes e.g. small fractures dominated by one orientation, and larger fractures by another. These relationships are important because the mechanical (e.g. strength, anisotropy) and transport (e.g. fluids, heat) properties of rock depend on these fracture patterns and fracture attributes. Based on previously published work (Oda, Cowin, Sayers & Kachanov) this presentation describes an integrated tensorial approach to quantifying fracture networks and predicting the key properties of fractured rock: permeability and elasticity (and in turn, seismic velocities). Each of these properties can be represented as tensors, and these entities capture the essential 'directionality', or anisotropy of the property. In structural geology, we are familiar with using tensors for stress and strain, where these concepts incorporate volume averaging of many forces (in the case of the stress tensor), or many displacements (for the strain tensor), to produce more tractable and more computationally efficient quantities. It is conceptually attractive to formulate both the structure (the fracture network) and the structure-dependent properties (permeability, elasticity) in a consistent way with tensors of 2nd and 4th rank, as appropriate. Examples are provided to highlight the interdependence of the property tensors with the geometry of the fracture network. The fabric tensor (or orientation tensor of Scheidegger, Woodcock) describes the orientation distribution of fractures in the network. The crack tensor combines the fabric tensor (orientation distribution) with information about the fracture density and fracture size distribution. Changes to the fracture network, manifested in the values of the fabric and crack tensors, translate into changes in predicted permeability and elasticity (seismic velocity). Conversely, this implies that measured changes in any of the in situ properties or responses in the subsurface (e.g. permeability, seismic velocity) could be used to predict, or at least constrain, the fracture network. Explicitly linking the fracture network geometry to the permeability and elasticity (seismic velocity) through a tensorial formulation provides an exciting and efficient alternative to existing approaches.

On symmetry inheritance of nonminimally coupled scalar fields

NASA Astrophysics Data System (ADS)

Barjašić, Irena; Smolić, Ivica

2018-04-01

We present the first symmetry inheritance analysis of fields non-minimally coupled to gravity. In this work we are focused on the real scalar field ϕ with nonminimal coupling of the form ξφ2 R . Possible cases of symmetry noninheriting fields are constrained by the properties of the Ricci tensor and the scalar potential. Examples of such spacetimes can be found among those which are ‘dressed’ with the stealth scalar field, a nontrivial scalar field configuration with the vanishing energy–momentum tensor. We classify the scalar field potentials which allow symmetry noninheriting stealth field configurations on top of the exact solutions of the Einstein’s gravitational field equation with the cosmological constant.

Effects of viscous pressure on warm inflationary generalized cosmic Chaplygin gas model

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

Sharif, M.; Saleem, Rabia, E-mail: msharif.math@pu.edu.pk, E-mail: rabiasaleem1988@yahoo.com

This paper is devoted to study the effects of bulk viscous pressure on an inflationary generalized cosmic Chaplygin gas model using FRW background. The matter contents of the universe are assumed to be inflaton and imperfect fluid. We evaluate inflaton fields, potentials and entropy density for variable as well as constant dissipation and bulk viscous coefficients in weak as well as high dissipative regimes during intermediate era. In order to discuss inflationary perturbations, we evaluate entropy density, scalar (tensor) power spectra, their corresponding spectral indices, tensor-scalar ratio and running of spectral index in terms of inflaton which are constrained usingmore » recent Planck, WMAP7 and Bicep2 probes.« less

Matter coupling in partially constrained vielbein formulation of massive gravity

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

Felice, Antonio De; Mukohyama, Shinji; Gümrükçüoğlu, A. Emir

2016-01-01

We consider a linear effective vielbein matter coupling without introducing the Boulware-Deser ghost in ghost-free massive gravity. This is achieved in the partially constrained vielbein formulation. We first introduce the formalism and prove the absence of ghost at all scales. As next we investigate the cosmological application of this coupling in this new formulation. We show that even if the background evolution accords with the metric formulation, the perturbations display important different features in the partially constrained vielbein formulation. We study the cosmological perturbations of the two branches of solutions separately. The tensor perturbations coincide with those in the metricmore » formulation. Concerning the vector and scalar perturbations, the requirement of absence of ghost and gradient instabilities yields slightly different allowed parameter space.« less

Matter coupling in partially constrained vielbein formulation of massive gravity

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

Felice, Antonio De; Gümrükçüoğlu, A. Emir; Heisenberg, Lavinia

2016-01-04

We consider a linear effective vielbein matter coupling without introducing the Boulware-Deser ghost in ghost-free massive gravity. This is achieved in the partially constrained vielbein formulation. We first introduce the formalism and prove the absence of ghost at all scales. As next we investigate the cosmological application of this coupling in this new formulation. We show that even if the background evolution accords with the metric formulation, the perturbations display important different features in the partially constrained vielbein formulation. We study the cosmological perturbations of the two branches of solutions separately. The tensor perturbations coincide with those in the metricmore » formulation. Concerning the vector and scalar perturbations, the requirement of absence of ghost and gradient instabilities yields slightly different allowed parameter space.« less

Influence of geometry variations on the gravitational focusing of timelike geodesic congruences

NASA Astrophysics Data System (ADS)

Seriu, Masafumi

2015-10-01

We derive a set of equations describing the linear response of the convergence properties of a geodesic congruence to arbitrary geometry variations. It is a combination of equations describing the deviations from the standard Raychaudhuri-type equations due to the geodesic shifts and an equation describing the geodesic shifts due to the geometry variations. In this framework, the geometry variations, which can be chosen arbitrarily, serve as probes to investigate the gravitational contraction processes from various angles. We apply the obtained framework to the case of conformal geometry variations, characterized by an arbitrary function f (x ), and see that the formulas get simplified to a great extent. We investigate the response of the convergence properties of geodesics in the latest phase of gravitational contractions by restricting the class of conformal geometry variations to the one satisfying the strong energy condition. We then find out that in the final stage, f and D .D f control the overall contraction behavior and that the contraction rate gets larger when f is negative and |f | is so large as to overwhelm |D .D f |. (Here D .D is the Laplacian operator on the spatial hypersurfaces orthogonal to the geodesic congruence in concern.) To get more concrete insights, we also apply the framework to the time-reversed Friedmann-Robertson-Walker model as the simplest case of the singularity formations.

Volume illustration of muscle from diffusion tensor images.

PubMed

Chen, Wei; Yan, Zhicheng; Zhang, Song; Crow, John Allen; Ebert, David S; McLaughlin, Ronald M; Mullins, Katie B; Cooper, Robert; Ding, Zi'ang; Liao, Jun

2009-01-01

Medical illustration has demonstrated its effectiveness to depict salient anatomical features while hiding the irrelevant details. Current solutions are ineffective for visualizing fibrous structures such as muscle, because typical datasets (CT or MRI) do not contain directional details. In this paper, we introduce a new muscle illustration approach that leverages diffusion tensor imaging (DTI) data and example-based texture synthesis techniques. Beginning with a volumetric diffusion tensor image, we reformulate it into a scalar field and an auxiliary guidance vector field to represent the structure and orientation of a muscle bundle. A muscle mask derived from the input diffusion tensor image is used to classify the muscle structure. The guidance vector field is further refined to remove noise and clarify structure. To simulate the internal appearance of the muscle, we propose a new two-dimensional example based solid texture synthesis algorithm that builds a solid texture constrained by the guidance vector field. Illustrating the constructed scalar field and solid texture efficiently highlights the global appearance of the muscle as well as the local shape and structure of the muscle fibers in an illustrative fashion. We have applied the proposed approach to five example datasets (four pig hearts and a pig leg), demonstrating plausible illustration and expressiveness.

Diffusion tensor optical coherence tomography

NASA Astrophysics Data System (ADS)

Marks, Daniel L.; Blackmon, Richard L.; Oldenburg, Amy L.

2018-01-01

In situ measurements of diffusive particle transport provide insight into tissue architecture, drug delivery, and cellular function. Analogous to diffusion-tensor magnetic resonance imaging (DT-MRI), where the anisotropic diffusion of water molecules is mapped on the millimeter scale to elucidate the fibrous structure of tissue, here we propose diffusion-tensor optical coherence tomography (DT-OCT) for measuring directional diffusivity and flow of optically scattering particles within tissue. Because DT-OCT is sensitive to the sub-resolution motion of Brownian particles as they are constrained by tissue macromolecules, it has the potential to quantify nanoporous anisotropic tissue structure at micrometer resolution as relevant to extracellular matrices, neurons, and capillaries. Here we derive the principles of DT-OCT, relating the detected optical signal from a minimum of six probe beams with the six unique diffusion tensor and three flow vector components. The optimal geometry of the probe beams is determined given a finite numerical aperture, and a high-speed hardware implementation is proposed. Finally, Monte Carlo simulations are employed to assess the ability of the proposed DT-OCT system to quantify anisotropic diffusion of nanoparticles in a collagen matrix, an extracellular constituent that is known to become highly aligned during tumor development.

Full paleostress tensor reconstruction using quartz veins of Panasqueira Mine, central Portugal; part I: Paleopressure determination

NASA Astrophysics Data System (ADS)

Jaques, Luís; Pascal, Christophe

2017-09-01

Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal exposures of mineralized quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. The present contribution focuses specifically on the determination of pore pressure. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of ∼300 MPa and formation depths of ∼10 km. Such formation depths are in good agreement with the regional geological evolution. The obtained pore pressure will be merged with vein inversion results, in order to achieve full paleostress tensor restoration, in a forthcoming companion paper.

Kinematic space and wormholes

NASA Astrophysics Data System (ADS)

Zhang, Jian-dong; Chen, Bin

2017-01-01

The kinematic space could play a key role in constructing the bulk geometry from dual CFT. In this paper, we study the kinematic space from geometric points of view, without resorting to differential entropy. We find that the kinematic space could be intrinsically defined in the embedding space. For each oriented geodesic in the Poincaré disk, there is a corresponding point in the kinematic space. This point is the tip of the causal diamond of the disk whose intersection with the Poincaré disk determines the geodesic. In this geometric construction, the causal structure in the kinematic space can be seen clearly. Moreover, we find that every transformation in the SL(2,R) leads to a geodesic in the kinematic space. In particular, for a hyperbolic transformation defining a BTZ black hole, it is a timelike geodesic in the kinematic space. We show that the horizon length of the static BTZ black hole could be computed by the geodesic length of corresponding points in the kinematic space. Furthermore, we discuss the fundamental regions in the kinematic space for the BTZ blackhole and multi-boundary wormholes.

The inherent dynamics of a molecular liquid: geodesic pathways through the potential energy landscape of a liquid of linear molecules.

PubMed

Jacobson, Daniel; Stratt, Richard M

2014-05-07

Because the geodesic pathways that a liquid follows through its potential energy landscape govern its slow, diffusive motion, we suggest that these pathways are logical candidates for the title of a liquid's "inherent dynamics." Like their namesake "inherent structures," these objects are simply features of the system's potential energy surface and thus provide views of the system's structural evolution unobstructed by thermal kinetic energy. This paper shows how these geodesic pathways can be computed for a liquid of linear molecules, allowing us to see precisely how such molecular liquids mix rotational and translational degrees of freedom into their dynamics. The ratio of translational to rotational components of the geodesic path lengths, for example, is significantly larger than would be expected on equipartition grounds, with a value that scales with the molecular aspect ratio. These and other features of the geodesics are consistent with a picture in which molecular reorientation adiabatically follows translation-molecules largely thread their way through narrow channels available in the potential energy landscape.

The inherent dynamics of a molecular liquid: Geodesic pathways through the potential energy landscape of a liquid of linear molecules

NASA Astrophysics Data System (ADS)

Jacobson, Daniel; Stratt, Richard M.

2014-05-01

Because the geodesic pathways that a liquid follows through its potential energy landscape govern its slow, diffusive motion, we suggest that these pathways are logical candidates for the title of a liquid's "inherent dynamics." Like their namesake "inherent structures," these objects are simply features of the system's potential energy surface and thus provide views of the system's structural evolution unobstructed by thermal kinetic energy. This paper shows how these geodesic pathways can be computed for a liquid of linear molecules, allowing us to see precisely how such molecular liquids mix rotational and translational degrees of freedom into their dynamics. The ratio of translational to rotational components of the geodesic path lengths, for example, is significantly larger than would be expected on equipartition grounds, with a value that scales with the molecular aspect ratio. These and other features of the geodesics are consistent with a picture in which molecular reorientation adiabatically follows translation—molecules largely thread their way through narrow channels available in the potential energy landscape.

Inflationary tensor fossils in large-scale structure

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

Dimastrogiovanni, Emanuela; Fasiello, Matteo; Jeong, Donghui

Inflation models make specific predictions for a tensor-scalar-scalar three-point correlation, or bispectrum, between one gravitational-wave (tensor) mode and two density-perturbation (scalar) modes. This tensor-scalar-scalar correlation leads to a local power quadrupole, an apparent departure from statistical isotropy in our Universe, as well as characteristic four-point correlations in the current mass distribution in the Universe. So far, the predictions for these observables have been worked out only for single-clock models in which certain consistency conditions between the tensor-scalar-scalar correlation and tensor and scalar power spectra are satisfied. Here we review the requirements on inflation models for these consistency conditions to bemore » satisfied. We then consider several examples of inflation models, such as non-attractor and solid-inflation models, in which these conditions are put to the test. In solid inflation the simplest consistency conditions are already violated whilst in the non-attractor model we find that, contrary to the standard scenario, the tensor-scalar-scalar correlator probes directly relevant model-dependent information. We work out the predictions for observables in these models. For non-attractor inflation we find an apparent local quadrupolar departure from statistical isotropy in large-scale structure but that this power quadrupole decreases very rapidly at smaller scales. The consistency of the CMB quadrupole with statistical isotropy then constrains the distance scale that corresponds to the transition from the non-attractor to attractor phase of inflation to be larger than the currently observable horizon. Solid inflation predicts clustering fossils signatures in the current galaxy distribution that may be large enough to be detectable with forthcoming, and possibly even current, galaxy surveys.« less

Space–time and spatial geodesic orbits in Schwarzschild geometry

NASA Astrophysics Data System (ADS)

Resca, Lorenzo

2018-05-01

Geodesic orbit equations in the Schwarzschild geometry of general relativity reduce to ordinary conic sections of Newtonian mechanics and gravity for material particles in the non-relativistic limit. On the contrary, geodesic orbit equations for a proper spatial submanifold of Schwarzschild metric at any given coordinate-time correspond to an unphysical gravitational repulsion in the non-relativistic limit. This demonstrates at a basic level the centrality and critical role of relativistic time and its intimate pseudo-Riemannian connection with space. Correspondingly, a commonly popularised depiction of geodesic orbits of planets as resulting from the curvature of space produced by the Sun, represented as a rubber sheet dipped in the middle by the weighing of that massive body, is mistaken and misleading for the essence of relativity, even in the non-relativistic limit.

Null geodesics and red-blue shifts of photons emitted from geodesic particles around a noncommutative black hole space-time

NASA Astrophysics Data System (ADS)

Kuniyal, Ravi Shankar; Uniyal, Rashmi; Biswas, Anindya; Nandan, Hemwati; Purohit, K. D.

2018-06-01

We investigate the geodesic motion of massless test particles in the background of a noncommutative geometry-inspired Schwarzschild black hole. The behavior of effective potential is analyzed in the equatorial plane and the possible motions of massless particles (i.e. photons) for different values of impact parameter are discussed accordingly. We have also calculated the frequency shift of photons in this space-time. Further, the mass parameter of a noncommutative inspired Schwarzschild black hole is computed in terms of the measurable redshift of photons emitted by massive particles moving along circular geodesics in equatorial plane. The strength of gravitational fields of noncommutative geometry-inspired Schwarzschild black hole and usual Schwarzschild black hole in General Relativity is also compared.

No-Go Theorem for Nonstandard Explanations of the τ → K S π ν τ C P Asymmetry

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

Cirigliano, Vincenzo; Crivellin, Andreas; Hoferichter, Martin

Tmore » he C P asymmetry in τ → K S π ν τ C P , as measured by the BABAR collaboration, differs from the standard model prediction by 2.8 σ . Most nonstandard interactions do not allow for the required strong phase needed to produce a nonvanishing C P asymmetry, leaving only new tensor interactions as a possible mechanism. We demonstrate that, contrary to previous assumptions in the literature, the crucial interference between vector and tensor phases is suppressed by at least 2 orders of magnitude due to Watson’s final-state-interaction theorem. Furthermore, we find that the strength of the relevant C P -violating tensor interaction is strongly constrained by bounds from the neutron electric dipole moment and D – ¯ D mixing. hese observations together imply that it is extremely difficult to explain the current τ → K S π ν τ C P measurement in terms of physics beyond the standard model originating in the ultraviolet.« less

No-Go Theorem for Nonstandard Explanations of the τ → K S π ν τ C P Asymmetry

DOE PAGES

Cirigliano, Vincenzo; Crivellin, Andreas; Hoferichter, Martin

2018-04-06

Tmore » he C P asymmetry in τ → K S π ν τ C P , as measured by the BABAR collaboration, differs from the standard model prediction by 2.8 σ . Most nonstandard interactions do not allow for the required strong phase needed to produce a nonvanishing C P asymmetry, leaving only new tensor interactions as a possible mechanism. We demonstrate that, contrary to previous assumptions in the literature, the crucial interference between vector and tensor phases is suppressed by at least 2 orders of magnitude due to Watson’s final-state-interaction theorem. Furthermore, we find that the strength of the relevant C P -violating tensor interaction is strongly constrained by bounds from the neutron electric dipole moment and D – ¯ D mixing. hese observations together imply that it is extremely difficult to explain the current τ → K S π ν τ C P measurement in terms of physics beyond the standard model originating in the ultraviolet.« less

Gravitational-wave cosmology across 29 decades in frequency

DOE PAGES

Lasky, Paul D.; Mingarelli, Chiara M. F.; Smith, Tristan L.; ...

2016-03-31

Here, quantum fluctuations of the gravitational field in the early Universe, amplified by inflation, produce a primordial gravitational-wave background across a broad frequency band. We derive constraints on the spectrum of this gravitational radiation, and hence on theories of the early Universe, by combining experiments that cover 29 orders of magnitude in frequency. These include Planck observations of cosmic microwave background temperature and polarization power spectra and lensing, together with baryon acoustic oscillations and big bang nucleosynthesis measurements, as well as new pulsar timing array and ground-based interferometer limits. While individual experiments constrain the gravitational-wave energy density in specific frequencymore » bands, the combination of experiments allows us to constrain cosmological parameters, including the inflationary spectral index n t and the tensor-to-scalar ratio r. Results from individual experiments include the most stringent nanohertz limit of the primordial background to date from the Parkes Pulsar Timing Array, Ω GW(f) < 2.3 × 10 -10. Observations of the cosmic microwave background alone limit the gravitational-wave spectral index at 95% confidence to n t ≲ 5 for a tensor-toscalar ratio of r = 0.11. However, the combination of all the above experiments limits n t < 0.36. Future Advanced LIGO observations are expected to further constrain n t < 0.34 by 2020. When cosmic microwave background experiments detect a nonzero r, our results will imply even more stringent constraints on n t and, hence, theories of the early Universe.« less

Geodesic curve-of-sight formulae for the cosmic microwave background: a unified treatment of redshift, time delay, and lensing

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

Saito, Ryo; Naruko, Atsushi; Hiramatsu, Takashi

2014-10-01

In this paper, we introduce a new approach to a treatment of the gravitational effects (redshift, time delay and lensing) on the observed cosmic microwave background (CMB) anisotropies based on the Boltzmann equation. From the Liouville's theorem in curved spacetime, the intensity of photons is conserved along a photon geodesic when non-gravitational scatterings are absent. Motivated by this fact, we derive a second-order line-of-sight formula by integrating the Boltzmann equation along a perturbed geodesic (curve) instead of a background geodesic (line). In this approach, the separation of the gravitational and intrinsic effects are manifest. This approach can be considered asmore » a generalization of the remapping approach of CMB lensing, where all the gravitational effects can be treated on the same footing.« less

A discrete model for geometrically nonlinear transverse free constrained vibrations of beams with various end conditions

NASA Astrophysics Data System (ADS)

Rahmouni, A.; Beidouri, Z.; Benamar, R.

2013-09-01

The purpose of the present paper was the development of a physically discrete model for geometrically nonlinear free transverse constrained vibrations of beams, which may replace, if sufficient degrees of freedom are used, the previously developed continuous nonlinear beam constrained vibration models. The discrete model proposed is an N-Degrees of Freedom (N-dof) system made of N masses placed at the ends of solid bars connected by torsional springs, presenting the beam flexural rigidity. The large transverse displacements of the bar ends induce a variation in their lengths giving rise to axial forces modelled by longitudinal springs. The calculations made allowed application of the semi-analytical model developed previously for nonlinear structural vibration involving three tensors, namely the mass tensor mij, the linear rigidity tensor kij and the nonlinearity tensor bijkl. By application of Hamilton's principle and spectral analysis, the nonlinear vibration problem is reduced to a nonlinear algebraic system, examined for increasing numbers of dof. The results obtained by the physically discrete model showed a good agreement and a quick convergence to the equivalent continuous beam model, for various fixed boundary conditions, for both the linear frequencies and the nonlinear backbone curves, and also for the corresponding mode shapes. The model, validated here for the simply supported and clamped ends, may be used in further works to present the flexural linear and nonlinear constrained vibrations of beams with various types of discontinuities in the mass or in the elasticity distributions. The development of an adequate discrete model including the effect of the axial strains induced by large displacement amplitudes, which is predominant in geometrically nonlinear transverse constrained vibrations of beams [1]. The investigation of the results such a discrete model may lead to in the case of nonlinear free vibrations. The development of the analogy between the previously developed models of geometrically nonlinear vibrations of Euler-Bernoulli continuous beams, and multidof system models made of N masses placed at the end of elastic bars connected by linear spiral springs, presenting the beam flexural rigidity. The validation of the new model via the analysis of the convergence conditions of the nonlinear frequencies obtained by the N-dof system, when N increases, and those obtained in previous works using a continuous description of the beam. In addition to the above points, the models developed in the present work, may constitute, in our opinion, a good illustration, from the didactic point of view, of the origin of the geometrical nonlinearity induced by large transverse vibration amplitudes of constrained continuous beams, which may appear as a Pythagorean Theorem effect. The first step of the work presented here was the formulation of the problem of nonlinear vibrations of the discrete system shown in Fig. 1 in terms of the semi-analytical method, denoted as SAA, developed in the early 90's by Benamar and coauthors [3], and discussed for example in [6,7]. This method has been applied successfully to various types of geometrically nonlinear problems of structural dynamics [1-3,6-8,10-12] and the objective here was to use it in order to develop a flexible discrete nonlinear model which may be useful for presenting in further works geometrically nonlinear vibrations of real beams with discontinuities in the mass, the section, or the stiffness distributions. The purpose in the present work was restricted to developing and validating the model, via comparison of the obtained dependence of the resonance frequencies of such a system on the amplitude of vibration, with the results obtained previously by continuous beams nonlinear models. In the SAA method, the dynamic system under consideration is described by the mass matrix [M], the rigidity matrix [K], and the nonlinear rigidity matrix [B], which depends on the amplitude of vibration, and involves a fourth-order nonlinearity tensor bijkl. Details are given below, corresponding to the definition of the tensors mentioned above. The analogy between the classical continuous Euler-Bernoulli model of beams and the present discrete model is developed, leading to the expressions for the equivalent spiral and axial stiffness, in terms of the continuous beam geometrical and mechanical characteristics. Some numerical results are also given, showing the amplitude dependence of the frequencies on the amplitude of vibration, and compared to the backbone curves obtained previously by the continuous nonlinear classical beam theory, presented for example in [3,5,8,15-22]. A convergence study is performed by increasing the number of masses and bars, showing a good convergence to the theoretical values of continuous beams.

How much can we learn about the physics of inflation?

PubMed

Dodelson, Scott

2014-05-16

The recent BICEP2 measurement of B modes in the polarization of the cosmic microwave background suggests that inflation was driven by a field at an energy scale of 2 × 10(16) GeV. I explore the potential of upcoming cosmic microwave radiation polarization experiments to further constrain the physics underlying inflation. If the signal is confirmed, then two sets of experiments covering a large area will shed light on inflation. Low-resolution measurements can pin down the tensor to scalar ratio at the percent level, thereby distinguishing models from one another. A high angular resolution experiment will be necessary to measure the tilt of the tensor spectrum, testing the consistency relation that relates the tilt to the amplitude.

Acoustic emission source location in composite structure by Voronoi construction using geodesic curve evolution.

PubMed

Gangadharan, R; Prasanna, G; Bhat, M R; Murthy, C R L; Gopalakrishnan, S

2009-11-01

Conventional analytical/numerical methods employing triangulation technique are suitable for locating acoustic emission (AE) source in a planar structure without structural discontinuities. But these methods cannot be extended to structures with complicated geometry, and, also, the problem gets compounded if the material of the structure is anisotropic warranting complex analytical velocity models. A geodesic approach using Voronoi construction is proposed in this work to locate the AE source in a composite structure. The approach is based on the fact that the wave takes minimum energy path to travel from the source to any other point in the connected domain. The geodesics are computed on the meshed surface of the structure using graph theory based on Dijkstra's algorithm. By propagating the waves in reverse virtually from these sensors along the geodesic path and by locating the first intersection point of these waves, one can get the AE source location. In this work, the geodesic approach is shown more suitable for a practicable source location solution in a composite structure with arbitrary surface containing finite discontinuities. Experiments have been conducted on composite plate specimens of simple and complex geometry to validate this method.

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2013-11-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. Uμ = γ (c , u (r --> , t)) denotes four-velocity field. Jμ = ρUμ denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. DJμ/Dτ =dJμ/Dτ +ΓαβμJαUβ =JνΩμν +∂νTμν +ΓαβμJαUβ Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is DJμ/Dτ =JνFμν +∂νTμν +ΓαβμJαUβ electromagnetism.

M-Isomap: Orthogonal Constrained Marginal Isomap for Nonlinear Dimensionality Reduction.

PubMed

Zhang, Zhao; Chow, Tommy W S; Zhao, Mingbo

2013-02-01

Isomap is a well-known nonlinear dimensionality reduction (DR) method, aiming at preserving geodesic distances of all similarity pairs for delivering highly nonlinear manifolds. Isomap is efficient in visualizing synthetic data sets, but it usually delivers unsatisfactory results in benchmark cases. This paper incorporates the pairwise constraints into Isomap and proposes a marginal Isomap (M-Isomap) for manifold learning. The pairwise Cannot-Link and Must-Link constraints are used to specify the types of neighborhoods. M-Isomap computes the shortest path distances over constrained neighborhood graphs and guides the nonlinear DR through separating the interclass neighbors. As a result, large margins between both interand intraclass clusters are delivered and enhanced compactness of intracluster points is achieved at the same time. The validity of M-Isomap is examined by extensive simulations over synthetic, University of California, Irvine, and benchmark real Olivetti Research Library, YALE, and CMU Pose, Illumination, and Expression databases. The data visualization and clustering power of M-Isomap are compared with those of six related DR methods. The visualization results show that M-Isomap is able to deliver more separate clusters. Clustering evaluations also demonstrate that M-Isomap delivers comparable or even better results than some state-of-the-art DR algorithms.

Self-consistent geodesic equation and quantum tunneling from charged AdS black holes

NASA Astrophysics Data System (ADS)

Deng, Gao-Ming

2017-12-01

Some urgent shortcomings in previous derivations of geodesic equations are remedied in this paper. In contrast to the unnatural and awkward treatment in previous works, here we derive the geodesic equations of massive and massless particles in a unified and self- consistent manner. Furthermore, we extend to investigate the Hawking radiation via tunneling from charged black holes in the context of AdS spacetime. Of special interest, the application of the first law of black hole thermodynamics in tunneling integration manifestly simplifies the calculation.

Singularities and the geometry of spacetime

NASA Astrophysics Data System (ADS)

Hawking, Stephen

2014-11-01

The aim of this essay is to investigate certain aspects of the geometry of the spacetime manifold in the General Theory of Relativity with particular reference to the occurrence of singularities in cosmological solutions and their relation with other global properties. Section 2 gives a brief outline of Riemannian geometry. In Section 3, the General Theory of Relativity is presented in the form of two postulates and two requirements which are common to it and to the Special Theory of Relativity, and a third requirement, the Einstein field equations, which distinguish it from the Special Theory. There does not seem to be any alternative set of field equations which would not have some undeseriable features. Some exact solutions are described. In Section 4, the physical significance of curvature is investigated using the deviation equation for timelike and null curves. The Riemann tensor is decomposed into the Ricci tensor which represents the gravitational effect at a point of matter at that point and the Welyl tensor which represents the effect at a point of gravitational radiation and matter at other points. The two tensors are related by the Bianchi identities which are presented in a form analogous to the Maxwell equations. Some lemmas are given for the occurrence of conjugate points on timelike and null geodesics and their relation with the variation of timelike and null curves is established. Section 5 is concerned with properties of causal relations between points of spacetime. It is shown that these could be used to determine physically the manifold structure of spacetime if the strong causality assumption held. The concepts of a null horizon and a partial Cauchy surface are introduced and are used to prove a number of lemmas relating to the existence of a timelike curve of maximum length between two sets. In Section 6, the definition of a singularity of spacetime is given in terms of geodesic incompleteness. The various energy assumptions needed to prove the occurrence of singularities are discussed and then a number of theorems are presented which prove the occurrence of singularities in most cosmological solutions. A procedure is given which could be used to describe and classify the singularites and their expected nature is discussed. Sections 2 and 3 are reviews of standard work. In Section 4, the deviation equation is standard but the matrix method used to analyse it is the author's own as is the decomposition given of the Bianchi identities (this was also obtained independently by Trümper). Variation of curves and conjugate points are standard in a positive-definite metric but this seems to be the first full account for timelike and null curves in a Lorentz metric. Except where otherwise indicated in the text, Sections 5 and 6 are the work of the author who, however, apologises if through ignorance or inadvertance he has failed to make acknowledgements where due. Some of this work has been described in [Hawking S.W. 1965b. Occurrence of singularities in open universes. Phys. Rev. Lett. 15: 689-690; Hawking S.W. and G.F.R. Ellis. 1965c. Singularities in homogeneous world models. Phys. Rev. Lett. 17: 246-247; Hawking S.W. 1966a. Singularities in the universe. Phys. Rev. Lett. 17: 444-445; Hawking S.W. 1966c. The occurrence of singularities in cosmology. Proc. Roy. Soc. Lond. A 294: 511-521]. Undoubtedly, the most important results are the theorems in Section 6 on the occurrence of singularities. These seem to imply either that the General Theory of Relativity breaks down or that there could be particles whose histories did not exist before (or after) a certain time. The author's own opinion is that the theory probably does break down, but only when quantum gravitational effects become important. This would not be expected to happen until the radius of curvature of spacetime became about 10-14 cm.

Exact Descriptions of General Relativity Derived from Newtonian Mechanics within Curved Geometries

NASA Astrophysics Data System (ADS)

Savickas, David

2015-04-01

General relativity and Newtonian mechanics are shown to be exactly related when Newton's second law is written in a curved geometry by using the physical components of a vector as is defined in tensor calculus. By replacing length within the momentum's velocity by the vector metric in a curved geometry the second law can then be shown to be exactly identical to the geodesic equation of motion occurring in general relativity. When time's vector direction is constant, as similarly occurs in Newtonian mechanics, this equation can be reduced to a curved three-dimensional equation of motion that yields the the Schwarzschild equations of motion for an isolated particle. They can be used to describe gravitational behavior for any array of masses for which the Newtonian gravitational potential is known, and is shown to describe a mass particle's behavior in the gravitational field of a thin mass-rod. This use of Newton's laws allows relativistic behavior to be described in a physically comprehensible manner. D. Savickas, Int. J. Mod. Phys. D 23 1430018, (2014).

Hamiltonian Systems and Optimal Control in Computational Anatomy: 100 Years Since D'Arcy Thompson.

PubMed

Miller, Michael I; Trouvé, Alain; Younes, Laurent

2015-01-01

The Computational Anatomy project is the morphome-scale study of shape and form, which we model as an orbit under diffeomorphic group action. Metric comparison calculates the geodesic length of the diffeomorphic flow connecting one form to another. Geodesic connection provides a positioning system for coordinatizing the forms and positioning their associated functional information. This article reviews progress since the Euler-Lagrange characterization of the geodesics a decade ago. Geodesic positioning is posed as a series of problems in Hamiltonian control, which emphasize the key reduction from the Eulerian momentum with dimension of the flow of the group, to the parametric coordinates appropriate to the dimension of the submanifolds being positioned. The Hamiltonian viewpoint provides important extensions of the core setting to new, object-informed positioning systems. Several submanifold mapping problems are discussed as they apply to metamorphosis, multiple shape spaces, and longitudinal time series studies of growth and atrophy via shape splines.

Superintegrability of geodesic motion on the sausage model

NASA Astrophysics Data System (ADS)

Arutyunov, Gleb; Heinze, Martin; Medina-Rincon, Daniel

2017-06-01

Reduction of the η-deformed sigma model on AdS_5× S5 to the two-dimensional squashed sphere (S^2)η can be viewed as a special case of the Fateev sausage model where the coupling constant ν is imaginary. We show that geodesic motion in this model is described by a certain superintegrable mechanical system with four-dimensional phase space. This is done by means of explicitly constructing three integrals of motion which satisfy the sl(2) Poisson algebra relations, albeit being non-polynomial in momenta. Further, we find a canonical transformation which transforms the Hamiltonian of this mechanical system to the one describing the geodesic motion on the usual two-sphere. By inverting this transformation we map geodesics on this auxiliary two-sphere back to the sausage model. This paper is a tribute to the memory of Prof Petr Kulish.

Geodesic regression on orientation distribution functions with its application to an aging study.

PubMed

Du, Jia; Goh, Alvina; Kushnarev, Sergey; Qiu, Anqi

2014-02-15

In this paper, we treat orientation distribution functions (ODFs) derived from high angular resolution diffusion imaging (HARDI) as elements of a Riemannian manifold and present a method for geodesic regression on this manifold. In order to find the optimal regression model, we pose this as a least-squares problem involving the sum-of-squared geodesic distances between observed ODFs and their model fitted data. We derive the appropriate gradient terms and employ gradient descent to find the minimizer of this least-squares optimization problem. In addition, we show how to perform statistical testing for determining the significance of the relationship between the manifold-valued regressors and the real-valued regressands. Experiments on both synthetic and real human data are presented. In particular, we examine aging effects on HARDI via geodesic regression of ODFs in normal adults aged 22 years old and above. © 2013 Elsevier Inc. All rights reserved.

Ray-tracing method for creeping waves on arbitrarily shaped nonuniform rational B-splines surfaces.

PubMed

Chen, Xi; He, Si-Yuan; Yu, Ding-Feng; Yin, Hong-Cheng; Hu, Wei-Dong; Zhu, Guo-Qiang

2013-04-01

An accurate creeping ray-tracing algorithm is presented in this paper to determine the tracks of creeping waves (or creeping rays) on arbitrarily shaped free-form parametric surfaces [nonuniform rational B-splines (NURBS) surfaces]. The main challenge in calculating the surface diffracted fields on NURBS surfaces is due to the difficulty in determining the geodesic paths along which the creeping rays propagate. On one single parametric surface patch, the geodesic paths need to be computed by solving the geodesic equations numerically. Furthermore, realistic objects are generally modeled as the union of several connected NURBS patches. Due to the discontinuity of the parameter between the patches, it is more complicated to compute geodesic paths on several connected patches than on one single patch. Thus, a creeping ray-tracing algorithm is presented in this paper to compute the geodesic paths of creeping rays on the complex objects that are modeled as the combination of several NURBS surface patches. In the algorithm, the creeping ray tracing on each surface patch is performed by solving the geodesic equations with a Runge-Kutta method. When the creeping ray propagates from one patch to another, a transition method is developed to handle the transition of the creeping ray tracing across the border between the patches. This creeping ray-tracing algorithm can meet practical requirements because it can be applied to the objects with complex shapes. The algorithm can also extend the applicability of NURBS for electromagnetic and optical applications. The validity and usefulness of the algorithm can be verified from the numerical results.

Finite Element Analysis of Geodesically Stiffened Cylindrical Composite Shells Using a Layerwise Theory

NASA Technical Reports Server (NTRS)

Gerhard, Craig Steven; Gurdal, Zafer; Kapania, Rakesh K.

1996-01-01

Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.

On actions for (entangling) surfaces and DCFTs

NASA Astrophysics Data System (ADS)

Armas, Jay; Tarrío, Javier

2018-04-01

The dynamics of surfaces and interfaces describe many physical systems, including fluid membranes, entanglement entropy and the coupling of defects to quantum field theories. Based on the formulation of submanifold calculus developed by Carter, we introduce a new variational principle for (entangling) surfaces. This principle captures all diffeomorphism constraints on surface/interface actions and their associated spacetime stress tensor. The different couplings to the geometric tensors appearing in the surface action are interpreted in terms of response coefficients within elasticity theory. An example of a surface action with edges at the two-derivative level is studied, including both the parity-even and parity-odd sectors. Its conformally invariant counterpart restricts the type of conformal anomalies that can appear in two-dimensional submanifolds with boundaries. Analogously to hydrodynamics, it is shown that classification methods can be used to constrain the stress tensor of (entangling) surfaces at a given order in derivatives. This analysis reveals a purely geometric parity-odd contribution to the Young modulus of a thin elastic membrane. Extending this novel variational principle to BCFTs and DCFTs in curved spacetimes allows to obtain the Ward identities for diffeomorphism and Weyl transformations. In this context, we provide a formal derivation of the contact terms in the stress tensor and of the displacement operator for a broad class of actions.

Full paleostress tensor reconstruction: case study of the Panasqueira Mine, Portugal.

NASA Astrophysics Data System (ADS)

Pascal, C.; Jaques Ribeiro, L. M.

2017-12-01

Paleostress tensor restoration methods are traditionally limited to reconstructing geometrical parameters and are unable to resolve stress magnitudes. Based on previous studies we further developed a methodology to restore full paleostress tensors. We concentrated on inversion of Mode I fractures and acquired data in Panasqueira Mine, Portugal, where optimal 3D exposures of mineralised quartz veins can be found. To carry out full paleostress restoration we needed to determine (1) pore (paleo)pressure and (2) vein attitudes. To these aims we conducted an extensive fluid inclusion study to derive fluid isochores from the quartz of the studied veins. To further constrain P-T conditions, we combined these isochores with crystallisation temperatures derived from geochemical analyses of coeval arsenopyrite. We also applied the sphalerite geobarometer and considered two other independent pressure indicators. Our results point to pore pressures of 300 MPa and formation depths of 10 km. As a second step, we measured 600 subhorizontal quartz veins in all the levels of the mine. The inversion of the attitudes of the veins allowed for reconstructing the orientations of the principal axes of stress, the unscaled Mohr circle and the relative pore pressure. After merging these results with the previously obtained absolute pore pressure we reconstructed the six parameters of the paleostress tensor.

Gravitational collapse in Husain space-time for Brans-Dicke gravity theory with power-law potential

NASA Astrophysics Data System (ADS)

Rudra, Prabir; Biswas, Ritabrata; Debnath, Ujjal

2014-12-01

The motive of this work is to study gravitational collapse in Husain space-time in Brans-Dicke gravity theory. Among many scalar-tensor theories of gravity, Brans-Dicke is the simplest and the impact of it can be regulated by two parameters associated with it, namely, the Brans-Dicke parameter, ω, and the potential-scalar field dependency parameter n respectively. V. Husain's work on exact solution for null fluid collapse in 1996 has influenced many authors to follow his way to find the end-state of the homogeneous/inhomogeneous dust cloud. Vaidya's metric is used all over to follow the nature of future outgoing radial null geodesics. Detecting whether the central singularity is naked or wrapped by an event horizon, by the existence of future directed radial null geodesic emitted in past from the singularity is the basic objective. To point out the existence of positive trajectory tangent solution, both particular parametric cases (through tabular forms) and wide range contouring process have been applied. Precisely, perfect fluid's EoS satisfies a wide range of phenomena: from dust to exotic fluid like dark energy. We have used the EoS parameter k to determine the end state of collapse in different cosmological era. Our main target is to check low ω (more deviations from Einstein gravity-more Brans Dicke effect) and negative k zones. This particularly throws light on the nature of the end-state of collapse in accelerated expansion in Brans Dicke gravity. It is seen that for positive values of EoS parameter k, the collapse results in a black hole, whereas for negative values of k, naked singularity is the only outcome. It is also to be noted that "low ω" leads to the possibility of getting more naked singularities even for a non-accelerating universe.

Gravitational Collapse in Husain space-time for Brans-Dicke Gravity Theory with Power-law Potential.

NASA Astrophysics Data System (ADS)

Rudra, Prabir

2016-07-01

The motive of this work is to study gravitational collapse in Husain space-time in Brans-Dicke gravity theory. Among many scalar-tensor theories of gravity, Brans-Dicke is the simplest and the impact of it can be regulated by two parameters associated with it, namely, the Brans-Dicke parameter, ω, and the potential-scalar field dependency parameter 'n' respectively. V. Husain's work on exact solution for null fluid collapse in 1996 has influenced many authors to follow his way to find the end-state of the homogeneous/inhomogeneous dust cloud. Vaidya's metric is used all over to follow the nature of future outgoing radial null geodesics. Detecting whether the central singularity is naked or wrapped by an event horizon, by the existence of future directed radial null geodesic emitted in past from the singularity is the basic objective. To point out the existence of positive trajectory tangent solution, both particular parametric cases(through tabular forms) and wide range contouring process have been applied. Precisely, perfect fluid's equation of state satisfies a wide range of phenomena : from dust to exotic fluid like dark energy. We have used the equation of state parameter 'k' to determine the end state of collapse in different cosmological era. Our main target is to check low ω (more deviations from Einstein gravity-more Brans Dicke effect) and negative 'k' zones. This particularly throws light on the nature of the end-state of collapse in accelerated expansion in Brans Dicke gravity. It is seen that for positive values of EoS parameter 'k', the collapse results in a black hole, whereas for negative values of 'k', naked singularity is the only outcome. It is also to be noted that "low ω" leads to the possibility of getting more naked singularities even for a non-accelerating universe.

BOOK REVIEW: Advanced Mechanics and General Relativity Advanced Mechanics and General Relativity

NASA Astrophysics Data System (ADS)

Louko, Jorma

2011-04-01

Joel Franklin's textbook `Advanced Mechanics and General Relativity' comprises two partially overlapping, partially complementary introductory paths into general relativity at advanced undergraduate level. Path I starts with the Lagrangian and Hamiltonian formulations of Newtonian point particle motion, emphasising the action principle and the connection between symmetries and conservation laws. The concepts are then adapted to point particle motion in Minkowski space, introducing Lorentz transformations as symmetries of the action. There follows a focused development of tensor calculus, parallel transport and curvature, using examples from Newtonian mechanics and special relativity, culminating in the field equations of general relativity. The Schwarzschild solution is analysed, including a detailed discussion of the tidal forces on a radially infalling observer. Basics of gravitational radiation are examined, highlighting the similarities to and differences from electromagnetic radiation. The final topics in Path I are equatorial geodesics in Kerr and the motion of a relativistic string in Minkowski space. Path II starts by introducing scalar field theory on Minkowski space as a limit of point masses connected by springs, emphasising the action principle, conservation laws and the energy-momentum tensor. The action principle for electromagnetism is introduced, and the coupling of electromagnetism to a complex scalar field is developed in a detailed and pedagogical fashion. A free symmetric second-rank tensor field on Minkowski space is introduced, and the action principle of general relativity is recovered from coupling the second-rank tensor to its own energy-momentum tensor. Path II then merges with Path I and, supplanted with judicious early selections from Path I, can proceed to the Schwarzschild solution. The choice of material in each path is logical and focused. A notable example in Path I is that Lorentz transformations in Minkowki space are introduced efficiently and with a minimum of fuss, as symmetries of a geodesic action principle. Another example is a similarly efficient and hands-on introduction of Killing vectors. A consequence of this focus is that some perhaps traditional material is omitted. For example, Lorentz contraction appears briefly in the incompatibility discussion of special relativity and Newtonian gravity but is not introduced in a more systematic manner. The style is informal and very readable, with detailed explanations, frequent summaries of what has been achieved and pointers to what is about to follow. There are plenty of examples and some 150 well-chosen exercises, and the author's website hosts relevant Maple sample scripts for tensor manipulations and variational problems. The text conveys an enthusiasm for explaining the subject, frequently reminiscent of the Feynman lectures. The presentation emphasises explicit calculations and examples, largely avoiding technical definitions of abstract mathematical concepts. The author negotiates the challenge between readability and technical accuracy with admirable skill, striking a balance that will be much appreciated by the target audience. For example, the notion of spherical symmetry in curved spacetime is introduced informally as a generalisation of a spherically symmetric vector field in Minkowski space, and spherically symmetric vacuum and electrovacuum solutions are then carefully discussed so that a formal definition of spherical symmetry is not required. A rare instance that may border on oversimplification is the brief discussion of curvature scalars versus spacetime singularities. Towards the end of the book, the text mentions with increasing explicitness that inserting a gauge condition or an ansatz in an action before varying may not always give the correct equations of motion. It would be useful to be more explicit about this point already earlier in the book. In particular, the text refers to the reparametrisation-invariant square root action of a relativistic point particle as being `in proper time parametrisation', while the actual calculations of course impose the proper time condition only in the equation of motion after the action has been varied. Two presentational conventions surprised me. First, the speed of light is throughout kept explicitly as c: might advanced undergraduates appreciate being trusted with geometric units, reinstating c by dimensional analysis when desired? Second, in Minkowski space field theory, the overall coefficient in the action is chosen so that the time derivative term is negative, with the consequence that the Hamiltonian is negative (as explicitly noted in an exercise) and the definition of the energy-momentum tensor must include a minus sign to achieve the usual choice T00 > 0. This convention eliminates some minus signs in the computations with the spin two field: does this computational saving outweigh the adjustment awaiting those who continue with the topic at graduate level? Overall, Franklin's book is an excellent addition to the literature, and its readability and explicitness will be appreciated by the target audience. Should I be teaching an introductory undergraduate class in general relativity in the near future, I would seriously consider this book for the main class text.

Constraining primordial vector mode from B-mode polarization

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

Saga, Shohei; Ichiki, Kiyotomo; Shiraishi, Maresuke, E-mail: saga.shohei@nagoya-u.jp, E-mail: maresuke.shiraishi@pd.infn.it, E-mail: ichiki@a.phys.nagoya-u.ac.jp

The B-mode polarization spectrum of the Cosmic Microwave Background (CMB) may be the smoking gun of not only the primordial tensor mode but also of the primordial vector mode. If there exist nonzero vector-mode metric perturbations in the early Universe, they are known to be supported by anisotropic stress fluctuations of free-streaming particles such as neutrinos, and to create characteristic signatures on both the CMB temperature, E-mode, and B-mode polarization anisotropies. We place constraints on the properties of the primordial vector mode characterized by the vector-to-scalar ratio r{sub v} and the spectral index n{sub v} of the vector-shear power spectrum,more » from the Planck and BICEP2 B-mode data. We find that, for scale-invariant initial spectra, the ΛCDM model including the vector mode fits the data better than the model including the tensor mode. The difference in χ{sup 2} between the vector and tensor models is Δχ{sup 2} = 3.294, because, on large scales the vector mode generates smaller temperature fluctuations than the tensor mode, which is preferred for the data. In contrast, the tensor mode can fit the data set equally well if we allow a significantly blue-tilted spectrum. We find that the best-fitting tensor mode has a large blue tilt and leads to an indistinct reionization bump on larger angular scales. The slightly red-tilted vector mode supported by the current data set can also create O(10{sup -22})-Gauss magnetic fields at cosmological recombination. Our constraints should motivate research that considers models of the early Universe that involve the vector mode.« less

Measurement of the β-asymmetry parameter of Cu67 in search for tensor-type currents in the weak interaction

NASA Astrophysics Data System (ADS)

Soti, G.; Wauters, F.; Breitenfeldt, M.; Finlay, P.; Herzog, P.; Knecht, A.; Köster, U.; Kraev, I. S.; Porobic, T.; Prashanth, P. N.; Towner, I. S.; Tramm, C.; Zákoucký, D.; Severijns, N.

2014-09-01

Background: Precision measurements at low energy search for physics beyond the standard model in a way complementary to searches for new particles at colliders. In the weak sector the most general β-decay Hamiltonian contains, besides vector and axial-vector terms, also scalar, tensor, and pseudoscalar terms. Current limits on the scalar and tensor coupling constants from neutron and nuclear β decay are on the level of several percent. Purpose: Extracting new information on tensor coupling constants by measuring the β-asymmetry parameter in the pure Gamow-Teller decay of Cu67, thereby testing the V-A structure of the weak interaction. Method: An iron sample foil into which the radioactive nuclei were implanted was cooled down to mK temperatures in a 3He-4He dilution refrigerator. An external magnetic field of 0.1 T, in combination with the internal hyperfine magnetic field, oriented the nuclei. The anisotropic β radiation was observed with planar high-purity germanium detectors operating at a temperature of about 10 K. An on-line measurement of the β asymmetry of Cu68 was performed as well for normalization purposes. Systematic effects were investigated using geant4 simulations. Results: The experimental value, Ã=0.587(14), is in agreement with the standard model value of 0.5991(2) and is interpreted in terms of physics beyond the standard model. The limits obtained on possible tensor-type charged currents in the weak interaction Hamiltonian are -0.045<(CT+CT')/CA<0.159 (90% C.L.). Conclusions: The obtained limits are comparable to limits from other correlation measurements in nuclear β decay and contribute to further constraining tensor coupling constants.

Uncertainty estimations for moment tensor inversions: the issue of the 2012 May 20 Emilia earthquake

NASA Astrophysics Data System (ADS)

Scognamiglio, Laura; Magnoni, Federica; Tinti, Elisa; Casarotti, Emanuele

2016-08-01

Seismic moment tensor is one of the most important source parameters defining the earthquake dimension and style of the activated fault. Geoscientists ordinarily use moment tensor catalogues, however, few attempts have been done to assess possible impacts of moment magnitude uncertainties upon their analysis. The 2012 May 20 Emilia main shock is a representative event since it is defined in literature with a moment magnitude value (Mw) spanning between 5.63 and 6.12. A variability of ˜0.5 units in magnitude leads to a controversial knowledge of the real size of the event and reveals how the solutions could be poorly constrained. In this work, we investigate the stability of the moment tensor solution for this earthquake, studying the effect of five different 1-D velocity models, the number and the distribution of the stations used in the inversion procedure. We also introduce a 3-D velocity model to account for structural heterogeneity. We finally estimate the uncertainties associated to the computed focal planes and the obtained Mw. We conclude that our reliable source solutions provide a moment magnitude that ranges from 5.87, 1-D model, to 5.96, 3-D model, reducing the variability of the literature to ˜0.1. We endorse that the estimate of seismic moment from moment tensor solutions, as well as the estimate of the other kinematic source parameters, requires coming out with disclosed assumptions and explicit processing workflows. Finally and, probably more important, when moment tensor solution is used for secondary analyses it has to be combined with the same main boundary conditions (e.g. wave-velocity propagation model) to avoid conflicting results.

Higher-order geodesic deviation for charged particles and resonance induced by gravitational waves

NASA Astrophysics Data System (ADS)

Heydari-Fard, M.; Hasani, S. N.

We generalize the higher-order geodesic deviation for the structure-less test particles to the higher-order geodesic deviation equations of the charged particles [R. Kerner, J. W. van Holten and R. Colistete Jr., Class. Quantum Grav. 18 (2001) 4725]. By solving these equations for charged particles moving in a constant magnetic field in the spacetime of a gravitational wave, we show for both cases when the gravitational wave is parallel and perpendicular to the constant magnetic field, a magnetic resonance appears at wg = Ω. This feature might be useful to detect the gravitational wave with high frequencies.

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

Kagramanova, Valeria; Kunz, Jutta; Hackmann, Eva

We present the complete set of analytical solutions of the geodesic equation in Taub-NUT space-times in terms of the Weierstrass elliptic functions. We systematically study the underlying polynomials and characterize the motion of test particles by its zeros. Since the presence of the 'Misner string' in the Taub-NUT metric has led to different interpretations, we consider these in terms of the geodesics of the space-time. In particular, we address the geodesic incompleteness at the horizons discussed by Misner and Taub [C. W. Misner and A. H. Taub, Sov. Phys. JETP 28, 122 (1969) [Zh. Eksp. Teor. Fiz. 55, 233 (1968)

Winding trajectories of noncircular composite shells

NASA Astrophysics Data System (ADS)

Nikityuk, V. A.; Fedorov, V. V.

1995-07-01

An approach has been proposed for determination of the trajectory parameters of a layer formed by winding of continuous ribbons on a complicated surface. An algorithm has been developed for determining the geodesic trajectories of the reinforcement fiber arrangement, reinforcement angles, and geodesic deviation angles. Conditions have been formulated for positional stability of the ribbons on the surface and avoidance of gaps and overlapping between the ribbons along with restrictions to the surface form. Results are given for a calculation of the geodesic turn parameters on a fuselage surface, which is not a surface of revolution, of a light airplane.

Geodesic motion around traversable wormholes supported by a massless conformally coupled scalar field

NASA Astrophysics Data System (ADS)

Willenborg, Felix; Grunau, Saskia; Kleihaus, Burkhard; Kunz, Jutta

2018-06-01

We consider a traversable wormhole solution of Einstein's gravity conformally coupled to a massless scalar field, a solution derived by Barcelo and Visser based on the Janis-Newman-Winicour-Wyman spacetime. We study the geodesic motion of timelike and spacelike particles in this spacetime. We solve the equations of motion analytically in terms of the Weierstraß functions and discuss all possible orbit types and their parameter dependence. Interestingly, bound orbits occur for timelike geodesics only in one of the two worlds. Moreover, under no conditions there exist timelike two world bound orbits.

Impact of energetic-particle-driven geodesic acoustic modes on turbulence.

PubMed

Zarzoso, D; Sarazin, Y; Garbet, X; Dumont, R; Strugarek, A; Abiteboul, J; Cartier-Michaud, T; Dif-Pradalier, G; Ghendrih, Ph; Grandgirard, V; Latu, G; Passeron, C; Thomine, O

2013-03-22

The impact on turbulent transport of geodesic acoustic modes excited by energetic particles is evidenced for the first time in flux-driven 5D gyrokinetic simulations using the Gysela code. Energetic geodesic acoustic modes (EGAMs) are excited in a regime with a transport barrier in the outer radial region. The interaction between EGAMs and turbulence is such that turbulent transport can be enhanced in the presence of EGAMs, with the subsequent destruction of the transport barrier. This scenario could be particularly critical in those plasmas, such as burning plasmas, exhibiting a rich population of suprathermal particles capable of exciting energetic modes.

Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity

NASA Astrophysics Data System (ADS)

Hoseini, Bahareh; Saffari, Reza; Soroushfar, Saheb

2017-03-01

A set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass \\wp function and the Kleinian σ function. Using conserved energy and angular momentum we can characterize the different orbits. Also, considering parametric diagrams and effective potentials, we plot some possible orbits. Moreover, with the help of analytical solutions, we investigate the light deflection for such an escape orbit. Finally, by using periastron advance we get to an upper bound for magnitude of γ.

Covariant Formulation of Fluid Dynamics and Estakhr's Material Geodesic Equation, far down the Rabbit hole

NASA Astrophysics Data System (ADS)

Estakhr, Ahmad Reza

2012-07-01

``When i meet God, I am going to ask him two questions, why relativity and why turbulence. A. Einstein'' You probably will not need to ask these questions of God, I've already answered both of them. U^{μ}=γ (c,u({r}, t)) denotes four-velocity field. J^ {μ}=ρ U^{μ} denotes four-current mass density. Estakhr's Material-Geodesic equation is developed analogy of Navier Stokes equation and Einstein Geodesic equation. {DJ^ {μ}}/{Dτ}={dJ^{μ}}/{D τ}+Γ^{μ}_{α β}J^{α}U^{β}=J_ {ν}Ω^{μν}+npartial_ {ν}T^{μν}+Γ^{μ} _{αβ}J^{α}U^{β} Covariant formulation of fluid dynamics, describe the motion of fluid substances. The local existence and uniqueness theorem for geodesics states that geodesics on a smooth manifold with an affine connection exist, and are unique. EMG equation is also applicable in different branches of physics, it all depend on what you mean by 4-current density, if you mean 4-current electron number density then it is plasma physics, if you mean 4-current electron charge density then it is {DJ^ {μ}}/{Dτ}=J_{ν}F^{μν} +partial_{ν}T^{μν}+ Γ^{μ}_{αβ}J^ {α}U^{β} electromagnetism.

Thermal Hawking radiation of black hole with supertranslation field

NASA Astrophysics Data System (ADS)

Iofa, Mikhail Z.

2018-01-01

Using the analytical solution for the Schwarzschild metric containing supertranslation field, we consider two main ingredients of calculation of the thermal Hawking black hole radiation: solution for eigenmodes of the d'Alambertian and solution of the geodesic equations for null geodesics. For calculation of Hawking radiation it is essential to determine the behavior of both the eigenmodes and geodesics in the vicinity of horizon. The equation for the eigenmodes is solved, first, perturbatively in the ratio O( C) /M of the supertranslation field to the mass of black hole, and, next, non-perturbatively in the near- horizon region. It is shown that in any order of perturbation theory solution for the eigenmodes in the metric containing supertranslation field differs from solution in the pure Schwarzschild metric by terms of order L 1/2 = (1 - 2 M/r)1/2. In the non-perturbative approach, solution for the eigenmodes differs from solution in the Schwarzschild metric by terms of order L 1/2 which vanish on horizon. Using the simplified form of geodesic equations in vicinity of horizon, it is shown that in vicinity of horizon the null geodesics have the same behavior as in the Schwarzschild metric. As a result, the density matrices of thermal radiation in both cases are the same.

Synthesis of Creep Measurements from Strainmeters and Creepmeters along the San Andreas Fault: Implications for Seismic vs. Aseismic Partitioning

NASA Astrophysics Data System (ADS)

Mencin, D.; Gottlieb, M. H.; Hodgkinson, K. M.; Bilham, R. G.; Mattioli, G. S.; Johnson, W.; Van Boskirk, E.; Meertens, C. M.

2015-12-01

Strainmeters and creepmeters have been operated along the San Andreas Fault, observing creep events for decades. In particular, the EarthScope Plate Boundary Observatory (PBO) has added a significant number of borehole strainmeters along the San Andreas Fault (SAF) over the last decade. The geodetic data cover a significant temporal portion of the inferred earthquake cycle along this portion of the SAF. Creepmeters measure the surface displacement over time (creep) with short apertures and have the ability to capture slow slip, coseismic rupture, and afterslip. Modern creepmeters deployed by the authors have a resolution of 5 µm over a range of 10 mm and a dynamic sensor with a resolution 25 µm over a range 2.2 m. Borehole strainmeters measure local deformation some distance from the fault with a broader aperture. Borehole tensor strainmeters principally deployed as part of the PBO, measure the horizontal strain tensor at a depth of 100-200 m with a resolution of 10-11 strain and are located 4 - 10 km from the fault with the ability to image a 1 mm creep event acting on an area of ~500 m2 from over 4 km away (fault perpendicular). A single borehole tensor strainmeter is capable of providing broad constraints on the creep event asperity size, location, direction and depth of a single creep event. The synthesis of these data from all the available geodetic instruments proximal to the SAF presents a unique opportunity to constrain the partitioning between aseismic and seismic slip on the central SAF. We show that simple elastic half-space models allow us to loosely constrain the location and depth of any individual creep event on the fault, even with a single instrument, and to image the accumulation of creep with time.

Shining light on modifications of gravity

NASA Astrophysics Data System (ADS)

Brax, Philippe; Burrage, Clare; Davis, Anne-Christine

2012-10-01

Many modifications of gravity introduce new scalar degrees of freedom, and in such theories matter fields typically couple to an effective metric that depends on both the true metric of spacetime and on the scalar field and its derivatives. Scalar field contributions to the effective metric can be classified as conformal and disformal. Disformal terms introduce gradient couplings between scalar fields and the energy momentum tensor of other matter fields, and cannot be constrained by fifth force experiments because the effects of these terms are trivial around static non-relativistic sources. The use of high-precision, low-energy photon experiments to search for conformally coupled scalar fields, called axion-like particles, is well known. In this article we show that these experiments are also constraining for disformal scalar field theories, and are particularly important because of the difficulty of constraining these couplings with other laboratory experiments.

Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Orlando, Giorgio

2017-07-01

Considering high-energy modifications of Einstein gravity during inflation is an interesting issue. We can constrain the strength of the new gravitational terms through observations of inflationary imprints in the actual universe. In this paper we analyze the effects on slow-roll models due to a Chern-Simons term coupled to the inflaton field through a generic coupling function f(phi). A well known result is the polarization of primordial gravitational waves (PGW) into left and right eigenstates, as a consequence of parity breaking. In such a scenario the modifications to the power spectrum of PGW are suppressed under the conditions that allow to avoid the production of ghost gravitons at a certain energy scale, the so-called Chern-Simons mass MCS. In general it has been recently pointed out that there is very little hope to efficiently constrain chirality of PGW on the basis solely of two-point statistics from future CMB data, even in the most optimistic cases. Thus we search if significant parity breaking signatures can arise at least in the bispectrum statistics. We find that the tensor-tensor-scalar bispectra langle γ γ ζ rangle for each polarization state are the only ones that are not suppressed. Their amplitude, setting the level of parity breaking during inflation, is proportional to the second derivative of the coupling function f(phi) and they turn out to be maximum in the squeezed limit. We comment on the squeezed-limit consistency relation arising in the case of chiral gravitational waves, and on possible observables to constrain these signatures.

Cosmic structures and gravitational waves in ghost-free scalar-tensor theories of gravity

NASA Astrophysics Data System (ADS)

Bartolo, Nicola; Karmakar, Purnendu; Matarrese, Sabino; Scomparin, Mattia

2018-05-01

We study cosmic structures in the quadratic Degenerate Higher Order Scalar Tensor (qDHOST) model, which has been proposed as the most general scalar-tensor theory (up to quadratic dependence on the covariant derivatives of the scalar field), which is not plagued by the presence of ghost instabilities. We then study a static, spherically symmetric object embedded in de Sitter space-time for the qDHOST model. This model exhibits breaking of the Vainshtein mechanism inside the cosmic structure and Schwarzschild-de Sitter space-time outside, where General Relativity (GR) can be recovered within the Vainshtein radius. We constrained the parameters of the qDHOST model by requiring the validity of the Vainshtein screening mechanism inside the cosmic structures and the consistency with the recently established bounds on gravitational wave speed from GW170817/GRB170817A event. We find that these two constraints rule out the same set of parameters, corresponding to the Lagrangians that are quadratic in second-order derivatives of the scalar field, for the shift symmetric qDHOST.

Geodesic congruences in warped spacetimes

NASA Astrophysics Data System (ADS)

Ghosh, Suman; Dasgupta, Anirvan; Kar, Sayan

2011-04-01

In this article, we explore the kinematics of timelike geodesic congruences in warped five-dimensional bulk spacetimes, with and without thick or thin branes. Beginning with geodesic flows in the Randall-Sundrum anti-de Sitter geometry without and with branes, we find analytical expressions for the expansion scalar and comment on the effects of including thin branes on its evolution. Later, we move on to congruences in more general warped bulk geometries with a cosmological thick brane and a time-dependent extra dimensional scale. Using analytical expressions for the velocity field, we interpret the expansion, shear and rotation (ESR) along the flows, as functions of the extra dimensional coordinate. The evolution of a cross-sectional area orthogonal to the congruence, as seen from a local observer’s point of view, is also shown graphically. Finally, the Raychaudhuri and geodesic equations in backgrounds with a thick brane are solved numerically in order to figure out the role of initial conditions (prescribed on the ESR) and spacetime curvature on the evolution of the ESR.

Light escape cones in local reference frames of Kerr-de Sitter black hole spacetimes and related black hole shadows

NASA Astrophysics Data System (ADS)

Stuchlík, Zdeněk; Charbulák, Daniel; Schee, Jan

2018-03-01

We construct the light escape cones of isotropic spot sources of radiation residing in special classes of reference frames in the Kerr-de Sitter (KdS) black hole spacetimes, namely in the fundamental class of `non-geodesic' locally non-rotating reference frames (LNRFs), and two classes of `geodesic' frames, the radial geodesic frames (RGFs), both falling and escaping, and the frames related to the circular geodesic orbits (CGFs). We compare the cones constructed in a given position for the LNRFs, RGFs, and CGFs. We have shown that the photons locally counter-rotating relative to LNRFs with positive impact parameter and negative covariant energy are confined to the ergosphere region. Finally, we demonstrate that the light escaping cones govern the shadows of black holes located in front of a radiating screen, as seen by the observers in the considered frames. For shadows related to distant static observers the LNRFs are relevant.

A Computational Model of Multidimensional Shape

PubMed Central

Liu, Xiuwen; Shi, Yonggang; Dinov, Ivo

2010-01-01

We develop a computational model of shape that extends existing Riemannian models of curves to multidimensional objects of general topological type. We construct shape spaces equipped with geodesic metrics that measure how costly it is to interpolate two shapes through elastic deformations. The model employs a representation of shape based on the discrete exterior derivative of parametrizations over a finite simplicial complex. We develop algorithms to calculate geodesics and geodesic distances, as well as tools to quantify local shape similarities and contrasts, thus obtaining a formulation that accounts for regional differences and integrates them into a global measure of dissimilarity. The Riemannian shape spaces provide a common framework to treat numerous problems such as the statistical modeling of shapes, the comparison of shapes associated with different individuals or groups, and modeling and simulation of shape dynamics. We give multiple examples of geodesic interpolations and illustrations of the use of the models in brain mapping, particularly, the analysis of anatomical variation based on neuroimaging data. PMID:21057668

Spectral edge: gradient-preserving spectral mapping for image fusion.

PubMed

Connah, David; Drew, Mark S; Finlayson, Graham D

2015-12-01

This paper describes a novel approach to image fusion for color display. Our goal is to generate an output image whose gradient matches that of the input as closely as possible. We achieve this using a constrained contrast mapping paradigm in the gradient domain, where the structure tensor of a high-dimensional gradient representation is mapped exactly to that of a low-dimensional gradient field which is then reintegrated to form an output. Constraints on output colors are provided by an initial RGB rendering. Initially, we motivate our solution with a simple "ansatz" (educated guess) for projecting higher-D contrast onto color gradients, which we expand to a more rigorous theorem to incorporate color constraints. The solution to these constrained optimizations is closed-form, allowing for simple and hence fast and efficient algorithms. The approach can map any N-D image data to any M-D output and can be used in a variety of applications using the same basic algorithm. In this paper, we focus on the problem of mapping N-D inputs to 3D color outputs. We present results in five applications: hyperspectral remote sensing, fusion of color and near-infrared or clear-filter images, multilighting imaging, dark flash, and color visualization of magnetic resonance imaging diffusion-tensor imaging.

A unifying theoretical and algorithmic framework for least squares methods of estimation in diffusion tensor imaging.

PubMed

Koay, Cheng Guan; Chang, Lin-Ching; Carew, John D; Pierpaoli, Carlo; Basser, Peter J

2006-09-01

A unifying theoretical and algorithmic framework for diffusion tensor estimation is presented. Theoretical connections among the least squares (LS) methods, (linear least squares (LLS), weighted linear least squares (WLLS), nonlinear least squares (NLS) and their constrained counterparts), are established through their respective objective functions, and higher order derivatives of these objective functions, i.e., Hessian matrices. These theoretical connections provide new insights in designing efficient algorithms for NLS and constrained NLS (CNLS) estimation. Here, we propose novel algorithms of full Newton-type for the NLS and CNLS estimations, which are evaluated with Monte Carlo simulations and compared with the commonly used Levenberg-Marquardt method. The proposed methods have a lower percent of relative error in estimating the trace and lower reduced chi2 value than those of the Levenberg-Marquardt method. These results also demonstrate that the accuracy of an estimate, particularly in a nonlinear estimation problem, is greatly affected by the Hessian matrix. In other words, the accuracy of a nonlinear estimation is algorithm-dependent. Further, this study shows that the noise variance in diffusion weighted signals is orientation dependent when signal-to-noise ratio (SNR) is low (

CONSTRAINTS ON SCALAR AND TENSOR PERTURBATIONS IN PHENOMENOLOGICAL AND TWO-FIELD INFLATION MODELS: BAYESIAN EVIDENCES FOR PRIMORDIAL ISOCURVATURE AND TENSOR MODES

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

Vaeliviita, Jussi; Savelainen, Matti; Talvitie, Marianne

2012-07-10

We constrain cosmological models where the primordial perturbations have an adiabatic and a (possibly correlated) cold dark matter (CDM) or baryon isocurvature component. We use both a phenomenological approach, where the power spectra of primordial perturbations are parameterized with amplitudes and spectral indices, and a slow-roll two-field inflation approach where slow-roll parameters are used as primary parameters, determining the spectral indices and the tensor-to-scalar ratio. In the phenomenological case, with CMB data, the upper limit to the CDM isocurvature fraction is {alpha} < 6.4% at k = 0.002 Mpc{sup -1} and 15.4% at k = 0.01 Mpc{sup -1}. The non-adiabaticmore » contribution to the CMB temperature variance is -0.030 < {alpha}{sub T} < 0.049 at the 95% confidence level. Including the supernova (SN) (or large-scale structure) data, these limits become {alpha} < 7.0%, 13.7%, and -0.048 < {alpha}{sub T} < 0.042 (or {alpha} < 10.2%, 16.0%, and -0.071 < {alpha}{sub T} < 0.024). The CMB constraint on the tensor-to-scalar ratio, r < 0.26 at k = 0.01 Mpc{sup -1}, is not affected by the non-adiabatic modes. In the slow-roll two-field inflation approach, the spectral indices are constrained close to 1. This leads to tighter limits on the isocurvature fraction; with the CMB data {alpha} < 2.6% at k = 0.01 Mpc{sup -1}, but the constraint on {alpha}{sub T} is not much affected, -0.058 < {alpha}{sub T} < 0.045. Including SN (or LSS) data, these limits become {alpha} < 3.2% and -0.056 < {alpha}{sub T} < 0.030 (or {alpha} < 3.4% and -0.063 < {alpha}{sub T} < -0.008). In addition to the generally correlated models, we study also special cases where the adiabatic and isocurvature modes are uncorrelated or fully (anti)correlated. We calculate Bayesian evidences (model probabilities) in 21 different non-adiabatic cases and compare them to the corresponding adiabatic models, and find that in all cases the data support the pure adiabatic model.« less

Geodesic Monte Carlo on Embedded Manifolds

PubMed Central

Byrne, Simon; Girolami, Mark

2013-01-01

Markov chain Monte Carlo methods explicitly defined on the manifold of probability distributions have recently been established. These methods are constructed from diffusions across the manifold and the solution of the equations describing geodesic flows in the Hamilton–Jacobi representation. This paper takes the differential geometric basis of Markov chain Monte Carlo further by considering methods to simulate from probability distributions that themselves are defined on a manifold, with common examples being classes of distributions describing directional statistics. Proposal mechanisms are developed based on the geodesic flows over the manifolds of support for the distributions, and illustrative examples are provided for the hypersphere and Stiefel manifold of orthonormal matrices. PMID:25309024

Some clarifications about the Bohmian geodesic deviation equation and Raychaudhuri’s equation

NASA Astrophysics Data System (ADS)

Rahmani, Faramarz; Golshani, Mehdi

2018-01-01

One of the important and famous topics in general theory of relativity and gravitation is the problem of geodesic deviation and its related singularity theorems. An interesting subject is the investigation of these concepts when quantum effects are considered. Since the definition of trajectory is not possible in the framework of standard quantum mechanics (SQM), we investigate the problem of geodesic equation and its related topics in the framework of Bohmian quantum mechanics in which the definition of trajectory is possible. We do this in a fixed background and we do not consider the backreaction effects of matter on the space-time metric.

Inversion of calcite twin data for paleostress (1) : improved Etchecopar technique tested on numerically-generated and natural data

NASA Astrophysics Data System (ADS)

Parlangeau, Camille; Lacombe, Olivier; Daniel, Jean-Marc; Schueller, Sylvie

2015-04-01

Inversion of calcite twin data are known to be a powerful tool to reconstruct the past-state of stress in carbonate rocks of the crust, especially in fold-and-thrust belts and sedimentary basins. This is of key importance to constrain results of geomechanical modelling. Without proposing a new inversion scheme, this contribution reports some recent improvements of the most efficient stress inversion technique to date (Etchecopar, 1984) that allows to reconstruct the 5 parameters of the deviatoric paleostress tensors (principal stress orientations and differential stress magnitudes) from monophase and polyphase twin data sets. The improvements consist in the search of the possible tensors that account for the twin data (twinned and untwinned planes) and the aid to the user to define the best stress tensor solution, among others. We perform a systematic exploration of an hypersphere in 4 dimensions by varying different parameters, Euler's angles and the stress ratio. We first record all tensors with a minimum penalization function accounting for 20% of the twinned planes. We then define clusters of tensors following a dissimilarity criterion based on the stress distance between the 4 parameters of the reduced stress tensors and a degree of disjunction of the related sets of twinned planes. The percentage of twinned data to be explained by each tensor is then progressively increased and tested using the standard Etchecopar procedure until the best solution that explains the maximum number of twinned planes and the whole set of untwinned planes is reached. This new inversion procedure is tested on monophase and polyphase numerically-generated as well as natural calcite twin data in order to more accurately define the ability of the technique to separate more or less similar deviatoric stress tensors applied in sequence on the samples, to test the impact of strain hardening through the change of the critical resolved shear stress for twinning as well as to evaluate the possible bias due to measurement uncertainties or clustering of grain optical axes in the samples.

Time-Dependent Moment Tensors of the First Four Source Physics Experiments (SPE) Explosions

NASA Astrophysics Data System (ADS)

Yang, X.

2015-12-01

We use mainly vertical-component geophone data within 2 km from the epicenter to invert for time-dependent moment tensors of the first four SPE explosions: SPE-1, SPE-2, SPE-3 and SPE-4Prime. We employ a one-dimensional (1D) velocity model developed from P- and Rg-wave travel times for Green's function calculations. The attenuation structure of the model is developed from P- and Rg-wave amplitudes. We select data for the inversion based on the criterion that they show consistent travel times and amplitude behavior as those predicted by the 1D model. Due to limited azimuthal coverage of the sources and the mostly vertical-component-only nature of the dataset, only long-period, diagonal components of the moment tensors are well constrained. Nevertheless, the moment tensors, particularly their isotropic components, provide reasonable estimates of the long-period source amplitudes as well as estimates of corner frequencies, albeit with larger uncertainties. The estimated corner frequencies, however, are consistent with estimates from ratios of seismogram spectra from different explosions. These long-period source amplitudes and corner frequencies cannot be fit by classical P-wave explosion source models. The results motivate the development of new P-wave source models suitable for these chemical explosions. To that end, we fit inverted moment-tensor spectra by modifying the classical explosion model using regressions of estimated source parameters. Although the number of data points used in the regression is small, the approach suggests a way for the new-model development when more data are collected.

Divergence correction schemes in finite difference method for 3D tensor CSAMT in axial anisotropic media

NASA Astrophysics Data System (ADS)

Wang, Kunpeng; Tan, Handong; Zhang, Zhiyong; Li, Zhiqiang; Cao, Meng

2017-05-01

Resistivity anisotropy and full-tensor controlled-source audio-frequency magnetotellurics (CSAMT) have gradually become hot research topics. However, much of the current anisotropy research for tensor CSAMT only focuses on the one-dimensional (1D) solution. As the subsurface is rarely 1D, it is necessary to study three-dimensional (3D) model response. The staggered-grid finite difference method is an effective simulation method for 3D electromagnetic forward modelling. Previous studies have suggested using the divergence correction to constrain the iterative process when using a staggered-grid finite difference model so as to accelerate the 3D forward speed and enhance the computational accuracy. However, the traditional divergence correction method was developed assuming an isotropic medium. This paper improves the traditional isotropic divergence correction method and derivation process to meet the tensor CSAMT requirements for anisotropy using the volume integral of the divergence equation. This method is more intuitive, enabling a simple derivation of a discrete equation and then calculation of coefficients related to the anisotropic divergence correction equation. We validate the result of our 3D computational results by comparing them to the results computed using an anisotropic, controlled-source 2.5D program. The 3D resistivity anisotropy model allows us to evaluate the consequences of using the divergence correction at different frequencies and for two orthogonal finite length sources. Our results show that the divergence correction plays an important role in 3D tensor CSAMT resistivity anisotropy research and offers a solid foundation for inversion of CSAMT data collected over an anisotropic body.

Free energy from molecular dynamics with multiple constraints

NASA Astrophysics Data System (ADS)

den Otter, W. K.; Briels, W. J.

In molecular dynamics simulations of reacting systems, the key step to determining the equilibrium constant and the reaction rate is the calculation of the free energy as a function of the reaction coordinate. Intuitively the derivative of the free energy is equal to the average force needed to constrain the reaction coordinate to a constant value, but the metric tensor effect of the constraint on the sampled phase space distribution complicates this relation. The appropriately corrected expression for the potential of mean constraint force method (PMCF) for systems in which only the reaction coordinate is constrained was published recently. Here we will consider the general case of a system with multiple constraints. This situation arises when both the reaction coordinate and the 'hard' coordinates are constrained, and also in systems with several reaction coordinates. The obvious advantage of this method over the established thermodynamic integration and free energy perturbation methods is that it avoids the cumbersome introduction of a full set of generalized coordinates complementing the constrained coordinates. Simulations of n -butane and n -pentane in vacuum illustrate the method.

Tensor-driven extraction of developmental features from varying paediatric EEG datasets.

PubMed

Kinney-Lang, Eli; Spyrou, Loukianos; Ebied, Ahmed; Chin, Richard Fm; Escudero, Javier

2018-05-21

Constant changes in developing children's brains can pose a challenge in EEG dependant technologies. Advancing signal processing methods to identify developmental differences in paediatric populations could help improve function and usability of such technologies. Taking advantage of the multi-dimensional structure of EEG data through tensor analysis may offer a framework for extracting relevant developmental features of paediatric datasets. A proof of concept is demonstrated through identifying latent developmental features in resting-state EEG. Approach. Three paediatric datasets (n = 50, 17, 44) were analyzed using a two-step constrained parallel factor (PARAFAC) tensor decomposition. Subject age was used as a proxy measure of development. Classification used support vector machines (SVM) to test if PARAFAC identified features could predict subject age. The results were cross-validated within each dataset. Classification analysis was complemented by visualization of the high-dimensional feature structures using t-distributed Stochastic Neighbour Embedding (t-SNE) maps. Main Results. Development-related features were successfully identified for the developmental conditions of each dataset. SVM classification showed the identified features could accurately predict subject at a significant level above chance for both healthy and impaired populations. t-SNE maps revealed suitable tensor factorization was key in extracting the developmental features. Significance. The described methods are a promising tool for identifying latent developmental features occurring throughout childhood EEG. © 2018 IOP Publishing Ltd.

Constraining f(R) gravity in solar system, cosmology and binary pulsar systems

NASA Astrophysics Data System (ADS)

Liu, Tan; Zhang, Xing; Zhao, Wen

2018-02-01

The f (R) gravity can be cast into the form of a scalar-tensor theory, and scalar degree of freedom can be suppressed in high-density regions by the chameleon mechanism. In this article, for the general f (R) gravity, using a scalar-tensor representation with the chameleon mechanism, we calculate the parametrized post-Newtonian parameters γ and β, the effective gravitational constant Geff, and the effective cosmological constant Λeff. In addition, for the general f (R) gravity, we also calculate the rate of orbital period decay of the binary system due to gravitational radiation. Then we apply these results to specific f (R) models (Hu-Sawicki model, Tsujikawa model and Starobinsky model) and derive the constraints on the model parameters by combining the observations in solar system, cosmological scales and the binary systems.

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

Ferreira, Pedro G.; Hill, Christopher T.; Ross, Graham G.

We revisit the possibility that the Planck mass is spontaneously generated in scale-invariant scalar-tensor theories of gravity, typically leading to a “dilaton.” The fifth force, arising from the dilaton, is severely constrained by astrophysical measurements. We explore the possibility that nature is fundamentally scale invariant and argue that, as a consequence, the fifth-force effects are dramatically suppressed and such models are viable. Finally, we discuss possible obstructions to maintaining scale invariance and how these might be resolved.

On the n-body problem on surfaces of revolution

NASA Astrophysics Data System (ADS)

Stoica, Cristina

2018-05-01

We explore the n-body problem, n ≥ 3, on a surface of revolution with a general interaction depending on the pairwise geodesic distance. Using the geometric methods of classical mechanics we determine a large set of properties. In particular, we show that Saari's conjecture fails on surfaces of revolution admitting a geodesic circle. We define homographic motions and, using the discrete symmetries, prove that when the masses are equal, they form an invariant manifold. On this manifold the dynamics are reducible to a one-degree of freedom system. We also find that for attractive interactions, regular n-gon shaped relative equilibria with trajectories located on geodesic circles typically experience a pitchfork bifurcation. Some applications are included.

Parity breaking signatures from a Chern-Simons coupling during inflation: the case of non-Gaussian gravitational waves

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

Bartolo, Nicola; Orlando, Giorgio, E-mail: nicola.bartolo@pd.infn.it, E-mail: giorgio.orlando@phd.unipd.it

Considering high-energy modifications of Einstein gravity during inflation is an interesting issue. We can constrain the strength of the new gravitational terms through observations of inflationary imprints in the actual universe. In this paper we analyze the effects on slow-roll models due to a Chern-Simons term coupled to the inflaton field through a generic coupling function f (φ). A well known result is the polarization of primordial gravitational waves (PGW) into left and right eigenstates, as a consequence of parity breaking. In such a scenario the modifications to the power spectrum of PGW are suppressed under the conditions that allowmore » to avoid the production of ghost gravitons at a certain energy scale, the so-called Chern-Simons mass M {sub CS}. In general it has been recently pointed out that there is very little hope to efficiently constrain chirality of PGW on the basis solely of two-point statistics from future CMB data, even in the most optimistic cases. Thus we search if significant parity breaking signatures can arise at least in the bispectrum statistics. We find that the tensor-tensor-scalar bispectra ( γ γ ζ ) for each polarization state are the only ones that are not suppressed. Their amplitude, setting the level of parity breaking during inflation, is proportional to the second derivative of the coupling function f (φ) and they turn out to be maximum in the squeezed limit. We comment on the squeezed-limit consistency relation arising in the case of chiral gravitational waves, and on possible observables to constrain these signatures.« less

Approximate geodesic distances reveal biologically relevant structures in microarray data.

PubMed

Nilsson, Jens; Fioretos, Thoas; Höglund, Mattias; Fontes, Magnus

2004-04-12

Genome-wide gene expression measurements, as currently determined by the microarray technology, can be represented mathematically as points in a high-dimensional gene expression space. Genes interact with each other in regulatory networks, restricting the cellular gene expression profiles to a certain manifold, or surface, in gene expression space. To obtain knowledge about this manifold, various dimensionality reduction methods and distance metrics are used. For data points distributed on curved manifolds, a sensible distance measure would be the geodesic distance along the manifold. In this work, we examine whether an approximate geodesic distance measure captures biological similarities better than the traditionally used Euclidean distance. We computed approximate geodesic distances, determined by the Isomap algorithm, for one set of lymphoma and one set of lung cancer microarray samples. Compared with the ordinary Euclidean distance metric, this distance measure produced more instructive, biologically relevant, visualizations when applying multidimensional scaling. This suggests the Isomap algorithm as a promising tool for the interpretation of microarray data. Furthermore, the results demonstrate the benefit and importance of taking nonlinearities in gene expression data into account.

New Methods For Interpretation Of Magnetic Gradient Tensor Data Using Eigenalysis And The Normalized Source Strength

NASA Astrophysics Data System (ADS)

Clark, D.

2012-12-01

In the future, acquisition of magnetic gradient tensor data is likely to become routine. New methods developed for analysis of magnetic gradient tensor data can also be applied to high quality conventional TMI surveys that have been processed using Fourier filtering techniques, or otherwise, to calculate magnetic vector and tensor components. This approach is, in fact, the only practical way at present to analyze vector component data, as measurements of vector components are seriously afflicted by motion noise, which is not as serious a problem for gradient components. In many circumstances, an optimal approach to extracting maximum information from magnetic surveys would be to combine analysis of measured gradient tensor data with vector components calculated from TMI measurements. New methods for inverting gradient tensor surveys to obtain source parameters have been developed for a number of elementary, but useful, models. These include point dipole (sphere), vertical line of dipoles (narrow vertical pipe), line of dipoles (horizontal cylinder), thin dipping sheet, horizontal line current and contact models. A key simplification is the use of eigenvalues and associated eigenvectors of the tensor. The normalized source strength (NSS), calculated from the eigenvalues, is a particularly useful rotational invariant that peaks directly over 3D compact sources, 2D compact sources, thin sheets and contacts, and is independent of magnetization direction for these sources (and only very weakly dependent on magnetization direction in general). In combination the NSS and its vector gradient enable estimation of the Euler structural index, thereby constraining source geometry, and determine source locations uniquely. NSS analysis can be extended to other useful models, such as vertical pipes, by calculating eigenvalues of the vertical derivative of the gradient tensor. Once source locations are determined, information of source magnetizations can be obtained by simple linear inversion of measured or calculated vector and/or tensor data. Inversions based on the vector gradient of the NSS over the Tallawang magnetite deposit in central New South Wales obtained good agreement between the inferred geometry of the tabular magnetite skarn body and drill hole intersections. Inverted magnetizations are consistent with magnetic property measurements on drill core samples from this deposit. Similarly, inversions of calculated tensor data over the Mount Leyshold gold-mineralized porphyry system in Queensland yield good estimates of the centroid location, total magnetic moment and magnetization direction of the magnetite-bearing potassic alteration zone that are consistent with geological and petrophysical information.

Light-Ring Stability for Ultracompact Objects.

PubMed

Cunha, Pedro V P; Berti, Emanuele; Herdeiro, Carlos A R

2017-12-22

We prove the following theorem: axisymmetric, stationary solutions of the Einstein field equations formed from classical gravitational collapse of matter obeying the null energy condition, that are everywhere smooth and ultracompact (i.e., they have a light ring) must have at least two light rings, and one of them is stable. It has been argued that stable light rings generally lead to nonlinear spacetime instabilities. Our result implies that smooth, physically and dynamically reasonable ultracompact objects are not viable as observational alternatives to black holes whenever these instabilities occur on astrophysically short time scales. The proof of the theorem has two parts: (i) We show that light rings always come in pairs, one being a saddle point and the other a local extremum of an effective potential. This result follows from a topological argument based on the Brouwer degree of a continuous map, with no assumptions on the spacetime dynamics, and, hence, it is applicable to any metric gravity theory where photons follow null geodesics. (ii) Assuming Einstein's equations, we show that the extremum is a local minimum of the potential (i.e., a stable light ring) if the energy-momentum tensor satisfies the null energy condition.

Light-Ring Stability for Ultracompact Objects

NASA Astrophysics Data System (ADS)

Cunha, Pedro V. P.; Berti, Emanuele; Herdeiro, Carlos A. R.

2017-12-01

We prove the following theorem: axisymmetric, stationary solutions of the Einstein field equations formed from classical gravitational collapse of matter obeying the null energy condition, that are everywhere smooth and ultracompact (i.e., they have a light ring) must have at least two light rings, and one of them is stable. It has been argued that stable light rings generally lead to nonlinear spacetime instabilities. Our result implies that smooth, physically and dynamically reasonable ultracompact objects are not viable as observational alternatives to black holes whenever these instabilities occur on astrophysically short time scales. The proof of the theorem has two parts: (i) We show that light rings always come in pairs, one being a saddle point and the other a local extremum of an effective potential. This result follows from a topological argument based on the Brouwer degree of a continuous map, with no assumptions on the spacetime dynamics, and, hence, it is applicable to any metric gravity theory where photons follow null geodesics. (ii) Assuming Einstein's equations, we show that the extremum is a local minimum of the potential (i.e., a stable light ring) if the energy-momentum tensor satisfies the null energy condition.

Evidence for Bouncing Evolution Before Inflation After BICEP2

NASA Astrophysics Data System (ADS)

Xia, Jun-Qing; Cai, Yi-Fu; Li, Hong; Zhang, Xinmin

2014-06-01

The BICEP2 Collaboration reports a detection of primordial cosmic microwave background (CMB) B mode with a tensor-to-scalar ratio r =0.20-0.05+0.07 (68% C.L.). However, this result disagrees with the recent Planck limit r<0.11 (95% C.L.) on constraining inflation models. In this Letter we consider an inflationary cosmology with a preceding nonsingular bounce, which gives rise to observable signatures on primordial perturbations. One interesting phenomenon is that both the primordial scalar and tensor modes can have a step feature on their power spectra, which nicely cancels the tensor excess power on the CMB temperature power spectrum. By performing a global analysis, we obtain the 68% C.L. constraints on the parameters of the model from the Planck+WP and BICEP2 data together: the jump scale log10(kB/Mpc-1)=-2.4±0.2 and the spectrum amplitude ratio of bounce to inflation rB≡Pm/As=0.71±0.09. Our result reveals that the bounce inflation scenario can simultaneously explain the Planck and BICEP2 observations better than the standard cold dark matter model with a cosmological constant, and can be verified by future CMB polarization measurements.

MOMENT TENSOR SOLUTIONS OF RECENT EARTHQUAKES IN THE CALABRIAN REGION (SOUTH ITALY)

NASA Astrophysics Data System (ADS)

Orecchio, B.; D'Amico, S.; Gervasi, A.; Guerra, I.; Presti, D.; Zhu, L.; Herrmann, R. B.; Neri, G.

2009-12-01

The aim of this study is to provide moment tensor solutions for recent events occurred in the Calabrian region (South Italy), an area struck by several destructive earthquakes in the last centuries. The seismicity of the area under investigation is actually characterized by low to moderate magnitude earthquakes (up to 4.5) not properly represented in the Italian national catalogues of focal mechanisms like RCMT (Regional Centroid Moment Tensor, Pondrelli et al., PEPI, 2006) and TDMT (Time Domain Moment Tensors, Dreger and Helmerger, BSSA, 1993). Also, the solutions estimated from P-onset polarities are often poorly constrained due to network geometry in the study area. We computed the moment tensor solutions using the “Cut And Paste” method originally proposed by Zhao and Helmerger (BSSA, 1994) and later modified by Zhu and Helmerger (BSSA, 1996). Each waveform is broken into the Pnl and surface wave segments and the source depth and focal mechanisms are determined using a grid search technique. The technique allows time shifts between synthetics and observed data in order to reduce dependence of the solution on the assumed velocity model and earthquake locations. This method has shown to provide good-quality solutions for earthquakes of magnitude as small as 2.5. The data set of the present study consists of waveforms from more than 100 earthquakes that were recorded by the permanent seismic network run by Istituto Nazionale di Geofisica e Vulcanologia (INGV) and about 40 stations of the NSF CAT/SCAN project. The results concur to check and better detail the regional geodynamic model assuming subduction of the Ionian lithosphere beneath the Tyrrhenian one and related response of the shallow structures in terms of normal and strike-slip faulting seismicity.

Which Way Is Jerusalem? Navigating on a Spheroid

ERIC Educational Resources Information Center

Schechter, Murray

2007-01-01

Given two points on a spheroidal planet, what is the direction from the first to the second? The answer depends, of course, on what path you take. This paper compares two paths which suggest themselves, namely, the loxodrome, which is the path in which the direction stays constant, and the geodesic, which is the shortest path. The geodesic does…

How well can future CMB missions constrain cosmic inflation?

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

Martin, Jérôme; Vennin, Vincent; Ringeval, Christophe, E-mail: jmartin@iap.fr, E-mail: christophe.ringeval@uclouvain.be, E-mail: vennin@iap.fr

2014-10-01

We study how the next generation of Cosmic Microwave Background (CMB) measurement missions (such as EPIC, LiteBIRD, PRISM and COrE) will be able to constrain the inflationary landscape in the hardest to disambiguate situation in which inflation is simply described by single-field slow-roll scenarios. Considering the proposed PRISM and LiteBIRD satellite designs, we simulate mock data corresponding to five different fiducial models having values of the tensor-to-scalar ratio ranging from 10{sup -1} down to 10{sup -7}. We then compute the Bayesian evidences and complexities of all Encyclopædia Inflationaris models in order to assess the constraining power of PRISM alone andmore » LiteBIRD complemented with the Planck 2013 data. Within slow-roll inflation, both designs have comparable constraining power and can rule out about three quarters of the inflationary scenarios, compared to one third for Planck 2013 data alone. However, we also show that PRISM can constrain the scalar running and has the capability to detect a violation of slow roll at second order. Finally, our results suggest that describing an inflationary model by its potential shape only, without specifying a reheating temperature, will no longer be possible given the accuracy level reached by the future CMB missions.« less

Removing Shape-Preserving Transformations in Square-Root Elastic (SRE) Framework for Shape Analysis of Curves

PubMed Central

Joshi, Shantanu H.; Klassen, Eric; Srivastava, Anuj; Jermyn, Ian

2011-01-01

This paper illustrates and extends an efficient framework, called the square-root-elastic (SRE) framework, for studying shapes of closed curves, that was first introduced in [2]. This framework combines the strengths of two important ideas - elastic shape metric and path-straightening methods - for finding geodesics in shape spaces of curves. The elastic metric allows for optimal matching of features between curves while path-straightening ensures that the algorithm results in geodesic paths. This paper extends this framework by removing two important shape preserving transformations: rotations and re-parameterizations, by forming quotient spaces and constructing geodesics on these quotient spaces. These ideas are demonstrated using experiments involving 2D and 3D curves. PMID:21738385

Tidal Forces in Dyonic Reissner-Nördstrom Black Hole

NASA Astrophysics Data System (ADS)

Sharif, M.; Kousar, Lubna

2018-03-01

This paper investigates the tidal as well as magnetic charge effects produced in dyonic Reissner-Nordström black hole. We evaluate Newtonian radial acceleration using radial geodesics for freely falling test particles. We establish system of equations governing radial and angular tidal forces using geodesic deviation equation and discuss their solutions for bodies falling freely towards this black hole. The radial tidal force turns out to be compressing outside the event horizon whereas the angular tidal force changes sign between event and Cauchy horizons unlike Schwarzschild black hole. The radial geodesic component starts decreasing in dyonic Reissner-Nordström black hole unlike Schwarzschild case. We conclude that magnetic charge strongly affects the radial as well as angular components of tidal force.

Evolution of geodesic congruences in a gravitationally collapsing scalar field background

NASA Astrophysics Data System (ADS)

Shaikh, Rajibul; Kar, Sayan; DasGupta, Anirvan

2014-12-01

The evolution of timelike geodesic congruences in a spherically symmetric, nonstatic, inhomogeneous spacetime representing gravitational collapse of a massless scalar field is studied. We delineate how initial values of the expansion, rotation, and shear of a congruence, as well as the spacetime curvature, influence the global behavior and focusing properties of a family of trajectories. Under specific conditions, the expansion scalar is shown to exhibit a finite jump (from negative to positive value) before focusing eventually occurs. This nonmonotonic behavior of the expansion, observed in our numerical work, is successfully explained through an analysis of the equation for the expansion. Finally, we bring out the role of the metric parameters (related to nonstaticity and spatial inhomogeneity) in shaping the overall behavior of geodesic congruences.

Completely integrable 2D Lagrangian systems and related integrable geodesic flows on various manifolds

NASA Astrophysics Data System (ADS)

Yehia, Hamad M.

2013-08-01

In this study we have formulated a theorem that generates deformations of the natural integrable conservative systems in the plane into integrable systems on Riemannian and other manifolds by introducing additional parameters into their structures. The relation of explicit solutions of the new and the original dynamics to the corresponding Jacobi (Maupertuis) geodesic flow is clarified. For illustration, we apply the result to three concrete examples of the many available integrable systems in the literature. Complementary integrals in those systems are polynomial in velocity with degrees 3, 4 and 6, respectively. As a special case of the first deformed system, a new several-parameter family of integrable mechanical systems (and geodesic flows) on S2 is constructed.

Conformal geodesics in spherically symmetric vacuum spacetimes with cosmological constant

NASA Astrophysics Data System (ADS)

García-Parrado Gómez-Lobo, A.; Gasperín, E.; Valiente Kroon, J. A.

2018-02-01

An analysis of conformal geodesics in the Schwarzschild–de Sitter and Schwarzschild–anti-de Sitter families of spacetimes is given. For both families of spacetimes we show that initial data on a spacelike hypersurface can be given such that the congruence of conformal geodesics arising from this data cover the whole maximal extension of canonical conformal representations of the spacetimes without forming caustic points. For the Schwarzschild–de Sitter family, the resulting congruence can be used to obtain global conformal Gaussian systems of coordinates of the conformal representation. In the case of the Schwarzschild–anti-de Sitter family, the natural parameter of the curves only covers a restricted time span so that these global conformal Gaussian systems do not exist.

Newtonian potential and geodesic completeness in infinite derivative gravity

NASA Astrophysics Data System (ADS)

Edholm, James; Conroy, Aindriú

2017-08-01

Recent study has shown that a nonsingular oscillating potential—a feature of infinite derivative gravity theories—matches current experimental data better than the standard General Relativity potential. In this work, we show that this nonsingular oscillating potential can be given by a wider class of theories which allows the defocusing of null rays and therefore geodesic completeness. We consolidate the conditions whereby null geodesic congruences may be made past complete, via the Raychaudhuri equation, with the requirement of a nonsingular Newtonian potential in an infinite derivative gravity theory. In doing so, we examine a class of Newtonian potentials characterized by an additional degree of freedom in the scalar propagator, which returns the familiar potential of General Relativity at large distances.

Comparison of magmatic and amagmatic rift zone kinematics using full moment tensor inversions of regional earthquakes

NASA Astrophysics Data System (ADS)

Jaye Oliva, Sarah; Ebinger, Cynthia; Shillington, Donna; Albaric, Julie; Deschamps, Anne; Keir, Derek; Drooff, Connor

2017-04-01

Temporary seismic networks deployed in the magmatic Eastern rift and the mostly amagmatic Western rift in East Africa present the opportunity to compare the depth distribution of strain, and fault kinematics in light of rift age and the presence or absence of surface magmatism. The largest events in local earthquake catalogs (ML > 3.5) are modeled using the Dreger and Ford full moment tensor algorithm (Dreger, 2003; Minson & Dreger, 2008) to better constrain source depth and to investigate non-double-couple components. A bandpass filter of 0.02 to 0.10 Hz is applied to the waveforms prior to inversion. Synthetics are based on 1D velocity models derived during seismic analysis and constrained by reflection and tomographic data where available. Results show significant compensated linear vector dipole (CLVD) and isotropic components for earthquakes in magmatic rift zones, whereas double-couple mechanisms predominate in weakly magmatic rift sectors. We interpret the isotropic components as evidence for fluid-involved faulting in the Eastern rift where volatile emissions are large, and dike intrusions well documented. Lower crustal earthquakes are found in both amagmatic and magmatic sectors. These results are discussed in the context of the growing database of complementary geophysical, geochemical, and geological studies in these regions as we seek to understand the role of magmatism and faulting in accommodating strain during early continental rifting.

Constraints on scalar-tensor theories of gravity from observations

NASA Astrophysics Data System (ADS)

Lee, Seokcheon

2011-03-01

In spite of their original discrepancy, both dark energy and modified theory of gravity can be parameterized by the effective equation of state (EOS) ω for the expansion history of the Universe. A useful model independent approach to the EOS of them can be given by so-called Chevallier-Polarski-Linder (CPL) parametrization where two parameters of it (ω0 and ωa) can be constrained by the geometrical observations which suffer from degeneracies between models. The linear growth of large scale structure is usually used to remove these degeneracies. This growth can be described by the growth index parameter γ and it can be parameterized by γ0+γa(1-a) in general. We use the scalar-tensor theories of gravity (STG) and show that the discernment between models is possible only when γa is not negligible. We show that the linear density perturbation of the matter component as a function of redshift severely constrains the viable subclasses of STG in terms of ω and γ. From this method, we can rule out or prove the viable STG in future observations. When we use Z(phi) = 1, F shows the convex shape of evolution in a viable STG model. The viable STG models with Z(phi) = 1 are not distinguishable from dark energy models when we strongly limit the solar system constraint.

Hydrodynamical model of anisotropic, polarized turbulent superfluids. I: constraints for the fluxes

NASA Astrophysics Data System (ADS)

Mongiovì, Maria Stella; Restuccia, Liliana

2018-02-01

This work is the first of a series of papers devoted to the study of the influence of the anisotropy and polarization of the tangle of quantized vortex lines in superfluid turbulence. A thermodynamical model of inhomogeneous superfluid turbulence previously formulated is here extended, to take into consideration also these effects. The model chooses as thermodynamic state vector the density, the velocity, the energy density, the heat flux, and a complete vorticity tensor field, including its symmetric traceless part and its antisymmetric part. The relations which constrain the constitutive quantities are deduced from the second principle of thermodynamics using the Liu procedure. The results show that the presence of anisotropy and polarization in the vortex tangle affects in a substantial way the dynamics of the heat flux, and allow us to give a physical interpretation of the vorticity tensor here introduced, and to better describe the internal structure of a turbulent superfluid.

Speed of gravitational waves and black hole hair

NASA Astrophysics Data System (ADS)

Tattersall, Oliver J.; Ferreira, Pedro G.; Lagos, Macarena

2018-04-01

The recent detection of GRB 170817A and GW170817 constrains the speed of gravity waves cT to be that of light, which severely restricts the landscape of modified gravity theories that impact the cosmological evolution of the Universe. In this work, we investigate the presence of black hole hair in the remaining viable cosmological theories of modified gravity that respect the constraint cT=1 . We focus mainly on scalar-tensor theories of gravity, analyzing static, asymptotically flat black holes in Horndeski, Beyond Horndeski, Einstein-scalar-Gauss-Bonnet, and Chern-Simons theories. We find that in all of the cases considered here, theories that are cosmologically relevant and respect cT=1 do not allow for hair, or have negligible hair. We further comment on vector-tensor theories including Einstein-Yang-Mills, Einstein-Aether, and generalized Proca theories, as well as bimetric theories.

Spontaneous Scalarization: Dead or Alive?

NASA Astrophysics Data System (ADS)

Berti, Emanuele; Crispino, Luis; Gerosa, Davide; Gualtieri, Leonardo; Horbatsch, Michael; Macedo, Caio; Okada da Silva, Hector; Pani, Paolo; Sotani, Hajime; Sperhake, Ulrich

2015-04-01

In 1993, Damour and Esposito-Farese showed that a wide class of scalar-tensor theories can pass weak-field gravitational tests and exhibit nonperturbative strong-field deviations away from General Relativity in systems involving neutron stars. These deviations are possible in the presence of ``spontaneous scalarization,'' a phase transition similar in nature to spontaneous magnetization in ferromagnets. More than twenty years after the original proposal, binary pulsar experiments have severely constrained the possibility of spontaneous scalarization occurring in nature. I will show that these experimental constraints have important implications for the torsional oscillation frequencies of neutron stars and for the so-called ``I-Love-Q'' relations in scalar-tensor theories. I will also argue that there is still hope to observe strong scalarization effects, despite the strong experimental bounds on the original mechanism. In particular, I will discuss two mechanisms that could produce strong scalarization in neutron stars: anisotropy and multiscalarization. This work was supported by NSF CAREER Award PHY-1055103.

Bounds on OPE coefficients from interference effects in the conformal collider

NASA Astrophysics Data System (ADS)

Córdova, Clay; Maldacena, Juan; Turiaci, Gustavo J.

2017-11-01

We apply the average null energy condition to obtain upper bounds on the three-point function coefficients of stress tensors and a scalar operator, < TTOi>, in general CFTs. We also constrain the gravitational anomaly of U(1) currents in four-dimensional CFTs, which are encoded in three-point functions of the form 〈 T T J 〉. In theories with a large N AdS dual we translate these bounds into constraints on the coefficient of a higher derivative bulk term of the form ∫ϕ W 2. We speculate that these bounds also apply in de-Sitter. In this case our results constrain inflationary observables, such as the amplitude for chiral gravity waves that originate from higher derivative terms in the Lagrangian of the form ϕ W W ∗.

Cosmology of non-minimal derivative coupling to gravity in Palatini formalism and its chaotic inflation

NASA Astrophysics Data System (ADS)

Kaewkhao, Narakorn; Gumjudpai, Burin

2018-06-01

We consider, in Palatini formalism, a modified gravity of which the scalar field derivative couples to Einstein tensor. In this scenario, Ricci scalar, Ricci tensor and Einstein tensor are functions of connection field. As a result, the connection field gives rise to relation, hμν = fgμν between effective metric, hμν and the usual metric gμν where f = 1 - κϕ,αϕ,α / 2. In FLRW universe, NMDC coupling constant is limited in a range of - 2 /ϕ˙2 < κ ≤ ∞ preserving Lorentz signature of the effective metric. Slowly-rolling regime provides κ < 0 forbidding graviton from traveling at superluminal speed. Effective gravitational coupling and entropy of blackhole's apparent horizon are derived. In case of negative coupling, acceleration could happen even with weff > - 1 / 3. Power-law potentials of chaotic inflation are considered. For V ∝ϕ2 and V ∝ϕ4, it is possible to obtain tensor-to-scalar ratio lower than that of GR so that it satisfies r < 0 . 12 as constrained by Planck 2015 (Ade et al., 2016). The V ∝ϕ2 case yields acceptable range of spectrum index and r values. The quartic potential's spectrum index is disfavored by the Planck results. Viable range of κ for V ∝ϕ2 case lies in positive region, resulting in less blackhole's entropy, superluminal metric, more amount of inflation, avoidance of super-Planckian field initial value and stronger gravitational constant.

Book Review:

NASA Astrophysics Data System (ADS)

Ellis, G. F. R.

2005-12-01

Wolfgang Rindler is known as a writer of exceptional clarity. This quality is evident in this book as it explores in depth first special relativity, then general relativity, and finally relativistic cosmology. He bases his writing in the fundamental underlying ideas and principles that so successfully guided Einstein in his work, clarifying their nature and implications in an illuminating way with many examples. The usual suspects are there: the relativity principle and equivalence principle, the abolishing of absolute space, invariance of the speed of light, analytic and geometric representations of the Lorentz transformation, its kinematic and dynamic consequences, relativistic optics, Minkowski spacetime, energy and momentum conservation, and the Compton effect. Particularly useful is the emphasis on the unity of the whole: for example (p 63) that the kinematic effect of length shortening must imply a corresponding detailed mechanical explanation of that shortening. The tensor formulation of Maxwell's equations leads to the transformation properties of the electromagnetic field and consequent elegant derivation of the field of an infinite straight current; in this case, relativity is important even for slowly moving charges because an ordinary current moves a very big charge (p 151). General relativity is systematically introduced in stages, starting with curved spaces and moving on through static and stationary spacetimes, geodesics, and tensor calculus to the field equations. A considerable strength of the book is the careful detailed examination of the local and global geometry of the major significant solutions of the equations: the Schwarzschild spacetime and its Kruskal extension, plane gravitational waves, de sitter and anti-de Sitter spacetimes, and Robertson-Walker cosmologies. The latter includes a clear presentation of the dust and radiation model dynamics for the variety of possible cases, a detailed examination of observational relations, and considered study of the properties of horizons. Linearized relativity is dealt with in depth leading to the standard weak field gravitational wave formulae and a study of their effects on test particles, together with a very useful discussion of the analogy between weak gravity and the electromagnetic field. Thus this is a straightforward detailed presentation of both special and general relativity theory and their applications. It has many examples and is well suited as a text on these topics, giving a clear relativists' view all the way through. It does not go into astrophysical or particle physics aspects, which is fine given its focus. Personally I would have liked a bit more emphasis on the geodesic deviation equation on the one hand, and on holonomy (which provides a link into particle gauge theories) on the other. But that is a matter of taste. This is an excellent book, which can be highly recommended. Just one quibble: what on earth is the reason for the irritating blurred picture of Einstein on the cover? The whole point of the book is its clarity: why the implication of this picture that it presents a blurred vision?

Geodesic detection of Agulhas rings

NASA Astrophysics Data System (ADS)

Beron-Vera, F. J.; Wang, Y.; Olascoaga, M. J.; Goni, G. J.; Haller, G.

2012-12-01

Mesoscale oceanic eddies are routinely detected from instantaneous velocities. While simple to implement, this Eulerian approach gives frame-dependent results and often hides true material transport by eddies. Building on the recent geodesic theory of transport barriers, we develop an objective (i.e., frame-independent) method for accurately locating coherent Lagrangian eddies. These eddies act as compact water bodies, with boundaries showing no leakage or filamentation over long periods of time. Applying the algorithm to altimetry-derived velocities in the South Atlantic, we detect, for the first time, Agulhas rings that preserve their material coherence for several months, while eddy candidates yielded by other approaches tend to disperse or leak within weeks. These findings suggest that current Eulerian estimates of the Agulhas leakage need significant revision.Temporal evolution of fluid patches identified as eddies by different methods. First column: eddies extracted using geodesic eddy identification [1,2]. Second column: eddies identified from sea surface height (SSH) using the methodology of Chelton et al. [2] with U/c > 1. Third column: eddies identified as elliptic regions by the Okubo-Weiss (OW) criterion [e.g., 3]. Fourth column: eddies identified as mesoelliptic (ME) regions by Mezic et al.'s [4] criterion. References: [1] Beron-Vera et al. (2012). Geodesic eddy detection suggests reassessment of Agulhas leakage. Proc. Nat. Acad. Sci. USA, submitted. [2] Haller & Beron-Vera (2012). Geodesic theory of transport barriers in two-dimensional flows. Physica D, in press. [2] Chelton et al. (2011). Prog. Oceanog. 91, 167. [3] Chelton et al. (2007). Geophys. Res. Lett. 34, L5606. [4] Mezic et al. (2010). Science 330, 486.

Strong Magnetic Field Fluctuations within Filamentary Auroral Density Cavities Interpreted as VLF Saucer Sources

NASA Technical Reports Server (NTRS)

Knudsen, D. L.; Kabirzadeh, R.; Burchill, J. K.; Pfaff, Robert F.; Wallis, D. D.; Bounds, S. R.; Clemmons, J. H.; Pincon, J.-L.

2012-01-01

The Geoelectrodynamics and Electro-Optical Detection of Electron and SuprathermalIon Currents (GEODESIC) sounding rocket encountered more than 100 filamentary densitycavities associated with enhanced plasma waves at ELF (3 kHz) and VLF (310 kHz)frequencies and at altitudes of 800990 km during an auroral substorm. These cavities weresimilar in size (20 m diameter in most cases) to so-called lower-hybrid cavities (LHCs)observed by previous sounding rockets and satellites; however, in contrast, many of theGEODESIC cavities exhibited up to tenfold enhancements in magnetic wave powerthroughout the VLF band. GEODESIC also observed enhancements of ELF and VLFelectric fields both parallel and perpendicular to the geomagnetic field B0 within cavities,though the VLF E field increases were often not as large proportionally as seen in themagnetic fields. This behavior is opposite to that predicted by previously published theoriesof LHCs based on passive scattering of externally incident auroral hiss. We argue thatthe GEODESIC cavities are active wave generation sites capable of radiating VLF wavesinto the surrounding plasma and producing VLF saucers, with energy supplied by cold,upward flowing electron beams composing the auroral return current. This interpretation issupported by the observation that the most intense waves, both inside and outside cavities,occurred in regions where energetic electron precipitation was largely inhibited orabsent altogether. We suggest that the wave-enhanced cavities encountered by GEODESICwere qualitatively different from those observed by earlier spacecraft because of thefortuitous timing of the GEODESIC launch, which placed the payload at apogee within asubstorm-related return current during its most intense phase, lasting only a few minutes.

Feature Extraction of High-Dimensional Structures for Exploratory Analytics

DTIC Science & Technology

2013-04-01

Comparison of Euclidean vs. geodesic distance. LDRs use metric based on the Euclidean distance between two points, while the NLDRs are based on...geodesic distance. An NLDR successfully unrolls the curved manifold, whereas an LDR fails. ...........................3 1 1. Introduction An...and classical metric multidimensional scaling, are a linear DR ( LDR ). An LDR is based on a linear combination of

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

Akers, Chris; Bousso, Raphael; Halpern, Illan F.

We prove that the boundary of the future of a surface K consists precisely of the points p that lie on a null geodesic orthogonal to K such that between K and p there are no points conjugate to K nor intersections with another such geodesic. Our theorem has applications to holographic screens and their associated light sheets and in particular enters the proof that holographic screens satisfy an area law.

Adaptive geodesic transform for segmentation of vertebrae on CT images

NASA Astrophysics Data System (ADS)

Gaonkar, Bilwaj; Shu, Liao; Hermosillo, Gerardo; Zhan, Yiqiang

2014-03-01

Vertebral segmentation is a critical first step in any quantitative evaluation of vertebral pathology using CT images. This is especially challenging because bone marrow tissue has the same intensity profile as the muscle surrounding the bone. Thus simple methods such as thresholding or adaptive k-means fail to accurately segment vertebrae. While several other algorithms such as level sets may be used for segmentation any algorithm that is clinically deployable has to work in under a few seconds. To address these dual challenges we present here, a new algorithm based on the geodesic distance transform that is capable of segmenting the spinal vertebrae in under one second. To achieve this we extend the theory of the geodesic distance transforms proposed in1 to incorporate high level anatomical knowledge through adaptive weighting of image gradients. Such knowledge may be provided by the user directly or may be automatically generated by another algorithm. We incorporate information 'learnt' using a previously published machine learning algorithm2 to segment the L1 to L5 vertebrae. While we present a particular application here, the adaptive geodesic transform is a generic concept which can be applied to segmentation of other organs as well.

NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface.

PubMed

Ingebrigtsen, Trond S; Toxvaerd, Søren; Heilmann, Ole J; Schrøder, Thomas B; Dyre, Jeppe C

2011-09-14

An algorithm is derived for computer simulation of geodesics on the constant-potential-energy hypersurface of a system of N classical particles. First, a basic time-reversible geodesic algorithm is derived by discretizing the geodesic stationarity condition and implementing the constant-potential-energy constraint via standard Lagrangian multipliers. The basic NVU algorithm is tested by single-precision computer simulations of the Lennard-Jones liquid. Excellent numerical stability is obtained if the force cutoff is smoothed and the two initial configurations have identical potential energy within machine precision. Nevertheless, just as for NVE algorithms, stabilizers are needed for very long runs in order to compensate for the accumulation of numerical errors that eventually lead to "entropic drift" of the potential energy towards higher values. A modification of the basic NVU algorithm is introduced that ensures potential-energy and step-length conservation; center-of-mass drift is also eliminated. Analytical arguments confirmed by simulations demonstrate that the modified NVU algorithm is absolutely stable. Finally, we present simulations showing that the NVU algorithm and the standard leap-frog NVE algorithm have identical radial distribution functions for the Lennard-Jones liquid. © 2011 American Institute of Physics

Crustal velocity structure and earthquake processes of Garhwal-Kumaun Himalaya: Constraints from regional waveform inversion and array beam modeling

NASA Astrophysics Data System (ADS)

Negi, Sanjay S.; Paul, Ajay; Cesca, Simone; Kamal; Kriegerowski, Marius; Mahesh, P.; Gupta, Sandeep

2017-08-01

In order to understand present day earthquake kinematics at the Indian plate boundary, we analyse seismic broadband data recorded between 2007 and 2015 by the regional network in the Garhwal-Kumaun region, northwest Himalaya. We first estimate a local 1-D velocity model for the computation of reliable Green's functions, based on 2837 P-wave and 2680 S-wave arrivals from 251 well located earthquakes. The resulting 1-D crustal structure yields a 4-layer velocity model down to the depths of 20 km. A fifth homogeneous layer extends down to 46 km, constraining the Moho using travel-time distance curve method. We then employ a multistep moment tensor (MT) inversion algorithm to infer seismic moment tensors of 11 moderate earthquakes with Mw magnitude in the range 4.0-5.0. The method provides a fast MT inversion for future monitoring of local seismicity, since Green's functions database has been prepared. To further support the moment tensor solutions, we additionally model P phase beams at seismic arrays at teleseismic distances. The MT inversion result reveals the presence of dominant thrust fault kinematics persisting along the Himalayan belt. Shallow low and high angle thrust faulting is the dominating mechanism in the Garhwal-Kumaun Himalaya. The centroid depths for these moderate earthquakes are shallow between 1 and 12 km. The beam modeling result confirm hypocentral depth estimates between 1 and 7 km. The updated seismicity, constrained source mechanism and depth results indicate typical setting of duplexes above the mid crustal ramp where slip is confirmed along out-of-sequence thrusting. The involvement of Tons thrust sheet in out-of-sequence thrusting indicate Tons thrust to be the principal active thrust at shallow depth in the Himalayan region. Our results thus support the critical taper wedge theory, where we infer the microseismicity cluster as a result of intense activity within the Lesser Himalayan Duplex (LHD) system.

Methods for determining remanent and total magnetisations of magnetic sources - a review

NASA Astrophysics Data System (ADS)

Clark, David A.

2014-07-01

Assuming without evidence that magnetic sources are magnetised parallel to the geomagnetic field can seriously mislead interpretation and can result in drill holes missing their targets. This article reviews methods that are available for estimating, directly or indirectly, the natural remanent magnetisation (NRM) and total magnetisation of magnetic sources, noting the strengths and weaknesses of each approach. These methods are: (i) magnetic property measurements of samples; (ii) borehole magnetic measurements; (iii) inference of properties from petrographic/petrological information, supplemented by palaeomagnetic databases; (iv) constrained modelling/inversion of magnetic sources; (v) direct inversions of measured or calculated vector and gradient tensor data for simple sources; (vi) retrospective inference of magnetisation of a mined deposit by comparing magnetic data acquired pre- and post-mining; (vii) combined analysis of magnetic and gravity anomalies using Poisson's theorem; (viii) using a controlled magnetic source to probe the susceptibility distribution of the subsurface; (ix) Helbig-type analysis of gridded vector components, gradient tensor elements, and tensor invariants; (x) methods based on reduction to the pole and related transforms; and (xi) remote in situ determination of NRM direction, total magnetisation direction and Koenigsberger ratio by deploying dual vector magnetometers or a single combined gradiometer/magnetometer to monitor local perturbation of natural geomagnetic variations, operating in base station mode within a magnetic anomaly of interest. Characterising the total and remanent magnetisations of sources is important for several reasons. Knowledge of total magnetisation is often critical for accurate determination of source geometry and position. Knowledge of magnetic properties such as magnetisation intensity and Koenigsberger ratio constrains the likely magnetic mineralogy (composition and grain size) of a source, which gives an indication of its geological nature. Determining the direction of a stable ancient remanence gives an indication of the age of magnetisation, which provides useful information about the geological history of the source and its environs.

The Weighted Burgers Vector: a new quantity for constraining dislocation densities and types using electron backscatter diffraction on 2D sections through crystalline materials.

PubMed

Wheeler, J; Mariani, E; Piazolo, S; Prior, D J; Trimby, P; Drury, M R

2009-03-01

The Weighted Burgers Vector (WBV) is defined here as the sum, over all types of dislocations, of [(density of intersections of dislocation lines with a map) x (Burgers vector)]. Here we show that it can be calculated, for any crystal system, solely from orientation gradients in a map view, unlike the full dislocation density tensor, which requires gradients in the third dimension. No assumption is made about gradients in the third dimension and they may be non-zero. The only assumption involved is that elastic strains are small so the lattice distortion is entirely due to dislocations. Orientation gradients can be estimated from gridded orientation measurements obtained by EBSD mapping, so the WBV can be calculated as a vector field on an EBSD map. The magnitude of the WBV gives a lower bound on the magnitude of the dislocation density tensor when that magnitude is defined in a coordinate invariant way. The direction of the WBV can constrain the types of Burgers vectors of geometrically necessary dislocations present in the microstructure, most clearly when it is broken down in terms of lattice vectors. The WBV has three advantages over other measures of local lattice distortion: it is a vector and hence carries more information than a scalar quantity, it has an explicit mathematical link to the individual Burgers vectors of dislocations and, since it is derived via tensor calculus, it is not dependent on the map coordinate system. If a sub-grain wall is included in the WBV calculation, the magnitude of the WBV becomes dependent on the step size but its direction still carries information on the Burgers vectors in the wall. The net Burgers vector content of dislocations intersecting an area of a map can be simply calculated by an integration round the edge of that area, a method which is fast and complements point-by-point WBV calculations.

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

Null geodesics and wave front singularities in the Gödel space-time

NASA Astrophysics Data System (ADS)

Kling, Thomas P.; Roebuck, Kevin; Grotzke, Eric

2018-01-01

We explore wave fronts of null geodesics in the Gödel metric emitted from point sources both at, and away from, the origin. For constant time wave fronts emitted by sources away from the origin, we find cusp ridges as well as blue sky metamorphoses where spatially disconnected portions of the wave front appear, connect to the main wave front, and then later break free and vanish. These blue sky metamorphoses in the constant time wave fronts highlight the non-causal features of the Gödel metric. We introduce a concept of physical distance along the null geodesics, and show that for wave fronts of constant physical distance, the reorganization of the points making up the wave front leads to the removal of cusp ridges.

Injection of a Body into a Geodesic: Lessons Learnt from the LISA Pathfinder Case

NASA Technical Reports Server (NTRS)

Bortoluzzi, Daniele; Armano, M.; Audley, H.; Auger, G.; Baird, J.; Binetruy, P.; Born, M.; Bortoluzzi, D.; Brandt, N.; Bursi, A.;

Simple inflationary quintessential model. II. Power law potentials

NASA Astrophysics Data System (ADS)

de Haro, Jaume; Amorós, Jaume; Pan, Supriya

2016-09-01

The present work is a sequel of our previous work [Phys. Rev. D 93, 084018 (2016)] which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs-type potential and the quintessential phase was responsible due to an exponential potential. Additionally, the model predicted a nonsingular universe in past which was geodesically past incomplete. Further, it was also found that the model is in agreement with the Planck 2013 data when running is allowed. But, this model provides a theoretical value of the running which is far smaller than the central value of the best fit in ns , r , αs≡d ns/d l n k parameter space where ns, r , αs respectively denote the spectral index, tensor-to-scalar ratio and the running of the spectral index associated with any inflationary model, and consequently to analyze the viability of the model one has to focus in the two-dimensional marginalized confidence level in the allowed domain of the plane (ns,r ) without taking into account the running. Unfortunately, such analysis shows that this model does not pass this test. However, in this sequel we propose a family of models runs by a single parameter α ∈[0 ,1 ] which proposes another "inflationary quintessential model" where the inflation and the quintessence regimes are respectively described by a power law potential and a cosmological constant. The model is also nonsingular although geodesically past incomplete as in the cited model. Moreover, the present one is found to be more simple compared to the previous model and it is in excellent agreement with the observational data. In fact, we note that, unlike the previous model, a large number of the models of this family with α ∈[0 ,1/2 ) match with both Planck 2013 and Planck 2015 data without allowing the running. Thus, the properties in the current family of models compared to its past companion justify its need for a better cosmological model with the successive improvement of the observational data.

No fifth force in a scale invariant universe

DOE PAGES

Ferreira, Pedro G.; Hill, Christopher T.; Ross, Graham G.

2017-03-15

We revisit the possibility that the Planck mass is spontaneously generated in scale-invariant scalar-tensor theories of gravity, typically leading to a “dilaton.” The fifth force, arising from the dilaton, is severely constrained by astrophysical measurements. We explore the possibility that nature is fundamentally scale invariant and argue that, as a consequence, the fifth-force effects are dramatically suppressed and such models are viable. Finally, we discuss possible obstructions to maintaining scale invariance and how these might be resolved.

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.

Minimum energy control and optimal-satisfactory control of Boolean control network

NASA Astrophysics Data System (ADS)

Li, Fangfei; Lu, Xiwen

2013-12-01

In the literatures, to transfer the Boolean control network from the initial state to the desired state, the expenditure of energy has been rarely considered. Motivated by this, this Letter investigates the minimum energy control and optimal-satisfactory control of Boolean control network. Based on the semi-tensor product of matrices and Floyd's algorithm, minimum energy, constrained minimum energy and optimal-satisfactory control design for Boolean control network are given respectively. A numerical example is presented to illustrate the efficiency of the obtained results.

Axisymmetric electrostatic magnetohydrodynamic oscillations in tokamaks with general cross-sections and toroidal flow

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

Chu, M. S.; Guo, Wenfeng

2016-06-15

The frequency spectrum and mode structure of axisymmetric electrostatic oscillations [the zonal flow (ZF), sound waves (SW), geodesic acoustic modes (GAM), and electrostatic mean flows (EMF)] in tokamaks with general cross-sections and toroidal flows are studied analytically using the electrostatic approximation for magnetohydrodynamic modes. These modes constitute the “electrostatic continua.” Starting from the energy principle for a tokamak plasma with toroidal rotation, we showed that these modes are completely stable. The ZF, the SW, and the EMF could all be viewed as special cases of the general GAM. The Euler equations for the general GAM are obtained and are solvedmore » analytically for both the low and high range of Mach numbers. The solution consists of the usual countable infinite set of eigen-modes with discrete eigen-frequencies, and two modes with lower frequencies. The countable infinite set is identified with the regular GAM. The lower frequency mode, which is also divergence free as the plasma rotation tends to zero, is identified as the ZF. The other lower (zero) frequency mode is a pure geodesic E×B flow and not divergence free is identified as the EMF. The frequency of the EMF is shown to be exactly 0 independent of plasma cross-section or its flow Mach number. We also show that in general, sound waves with no geodesic components are (almost) completely lost in tokamaks with a general cross-sectional shape. The exception is the special case of strict up-down symmetry. In this case, half of the GAMs would have no geodesic displacements. They are identified as the SW. Present day tokamaks, although not strictly up-down symmetric, usually are only slightly up-down asymmetric. They are expected to share the property with the up-down symmetric tokamak in that half of the GAMs would be more sound wave-like, i.e., have much weaker coupling to the geodesic components than the other half of non-sound-wave-like modes with stronger coupling to the geodesic displacements. Based on the general notion that the geodesic component of the GAM is more effective in tearing up the eddies in the electrostatic turbulence, it is important to preferentially excite the GAMs that are non-sound-wave like to maximize the efficiency on turbulence suppression through external means. Finally, approximate formulae for the frequencies of the EMF, ZF, SW, and the GAM for a large aspect ratio circular tokamak rotating at low Mach numbers are also provided.« less

Calculating the Sachs-Wolfe Effect from Solutions of Null Geodesics in Perturbed FRW Spacetime

NASA Astrophysics Data System (ADS)

Arroyo-Cárdenas, C. A.; Muñoz-Cuartas, J. C.

2017-07-01

In the upcoming precision era in cosmology, fine grained effects will be measured accurately. In particular, the late integrated Sachs-Wolfe (ISW) effect measurements will be improved to levels of unprecedented precision. The ISW consists on temperature fluctuations in the CMB due to gravitational redshift induced by the evolving potential well of large scale structure in the Universe. Currently there is large controversy related to the actual observability of the ISW effect. In principle, it is expected that, as an effect of the late accelerated expansion of the universe motivated by the current amount of dark energy, large scale structures may evolve rapidly, inducing an observable signature in the CMB photons in the way of a ISW anisotropy in the CMB. Tension arises since using galaxy redshift surveys some works report a temperature fluctuations with amplitude smaller than predicted by the Lambda-CDM. We argue that these discrepancies may be originated in the approximation that one has to make to get the classic Sachs-Wolfe effect. In this work, we compare the classic Sachs-Wolfe approximation with an exact solution to the propagation of photons in a dynamical background. We solve numerically the null geodesics on a perturbed FRW spacetime in the Newtonian gauge. From null geodesics, temperature fluctuations in the CMB due to the evolving potential has been calculated. Since solving geodesics accounts for more terms than solving the Sachs-Wolfe (approximated) integral, our results are more accurate. We have been able to substract the background cosmological redshift with the information provided by null geodesics, which allows to get an estimate of the integrated Sachs-Wolfe effect contribution to the temperature of the CMB.

Metric Properties of Relativistic Rotating Frames with Axial Symmetry

NASA Astrophysics Data System (ADS)

Torres, S. A.; Arenas, J. R.

2017-07-01

This abstract summarizes our poster contribution to the conference. We study the properties of an axially symmetric stationary gravitational field, by considering the spacetime properties of an uniformly rotating frame and the Einstein's Equivalence Principle (EEP). To undertake this, the weak field and slow-rotation limit of the kerr metric are determined, by making a first-order perturbation to the metric of a rotating frame. Also, we show a local connection between the effects of centrifugal and Coriolis forces with the effects of an axially symmetric stationary weak gravitational field, by calculating the geodesic equations of a free particle. It is observed that these geodesic, applying the (EEP), are locally equivalent to the geodesic equations of a free particle on a rotating frame. Furthermore, some aditional properties as the Lense-Thirring effect, the Sagnac effect, among others are studied.

Geodesic least squares regression for scaling studies in magnetic confinement fusion

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

Verdoolaege, Geert

In regression analyses for deriving scaling laws that occur in various scientific disciplines, usually standard regression methods have been applied, of which ordinary least squares (OLS) is the most popular. However, concerns have been raised with respect to several assumptions underlying OLS in its application to scaling laws. We here discuss a new regression method that is robust in the presence of significant uncertainty on both the data and the regression model. The method, which we call geodesic least squares regression (GLS), is based on minimization of the Rao geodesic distance on a probabilistic manifold. We demonstrate the superiority ofmore » the method using synthetic data and we present an application to the scaling law for the power threshold for the transition to the high confinement regime in magnetic confinement fusion devices.« less

Spherical cows in the sky with fab four

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

Kaloper, Nemanja; Sandora, McCullen, E-mail: kaloper@physics.ucdavis.edu, E-mail: mesandora@ucdavis.edu

2014-05-01

We explore spherically symmetric static solutions in a subclass of unitary scalar-tensor theories of gravity, called the 'Fab Four' models. The weak field large distance solutions may be phenomenologically viable, but only if the Gauss-Bonnet term is negligible. Only in this limit will the Vainshtein mechanism work consistently. Further, classical constraints and unitarity bounds constrain the models quite tightly. Nevertheless, in the limits where the range of individual terms at large scales is respectively Kinetic Braiding, Horndeski, and Gauss-Bonnet, the horizon scale effects may occur while the theory satisfies Solar system constraints and, marginally, unitarity bounds. On the other hand,more » to bring the cutoff down to below a millimeter constrains all the couplings scales such that 'Fab Fours' can't be heard outside of the Solar system.« less

Resonant Raman spectra of diindenoperylene thin films

NASA Astrophysics Data System (ADS)

Scholz, R.; Gisslén, L.; Schuster, B.-E.; Casu, M. B.; Chassé, T.; Heinemeyer, U.; Schreiber, F.

2011-01-01

Resonant and preresonant Raman spectra obtained on diindenoperylene (DIP) thin films are interpreted with calculations of the deformation of a relaxed excited molecule with density functional theory (DFT). The comparison of excited state geometries based on time-dependent DFT or on a constrained DFT scheme with observed absorption spectra of dissolved DIP reveals that the deformation pattern deduced from constrained DFT is more reliable. Most observed Raman peaks can be assigned to calculated A_g-symmetric breathing modes of DIP or their combinations. As the position of one of the laser lines used falls into a highly structured absorption band, we have carefully analyzed the Raman excitation profile arising from the frequency dependence of the dielectric tensor. This procedure gives Raman cross sections in good agreement with the observed relative intensities, both in the fully resonant and in the preresonant case.

Resonant Raman spectra of diindenoperylene thin films.

PubMed

Scholz, R; Gisslén, L; Schuster, B-E; Casu, M B; Chassé, T; Heinemeyer, U; Schreiber, F

2011-01-07

Resonant and preresonant Raman spectra obtained on diindenoperylene (DIP) thin films are interpreted with calculations of the deformation of a relaxed excited molecule with density functional theory (DFT). The comparison of excited state geometries based on time-dependent DFT or on a constrained DFT scheme with observed absorption spectra of dissolved DIP reveals that the deformation pattern deduced from constrained DFT is more reliable. Most observed Raman peaks can be assigned to calculated A(g)-symmetric breathing modes of DIP or their combinations. As the position of one of the laser lines used falls into a highly structured absorption band, we have carefully analyzed the Raman excitation profile arising from the frequency dependence of the dielectric tensor. This procedure gives Raman cross sections in good agreement with the observed relative intensities, both in the fully resonant and in the preresonant case.

Testing the equivalence principle on cosmological scales

NASA Astrophysics Data System (ADS)

Bonvin, Camille; Fleury, Pierre

2018-05-01

The equivalence principle, that is one of the main pillars of general relativity, is very well tested in the Solar system; however, its validity is more uncertain on cosmological scales, or when dark matter is concerned. This article shows that relativistic effects in the large-scale structure can be used to directly test whether dark matter satisfies Euler's equation, i.e. whether its free fall is characterised by geodesic motion, just like baryons and light. After having proposed a general parametrisation for deviations from Euler's equation, we perform Fisher-matrix forecasts for future surveys like DESI and the SKA, and show that such deviations can be constrained with a precision of order 10%. Deviations from Euler's equation cannot be tested directly with standard methods like redshift-space distortions and gravitational lensing, since these observables are not sensitive to the time component of the metric. Our analysis shows therefore that relativistic effects bring new and complementary constraints to alternative theories of gravity.

Horndeski theories confront the Gravity Probe B experiment

NASA Astrophysics Data System (ADS)

Mukherjee, Sajal; Chakraborty, Sumanta

2018-06-01

In this work we have investigated various properties of a spinning gyroscope in the context of Horndeski theories. In particular, we have focused on two specific situations—(a) when the gyroscope follows a geodesic trajectory and (b) when it is endowed with an acceleration. In both these cases, besides developing the basic formalism, we have also applied the same to understand the motion of a spinning gyroscope in various static and spherically symmetric spacetimes pertaining to Horndeski theories. Starting with the Schwarzschild de Sitter spacetime as a warm up exercise, we have presented our results for two charged Galileon black holes as well as for a black hole in scalar coupled Einstein-Gauss-Bonnet gravity. In all these cases we have shown that the spinning gyroscope can be used to distinguish black holes from naked singularities. Moreover, using the numerical estimation of the geodetic precession from the Gravity Probe B experiment, we have constrained the gauge/scalar charge of the black holes in these Horndeski theories. Implications are also discussed.

Moment tensor solutions estimated using optimal filter theory for 51 selected earthquakes, 1980-1984

USGS Publications Warehouse

Sipkin, S.A.

1987-01-01

The 51 global events that occurred from January 1980 to March 1984, which were chosen by the convenors of the Symposium on Seismological Theory and Practice, have been analyzed using a moment tensor inversion algorithm (Sipkin). Many of the events were routinely analyzed as part of the National Earthquake Information Center's (NEIC) efforts to publish moment tensor and first-motion fault-plane solutions for all moderate- to large-sized (mb>5.7) earthquakes. In routine use only long-period P-waves are used and the source-time function is constrained to be a step-function at the source (??-function in the far-field). Four of the events were of special interest, and long-period P, SH-wave solutions were obtained. For three of these events, an unconstrained inversion was performed. The resulting time-dependent solutions indicated that, for many cases, departures of the solutions from pure double-couples are caused by source complexity that has not been adequately modeled. These solutions also indicate that source complexity of moderate-sized events can be determined from long-period data. Finally, for one of the events of special interest, an inversion of the broadband P-waveforms was also performed, demonstrating the potential for using broadband waveform data in inversion procedures. ?? 1987.

Boundary of the future of a surface

DOE PAGES

Akers, Chris; Bousso, Raphael; Halpern, Illan F.; ...

2018-01-12

We prove that the boundary of the future of a surface K consists precisely of the points p that lie on a null geodesic orthogonal to K such that between K and p there are no points conjugate to K nor intersections with another such geodesic. Our theorem has applications to holographic screens and their associated light sheets and in particular enters the proof that holographic screens satisfy an area law.

Measurement of momentum transfer due to adhesive forces: on-ground testing of in-space body injection into geodesic motion.

PubMed

Bortoluzzi, D; Benedetti, M; Baglivo, L; De Cecco, M; Vitale, S

2011-12-01

In the frame of many scientific space missions, a massive free-falling object is required to mark a geodesic trajectory, i.e., to follow inside a spacecraft an orbit that is determined only by the planetary gravity field. The achievement of high-purity geodesic trajectories sets tight design constraints on the reference sensor that hosts and controls the reference body. Among these, a mechanism may be required to cage the reference body during the spacecraft launch and to inject it into the geodesic trajectory once on-orbit. The separation of the body from the injection mechanism must be realized against the action of adhesion forces, and in the worst case this is performed dynamically, relying on the body's inertia through a quick retraction of the holding finger(s). Unfortunately, this manoeuvre may not avoid transferring some momentum to the body, which may affect or even jeopardize the subsequent spacecraft control if the residual velocity is too large. The transferred momentum measurement facility (TMMF) was developed to reproduce representative conditions of the in-flight dynamic injection and to measure the transferred momentum to the released test mass. In this paper, we describe the design and development of the TMMF together with the achieved measurement performance.

On static solutions of the Einstein-Scalar Field equations

NASA Astrophysics Data System (ADS)

Reiris, Martín

2017-03-01

In this article we study self-gravitating static solutions of the Einstein-Scalar Field system in arbitrary dimensions. We discuss the existence of geodesically complete solutions depending on the form of the scalar field potential V(φ ), and provide full global geometric estimates when the solutions exist. The most complete results are obtained for the physically important Klein-Gordon field and are summarised as follows. When V(φ )=m2|φ |2, it is proved that geodesically complete solutions have Ricci-flat spatial metric, have constant lapse and are vacuum, (that is φ is constant and equal to zero if m≠ 0). In particular, when the spatial dimension is three, the only such solutions are either Minkowski or a quotient thereof (no nontrivial solutions exist). When V(φ )=m2|φ |2+2Λ , that is, when a vacuum energy or a cosmological constant is included, it is proved that no geodesically complete solution exists when Λ >0, whereas when Λ <0 it is proved that no non-vacuum geodesically complete solution exists unless m2<-2Λ /(n-1), ( n is the spatial dimension) and the spatial manifold is non-compact. The proofs are based on novel techniques in comparison geometry á la Bakry-Émery that have their own interest.

A cut-&-paste strategy for the 3-D inversion of helicopter-borne electromagnetic data - I. 3-D inversion using the explicit Jacobian and a tensor-based formulation

NASA Astrophysics Data System (ADS)

Scheunert, M.; Ullmann, A.; Afanasjew, M.; Börner, R.-U.; Siemon, B.; Spitzer, K.

2016-06-01

We present an inversion concept for helicopter-borne frequency-domain electromagnetic (HEM) data capable of reconstructing 3-D conductivity structures in the subsurface. Standard interpretation procedures often involve laterally constrained stitched 1-D inversion techniques to create pseudo-3-D models that are largely representative for smoothly varying conductivity distributions in the subsurface. Pronounced lateral conductivity changes may, however, produce significant artifacts that can lead to serious misinterpretation. Still, 3-D inversions of entire survey data sets are numerically very expensive. Our approach is therefore based on a cut-&-paste strategy whereupon the full 3-D inversion needs to be applied only to those parts of the survey where the 1-D inversion actually fails. The introduced 3-D Gauss-Newton inversion scheme exploits information given by a state-of-the-art (laterally constrained) 1-D inversion. For a typical HEM measurement, an explicit representation of the Jacobian matrix is inevitable which is caused by the unique transmitter-receiver relation. We introduce tensor quantities which facilitate the matrix assembly of the forward operator as well as the efficient calculation of the Jacobian. The finite difference forward operator incorporates the displacement currents because they may seriously affect the electromagnetic response at frequencies above 100. Finally, we deliver the proof of concept for the inversion using a synthetic data set with a noise level of up to 5%.

Motion of small bodies in classical field theory

NASA Astrophysics Data System (ADS)

Gralla, Samuel E.

2010-04-01

I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body’s composition (and, e.g., black holes are allowed). The worldline “left behind” by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the “Bianchi identity” for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the “monopoles” of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of “chameleon” bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.

On six-dimensional pseudo-Riemannian almost g.o. spaces

NASA Astrophysics Data System (ADS)

Dušek, Zdeněk; Kowalski, Oldřich

2007-09-01

We modify the "Kaplan example" (a six-dimensional nilpotent Lie group which is a Riemannian g.o. space) and we obtain two pseudo-Riemannian homogeneous spaces with noncompact isotropy group. These examples have the property that all geodesics are homogeneous up to a set of measure zero. We also show that the (incomplete) geodesic graphs are strongly discontinuous at the boundary, i.e., the limits along certain curves are always infinite.

Using Riemannian geometry to obtain new results on Dikin and Karmarkar methods

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

Oliveira, P.; Joao, X.; Piaui, T.

1994-12-31

We are motivated by a 1990 Karmarkar paper on Riemannian geometry and Interior Point Methods. In this talk we show 3 results. (1) Karmarkar direction can be derived from the Dikin one. This is obtained by constructing a certain Z(x) representation of the null space of the unitary simplex (e, x) = 1; then the projective direction is the image under Z(x) of the affine-scaling one, when it is restricted to that simplex. (2) Second order information on Dikin and Karmarkar methods. We establish computable Hessians for each of the metrics corresponding to both directions, thus permitting the generation ofmore » {open_quotes}second order{close_quotes} methods. (3) Dikin and Karmarkar geodesic descent methods. For those directions, we make computable the theoretical Luenberger geodesic descent method, since we are able to explicit very accurate expressions of the corresponding geodesics. Convergence results are given.« less

Gravitational attraction until relativistic equipartition of internal and translational kinetic energies

NASA Astrophysics Data System (ADS)

Bulyzhenkov, I. E.

2018-02-01

Translational ordering of the internal kinematic chaos provides the Special Relativity referents for the geodesic motion of warm thermodynamical bodies. Taking identical mathematics, relativistic physics of the low speed transport of time-varying heat-energies differs from Newton's physics of steady masses without internal degrees of freedom. General Relativity predicts geodesic changes of the internal heat-energy variable under the free gravitational fall and the geodesic turn in the radial field center. Internal heat variations enable cyclic dynamics of decelerated falls and accelerated takeoffs of inertial matter and its structural self-organization. The coordinate speed of the ordered spatial motion takes maximum under the equipartition of relativistic internal and translational kinetic energies. Observable predictions are discussed for verification/falsification of the principle of equipartition as a new basic for the ordered motion and self-organization in external fields, including gravitational, electromagnetic, and thermal ones.

Exact moduli space metrics for hyperbolic vortex polygons

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

Krusch, S.; Speight, J. M.

2010-02-15

Exact metrics on some totally geodesic submanifolds of the moduli space of static hyperbolic N-vortices are derived. These submanifolds, denoted as {sigma}{sub n,m}, are spaces of C{sub n}-invariant vortex configurations with n single vortices at the vertices of a regular polygon and m=N-n coincident vortices at the polygon's center. The geometric properties of {sigma}{sub n,m} are investigated, and it is found that {sigma}{sub n,n-1} is isometric to the hyperbolic plane of curvature -(3{pi}n){sup -1}. The geodesic flow on {sigma}{sub n,m} and a geometrically natural variant of geodesic flow recently proposed by Collie and Tong ['The dynamics of Chern-Simons vortices', Phys.more » Rev. D Part. Fields Gravit. Cosmol. 78, 065013 (2008);e-print arXiv:hep-th/0805.0602] are analyzed in detail.« less

Automated detection of Lagrangian eddies and coherent transport of heat and salinity in the Agulhas leakage

NASA Astrophysics Data System (ADS)

Huhn, Florian; Haller, George

2014-05-01

Haller and Beron-Vera(2013) have recently introduced a new objective method to detect coherent Lagrangian eddies in turbulence. They find that closed null-geodesics of a generalized Green-Lagrange strain tensor act as coherent Lagrangian eddy boundaries, showing near-zero and uniform material stretching. We make use of this method to develop an automated detection procedure for coherent Lagrangian eddies in large-scale ocean data. We apply our results to a recent 3D general circulation model, the Southern Ocean State Estimate (SOSE), with focus on the South Atlantic Ocean and the inter-ocean exchange between the Indian and Atlantic ocean. We detect a large number of coherent Lagrangian eddies and present statistics of their properties. The largest and most circular eddy boundaries represent Lagrangian Agulhas rings. Circular regions inside these rings with higher temperature and salinity than the surrounding waters can be explained by the coherent eddy boundaries that enclose and isolate the eddy interiors. We compare eddy boundaries at different depths with eddy boundaries obtained from geostrophic velocities derived from the model's sea surface height (SSH). The transport of mass, heat and salinity enclosed by coherent eddies through a section in the Cape basin is quantified and compared to the non-coherent transport by the background flow.

Unveiling the nucleon tensor charge at Jefferson Lab: A study of the SoLID case

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

Ye, Zhihong; Sato, Nobuo; Allada, Kalyan

© 2017 The Authors Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the quark transversity distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID experiments. Especially, we develop a simple strategy based on the Hessian matrix analysis that allows one to estimate themore » uncertainties of the transversity quark distributions and their tensor charges extracted from SoLID data simulation. We find that the SoLID measurements with the proton and the effective neutron targets can improve the precision of the u- and d-quark transversity distributions up to one order of magnitude in the range 0.05 < x < 0.6.« less

Neotectonic activity and parameters of seismotectonic deformations of seismic belts in Northeast Asia

NASA Astrophysics Data System (ADS)

Imaeva, Lyudmila; Gusev, Georgy; Imaev, Valerii; Mel'nikova, Valentina

2017-10-01

The Arctic-Asian and Okhotsk-Chukotka seismic belts bordering the Kolyma-Chukotka crustal plate are the subject of our study aimed at reconstructing the stress-strain state of the crust and defining the types of seismotectonic deformation (STD) in the region. Based on the degrees of activity of geodynamic processes, the regional principles for ranking neotectonic structures were constrained, and the corresponding classes of the discussed neotectonic structures were substantiated. We analyzed the structural tectonic positions of the modern structures, their deep structure parameters, and the systems of active faults in the Laptev, Kharaulakh, Koryak, and Chukotka segments and Chersky seismotectonic zone, as well as the tectonic stress fields revealed by tectonophysical analysis of the Late Cenozoic faults and folds. From the earthquake focal mechanisms, the average seismotectonic strain tensors were estimated. Using the geological, geostructural, geophysical and GPS data, and corresponding average tensors, the directions of the principal stress axes were determined. A regularity in the changes of tectonic settings in the Northeast Arctic was revealed.

Casimir Effect in de Sitter Spacetime

NASA Astrophysics Data System (ADS)

Saharian, A. A.

2011-06-01

The vacuum expectation value of the energy-momentum tensor and the Casimir forces are investigated for a massive scalar field with an arbitrary curvature coupling parameter in the geometry of two parallel plates, on the background of de Sitter spacetime. The field is prepared in the Bunch-Davies vacuum state and is constrained to satisfy Robin boundary conditions on the plates. The vacuum energy-momentum tensor is non-diagonal, with the off-diagonal component corresponding to the energy flux along the direction normal to the plates. It is shown that the curvature of the background spacetime decisively influences the behavior of the Casimir forces at separations larger than the curvature radius of de Sitter spacetime. In dependence of the curvature coupling parameter and the mass of the field, two different regimes are realized, which exhibit monotonic or oscillatory behavior of the forces. The decay of the Casimir force at large plate separation is shown to be power-law, with independence of the value of the field mass.

Simulations of Ground Motion in Southern California based upon the Spectral-Element Method

NASA Astrophysics Data System (ADS)

Tromp, J.; Komatitsch, D.; Liu, Q.

2003-12-01

We use the spectral-element method to simulate ground motion generated by recent well-recorded small earthquakes in Southern California. Simulations are performed using a new sedimentary basin model that is constrained by hundreds of petroleum industry well logs and more than twenty thousand kilometers of seismic reflection profiles. The numerical simulations account for 3D variations of seismic wave speeds and density, topography and bathymetry, and attenuation. Simulations for several small recent events demonstrate that the combination of a detailed sedimentary basin model and an accurate numerical technique facilitates the simulation of ground motion at periods of 2 seconds and longer inside the Los Angeles basin and 6 seconds and longer elsewhere. Peak ground displacement, velocity and acceleration maps illustrate that significant amplification occurs in the basin. Centroid-Moment Tensor mechanisms are obtained based upon Pnl and surface waveforms and numerically calculated 3D Frechet derivatives. We use a combination of waveform and waveform-envelope misfit criteria, and facilitate pure double-couple or zero-trace moment-tensor inversions.

The dynamic generalization of the Eshelby inclusion problem and its static limit

PubMed Central

2016-01-01

The dynamic generalization of the celebrated Eshelby inclusion with transformation strain is the (subsonically) self-similarly expanding ellipsoidal inclusion starting from the zero dimension. The solution of the governing system of partial differential equations was obtained recently by Ni & Markenscoff (In press. J. Mech. Phys. Solids (doi:10.1016/j.jmps.2016.02.025)) on the basis of the Radon transformation, while here an alternative method is presented. In the self-similarly expanding motion, the Eshelby property of constant constrained strain is valid in the interior domain of the expanding ellipsoid where the particle velocity vanishes (lacuna). The dynamic Eshelby tensor is obtained in integral form. From it, the static Eshelby tensor is obtained by a limiting procedure, as the axes' expansion velocities tend to zero and time to infinity, while their product is equal to the length of the static axis. This makes the Eshelby problem the limit of its dynamic generalization. PMID:27493574

On the running of the spectral index to all orders: a new model-dependent approach to constrain inflationary models

NASA Astrophysics Data System (ADS)

Zarei, Moslem

2016-06-01

In conventional model-independent approaches, the power spectrum of primordial perturbations is characterized by such free parameters as the spectral index, its running, the running of running, and the tensor-to-scalar ratio. In this work we show that, at least for simple inflationary potentials, one can find the primordial scalar and tensor power spectra exactly by resumming over all the running terms. In this model-dependent method, we expand the power spectra about the pivot scale to find the series terms as functions of the e-folding number for some single field models of inflation. Interestingly, for the viable models studied here, one can sum over all the terms and evaluate the exact form of the power spectra. This in turn gives more accurate parametrization of the specific models studied in this work. We finally compare our results with recent cosmic microwave background data to find that our new power spectra are in good agreement with the data.

Unveiling the nucleon tensor charge at Jefferson Lab: A study of the SoLID case

NASA Astrophysics Data System (ADS)

Ye, Zhihong; Sato, Nobuo; Allada, Kalyan; Liu, Tianbo; Chen, Jian-Ping; Gao, Haiyan; Kang, Zhong-Bo; Prokudin, Alexei; Sun, Peng; Yuan, Feng

2017-04-01

Future experiments at the Jefferson Lab 12 GeV upgrade, in particular, the Solenoidal Large Intensity Device (SoLID), aim at a very precise data set in the region where the partonic structure of the nucleon is dominated by the valence quarks. One of the main goals is to constrain the quark transversity distributions. We apply recent theoretical advances of the global QCD extraction of the transversity distributions to study the impact of future experimental data from the SoLID experiments. Especially, we develop a simple strategy based on the Hessian matrix analysis that allows one to estimate the uncertainties of the transversity quark distributions and their tensor charges extracted from SoLID data simulation. We find that the SoLID measurements with the proton and the effective neutron targets can improve the precision of the u- and d-quark transversity distributions up to one order of magnitude in the range 0.05 < x < 0.6.

Glueballs on the baryonic branch of Klebanov-Strassler: dimensional deconstruction and a light scalar particle

NASA Astrophysics Data System (ADS)

Elander, Daniel; Piai, Maurizio

2017-06-01

Within gauge/gravity duality, we compute the scalar and tensor mass spectrum in the boundary theory defined by the five-dimensional sigma-model coupled to gravity obtained by constraining to eight scalars the truncation on T 1,1 that corresponds to the Papadopoulos-Tseytlin (PT) ansatz. We study fluctuations around the 1-parameter family of backgrounds that lift to the baryonic branch of the Klebanov-Strassler (KS) system, and interpolates between the KS background and the Maldacena-Nunez one (CVMN). We adopt a gauge invariant formalism in the treatment of the fluctuations that we interpret as states of the dual theory. The tensor spectrum interpolates between the discrete spectrum of the KS background and the continuum spectrum of the CVMN background, in particular showing the emergence of a finite energy range containing a dense set of states, as expected from dimensional deconstruction. The scalar spectrum shows analogous features, and in addition it contains one state that becomes parametrically light far from the origin along the baryonic branch.

First direct constraints on Fierz interference in free-neutron β decay

NASA Astrophysics Data System (ADS)

Hickerson, K. P.; Sun, X.; Bagdasarova, Y.; Bravo-Berguño, D.; Broussard, L. J.; Brown, M. A.-P.; Carr, R.; Currie, S.; Ding, X.; Filippone, B. W.; García, A.; Geltenbort, P.; Hoagland, J.; Holley, A. T.; Hong, R.; Ito, T. M.; Knecht, A.; Liu, C.-Y.; Liu, J. L.; Makela, M.; Mammei, R. R.; Martin, J. W.; Melconian, D.; Mendenhall, M. P.; Moore, S. D.; Morris, C. L.; Pattie, R. W.; Pérez Galván, A.; Picker, R.; Pitt, M. L.; Plaster, B.; Ramsey, J. C.; Rios, R.; Saunders, A.; Seestrom, S. J.; Sharapov, E. I.; Sondheim, W. E.; Tatar, E.; Vogelaar, R. B.; VornDick, B.; Wrede, C.; Young, A. R.; Zeck, B. A.; UCNA Collaboration

2017-10-01

Precision measurements of free-neutron β decay have been used to precisely constrain our understanding of the weak interaction. However, the neutron Fierz interference term bn, which is particularly sensitive to beyond-standard-model tensor currents at the TeV scale, has thus far eluded measurement. Here we report the first direct constraints on this term, finding bn=0.067 ±0 .005stat-0.061+0.090sys , consistent with the standard model. The uncertainty is dominated by absolute energy reconstruction and the linearity of the β spectrometer energy response.

Average geodesic distance of skeleton networks of Sierpinski tetrahedron

NASA Astrophysics Data System (ADS)

Yang, Jinjin; Wang, Songjing; Xi, Lifeng; Ye, Yongchao

2018-04-01

The average distance is concerned in the research of complex networks and is related to Wiener sum which is a topological invariant in chemical graph theory. In this paper, we study the skeleton networks of the Sierpinski tetrahedron, an important self-similar fractal, and obtain their asymptotic formula for average distances. To provide the formula, we develop some technique named finite patterns of integral of geodesic distance on self-similar measure for the Sierpinski tetrahedron.

Strolling along gauge theory vacua

NASA Astrophysics Data System (ADS)

Seraj, Ali; Van den Bleeken, Dieter

2017-08-01

We consider classical, pure Yang-Mills theory in a box. We show how a set of static electric fields that solve the theory in an adiabatic limit correspond to geodesic motion on the space of vacua, equipped with a particular Riemannian metric that we identify. The vacua are generated by spontaneously broken global gauge symmetries, leading to an infinite number of conserved momenta of the geodesic motion. We show that these correspond to the soft multipole charges of Yang-Mills theory.

Beyond Higgs couplings: Probing the Higgs with angular observables at future e$$^{+}$$e$$^{-}$$ colliders

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

Craig, Nathaniel; Gu, Jiayin; Liu, Zhen

Here, we study angular observables in themore » $$ {e}^{+}{e}^{-}\\to ZH\\to {\\ell}^{+}{\\ell}^{-}b\\overline{b} $$ channel at future circular e$$^{+}$$ e$$^{-}$$ colliders such as CEPC and FCC-ee. Taking into account the impact of realistic cut acceptance and detector effects, we forecast the precision of six angular asymmetries at CEPC (FCC-ee) with center-of-mass energy $$ \\sqrt{s}=240 $$ GeV and 5 (30) ab$$^{-1}$$ integrated luminosity. We then determine the projected sensitivity to a range of operators relevant for he Higgs-strahlung process in the dimension-6 Higgs EFT. Our results show that angular observables provide complementary sensitivity to rate measurements when constraining various tensor structures arising from new physics. We further find that angular asymmetries provide a novel means of both probing BSM corrections to the HZγ coupling and constraining the “blind spot” in indirect limits on supersymmetric scalar top partners.« less

Beyond Higgs couplings: Probing the Higgs with angular observables at future e$$^{+}$$e$$^{-}$$ colliders

DOE PAGES

Craig, Nathaniel; Gu, Jiayin; Liu, Zhen; ...

2016-03-09

Here, we study angular observables in themore » $$ {e}^{+}{e}^{-}\\to ZH\\to {\\ell}^{+}{\\ell}^{-}b\\overline{b} $$ channel at future circular e$$^{+}$$ e$$^{-}$$ colliders such as CEPC and FCC-ee. Taking into account the impact of realistic cut acceptance and detector effects, we forecast the precision of six angular asymmetries at CEPC (FCC-ee) with center-of-mass energy $$ \\sqrt{s}=240 $$ GeV and 5 (30) ab$$^{-1}$$ integrated luminosity. We then determine the projected sensitivity to a range of operators relevant for he Higgs-strahlung process in the dimension-6 Higgs EFT. Our results show that angular observables provide complementary sensitivity to rate measurements when constraining various tensor structures arising from new physics. We further find that angular asymmetries provide a novel means of both probing BSM corrections to the HZγ coupling and constraining the “blind spot” in indirect limits on supersymmetric scalar top partners.« less

Geodesic denoising for optical coherence tomography images

NASA Astrophysics Data System (ADS)

Shahrian Varnousfaderani, Ehsan; Vogl, Wolf-Dieter; Wu, Jing; Gerendas, Bianca S.; Simader, Christian; Langs, Georg; Waldstein, Sebastian M.; Schmidt-Erfurth, Ursula

2016-03-01

Optical coherence tomography (OCT) is an optical signal acquisition method capturing micrometer resolution, cross-sectional three-dimensional images. OCT images are used widely in ophthalmology to diagnose and monitor retinal diseases such as age-related macular degeneration (AMD) and Glaucoma. While OCT allows the visualization of retinal structures such as vessels and retinal layers, image quality and contrast is reduced by speckle noise, obfuscating small, low intensity structures and structural boundaries. Existing denoising methods for OCT images may remove clinically significant image features such as texture and boundaries of anomalies. In this paper, we propose a novel patch based denoising method, Geodesic Denoising. The method reduces noise in OCT images while preserving clinically significant, although small, pathological structures, such as fluid-filled cysts in diseased retinas. Our method selects optimal image patch distribution representations based on geodesic patch similarity to noisy samples. Patch distributions are then randomly sampled to build a set of best matching candidates for every noisy sample, and the denoised value is computed based on a geodesic weighted average of the best candidate samples. Our method is evaluated qualitatively on real pathological OCT scans and quantitatively on a proposed set of ground truth, noise free synthetic OCT scans with artificially added noise and pathologies. Experimental results show that performance of our method is comparable with state of the art denoising methods while outperforming them in preserving the critical clinically relevant structures.

New perspectives for high accuracy SLR with second generation geodesic satellites

NASA Technical Reports Server (NTRS)

Lund, Glenn

1993-01-01

This paper reports on the accuracy limitations imposed by geodesic satellite signatures, and on the potential for achieving millimetric performances by means of alternative satellite concepts and an optimized 2-color system tradeoff. Long distance laser ranging, when performed between a ground (emitter/receiver) station and a distant geodesic satellite, is now reputed to enable short arc trajectory determinations to be achieved with an accuracy of 1 to 2 centimeters. This state-of-the-art accuracy is limited principally by the uncertainties inherent to single-color atmospheric path length correction. Motivated by the study of phenomena such as postglacial rebound, and the detailed analysis of small-scale volcanic and strain deformations, the drive towards millimetric accuracies will inevitably be felt. With the advent of short pulse (less than 50 ps) dual wavelength ranging, combined with adequate detection equipment (such as a fast-scanning streak camera or ultra-fast solid-state detectors) the atmospheric uncertainty could potentially be reduced to the level of a few millimeters, thus, exposing other less significant error contributions, of which by far the most significant will then be the morphology of the retroreflector satellites themselves. Existing geodesic satellites are simply dense spheres, several 10's of cm in diameter, encrusted with a large number (426 in the case of LAGEOS) of small cube-corner reflectors. A single incident pulse, thus, results in a significant number of randomly phased, quasi-simultaneous return pulses. These combine coherently at the receiver to produce a convolved interference waveform which cannot, on a shot to shot basis, be accurately and unambiguously correlated to the satellite center of mass. This paper proposes alternative geodesic satellite concepts, based on the use of a very small number of cube-corner retroreflectors, in which the above difficulties are eliminated while ensuring, for a given emitted pulse, the return of a single clean pulse with an adequate cross-section.

Nanoscale multiphase phase field approach for stress- and temperature-induced martensitic phase transformations with interfacial stresses at finite strains

NASA Astrophysics Data System (ADS)

Basak, Anup; Levitas, Valery I.

2018-04-01

A thermodynamically consistent, novel multiphase phase field approach for stress- and temperature-induced martensitic phase transformations at finite strains and with interfacial stresses has been developed. The model considers a single order parameter to describe the austenite↔martensitic transformations, and another N order parameters describing N variants and constrained to a plane in an N-dimensional order parameter space. In the free energy model coexistence of three or more phases at a single material point (multiphase junction), and deviation of each variant-variant transformation path from a straight line have been penalized. Some shortcomings of the existing models are resolved. Three different kinematic models (KMs) for the transformation deformation gradient tensors are assumed: (i) In KM-I the transformation deformation gradient tensor is a linear function of the Bain tensors for the variants. (ii) In KM-II the natural logarithms of the transformation deformation gradient is taken as a linear combination of the natural logarithm of the Bain tensors multiplied with the interpolation functions. (iii) In KM-III it is derived using the twinning equation from the crystallographic theory. The instability criteria for all the phase transformations have been derived for all the kinematic models, and their comparative study is presented. A large strain finite element procedure has been developed and used for studying the evolution of some complex microstructures in nanoscale samples under various loading conditions. Also, the stresses within variant-variant boundaries, the sample size effect, effect of penalizing the triple junctions, and twinned microstructures have been studied. The present approach can be extended for studying grain growth, solidifications, para↔ferro electric transformations, and diffusive phase transformations.

Moment tensor inversion of the 2016 southeast offshore Mie earthquake in the Tonankai region using a three-dimensional velocity structure model: effects of the accretionary prism and subducting oceanic plate

NASA Astrophysics Data System (ADS)

Takemura, Shunsuke; Kimura, Takeshi; Saito, Tatsuhiko; Kubo, Hisahiko; Shiomi, Katsuhiko

2018-03-01

The southeast offshore Mie earthquake occurred on April 1, 2016 near the rupture area of the 1944 Tonankai earthquake, where seismicity around the interface of the Philippine Sea plate had been very low until this earthquake. Since this earthquake occurred outside of seismic arrays, the focal mechanism and depth were not precisely constrained using a one-dimensional velocity model, as in a conventional approach. We conducted a moment tensor inversion of this earthquake by using a three-dimensional velocity structure model. Before the analysis of observed data, we investigated the effects of offshore heterogeneous structures such as the seawater, accretionary prism, and subducting oceanic plate by using synthetic seismograms in a full three-dimensional model and simpler models. The accretionary prism and subducting oceanic plate play important roles in the moment tensor inversion for offshore earthquakes in the subduction zone. Particularly, the accretionary prism, which controls the excitation and propagation of long-period surface waves around the offshore region, provides better estimations of the centroid depths and focal mechanisms of earthquakes around the Nankai subduction zone. The result of moment tensor inversion for the 2016 southeast offshore Mie earthquake revealed low-angle thrust faulting with a moment magnitude of 5.6. According to geophysical surveys in the Nankai Trough, our results suggest that the rupture of this earthquake occurred on the interface of the Philippine Sea plate, rather than on a mega-splay fault. Detailed comparisons of first-motion polarizations provided additional constraints of the rupture that occurred on the interface of the Philippine Sea plate.

Towards timelike singularity via AdS dual

NASA Astrophysics Data System (ADS)

Bhowmick, Samrat; Chatterjee, Soumyabrata

2017-07-01

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

Vortex pairs on surfaces

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

Koiller, Jair; Boatto, Stefanella

2009-05-06

A pair of infinitesimally close opposite vortices moving on a curved surface moves along a geodesic, according to a conjecture by Kimura. We outline a proof. Numerical simulations are presented for a pair of opposite vortices at a close but nonzero distance on a surface of revolution, the catenoid. We conjecture that the vortex pair system on a triaxial ellipsoid is a KAM perturbation of Jacobi's geodesic problem. We outline some preliminary calculations required for this study. Finding the surfaces for which the vortex pair system is integrable is in order.

Lagrangian averaging with geodesic mean

NASA Astrophysics Data System (ADS)

Oliver, Marcel

2017-11-01

This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler-α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.

Lagrangian averaging with geodesic mean.

PubMed

Oliver, Marcel

2017-11-01

This paper revisits the derivation of the Lagrangian averaged Euler (LAE), or Euler- α equations in the light of an intrinsic definition of the averaged flow map as the geodesic mean on the volume-preserving diffeomorphism group. Under the additional assumption that first-order fluctuations are statistically isotropic and transported by the mean flow as a vector field, averaging of the kinetic energy Lagrangian of an ideal fluid yields the LAE Lagrangian. The derivation presented here assumes a Euclidean spatial domain without boundaries.

On geodesics of the rotation group SO(3)

NASA Astrophysics Data System (ADS)

Novelia, Alyssa; O'Reilly, Oliver M.

2015-11-01

Geodesics on SO(3) are characterized by constant angular velocity motions and as great circles on a three-sphere. The former interpretation is widely used in optometry and the latter features in the interpolation of rotations in computer graphics. The simplicity of these two disparate interpretations belies the complexity of the corresponding rotations. Using a quaternion representation for a rotation, we present a simple proof of the equivalence of the aforementioned characterizations and a straightforward method to establish features of the corresponding rotations.

Energetic-particle-induced geodesic acoustic mode.

PubMed

Fu, G Y

2008-10-31

A new energetic particle-induced geodesic acoustic mode (EGAM) is shown to exist. The mode frequency and mode structure are determined nonperturbatively by energetic particle kinetic effects. In particular the EGAM frequency is found to be substantially lower than the standard GAM frequency. The radial mode width is determined by the energetic particle drift orbit width and can be fairly large for high energetic particle pressure and large safety factor. These results are consistent with the recent experimental observation of the beam-driven n=0 mode in DIII-D.

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

NASA Astrophysics Data System (ADS)

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

2014-07-01

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

Optimal design of geodesically stiffened composite cylindrical shells

NASA Technical Reports Server (NTRS)

Gendron, G.; Guerdal, Z.

1992-01-01

An optimization system based on the finite element code Computations Structural Mechanics (CSM) Testbed and the optimization program, Automated Design Synthesis (ADS), is described. The optimization system can be used to obtain minimum-weight designs of composite stiffened structures. Ply thickness, ply orientations, and stiffener heights can be used as design variables. Buckling, displacement, and material failure constraints can be imposed on the design. The system is used to conduct a design study of geodesically stiffened shells. For comparison purposes, optimal designs of unstiffened shells and shells stiffened by rings and stingers are also obtained. Trends in the design of geodesically stiffened shells are identified. An approach to include local stress concentrations during the design optimization process is then presented. The method is based on a global/local analysis technique. It employs spline interpolation functions to determine displacements and rotations from a global model which are used as 'boundary conditions' for the local model. The organization of the strategy in the context of an optimization process is described. The method is validated with an example.

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

NASA Astrophysics Data System (ADS)

Chekhov, Leonid; Mazzocco, Marta

2010-11-01

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

Cascades of Particles Moving at Finite Velocity in Hyperbolic Spaces

NASA Astrophysics Data System (ADS)

Cammarota, V.; Orsingher, E.

2008-12-01

A branching process of particles moving at finite velocity over the geodesic lines of the hyperbolic space (Poincaré half-plane and Poincaré disk) is examined. Each particle can split into two particles only once at Poisson spaced times and deviates orthogonally when splitted. At time t, after N( t) Poisson events, there are N( t)+1 particles moving along different geodesic lines. We are able to obtain the exact expression of the mean hyperbolic distance of the center of mass of the cloud of particles. We derive such mean hyperbolic distance from two different and independent ways and we study the behavior of the relevant expression as t increases and for different values of the parameters c (hyperbolic velocity of motion) and λ (rate of reproduction). The mean hyperbolic distance of each moving particle is also examined and a useful representation, as the distance of a randomly stopped particle moving over the main geodesic line, is presented.

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.

Newton's absolute time and space in general relativity

NASA Astrophysics Data System (ADS)

Gautreau, Ronald

2000-04-01

I describe a reference system in a spherically symmetric gravitational field that is built around times recorded by radially moving geodesic clocks. The geodesic time coordinate t and the curvature spatial radial coordinate R result in spacetime descriptions of the motion of the geodesic clocks that are exactly identical with equations following from Newton's absolute time and space used with his inverse square law. I show how to use the resulting Newtonian/general-relativistic equations for geodesic clocks to generate exact relativistic metric forms in terms of the coordinates (R,t). Newtonian theory does not describe light. However, the motion of light can be determined from the (R,t) general-relativistic metric forms obtained from Newtonian theory by setting ds2(R,t)=0. In this sense, a theory of light can be related to absolute time and space of Newtonian gravitational theory. I illustrate the (R,t) methodology by first solving the equations that result from a Newtonian picture and then examining the exact metric forms for the general-relativistic problems of the Schwarzschild field, gravitational collapse and expansion of a zero-pressure perfect fluid, and zero-pressure big-bang cosmology. I also briefly describe other applications of the Newtonian/general-relativistic formulation to: embedding a Schwarzschild mass into cosmology; continuously following an expanding universe from radiation to matter domination; Dirac's Large Numbers hypothesis; the incompleteness of Kruskal-Szekeres spacetime; double valuedness in cosmology; and the de Sitter universe.

Use of non-fault fractures in stress tensor reconstruction using the Mohr Circle with the Win-tensor program

NASA Astrophysics Data System (ADS)

Delvaux, Damien

2016-04-01

Paleostress inversion of geological fault-slip data is usually done using the directional part of the applied stress tensor on a slip plane and comparing it with the observed slip lines. However, this method do not fully exploit the brittle data sets as those are composed of shear and tension fractures, in addition to faults. Brittle deformation can be decomposed in two steps. An initial fracture/failure in previously intact rock generate extension/tensile fractures or shear fractures, both without visible opening or displacement. This first step may or not be followed by fracture opening to form tension joints, frictional shearing to form shear faults, or a combination of opening and shearing which produces hybrid fractures. Fractured rock outcrop contain information of the stress conditions that acted during both brittle deformation steps. The purpose here is to investigate how the fracture pattern generated during the initial fracture/failure step might be used in paleostress reconstruction. Each fracture is represented on the Mohr Circle by its resolved normal and shear stress magnitudes. We consider the typical domains on the Mohr circle where the different types de fractures nucleate (tension, hybrid, shear and compression fractures), as well the domain which contain reactivated fractures (faults reactivating an initial fracture plane). In function of the fracture type defined in the field, a "distance" is computed on the Mohr circle between each point and its expected corresponding nucleation/reactivation domain. This "Mohr Distance" is then used as function to minimize during the inversion. We implemented this new function in the Win-Tensor program, and tested it with natural and synthetic data sets from different stress regimes. It can be used alone using only the Mohr Distance on each plane (function F10), or combined with the angular misfit between observed striae and resolved shear directions (composite function F11). When used alone (F10), only the 3 stress axes can be determined and the stress ratio R (sigma 2-3)/sigma1-3) has to be pre-determined. With the combined function (F11), it provide an additional constrain to the classical angular misfit. With data sets composed of a majority of neoformed fractures, stress inversion using the Mohr Distance F10 function provide a good approximation of the 3 stress axes (using only the fracture data) as compared with the results of the F11 composite function (using also the observed slip lines). Tensor program is available at (http://www.damiendelvaux.be/Tensor/tensor-index.html).

Neutrino Masses in the Landscape and Global-Local Dualities in Eternal Inflation

NASA Astrophysics Data System (ADS)

Mainemer Katz, Dan

In this dissertation we study two topics in Theoretical Cosmology: one more formal, the other more phenomenological. We work in the context of eternally inflating cosmologies. These arise in any fundamental theory that contains at least one stable or metastable de Sitter vacuum. Each topic is presented in a different chapter: Chapter 1 deals with the measure problem in eternal inflation. Global-local duality is the equivalence of seemingly different regulators in eternal inflation. For example, the light- cone time cutoff (a global measure, which regulates time) makes the same predictions as the causal patch (a local measure that cuts off space). We show that global-local duality is far more general. It rests on a redundancy inherent in any global cutoff: at late times, an attractor regime is reached, characterized by the unlimited exponential self-reproduction of a certain fundamental region of spacetime. An equivalent local cutoff can be obtained by restricting to this fundamental region. We derive local duals to several global cutoffs of interest. The New Scale Factor Cutoff is dual to the Short Fat Geodesic, a geodesic of fixed infinitesimal proper width. Vilenkin's CAH Cutoff is equivalent to the Hubbletube, whose width is proportional to the local Hubble volume. The famous youngness problem of the Proper Time Cutoff can be readily understood by considering its local dual, the Incredible Shrinking Geodesic. The chapter closely follows our paper. Chapter 2 deals with the question of whether neutrino masses could be anthropically explained. The sum of active neutrino masses is well constrained, 58 meV ≤ mupsilon [is approximately less than] 0.23 eV, but the origin of this scale is not well understood. Here we investigate the possibility that it arises by environmental selection in a large landscape of vacua. Earlier work had noted the detrimental effects of neutrinos on large scale structure. However, using Boltzmann codes to compute the smoothed density contrast on Mpc scales, we find that dark matter halos form abundantly for mupsilon [is approximately greater than] 10eV. This finding rules out an anthropic origin of mupsilon, unless a different catastrophic boundary can be identified. Here we argue that galaxy formation becomes inefficient for mupsilon [is approximately greater than] 10 eV. We show that in this regime, structure forms late and is dominated by cluster scales, as in a top-down scenario. This is catastrophic: baryonic gas will cool too slowly to form stars in an abundance comparable to our universe. With this novel cooling boundary, we find that the anthropic prediction for mupsilon agrees at better than 2sigma with current observational bounds. A degenerate hierarchy is mildly preferred. The chapter closely follows our paper.

Stress field modeling of the Carpathian Basin based on compiled tectonic maps

NASA Astrophysics Data System (ADS)

Albert, Gáspár; Ungvári, Zsuzsanna; Szentpéteri, Krisztián

2014-05-01

The estimation of the stress field in the Carpathian Basin is tackled by several authors. Their modeling methods usually based on measurements (borehole-, focal mechanism- and geodesic data) and the result is a possible structural pattern of the region. Our method works indirectly: the analysis is aimed to project a possible 2D stress field over the already mapped/known/compiled lineament pattern. This includes a component-wise interpolation of the tensor-field, which is based on the generated irregular point cloud in the puffer zone of the mapped lineaments. The interpolated values appear on contour and tensor maps, and show the relative stress field of the area. In 2006 Horváth et al. compiled the 'Atlas of the present-day geodynamics of the Pannonian basin'. To test our method we processed the lineaments of the 1:1 500 000 scale 'Map of neotectonic (active) structures' published in this atlas. The geodynamic parameters (i.e. normal, reverse, right- and left lateral strike-slip faults, etc.) of the lines on this map were mostly explained in the legend. We classified the linear elements according to these parameters and created a geo-referenced mapping database. This database contains the polyline sections of the map lineaments as vectors (i.e. line sections), and the directions of the stress field as attributes of these vectors. The directions of the dip-parallel-, strike-parallel- and vertical stress-vectors are calculated from the geodynamical parameters of the line section. Since we created relative stress field properties, the eigenvalues of the vectors were maximized to one. Each point in the point cloud inherits the stress property of the line section, from which it was derived. During the modeling we tried several point-cloud generating- and interpolation methods. The analysis of the interpolated tensor fields revealed that the model was able to reproduce a geodynamic synthesis of the Carpathian Basin, which can be correlated with the synthesis of the Atlas published in 2006. The method was primarily aimed to reconstruct paleo-stress fields. References Horváth, F., Bada, G., Windhoffer, G., Csontos, L., Dombrádi, E., Dövényi, P., Fodor, L., Grenerczy, G., Síkhegyi, F., Szafián, P., Székely, B., Timár, G., Tóth, L., Tóth, T. 2006: Atlas of the present-day geodynamics of the Pannonian basin: Euroconform maps with explanatory text. Magyar Geofizika 47, 133-137.

Constraining modified theories of gravity with the galaxy bispectrum

NASA Astrophysics Data System (ADS)

Yamauchi, Daisuke; Yokoyama, Shuichiro; Tashiro, Hiroyuki

2017-12-01

We explore the use of the galaxy bispectrum induced by the nonlinear gravitational evolution as a possible probe to test general scalar-tensor theories with second-order equations of motion. We find that time dependence of the leading second-order kernel is approximately characterized by one parameter, the second-order index, which is expected to trace the higher-order growth history of the Universe. We show that our new parameter can significantly carry new information about the nonlinear growth of structure. We forecast future constraints on the second-order index as well as the equation-of-state parameter and the growth index.

Geodesic acoustic modes in noncircular cross section tokamaks

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

Sorokina, E. A., E-mail: sorokina.ekaterina@gmail.com; Lakhin, V. P.; Konovaltseva, L. V.

2017-03-15

The influence of the shape of the plasma cross section on the continuous spectrum of geodesic acoustic modes (GAMs) in a tokamak is analyzed in the framework of the MHD model. An expression for the frequency of a local GAM for a model noncircular cross section plasma equilibrium is derived. Amendments to the oscillation frequency due to the plasma elongation and triangularity and finite tokamak aspect ratio are calculated. It is shown that the main factor affecting the GAM spectrum is the plasma elongation, resulting in a significant decrease in the mode frequency.

MHD-model for low-frequency waves in a tokamak with toroidal plasma rotation and problem of existence of global geodesic acoustic modes

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

Lakhin, V. P.; Sorokina, E. A., E-mail: sorokina.ekaterina@gmail.com, E-mail: vilkiae@gmail.com; Ilgisonis, V. I.

2015-12-15

A set of reduced linear equations for the description of low-frequency perturbations in toroidally rotating plasma in axisymmetric tokamak is derived in the framework of ideal magnetohydrodynamics. The model suitable for the study of global geodesic acoustic modes (GGAMs) is designed. An example of the use of the developed model for derivation of the integral conditions for GGAM existence and of the corresponding dispersion relation is presented. The paper is dedicated to the memory of academician V.D. Shafranov.

Observed angles and geodesic light-cone coordinates

NASA Astrophysics Data System (ADS)

Mitsou, Ermis; Scaccabarozzi, Fulvio; Fanizza, Giuseppe

2018-05-01

We discuss the interpretation of the angles in the geodesic light-cone (GLC) coordinates. In particular, we clarify the way in which these angles can be identified with the observed ones. We show that, although this identification is always possible in principle, one cannot implement it in the usual gauge-fixing way, i.e. through a set of conditions on the GLC metric. Rather, one needs to invoke a tetrad at the observer and a Cartesian-like coordinate system in order to obtain the desired map globally on the observed sky.

Quantum computational complexity, Einstein's equations and accelerated expansion of the Universe

NASA Astrophysics Data System (ADS)

Ge, Xian-Hui; Wang, Bin

2018-02-01

We study the relation between quantum computational complexity and general relativity. The quantum computational complexity is proposed to be quantified by the shortest length of geodesic quantum curves. We examine the complexity/volume duality in a geodesic causal ball in the framework of Fermi normal coordinates and derive the full non-linear Einstein equation. Using insights from the complexity/action duality, we argue that the accelerated expansion of the universe could be driven by the quantum complexity and free from coincidence and fine-tunning problems.

Pure state consciousness and its local reduction to neuronal space

NASA Astrophysics Data System (ADS)

Duggins, A. J.

2013-01-01

The single neuronal state can be represented as a vector in a complex space, spanned by an orthonormal basis of integer spike counts. In this model a scalar element of experience is associated with the instantaneous firing rate of a single sensory neuron over repeated stimulus presentations. Here the model is extended to composite neural systems that are tensor products of single neuronal vector spaces. Depiction of the mental state as a vector on this tensor product space is intended to capture the unity of consciousness. The density operator is introduced as its local reduction to the single neuron level, from which the firing rate can again be derived as the objective correlate of a subjective element. However, the relational structure of perceptual experience only emerges when the non-local mental state is considered. A metric of phenomenal proximity between neuronal elements of experience is proposed, based on the cross-correlation function of neurophysiology, but constrained by the association of theoretical extremes of correlation/anticorrelation in inseparable 2-neuron states with identical and opponent elements respectively.

Planck limits on non-canonical generalizations of large-field inflation models

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

Stein, Nina K.; Kinney, William H., E-mail: ninastei@buffalo.edu, E-mail: whkinney@buffalo.edu

2017-04-01

In this paper, we consider two case examples of Dirac-Born-Infeld (DBI) generalizations of canonical large-field inflation models, characterized by a reduced sound speed, c {sub S} < 1. The reduced speed of sound lowers the tensor-scalar ratio, improving the fit of the models to the data, but increases the equilateral-mode non-Gaussianity, f {sup equil.}{sub NL}, which the latest results from the Planck satellite constrain by a new upper bound. We examine constraints on these models in light of the most recent Planck and BICEP/Keck results, and find that they have a greatly decreased window of viability. The upper bound onmore » f {sup equil.}{sub NL} corresponds to a lower bound on the sound speed and a corresponding lower bound on the tensor-scalar ratio of r ∼ 0.01, so that near-future Cosmic Microwave Background observations may be capable of ruling out entire classes of DBI inflation models. The result is, however, not universal: infrared-type DBI inflation models, where the speed of sound increases with time, are not subject to the bound.« less

Association Fields via Cuspless Sub-Riemannian Geodesics in SE(2).

PubMed

Duits, R; Boscain, U; Rossi, F; Sachkov, Y

To model association fields that underly perceptional organization (gestalt) in psychophysics we consider the problem P curve of minimizing [Formula: see text] for a planar curve having fixed initial and final positions and directions. Here κ ( s ) is the curvature of the curve with free total length ℓ . This problem comes from a model of geometry of vision due to Petitot (in J. Physiol. Paris 97:265-309, 2003; Math. Inf. Sci. Humaines 145:5-101, 1999), and Citti & Sarti (in J. Math. Imaging Vis. 24(3):307-326, 2006). In previous work we proved that the range [Formula: see text] of the exponential map of the underlying geometric problem formulated on SE(2) consists of precisely those end-conditions ( x fin , y fin , θ fin ) that can be connected by a globally minimizing geodesic starting at the origin ( x in , y in , θ in )=(0,0,0). From the applied imaging point of view it is relevant to analyze the sub-Riemannian geodesics and [Formula: see text] in detail. In this article we show that [Formula: see text] is contained in half space x ≥0 and (0, y fin )≠(0,0) is reached with angle π ,show that the boundary [Formula: see text] consists of endpoints of minimizers either starting or ending in a cusp,analyze and plot the cones of reachable angles θ fin per spatial endpoint ( x fin , y fin ),relate the endings of association fields to [Formula: see text] and compute the length towards a cusp,analyze the exponential map both with the common arc-length parametrization t in the sub-Riemannian manifold [Formula: see text] and with spatial arc-length parametrization s in the plane [Formula: see text]. Surprisingly, s -parametrization simplifies the exponential map, the curvature formulas, the cusp-surface, and the boundary value problem,present a novel efficient algorithm solving the boundary value problem,show that sub-Riemannian geodesics solve Petitot's circle bundle model (cf. Petitot in J. Physiol. Paris 97:265-309, [2003]),show a clear similarity with association field lines and sub-Riemannian geodesics.

BMS in cosmology

NASA Astrophysics Data System (ADS)

Kehagias, A.; Riotto, A.

2016-05-01

Symmetries play an interesting role in cosmology. They are useful in characterizing the cosmological perturbations generated during inflation and lead to consistency relations involving the soft limit of the statistical correlators of large-scale structure dark matter and galaxies overdensities. On the other hand, in observational cosmology the carriers of the information about these large-scale statistical distributions are light rays traveling on null geodesics. Motivated by this simple consideration, we study the structure of null infinity and the associated BMS symmetry in a cosmological setting. For decelerating Friedmann-Robertson-Walker backgrounds, for which future null infinity exists, we find that the BMS transformations which leaves the asymptotic metric invariant to leading order. Contrary to the asymptotic flat case, the BMS transformations in cosmology generate Goldstone modes corresponding to scalar, vector and tensor degrees of freedom which may exist at null infinity and perturb the asymptotic data. Therefore, BMS transformations generate physically inequivalent vacua as they populate the universe at null infinity with these physical degrees of freedom. We also discuss the gravitational memory effect when cosmological expansion is taken into account. In this case, there are extra contribution to the gravitational memory due to the tail of the retarded Green functions which are supported not only on the light-cone, but also in its interior. The gravitational memory effect can be understood also from an asymptotic point of view as a transition among cosmological BMS-related vacua.

Gravitational waves in Einstein-æther and generalized TeVeS theory after GW170817

NASA Astrophysics Data System (ADS)

Gong, Yungui; Hou, Shaoqi; Liang, Dicong; Papantonopoulos, Eleftherios

2018-04-01

In this work we discuss the polarization contents of Einstein-æther theory and the generalized tensor-vector-scalar (TeVeS) theory, as both theories have a normalized timelike vector field. We derive the linearized equations of motion around the flat spacetime background using the gauge-invariant variables to easily separate physical degrees of freedom. We find the plane wave solutions and identify the polarizations by examining the geodesic deviation equations. We find that there are five polarizations in Einstein-æther theory and six polarizations in the generalized TeVeS theory. In particular, the transverse breathing mode is mixed with the pure longitudinal mode. We also discuss the experimental tests of the extra polarizations in Einstein-æther theory using pulsar timing arrays combined with the gravitational-wave speed bound derived from the observations on GW 170817 and GRB 170817A. It turns out that it might be difficult to use pulsar timing arrays to distinguish different polarizations in Einstein-æther theory. The same speed bound also forces one of the propagating modes in the generalized TeVeS theory to travel much faster than the speed of light. Since the strong coupling problem does not exist in some parameter subspaces, the generalized TeVeS theory is excluded in these parameter subspaces.

BMS in cosmology

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

Kehagias, A.; Riotto, A.; Center for Astroparticle Physics

Symmetries play an interesting role in cosmology. They are useful in characterizing the cosmological perturbations generated during inflation and lead to consistency relations involving the soft limit of the statistical correlators of large-scale structure dark matter and galaxies overdensities. On the other hand, in observational cosmology the carriers of the information about these large-scale statistical distributions are light rays traveling on null geodesics. Motivated by this simple consideration, we study the structure of null infinity and the associated BMS symmetry in a cosmological setting. For decelerating Friedmann-Robertson-Walker backgrounds, for which future null infinity exists, we find that the BMS transformationsmore » which leaves the asymptotic metric invariant to leading order. Contrary to the asymptotic flat case, the BMS transformations in cosmology generate Goldstone modes corresponding to scalar, vector and tensor degrees of freedom which may exist at null infinity and perturb the asymptotic data. Therefore, BMS transformations generate physically inequivalent vacua as they populate the universe at null infinity with these physical degrees of freedom. We also discuss the gravitational memory effect when cosmological expansion is taken into account. In this case, there are extra contribution to the gravitational memory due to the tail of the retarded Green functions which are supported not only on the light-cone, but also in its interior. The gravitational memory effect can be understood also from an asymptotic point of view as a transition among cosmological BMS-related vacua.« less

Velocity model calibration as a tool to improve regional wave moment tensors: Application to the Basin and Range Province

NASA Astrophysics Data System (ADS)

Ichinose, G. A.

2006-12-01

Many scientific issues for the Basin and Range Province (BRP) remain unsettled including structural evolution, strain rates, slip partitioning and earthquake source physics. A catalog of earthquake source parameters including locations and moment tensors is the basis for tectonic and geophysical study. New instrumentation from the Advance National Seismic System, EarthScope Plate Boundary Observatory, Bigfoot and US-Array brings the opportunity for high quality research; therefore, a catalog is an underlying foundation for examining the BRP. We are continuing to generate a moment tensor catalog for the BRP (Mw<3.5) using long-period regional waves spanning back to 1990. Iterative waveform inversion method (e.g., Nolet et al., 1986, Randell, 1994) is used to calibrate the BRP velocity and density structure using two northern and southern BRP earthquakes. The calibrated models generate realistic synthetics for (f<0.5Hz) with ~50-80% variance reduction. We averaged all path specific models to construct a 1-D BRP community background model. The crust is relatively simple between 5-20km (~6.12km/s) and there is a strong velocity gradient in the upper 5- km. There are lower velocities in the upper crust but higher velocities in the mid-crust for the Sierra Nevada paths relative to BRP. There is also a lower crust high-velocity anomaly near Battle Mountain and Elko that is faster by ~5% and may indicate a wider area of under-plating by basaltic magmas. There are significant low velocity zones in the upper and mid crust mainly across the Walker Lane Belt that may indicate the presence of fluids. We are continuing to work on assessing the performance of these newly calibrated models in improving the estimation of moment tensors down to lower magnitudes and mapping out holes in the seismic network which can be filled to improve moment tensor catalog. We also are looking at how these models work at locating earthquakes and comparing synthetics with those computed from models constrained from different data including refraction, surface wave dispersion, and travel-time tomography.

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

Gravitational Self-Force: Orbital Mechanics Beyond Geodesic Motion

NASA Astrophysics Data System (ADS)

Barack, Leor

The question of motion in a gravitationally bound two-body system is a longstanding open problem of General Relativity. When the mass ratio eta; is small, the problem lends itself to a perturbative treatment, wherein corrections to the geodesic motion of the smaller object (due to radiation reaction, internal structure, etc.) are accounted for order by order in η, using the language of an effective gravitational self-force. The prospect for observing gravitational waves from compact objects inspiralling into massive black holes in the foreseeable future has in the past 15 years motivated a program to obtain a rigorous formulation of the self-force and compute it for astrophysically interesting systems. I will give a brief survey of this activity and its achievements so far, and will identify the challenges that lie ahead. As concrete examples, I will discuss recent calculations of certain conservative post-geodesic effects of the self-force, including the O(η ) correction to the precession rate of the periastron. I will highlight the way in which such calculations allow us to make a fruitful contact with other approaches to the two-body problem.

Pulmonary parenchyma segmentation in thin CT image sequences with spectral clustering and geodesic active contour model based on similarity

NASA Astrophysics Data System (ADS)

He, Nana; Zhang, Xiaolong; Zhao, Juanjuan; Zhao, Huilan; Qiang, Yan

2017-07-01

While the popular thin layer scanning technology of spiral CT has helped to improve diagnoses of lung diseases, the large volumes of scanning images produced by the technology also dramatically increase the load of physicians in lesion detection. Computer-aided diagnosis techniques like lesions segmentation in thin CT sequences have been developed to address this issue, but it remains a challenge to achieve high segmentation efficiency and accuracy without much involvement of human manual intervention. In this paper, we present our research on automated segmentation of lung parenchyma with an improved geodesic active contour model that is geodesic active contour model based on similarity (GACBS). Combining spectral clustering algorithm based on Nystrom (SCN) with GACBS, this algorithm first extracts key image slices, then uses these slices to generate an initial contour of pulmonary parenchyma of un-segmented slices with an interpolation algorithm, and finally segments lung parenchyma of un-segmented slices. Experimental results show that the segmentation results generated by our method are close to what manual segmentation can produce, with an average volume overlap ratio of 91.48%.

Measuring Alignments between Galaxies and the Cosmic Web at z ˜ 2-3 Using IGM Tomography

NASA Astrophysics Data System (ADS)

Krolewski, Alex; Lee, Khee-Gan; Lukić, Zarija; White, Martin

2017-03-01

Many galaxy formation models predict alignments between galaxy spin and the cosmic web (I.e., directions of filaments and sheets), leading to an intrinsic alignment between galaxies that creates a systematic error in weak-lensing measurements. These effects are often predicted to be stronger at high redshifts (z ≳ 1) that are inaccessible to massive galaxy surveys on foreseeable instrumentation, but IGM tomography of the Lyα forest from closely spaced quasars and galaxies is starting to measure the z ˜ 2-3 cosmic web with requisite fidelity. Using mock surveys from hydrodynamical simulations, we examine the utility of this technique, in conjunction with coeval galaxy samples, to measure alignment between galaxies and the cosmic web at z ˜ 2.5. We show that IGM tomography surveys with ≲5 h -1 Mpc sightline spacing can accurately recover the eigenvectors of the tidal tensor, which we use to define the directions of the cosmic web. For galaxy spins and shapes, we use a model parameterized by the alignment strength, {{Δ }}< \\cos θ > , with respect to the tidal tensor eigenvectors from the underlying density field, and also consider observational effects such as errors in the galaxy position angle, inclination, and redshift. Measurements using the upcoming ˜1 deg2 CLAMATO tomographic survey and 600 coeval zCOSMOS-Deep galaxies should place 3σ limits on extreme alignment models with {{Δ }}< \\cos θ > ˜ 0.1, but much larger surveys encompassing >10,000 galaxies, such as Subaru PFS, will be required to constrain models with {{Δ }}< \\cos θ > ˜ 0.03. These measurements will constrain models of galaxy-cosmic web alignment and test tidal torque theory at z ˜ 2, improving our understanding of the physics of intrinsic alignments.

Measuring Alignments between Galaxies and the Cosmic Web at z ~ 2–3 Using IGM Tomography

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

Krolewski, Alex; Lee, Khee-Gan; Luki?, Zarija

Many galaxy formation models predict alignments between galaxy spin and the cosmic web (i.e., directions of filaments and sheets), leading to an intrinsic alignment between galaxies that creates a systematic error in weak-lensing measurements. These effects are often predicted to be stronger at high redshifts (z ≳ 1) that are inaccessible to massive galaxy surveys on foreseeable instrumentation, but IGM tomography of the Lyα forest from closely spaced quasars and galaxies is starting to measure the z ~ 2-3 cosmic web with requisite fidelity. Using mock surveys from hydrodynamical simulations, we examine the utility of this technique, in conjunction withmore » coeval galaxy samples, to measure alignment between galaxies and the cosmic web at z ~ 2.5. We show that IGM tomography surveys with ≲ 5 h -1 Mpc sightline spacing can accurately recover the eigenvectors of the tidal tensor, which we use to define the directions of the cosmic web. For galaxy spins and shapes, we use a model parameterized by the alignment strength, Δ (cos θ), with respect to the tidal tensor eigenvectors from the underlying density field, and also consider observational effects such as errors in the galaxy position angle, inclination, and redshift. Measurements using the upcoming ~ 1 deg 2 CLAMATO tomographic survey and 600 coeval zCOSMOS-Deep galaxies should place 3σ limits on extreme alignment models with Δ (cos θ) ~ 0.1, but much larger surveys encompassing > 10,000 galaxies, such as Subaru PFS, will be required to constrain models with Δ (cos θ) ~ 0.3. These measurements will constrain models of galaxy-cosmic web alignment and test tidal torque theory at z ~ 2, improving our understanding of the physics of intrinsic alignments.« less

Measuring Alignments between Galaxies and the Cosmic Web at z ~ 2–3 Using IGM Tomography

DOE PAGES

Krolewski, Alex; Lee, Khee-Gan; Luki?, Zarija; ...

2017-02-28

Many galaxy formation models predict alignments between galaxy spin and the cosmic web (i.e., directions of filaments and sheets), leading to an intrinsic alignment between galaxies that creates a systematic error in weak-lensing measurements. These effects are often predicted to be stronger at high redshifts (z ≳ 1) that are inaccessible to massive galaxy surveys on foreseeable instrumentation, but IGM tomography of the Lyα forest from closely spaced quasars and galaxies is starting to measure the z ~ 2-3 cosmic web with requisite fidelity. Using mock surveys from hydrodynamical simulations, we examine the utility of this technique, in conjunction withmore » coeval galaxy samples, to measure alignment between galaxies and the cosmic web at z ~ 2.5. We show that IGM tomography surveys with ≲ 5 h -1 Mpc sightline spacing can accurately recover the eigenvectors of the tidal tensor, which we use to define the directions of the cosmic web. For galaxy spins and shapes, we use a model parameterized by the alignment strength, Δ (cos θ), with respect to the tidal tensor eigenvectors from the underlying density field, and also consider observational effects such as errors in the galaxy position angle, inclination, and redshift. Measurements using the upcoming ~ 1 deg 2 CLAMATO tomographic survey and 600 coeval zCOSMOS-Deep galaxies should place 3σ limits on extreme alignment models with Δ (cos θ) ~ 0.1, but much larger surveys encompassing > 10,000 galaxies, such as Subaru PFS, will be required to constrain models with Δ (cos θ) ~ 0.3. These measurements will constrain models of galaxy-cosmic web alignment and test tidal torque theory at z ~ 2, improving our understanding of the physics of intrinsic alignments.« less

Testing general relativity and alternative theories of gravity with space-based atomic clocks and atom interferometers

NASA Astrophysics Data System (ADS)

Bondarescu, Ruxandra; Schärer, Andreas; Jetzer, Philippe; Angélil, Raymond; Saha, Prasenjit; Lundgren, Andrew

2015-05-01

The successful miniaturisation of extremely accurate atomic clocks and atom interferometers invites prospects for satellite missions to perform precision experiments. We discuss the effects predicted by general relativity and alternative theories of gravity that can be detected by a clock, which orbits the Earth. Our experiment relies on the precise tracking of the spacecraft using its observed tick-rate. The spacecraft's reconstructed four-dimensional trajectory will reveal the nature of gravitational perturbations in Earth's gravitational field, potentially differentiating between different theories of gravity. This mission can measure multiple relativistic effects all during the course of a single experiment, and constrain the Parametrized Post-Newtonian Parameters around the Earth. A satellite carrying a clock of fractional timing inaccuracy of Δ f / f ˜ 10-16 in an elliptic orbit around the Earth would constrain the PPN parameters |β - 1|, |γ - 1| ≲ 10-6. We also briefly review potential constraints by atom interferometers on scalar tensor theories and in particular on Chameleon and dilaton models.

Cosmological constraints on Brans-Dicke theory.

PubMed

Avilez, A; Skordis, C

2014-07-04

We report strong cosmological constraints on the Brans-Dicke (BD) theory of gravity using cosmic microwave background data from Planck. We consider two types of models. First, the initial condition of the scalar field is fixed to give the same effective gravitational strength Geff today as the one measured on Earth, GN. In this case, the BD parameter ω is constrained to ω>692 at the 99% confidence level, an order of magnitude improvement over previous constraints. In the second type, the initial condition for the scalar is a free parameter leading to a somewhat stronger constraint of ω>890, while Geff is constrained to 0.981

The Olfactory System Revealed: Non-Invasive Mapping by using Constrained Spherical Deconvolution Tractography in Healthy Humans

PubMed Central

Milardi, Demetrio; Cacciola, Alberto; Calamuneri, Alessandro; Ghilardi, Maria F.; Caminiti, Fabrizia; Cascio, Filippo; Andronaco, Veronica; Anastasi, Giuseppe; Mormina, Enricomaria; Arrigo, Alessandro; Bruschetta, Daniele; Quartarone, Angelo

2017-01-01

Although the olfactory sense has always been considered with less interest than the visual, auditive or somatic senses, it does plays a major role in our ordinary life, with important implication in dangerous situations or in social and emotional behaviors. Traditional Diffusion Tensor signal model and related tractography have been used in the past years to reconstruct the cranial nerves, including the olfactory nerve (ON). However, no supplementary information with regard to the pathways of the olfactory network have been provided. Here, by using the more advanced Constrained Spherical Deconvolution (CSD) diffusion model, we show for the first time in vivo and non-invasively that, in healthy humans, the olfactory system has a widely distributed anatomical network to several cortical regions as well as to many subcortical structures. Although the present study focuses on an healthy sample size, a similar approach could be applied in the near future to gain important insights with regard to the early involvement of olfaction in several neurodegenerative disorders. PMID:28443000

Two-dimensional mapping of triaxial strain fields in a multiferroic BiFeO3 thin film using scanning x-ray microdiffraction

NASA Astrophysics Data System (ADS)

Bark, Chung W.; Cho, Kyung C.; Koo, Yang M.; Tamura, Nobumichi; Ryu, Sangwoo; Jang, Hyun M.

2007-03-01

The dramatically enhanced polarizations and saturation magnetizations observed in the epitaxially constrained BiFeO3 (BFO) thin films with their pronounced grain-orientation dependence have attracted much attention and are attributed largely to the constrained in-plane strain. Thus, it is highly desirable to directly obtain information on the two-dimensional (2D) distribution of the in-plane strain and its correlation with the grain orientation of each corresponding microregion. Here the authors report a 2D quantitative mapping of the grain orientation and the local triaxial strain field in a 250nm thick multiferroic BFO film using a synchrotron x-ray microdiffraction technique. This direct scanning measurement demonstrates that the deviatoric component of the in-plane strain tensor is between 5×10-3 and 6×10-3 and that the local triaxial strain is fairly well correlated with the grain orientation in that particular region.

Tidal stresses and energy gaps in microstate geometries

NASA Astrophysics Data System (ADS)

Tyukov, Alexander; Walker, Robert; Warner, Nicholas P.

2018-02-01

We compute energy gaps and study infalling massive geodesic probes in the new families of scaling, microstate geometries that have been constructed recently and for which the holographic duals are known. We find that in the deepest geometries, which have the lowest energy gaps, the geodesic deviation shows that the stress reaches the Planck scale long before the probe reaches the cap of the geometry. Such probes must therefore undergo a stringy transition as they fall into microstate geometry. We discuss the scales associated with this transition and comment on the implications for scrambling in microstate geometries.

Comparing an analytical spacetime metric for a merging binary to a fully nonlinear numerical evolution using curvature scalars

NASA Astrophysics Data System (ADS)

Sadiq, Jam; Zlochower, Yosef; Nakano, Hiroyuki

2018-04-01

We introduce a new geometrically invariant prescription for comparing two different spacetimes based on geodesic deviation. We use this method to compare a family of recently introduced analytical spacetime representing inspiraling black-hole binaries to fully nonlinear numerical solutions to the Einstein equations. Our method can be used to improve analytical spacetime models by providing a local measure of the effects that violations of the Einstein equations will have on timelike geodesics, and indirectly, gas dynamics. We also discuss the advantages and limitations of this method.

Aspects of Geodesical Motion with Fisher-Rao Metric: Classical and Quantum

NASA Astrophysics Data System (ADS)

Ciaglia, Florio M.; Cosmo, Fabio Di; Felice, Domenico; Mancini, Stefano; Marmo, Giuseppe; Pérez-Pardo, Juan M.

The purpose of this paper is to exploit the geometric structure of quantum mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that the end points of geodesics in the classical setting coincide with the probability distributions that minimise Shannon’s entropy, i.e. with distributions of zero dispersion. In the quantum setting this happens only for particular initial conditions, which in turn correspond to classical submanifolds. This result can be interpreted as a geometric manifestation of the uncertainty principle.

Arcmancer: Geodesics and polarized radiative transfer library

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli; Mannerkoski, Matias; Nättilä, Joonas; Johansson, Peter H.

2018-05-01

Arcmancer computes geodesics and performs polarized radiative transfer in user-specified spacetimes. The library supports Riemannian and semi-Riemannian spaces of any dimension and metric; it also supports multiple simultaneous coordinate charts, embedded geometric shapes, local coordinate systems, and automatic parallel propagation. Arcmancer can be used to solve various problems in numerical geometry, such as solving the curve equation of motion using adaptive integration with configurable tolerances and differential equations along precomputed curves. It also provides support for curves with an arbitrary acceleration term and generic tools for generating ray initial conditions and performing parallel computation over the image, among other tools.

From GLC to double-null coordinates and illustration with static black holes

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

Nugier, Fabien, E-mail: fnugier@ntu.edu.tw

We present a system of coordinates deriving directly from the so-called Geodesic Light-Cone (GLC) coordinates and made of two null scalars intersecting on a 2-dimensional sphere parameterized by two constant angles along geodesics. These coordinates are shown to be equivalent to the well-known double-null coordinates. As GLC, they present interesting properties for cosmology and astrophysics. We discuss this latter topic for static black holes, showing simple descriptions for the metric or particles and photons trajectories. We also briefly comment on the time of flight of ultra-relativistic particles.

Tempest Simulations of Collisionless Damping of the Geodesic-Acoustic Mode in Edge-Plasma Pedestals

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

Xu, X. Q.; Xiong, Z.; Nevins, W. M.

The fully nonlinear (full-f) four-dimensional TEMPEST gyrokinetic continuum code correctly produces the frequency and collisionless damping of geodesic-acoustic modes (GAMs) and zonal flow, with fully nonlinear Boltzmann electrons for the inverse aspect ratio {epsilon} scan and the tokamak safety factor q scan in homogeneous plasmas. TEMPEST simulations show that the GAMs exist in the edge pedestal for steep density and temperature gradients in the form of outgoing waves. The enhanced GAM damping may explain experimental beam emission spectroscopy measurements on the edge q scaling of the GAM amplitude.

Tempest Simulations of Collisionless Damping of the Geodesic-Acoustic Mode in Edge-Plasma Pedestals

NASA Astrophysics Data System (ADS)

Xu, X. Q.; Xiong, Z.; Gao, Z.; Nevins, W. M.; McKee, G. R.

2008-05-01

The fully nonlinear (full-f) four-dimensional TEMPEST gyrokinetic continuum code correctly produces the frequency and collisionless damping of geodesic-acoustic modes (GAMs) and zonal flow, with fully nonlinear Boltzmann electrons for the inverse aspect ratio γ scan and the tokamak safety factor q scan in homogeneous plasmas. TEMPEST simulations show that the GAMs exist in the edge pedestal for steep density and temperature gradients in the form of outgoing waves. The enhanced GAM damping may explain experimental beam emission spectroscopy measurements on the edge q scaling of the GAM amplitude.

Analytical collisionless damping rate of geodesic acoustic mode

NASA Astrophysics Data System (ADS)

Ren, H.; Xu, X. Q.

2016-10-01

Collisionless damping of geodesic acoustic mode (GAM) is analytically investigated by considering the finite-orbit-width (FOW) resonance effect to the 3rd order in the gyro-kinetic equations. A concise and transparent expression for the damping rate is presented for the first time. Good agreement is found between the analytical damping rate and the previous TEMPEST simulation result (Xu 2008 et al Phys. Rev. Lett. 100 215001) for systematic q scans. Our result also shows that it is of sufficient accuracy and has to take into account the FOW effect to the 3rd order.

TEMPEST simulations of collisionless damping of the geodesic-acoustic mode in edge-plasma pedestals.

PubMed

Xu, X Q; Xiong, Z; Gao, Z; Nevins, W M; McKee, G R

2008-05-30

The fully nonlinear (full-f) four-dimensional TEMPEST gyrokinetic continuum code correctly produces the frequency and collisionless damping of geodesic-acoustic modes (GAMs) and zonal flow, with fully nonlinear Boltzmann electrons for the inverse aspect ratio scan and the tokamak safety factor q scan in homogeneous plasmas. TEMPEST simulations show that the GAMs exist in the edge pedestal for steep density and temperature gradients in the form of outgoing waves. The enhanced GAM damping may explain experimental beam emission spectroscopy measurements on the edge q scaling of the GAM amplitude.

Effect of the chameleon scalar field on brane cosmological evolution

NASA Astrophysics Data System (ADS)

Bisabr, Y.; Ahmadi, F.

2017-11-01

We have investigated a brane world model in which the gravitational field in the bulk is described both by a metric tensor and a minimally coupled scalar field. This scalar field is taken to be a chameleon with an appropriate potential function. The scalar field interacts with matter and there is an energy transfer between the two components. We find a late-time asymptotic solution which exhibits late-time accelerating expansion. We also show that the Universe recently crosses the phantom barrier without recourse to any exotic matter. We provide some thermodynamic arguments which constrain both the direction of energy transfer and dynamics of the extra dimension.

Circular geodesic of Bardeen and Ayon-Beato-Garcia regular black-hole and no-horizon spacetimes

NASA Astrophysics Data System (ADS)

Stuchlík, Zdeněk; Schee, Jan

2015-12-01

In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an antigravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN naked singularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static antigravity sphere. Properties of the geodesic structure are reflected by simple observationally relevant optical phenomena. We give silhouette of the regular black-hole and no-horizon spacetimes, and profiled spectral lines generated by Keplerian rings radiating at a fixed frequency and located in strong gravity region at or nearby the marginally stable circular geodesics. We demonstrate that the profiled spectral lines related to the regular black-holes are qualitatively similar to those of the Schwarzschild black-holes, giving only small quantitative differences. On the other hand, the regular no-horizon spacetimes give clear qualitative signatures of their presence while compared to the Schwarschild spacetimes. Moreover, it is possible to distinguish the Bardeen and ABG no-horizon spacetimes, if the inclination angle to the observer is known.

Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos

NASA Astrophysics Data System (ADS)

Stuchlík, Zdeněk; Schee, Jan; Toshmatov, Bobir; Hladík, Jan; Novotný, Jan

2017-06-01

We study behaviour of gravitational waves in the recently introduced general relativistic polytropic spheres containing a region of trapped null geodesics extended around radius of the stable null circular geodesic that can exist for the polytropic index N > 2.138 and the relativistic parameter, giving ratio of the central pressure pc to the central energy density ρc, higher than σ = 0.677. In the trapping zones of such polytropes, the effective potential of the axial gravitational wave perturbations resembles those related to the ultracompact uniform density objects, giving thus similar long-lived axial gravitational modes. These long-lived linear perturbations are related to the stable circular null geodesic and due to additional non-linear phenomena could lead to conversion of the trapping zone to a black hole. We give in the eikonal limit examples of the long-lived gravitational modes, their oscillatory frequencies and slow damping rates, for the trapping zones of the polytropes with N in (2.138,4). However, in the trapping polytropes the long-lived damped modes exist only for very large values of the multipole number l > 50, while for smaller values of l the numerical calculations indicate existence of fast growing unstable axial gravitational modes. We demonstrate that for polytropes with N >= 3.78, the trapping region is by many orders smaller than extension of the polytrope, and the mass contained in the trapping zone is about 10-3 of the total mass of the polytrope. Therefore, the gravitational instability of such trapping zones could serve as a model explaining creation of central supermassive black holes in galactic halos or galaxy clusters.

Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos

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

Stuchlík, Zdeněk; Schee, Jan; Toshmatov, Bobir

We study behaviour of gravitational waves in the recently introduced general relativistic polytropic spheres containing a region of trapped null geodesics extended around radius of the stable null circular geodesic that can exist for the polytropic index N > 2.138 and the relativistic parameter, giving ratio of the central pressure p {sub c} to the central energy density ρ{sub c}, higher than σ = 0.677. In the trapping zones of such polytropes, the effective potential of the axial gravitational wave perturbations resembles those related to the ultracompact uniform density objects, giving thus similar long-lived axial gravitational modes. These long-lived linearmore » perturbations are related to the stable circular null geodesic and due to additional non-linear phenomena could lead to conversion of the trapping zone to a black hole. We give in the eikonal limit examples of the long-lived gravitational modes, their oscillatory frequencies and slow damping rates, for the trapping zones of the polytropes with N element of (2.138,4). However, in the trapping polytropes the long-lived damped modes exist only for very large values of the multipole number ℓ > 50, while for smaller values of ℓ the numerical calculations indicate existence of fast growing unstable axial gravitational modes. We demonstrate that for polytropes with N ≥ 3.78, the trapping region is by many orders smaller than extension of the polytrope, and the mass contained in the trapping zone is about 10{sup −3} of the total mass of the polytrope. Therefore, the gravitational instability of such trapping zones could serve as a model explaining creation of central supermassive black holes in galactic halos or galaxy clusters.« less

Airborne full tensor magnetic gradiometry surveys in the Thuringian basin, Germany

NASA Astrophysics Data System (ADS)

Queitsch, M.; Schiffler, M.; Goepel, A.; Stolz, R.; Meyer, M.; Meyer, H.; Kukowski, N.

2013-12-01

In this contribution we introduce a newly developed fully operational full tensor magnetic gradiometer (FTMG) instrument based on Superconducting Quantum Interference Devices (SQUIDs) and show example data acquired in 2012 within the framework of the INFLUINS (Integrated Fluid Dynamics in Sedimentary basins) project. This multidisciplinary project aims for a better understanding of movements and interaction between shallow and deep fluids in the Thuringian Basin in the center of Germany. In contrast to mapping total magnetic field intensity (TMI) in conventional airborne magnetic surveys for industrial exploration of mineral deposits and sedimentary basins, our instrument measures all components of the magnetic field gradient tensor using highly sensitive SQUID gradiometers. This significantly constrains the solutions of the inverse problem. Furthermore, information on the ratio between induced and remanent magnetization is obtained. Special care has been taken to reduce motion noise while acquiring data in airborne operation. Therefore, the sensors are mounted in a nonmagnetic and aerodynamically shaped bird made of fiberglas with a high drag tail which stabilizes the bird even at low velocities. The system is towed by a helicopter and kept at 30m above ground during data acquisition. Additionally, the system in the bird incorporates an inertial unit for geo-referencing and enhanced motion noise compensation, a radar altimeter for topographic correction and a GPS system for high precision positioning. Advanced data processing techniques using reference magnetometer and inertial unit data result in a very low system noise of less than 60 pT/m peak to peak in airborne operation. To show the performance of the system we present example results from survey areas within the Thuringian basin and along its bordering highlands. The mapped gradient tensor components show a high correlation to existing geologic maps. Furthermore, the measured gradient components indicate that some of the observed magnetic anomalies have a strong remanent magnetization. One example of interpretation of the acquired data of a magnetic anomaly related to a larger gabbro formation is presented.

Deployable geodesic truss structure

NASA Technical Reports Server (NTRS)

Mikulas, Martin M., Jr. (Inventor); Rhodes, Marvin D. (Inventor); Simonton, J. Wayne (Inventor)

1987-01-01

A deployable geodesic truss structure which can be deployed from a stowed state to an erected state is described. The truss structure includes a series of bays, each bay having sets of battens connected by longitudinal cross members which give the bay its axial and torsional stiffness. The cross members are hinged at their mid point by a joint so that the cross members are foldable for deployment or collapsing. The bays are deployed and stabilized by actuator means connected between the mid point joints of the cross members. Hinged longerons may be provided to also connect the sets of battens and to collapse for stowing with the rest of the truss structure.

OPTOELECTRONICS, FIBER OPTICS, AND OTHER ASPECTS OF QUANTUM ELECTRONICS: Integrated-optical spectrum analyzer based on Ti:LiNbO3 with an optimized system of interdigital transducers and spherical geodesic lenses

NASA Astrophysics Data System (ADS)

Golovanova, T. M.; Gryaznov, Yu M.; Dianov, Evgenii M.; Dobryakova, N. G.; Kiselev, A. V.; Prokhorov, A. M.; Shcherbakov, E. A.

1989-08-01

An investigation was made of the parameters of an integrated-optical spectrum analyzer consisting of a Ti:LiNbO3 crystal and a semiconductor laser with a built-in microobjective, spherical geodesic lenses, and an optimized system of interdigital (opposed-comb) transducers. The characteristics of this spectrum analyzer were as follows: the band of operating frequencies was 181 MHz (at the 3 dB level); the resolution was 2.8 MHz; the signal/noise ratio (under a control voltage of 4 V) was 20 dB.

TEMPEST Simulations of Collisionless Damping of Geodesic-Acoustic Mode in Edge Plasma Pedestal

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

Xu, X; Xiong, Z; Nevins, W

The fully nonlinear 4D TEMPEST gyrokinetic continuum code produces frequency, collisionless damping of geodesic-acoustic mode (GAM) and zonal flow with fully nonlinear Boltzmann electrons for the inverse aspect ratio {epsilon}-scan and the tokamak safety factor q-scan in homogeneous plasmas. The TEMPEST simulation shows that GAM exists in edge plasma pedestal for steep density and temperature gradients, and an initial GAM relaxes to the standard neoclassical residual, rather than Rosenbluth-Hinton residual due to the presence of ion-ion collisions. The enhanced GAM damping explains experimental BES measurements on the edge q scaling of the GAM amplitude.

Investigation of energetic particle induced geodesic acoustic mode

NASA Astrophysics Data System (ADS)

Schneller, Mirjam; Fu, Guoyong; Chavdarovski, Ilija; Wang, Weixing; Lauber, Philipp; Lu, Zhixin

2017-10-01

Energetic particles are ubiquitous in present and future tokamaks due to heating systems and fusion reactions. Anisotropy in the distribution function of the energetic particle population is able to excite oscillations from the continuous spectrum of geodesic acoustic modes (GAMs), which cannot be driven by plasma pressure gradients due to their toroidally and nearly poloidally symmetric structures. These oscillations are known as energetic particle-induced geodesic acoustic modes (EGAMs) [G.Y. Fu'08] and have been observed in recent experiments [R. Nazikian'08]. EGAMs are particularly attractive in the framework of turbulence regulation, since they lead to an oscillatory radial electric shear which can potentially saturate the turbulence. For the presented work, the nonlinear gyrokinetic, electrostatic, particle-in-cell code GTS [W.X. Wang'06] has been extended to include an energetic particle population following either bump-on-tail Maxwellian or slowing-down [Stix'76] distribution function. With this new tool, we study growth rate, frequency and mode structure of the EGAM in an ASDEX Upgrade-like scenario. A detailed understanding of EGAM excitation reveals essential for future studies of EGAM interaction with micro-turbulence. Funded by the Max Planck Princeton Research Center. Computational resources of MPCDF and NERSC are greatefully acknowledged.

On the transformations of the dynamical equations

NASA Astrophysics Data System (ADS)

Levi-Civita, T.

2009-08-01

In this issue we bring to the reader’s attention a translation of Levi-Civita’s work “Sulle trasformazioni delle equazioni dinamiche”. This paper, written by Levi-Civita at the onset of his career, is remarkable in many respects. Both the main result and the method developed in the paper brought the author in line with the greatest mathematicians of his day and seriously influenced the further progress of geometry and the theory of integrable systems. Speaking modern language the main result of his paper is the deduction of the general geodesic equivalence equation in invariant form and local classification of geodesically equivalent Riemannian metrics in the case of arbitrary dimension, i.e., metrics having the same geodesics considered as unparameterized curves (this classification problem was formulated by Beltrami in 1865). Levi-Civita’s work produced a great impact on further development of the theory of geodesically equivalent metrics and geodesic mappings, and still remains one of the most important tools in this area of differential geometry. In this paper the author uses a new method based on the concept of Riemannian connection, which later has been also referred to as the Levi-Civita connection. This paper is truly a pioneering work in the sense that the real power of covariant differentiation techniques in solving a concrete and highly nontrivial problem from the theory of dynamical systems was demonstrated. The author skillfully operates and weaves together many of the most advanced (for that times) algebraic, geometric and analytic methods. Moreover, an attentive reader can also notice several forerunning ideas of the method of moving frames, which was developed a few decades later by E. Cartan. We hope that the reader will appreciate the style of exposition as well. This work, focused on the essence of the problem and free of manipulation with abstract mathematical terms, is a good example of a classical text of the late 19th century. Owing to this, the paper is easy to read and understand in spite of some different notation and terminology. The Editorial Board is very grateful to Professor Sergio Benenti for the translation of the original Italian text and valuable comments (see marginal notes at the end of the text, p. 612).

Seismic velocity structure and microearthquake source properties at The Geysers, California, geothermal area

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

O'Connell, D.R.

1986-12-01

The method of progressive hypocenter-velocity inversion has been extended to incorporate S-wave arrival time data and to estimate S-wave velocities in addition to P-wave velocities. S-wave data to progressive inversion does not completely eliminate hypocenter-velocity tradeoffs, but they are substantially reduced. Results of a P and S-wave progressive hypocenter-velocity inversion at The Geysers show that the top of the steam reservoir is clearly defined by a large decrease of V/sub p//V/sub s/ at the condensation zone-production zone contact. The depth interval of maximum steam production coincides with minimum observed V/sub p//V/sub s/, and V/sub p//V/sub s/ increses below the shallowmore » primary production zone suggesting that reservoir rock becomes more fluid saturated. The moment tensor inversion method was applied to three microearthquakes at The Geysers. Estimated principal stress orientations were comparable to those estimated using P-wave firstmotions as constraints. Well constrained principal stress orientations were obtained for one event for which the 17 P-first motions could not distinguish between normal-slip and strike-slip mechanisms. The moment tensor estimates of principal stress orientations were obtained using far fewer stations than required for first-motion focal mechanism solutions. The three focal mechanisms obtained here support the hypothesis that focal mechanisms are a function of depth at The Geysers. Progressive inversion as developed here and the moment tensor inversion method provide a complete approach for determining earthquake locations, P and S-wave velocity structure, and earthquake source mechanisms.« less

Green-Kubo relations for the viscosity of biaxial nematic liquid crystals

NASA Astrophysics Data System (ADS)

Sarman, Sten

1996-09-01

We derive Green-Kubo relations for the viscosities of a biaxial nematic liquid crystal. In this system there are seven shear viscosities, three twist viscosities, and three cross coupling coefficients between the antisymmetric strain rate and the symmetric traceless pressure tensor. According to the Onsager reciprocity relations these couplings are equal to the cross couplings between the symmetric traceless strain rate and the antisymmetric pressure. Our method is based on a comparison of the microscopic linear response generated by the SLLOD equations of motion for planar Couette flow (so named because of their close connection to the Doll's tensor Hamiltonian) and the macroscopic linear phenomenological relations between the pressure tensor and the strain rate. In order to obtain simple Green-Kubo relations we employ an equilibrium ensemble where the angular velocities of the directors are identically zero. This is achieved by adding constraint torques to the equations for the molecular angular accelerations. One finds that all the viscosity coefficients can be expressed as linear combinations of time correlation function integrals (TCFIs). This is much simpler compared to the expressions in the conventional canonical ensemble, where the viscosities are complicated rational functions of the TCFIs. The reason for this is, that in the constrained angular velocity ensemble, the thermodynamic forces are given external parameters whereas the thermodynamic fluxes are ensemble averages of phase functions. This is not the case in the canonical ensemble. The simplest way of obtaining numerical estimates of viscosity coefficients of a particular molecular model system is to evaluate these fluctuation relations by equilibrium molecular dynamics simulations.

Multiple seismogenic processes for high-frequency earthquakes at Katmai National Park, Alaska: Evidence from stress tensor inversions of fault-plane solutions

USGS Publications Warehouse

Moran, S.C.

2003-01-01

The volcanological significance of seismicity within Katmai National Park has been debated since the first seismograph was installed in 1963, in part because Katmai seismicity consists almost entirely of high-frequency earthquakes that can be caused by a wide range of processes. I investigate this issue by determining 140 well-constrained first-motion fault-plane solutions for shallow (depth < 9 km) earthquakes occuring between 1995 and 2001 and inverting these solutions for the stress tensor in different regions within the park. Earthquakes removed by several kilometers from the volcanic axis occur in a stress field characterized by horizontally oriented ??1 and ??3 axes, with ??1 rotated slightly (12??) relative to the NUVELIA subduction vector, indicating that these earthquakes are occurring in response to regional tectonic forces. On the other hand, stress tensors for earthquake clusters beneath several Katmai cluster volcanoes have vertically oriented ??1 axes, indicating that these events are occuring in response to local, not regional, processes. At Martin-Mageik, vertically oriented ??1 is most consistent with failure under edifice loading conditions in conjunction with localized pore pressure increases associated with hydrothermal circulation cells. At Trident-Novarupta, it is consistent with a number of possible models, including occurence along fractures formed during the 1912 eruption that now serve as horizontal conduits for migrating fluids and/or volatiles from nearby degassing and cooling magma bodies. At Mount Katmai, it is most consistent with continued seismicity along ring-fracture systems created in the 1912 eruption, perhaps enhanced by circulating hydrothermal fluids and/or seepage from the caldera-filling lake.

A framework for fast probabilistic centroid-moment-tensor determination—inversion of regional static displacement measurements

NASA Astrophysics Data System (ADS)

Käufl, Paul; Valentine, Andrew P.; O'Toole, Thomas B.; Trampert, Jeannot

2014-03-01

The determination of earthquake source parameters is an important task in seismology. For many applications, it is also valuable to understand the uncertainties associated with these determinations, and this is particularly true in the context of earthquake early warning (EEW) and hazard mitigation. In this paper, we develop a framework for probabilistic moment tensor point source inversions in near real time. Our methodology allows us to find an approximation to p(m|d), the conditional probability of source models (m) given observations (d). This is obtained by smoothly interpolating a set of random prior samples, using Mixture Density Networks (MDNs)-a class of neural networks which output the parameters of a Gaussian mixture model. By combining multiple networks as `committees', we are able to obtain a significant improvement in performance over that of a single MDN. Once a committee has been constructed, new observations can be inverted within milliseconds on a standard desktop computer. The method is therefore well suited for use in situations such as EEW, where inversions must be performed routinely and rapidly for a fixed station geometry. To demonstrate the method, we invert regional static GPS displacement data for the 2010 MW 7.2 El Mayor Cucapah earthquake in Baja California to obtain estimates of magnitude, centroid location and depth and focal mechanism. We investigate the extent to which we can constrain moment tensor point sources with static displacement observations under realistic conditions. Our inversion results agree well with published point source solutions for this event, once the uncertainty bounds of each are taken into account.

Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity

NASA Astrophysics Data System (ADS)

Veraguth, Olivier J.; Wang, Charles H.-T.

2017-10-01

Conformal loop quantum gravity provides an approach to loop quantization through an underlying conformal structure i.e. conformally equivalent class of metrics. The property that general relativity itself has no conformal invariance is reinstated with a constrained scalar field setting the physical scale. Conformally equivalent metrics have recently been shown to be amenable to loop quantization including matter coupling. It has been suggested that conformal geometry may provide an extended symmetry to allow a reformulated Immirzi parameter necessary for loop quantization to behave like an arbitrary group parameter that requires no further fixing as its present standard form does. Here, we find that this can be naturally realized via conformal frame transformations in scalar-tensor gravity. Such a theory generally incorporates a dynamical scalar gravitational field and reduces to general relativity when the scalar field becomes a pure gauge. In particular, we introduce a conformal Einstein frame in which loop quantization is implemented. We then discuss how different Immirzi parameters under this description may be related by conformal frame transformations and yet share the same quantization having, for example, the same area gaps, modulated by the scalar gravitational field.

A seismological overview of the induced earthquakes in the Duvernay play near Fox Creek, Alberta

NASA Astrophysics Data System (ADS)

Schultz, Ryan; Wang, Ruijia; Gu, Yu Jeffrey; Haug, Kristine; Atkinson, Gail

2017-01-01

This paper summarizes the current state of understanding regarding the induced seismicity in connection with hydraulic fracturing operations targeting the Duvernay Formation in central Alberta, near the town of Fox Creek. We demonstrate that earthquakes in this region cluster into distinct sequences in time, space, and focal mechanism using (i) cross-correlation detection methods to delineate transient temporal relationships, (ii) double-difference relocations to confirm spatial clustering, and (iii) moment tensor solutions to assess fault motion consistency. The spatiotemporal clustering of the earthquake sequences is strongly related to the nearby hydraulic fracturing operations. In addition, we identify a preference for strike-slip motions on subvertical faults with an approximate 45° P axis orientation, consistent with expectation from the ambient stress field. The hypocentral geometries for two of the largest-magnitude (M 4) sequences that are robustly constrained by local array data provide compelling evidence for planar features starting at Duvernay Formation depths and extending into the shallow Precambrian basement. We interpret these lineaments as subvertical faults orientated approximately north-south, consistent with the regional moment tensor solutions. Finally, we conclude that the sequences were triggered by pore pressure increases in response to hydraulic fracturing stimulations along previously existing faults.

A Comprehensive Overview of the Duvernay Induced Seismicity near Fox Creek, Alberta

NASA Astrophysics Data System (ADS)

Schultz, R.; Wang, R.; Gu, Y. J.; Haug, K.; Atkinson, G. M.

2016-12-01

In this work we summarize the current state of understanding regarding the induced seismicity related to Duvernay hydraulic fracturing operations in central Alberta, near the town of Fox Creek. Earthquakes in this region cluster into distinct sequences in time, space, and focal mechanism. To corroborate this point, we use cross-correlation detection methods to delineate transient temporal relationships, double-difference relocations to confirm spatial clustering, and moment tensor determinations to show fault motion consistency. The spatiotemporal clustering of sequences is strongly related to nearby hydraulic fracturing operations. In addition, we identify a strong preference for subvertical strike-slip motion with a roughly 45º P-axis orientation, consistent with ambient stress field considerations. The hypocentral geometry in two red traffic light protocol cases, that are robustly constrained by local array data, provide compelling evidence for planar features starting at Duvernay Formation depths and extending into the shallow Precambrian basement. We interpret these features as faults orientated approximately north-south and subvertically, consistent with moment tensor determinations. Finally, we conclude that the primary sequences are best explained as induced events in response to effective stress changes as a result of pore-pressure increase along previously existing faults due to hydraulic fracturing stimulations.

Vainshtein screening in scalar-tensor theories before and after GW170817: Constraints on theories beyond Horndeski

NASA Astrophysics Data System (ADS)

Dima, Alexandru; Vernizzi, Filippo

2018-05-01

Screening mechanisms are essential features of dark energy models mediating a fifth force on large scales. We study the regime of strong scalar field nonlinearities, known as Vainshtein screening, in the most general scalar-tensor theories propagating a single scalar degree of freedom. We first develop an effective approach to parametrize cosmological perturbations beyond linear order for these theories. In the quasistatic limit, the fully nonlinear effective Lagrangian contains six independent terms, one of which starts at cubic order in perturbations. We compute the two gravitational potentials around a spherical body. Outside and near the body, screening reproduces standard gravity, with a modified gravitational coupling. Inside the body, the two potentials are different and depend on the density profile, signalling the breaking of the Vainshtein screening. We provide the most general expressions for these modifications, revising and extending previous results. We apply our findings to show that the combination of the GW170817 event, the Hulse-Taylor pulsar and stellar structure physics, constrain the parameters of these general theories at the level of 10-1, and of Gleyzes-Langlois-Piazza-Vernizzi theories at the level of 10-2.

The conformal limit of inflation in the era of CMB polarimetry

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

Pajer, Enrico; Wijck, Jaap V.S. van; Pimentel, Guilherme L., E-mail: enrico.pajer@gmail.com, E-mail: g.leitepimentel@uva.nl, E-mail: j.v.s.vanwijck@uu.nl

2017-06-01

We argue that the non-detection of primordial tensor modes has taught us a great deal about the primordial universe. In single-field slow-roll inflation, the current upper bound on the tensor-to-scalar ratio, r <0.07 (95% CL), implies that the Hubble slow-roll parameters obey ε||η , and therefore establishes the existence of a new hierarchy. We dub this regime the conformal limit of (slow-roll) inflation, and show that it includes Starobinsky-like inflation as well as all viable single-field models with a sub-Planckian field excursion. In this limit, all primordial correlators are constrained by the full conformal group to leading non-trivial order inmore » slow-roll. This fixes the power spectrum and the full bispectrum, and leads to the ''conformal'' shape of non-Gaussianity. The size of non-Gaussianity is related to the running of the spectral index by a consistency condition, and therefore it is expected to be small. In passing, we clarify the role of boundary terms in the ζ action, the order to which constraint equations need to be solved, and re-derive our results using the Wheeler-deWitt formalism.« less

Finite temperature behavior of the CPT-even and parity-even electrodynamics of the standard model extension

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

Casana, Rodolfo; Ferreira, Manoel M. Jr; Rodrigues, Josberg S.

2009-10-15

In this work, we examine the finite temperature properties of the CPT-even and Lorentz-invariance-violating (LIV) electrodynamics of the standard model extension, represented by the term W{sub {alpha}}{sub {nu}}{sub {rho}}{sub {phi}}F{sup {alpha}}{sup {nu}}F{sup {rho}}{sup {phi}}. We begin analyzing the Hamiltonian structure following the Dirac's procedure for constrained systems and construct a well-defined and gauge invariant partition function in the functional integral formalism. Next, we specialize for the nonbirefringent coefficients of the tensor W{sub {alpha}}{sub {nu}}{sub {rho}}{sub {phi}}. In the sequel, the partition function is explicitly carried out for the parity-even sector of the tensor W{sub {alpha}}{sub {nu}}{sub {rho}}{sub {phi}}. The modifiedmore » partition function is a power of the Maxwell's partition function. It is observed that the LIV coefficients induce an anisotropy in the black body angular energy density distribution. The Planck's radiation law, however, retains its frequency dependence and the Stefan-Boltzmann law keeps the usual form, except for a change in the Stefan-Boltzmann constant by a factor containing the LIV contributions.« less

Coupled Segmentation of Nuclear and Membrane-bound Macromolecules through Voting and Multiphase Level Set

PubMed Central

Wen, Quan

2014-01-01

Membrane-bound macromolecules play an important role in tissue architecture and cell-cell communication, and is regulated by almost one-third of the genome. At the optical scale, one group of membrane proteins expresses themselves as linear structures along the cell surface boundaries, while others are sequestered; and this paper targets the former group. Segmentation of these membrane proteins on a cell-by-cell basis enables the quantitative assessment of localization for comparative analysis. However, such membrane proteins typically lack continuity, and their intensity distributions are often very heterogeneous; moreover, nuclei can form large clump, which further impedes the quantification of membrane signals on a cell-by-cell basis. To tackle these problems, we introduce a three-step process to (i) regularize the membrane signal through iterative tangential voting, (ii) constrain the location of surface proteins by nuclear features, where clumps of nuclei are segmented through a delaunay triangulation approach, and (iii) assign membrane-bound macromolecules to individual cells through an application of multi-phase geodesic level-set. We have validated our method using both synthetic data and a dataset of 200 images, and are able to demonstrate the efficacy of our approach with superior performance. PMID:25530633

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.

Source-Type Identification Analysis Using Regional Seismic Moment Tensors

NASA Astrophysics Data System (ADS)

Chiang, A.; Dreger, D. S.; Ford, S. R.; Walter, W. R.

2012-12-01

Waveform inversion to determine the seismic moment tensor is a standard approach in determining the source mechanism of natural and manmade seismicity, and may be used to identify, or discriminate different types of seismic sources. The successful applications of the regional moment tensor method at the Nevada Test Site (NTS) and the 2006 and 2009 North Korean nuclear tests (Ford et al., 2009a, 2009b, 2010) show that the method is robust and capable for source-type discrimination at regional distances. The well-separated populations of explosions, earthquakes and collapses on a Hudson et al., (1989) source-type diagram enables source-type discrimination; however the question remains whether or not the separation of events is universal in other regions, where we have limited station coverage and knowledge of Earth structure. Ford et al., (2012) have shown that combining regional waveform data and P-wave first motions removes the CLVD-isotropic tradeoff and uniquely discriminating the 2009 North Korean test as an explosion. Therefore, including additional constraints from regional and teleseismic P-wave first motions enables source-type discrimination at regions with limited station coverage. We present moment tensor analysis of earthquakes and explosions (M6) from Lop Nor and Semipalatinsk test sites for station paths crossing Kazakhstan and Western China. We also present analyses of smaller events from industrial sites. In these sparse coverage situations we combine regional long-period waveforms, and high-frequency P-wave polarity from the same stations, as well as from teleseismic arrays to constrain the source type. Discrimination capability with respect to velocity model and station coverage is examined, and additionally we investigate the velocity model dependence of vanishing free-surface traction effects on seismic moment tensor inversion of shallow sources and recovery of explosive scalar moment. Our synthetic data tests indicate that biases in scalar seismic moment and discrimination for shallow sources are small and can be understood in a systematic manner. We are presently investigating the frequency dependence of vanishing traction of a very shallow (10m depth) M2+ chemical explosion recorded at several kilometer distances, and preliminary results indicate at the typical frequency passband we employ the bias does not affect our ability to retrieve the correct source mechanism but may affect the retrieval of the correct scalar seismic moment. Finally, we assess discrimination capability in a composite P-value statistical framework.

Surprising structures hiding in Penrose’s future null infinity

NASA Astrophysics Data System (ADS)

Newman, Ezra T.

2017-07-01

Since the late1950s, almost all discussions of asymptotically flat (Einstein-Maxwell) space-times have taken place in the context of Penrose’s null infinity, I+. In addition, almost all calculations have used the Bondi coordinate and tetrad systems. Beginning with a known asymptotically flat solution to the Einstein-Maxwell equations, we show first, that there are other natural coordinate systems, near I+, (analogous to light-cones in flat-space) that are based on (asymptotically) shear-free null geodesic congruences (analogous to the flat-space case). Using these new coordinates and their associated tetrad, we define the complex dipole moment, (the mass dipole plus i times angular momentum), from the l  =  1 harmonic coefficient of a component of the asymptotic Weyl tensor. Second, from this definition, from the Bianchi identities and from the Bondi-Sachs mass and linear momentum, we show that there exists a large number of results—identifications and dynamics—identical to those of classical mechanics and electrodynamics. They include, among many others, {P}=M{v}+..., {L}= {r} × {P} , spin, Newton’s second law with the rocket force term (\\dotM v) and radiation reaction, angular momentum conservation and others. All these relations take place in the rather mysterious H-space rather than in space-time. This leads to the enigma: ‘why do these well known relations of classical mechanics take place in H-space?’ and ‘What is the physical meaning of H-space?’

Information geometric methods for complexity

NASA Astrophysics Data System (ADS)

Felice, Domenico; Cafaro, Carlo; Mancini, Stefano

2018-03-01

Research on the use of information geometry (IG) in modern physics has witnessed significant advances recently. In this review article, we report on the utilization of IG methods to define measures of complexity in both classical and, whenever available, quantum physical settings. A paradigmatic example of a dramatic change in complexity is given by phase transitions (PTs). Hence, we review both global and local aspects of PTs described in terms of the scalar curvature of the parameter manifold and the components of the metric tensor, respectively. We also report on the behavior of geodesic paths on the parameter manifold used to gain insight into the dynamics of PTs. Going further, we survey measures of complexity arising in the geometric framework. In particular, we quantify complexity of networks in terms of the Riemannian volume of the parameter space of a statistical manifold associated with a given network. We are also concerned with complexity measures that account for the interactions of a given number of parts of a system that cannot be described in terms of a smaller number of parts of the system. Finally, we investigate complexity measures of entropic motion on curved statistical manifolds that arise from a probabilistic description of physical systems in the presence of limited information. The Kullback-Leibler divergence, the distance to an exponential family and volumes of curved parameter manifolds, are examples of essential IG notions exploited in our discussion of complexity. We conclude by discussing strengths, limits, and possible future applications of IG methods to the physics of complexity.

Topology and incompleteness for 2+1-dimensional cosmological spacetimes

NASA Astrophysics Data System (ADS)

Fajman, David

2017-06-01

We study the long-time behavior of the Einstein flow coupled to matter on 2-dimensional surfaces. We consider massless matter models such as collisionless matter composed of massless particles, massless scalar fields and radiation fluids and show that the maximal globally hyperbolic development of homogeneous and isotropic initial data on the 2-sphere is geodesically incomplete in both time directions, i.e. the spacetime recollapses. This behavior also holds for open sets of initial data. In particular, we construct classes of recollapsing 2+1-dimensional spacetimes with spherical spatial topology which provide evidence for a closed universe recollapse conjecture for massless matter models in 2+1 dimensions. Furthermore, we construct solutions with toroidal and higher genus topology for the massless matter fields, which in both cases are future complete. The spacetimes with toroidal topology are 2+1-dimensional analogies of the Einstein-de Sitter model. In addition, we point out a general relation between the energy-momentum tensor and the Kretschmann scalar in 2+1 dimensions and use it to infer strong cosmic censorship for all these models. In view of this relation, we also recall corresponding models containing massive particles, constructed in a previous work and determine the nature of their initial singularities. We conclude that the global structure of non-vacuum cosmological spacetimes in 2+1 dimensions is determined by the mass of particles and—in the homogeneous and isotropic setting studied here—verifies strong cosmic censorship.

Quantum Computational Geodesics

DTIC Science & Technology

2010-01-01

dtU (t)†  unvec κt   t ∫ 0 drκ−1r vec C(r...U(t). (209) If J(T ) = 0 in equation 209, then d dt J(0) = j−1T   T ∫ 0 dtU (t)†  unvec κt   t ∫ 0 drκ−1r vec C(r)    U(t)   . (210...equation 211, one obtains the so-called geodesic derivative (1) d dq Hq(0) = j −1 T   T ∫ 0 dtU (t)†unvec   κt   t ∫ 0 drκ−1r vec C(r)   

VizieR Online Data Catalog: ynogkm: code for calculating time-like geodesics (Yang+, 2014)

NASA Astrophysics Data System (ADS)

Yang, X.-L.; Wang, J.-C.

2013-11-01

Here we present the source file for a new public code named ynogkm, aim on calculating the time-like geodesics in a Kerr-Newmann spacetime fast. In the code the four Boyer-Lindquis coordinates and proper time are expressed as functions of a parameter p semi-analytically, i.e., r(p), μ(p), φ(p), t(p), and σ(p), by using the Weiers- trass' and Jacobi's elliptic functions and integrals. All of the ellip- tic integrals are computed by Carlson's elliptic integral method, which guarantees the fast speed of the code.The source Fortran file ynogkm.f90 contains three modules: constants, rootfind, ellfunction, and blcoordinates. (3 data files).

Influence of a weak gravitational wave on a bound system of two point-masses. [of binary stars

NASA Technical Reports Server (NTRS)

Turner, M. S.

1979-01-01

The problem of a weak gravitational wave impinging upon a nonrelativistic bound system of two point masses is considered. The geodesic equation for each mass is expanded in terms of two small parameters, v/c and dimensionless wave amplitude, in a manner similar to the post-Newtonian expansion; the geodesic equations are resolved into orbital and center-of-mass equations of motion. The effect of the wave on the orbit is determined by using Lagrange's planetary equations to calculate the time evolution of the orbital elements. The gauge properties of the solutions and, in particular, the gauge invariance of the secular effects are discussed.

Pragmatic approach to gravitational radiation reaction in binary black holes

PubMed

Lousto

2000-06-05

We study the relativistic orbit of binary black holes in systems with small mass ratio. The trajectory of the smaller object (another black hole or a neutron star), represented as a particle, is determined by the geodesic equation on the perturbed massive black hole spacetime. Here we study perturbations around a Schwarzschild black hole using Moncrief's gauge invariant formalism. We decompose the perturbations into l multipoles to show that all l-metric coefficients are C0 at the location of the particle. Summing over l, to reconstruct the full metric, gives a formally divergent result. We succeed in bringing this sum to a Riemann's zeta-function regularization scheme and numerically compute the first-order geodesics.

Witten diagrams revisited: the AdS geometry of conformal blocks

DOE PAGES

Hijano, Eliot; Kraus, Per; Perlmutter, Eric; ...

2016-01-25

Here, we develop a new method for decomposing blocks. The steps involved are elementary, requiring no explicit integration, and operate directly in position space. Central to this construction is an appealingly simple answer to the question: what object in AdS computes a conformal block? The answer is a "geodesic Witten diagram", which is essentially an ordinary exchange Witten diagram, except that the cubic vertices are not integrated over all of AdS, but only over bulk geodesics connecting the boundary operators. In particular, we also consider the case of four-point functions of scalar operators, and show how to easily reproduce existingmore » results for the relevant conformal blocks in arbitrary dimension.« less

A type N radiation field solution with Λ <0 in a curved space-time and closed time-like curves

NASA Astrophysics Data System (ADS)

Ahmed, Faizuddin

2018-05-01

An anti-de Sitter background four-dimensional type N solution of the Einstein's field equations, is presented. The matter-energy content pure radiation field satisfies the null energy condition (NEC), and the metric is free-from curvature divergence. In addition, the metric admits a non-expanding, non-twisting and shear-free geodesic null congruence which is not covariantly constant. The space-time admits closed time-like curves which appear after a certain instant of time in a causally well-behaved manner. Finally, the physical interpretation of the solution, based on the study of the equation of the geodesics deviation, is analyzed.

Weak lensing in a plasma medium and gravitational deflection of massive particles using the Gauss-Bonnet theorem. A unified treatment

NASA Astrophysics Data System (ADS)

Crisnejo, Gabriel; Gallo, Emanuel

2018-06-01

We apply the Gauss-Bonnet theorem to the study of light rays in a plasma medium in a static and spherically symmetric gravitational field and also to the study of timelike geodesics followed for test massive particles in a spacetime with the same symmetries. The possibility of using the theorem follows from a correspondence between timelike curves followed by light rays in a plasma medium and spatial geodesics in an associated Riemannian optical metric. A similar correspondence follows for massive particles. For some examples and applications, we compute the deflection angle in weak gravitational fields for different plasma density profiles and gravitational fields.

Active motion on curved surfaces

NASA Astrophysics Data System (ADS)

Castro-Villarreal, Pavel; Sevilla, Francisco J.

2018-05-01

A theoretical analysis of active motion on curved surfaces is presented in terms of a generalization of the telegrapher equation. Such a generalized equation is explicitly derived as the polar approximation of the hierarchy of equations obtained from the corresponding Fokker-Planck equation of active particles diffusing on curved surfaces. The general solution to the generalized telegrapher equation is given for a pulse with vanishing current as initial data. Expressions for the probability density and the mean squared geodesic displacement are given in the limit of weak curvature. As an explicit example of the formulated theory, the case of active motion on the sphere is presented, where oscillations observed in the mean squared geodesic displacement are explained.

Robust analysis of trends in noisy tokamak confinement data using geodesic least squares regression

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

Verdoolaege, G., E-mail: geert.verdoolaege@ugent.be; Laboratory for Plasma Physics, Royal Military Academy, B-1000 Brussels; Shabbir, A.

Regression analysis is a very common activity in fusion science for unveiling trends and parametric dependencies, but it can be a difficult matter. We have recently developed the method of geodesic least squares (GLS) regression that is able to handle errors in all variables, is robust against data outliers and uncertainty in the regression model, and can be used with arbitrary distribution models and regression functions. We here report on first results of application of GLS to estimation of the multi-machine scaling law for the energy confinement time in tokamaks, demonstrating improved consistency of the GLS results compared to standardmore » least squares.« less

Geodesic regression for image time-series.

PubMed

Niethammer, Marc; Huang, Yang; Vialard, François-Xavier

2011-01-01

Registration of image-time series has so far been accomplished (i) by concatenating registrations between image pairs, (ii) by solving a joint estimation problem resulting in piecewise geodesic paths between image pairs, (iii) by kernel based local averaging or (iv) by augmenting the joint estimation with additional temporal irregularity penalties. Here, we propose a generative model extending least squares linear regression to the space of images by using a second-order dynamic formulation for image registration. Unlike previous approaches, the formulation allows for a compact representation of an approximation to the full spatio-temporal trajectory through its initial values. The method also opens up possibilities to design image-based approximation algorithms. The resulting optimization problem is solved using an adjoint method.

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.

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

Karch, Andreas; Sato, Yoshiki

In this paper we discuss geodesic Witten diagrams in generic holographic conformal field theories with boundary or defect. Boundary CFTs allow two different de-compositions of two-point functions into conformal blocks: boundary channel and ambient channel. Building on earlier work, we derive a holographic dual of the boundary channel decomposition in terms of bulk-to-bulk propagators on lower dimensional AdS slices. In the situation in which we can treat the boundary or defect as a perturbation around pure AdS spacetime, we obtain the leading corrections to the two-point function both in boundary and ambient channel in terms of geodesic Witten diagrams whichmore » exactly reproduce the decomposition into corresponding conformal blocks on the field theory side.« less

Optimum design of Geodesic dome’s jointing system

NASA Astrophysics Data System (ADS)

Tran, Huy. T.

2018-04-01

This study attempts to create a new design for joint connector of Geodesic dome. A new type of joint connector design is proposed for flexible rotating connection; comparing it to another, this design is cheaper and workable. After calculating the bearing capacity of the sample according to EC3 and Vietnam standard TCVN 5575-2012, FEM model of the design sample is carried out in many specific situation to consider the stress distribution, the deformation, the local destruction… in the connector. The analytical results and the FE data are consistent. The FE analysis also points out the behavior of some details that simple calculation cannot show. Hence, we can choose the optimum design of joint connector.

Fractal spectral triples on Kellendonk's C∗-algebra of a substitution tiling

NASA Astrophysics Data System (ADS)

Mampusti, Michael; Whittaker, Michael F.

2017-02-01

We introduce a new class of noncommutative spectral triples on Kellendonk's C∗-algebra associated with a nonperiodic substitution tiling. These spectral triples are constructed from fractal trees on tilings, which define a geodesic distance between any two tiles in the tiling. Since fractals typically have infinite Euclidean length, the geodesic distance is defined using Perron-Frobenius theory, and is self-similar with scaling factor given by the Perron-Frobenius eigenvalue. We show that each spectral triple is θ-summable, and respects the hierarchy of the substitution system. To elucidate our results, we construct a fractal tree on the Penrose tiling, and explicitly show how it gives rise to a collection of spectral triples.

CMB B-mode auto-bispectrum produced by primordial gravitational waves

NASA Astrophysics Data System (ADS)

Tahara, Hiroaki W. H.; Yokoyama, Jun'ichi

2018-01-01

Gravitational waves from inflation induce polarization patterns in the cosmic microwave background (CMB). It is known that there are only two types of non-Gaussianities of the gravitational waves in the most general covariant scalar field theory having second-order field equations, namely, generalized G-inflation. One originates from the inherent non-Gaussianity in general relativity, and the other from a derivative coupling between the Einstein tensor and the scalar field. We calculate polarization bispectra induced by these non-Gaussianities by transforming them into separable forms by virtue of the Laplace transformation. It is shown that future experiments can constrain the new one but cannot detect the general relativistic one.

Testing chirality of primordial gravitational waves with Planck and future CMB data: no hope from angular power spectra

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

Gerbino, Martina; Gruppuso, Alessandro; Natoli, Paolo

We use the 2015 Planck likelihood in combination with the Bicep2/Keck likelihood (BKP and BK14) to constrain the chirality, χ, of primordial gravitational waves in a scale-invariant scenario. In this framework, the parameter χ enters theory always coupled to the tensor-to-scalar ratio, r , e.g. in combination of the form χ ⋅ r . Thus, the capability to detect χ critically depends on the value of r . We find that with present data sets χ is de facto unconstrained. We also provide forecasts for χ from future CMB experiments, including COrE+, exploring several fiducial values of r . Wemore » find that the current limit on r is tight enough to disfavor a neat detection of χ. For example, in the unlikely case in which r ∼0.1(0.05), the maximal chirality case, i.e. χ = ±1, could be detected with a significance of ∼2.5(1.5)σ at best. We conclude that the two-point statistics at the basis of CMB likelihood functions is currently unable to constrain chirality and may only provide weak limits on χ in the most optimistic scenarios. Hence, it is crucial to investigate the use of other observables, e.g. provided by higher order statistics, to constrain these kinds of parity violating theories with the CMB.« less

Rapid geodesic mapping of brain functional connectivity: implementation of a dedicated co-processor in a field-programmable gate array (FPGA) and application to resting state functional MRI.

PubMed

Minati, Ludovico; Cercignani, Mara; Chan, Dennis

2013-10-01

Graph theory-based analyses of brain network topology can be used to model the spatiotemporal correlations in neural activity detected through fMRI, and such approaches have wide-ranging potential, from detection of alterations in preclinical Alzheimer's disease through to command identification in brain-machine interfaces. However, due to prohibitive computational costs, graph-based analyses to date have principally focused on measuring connection density rather than mapping the topological architecture in full by exhaustive shortest-path determination. This paper outlines a solution to this problem through parallel implementation of Dijkstra's algorithm in programmable logic. The processor design is optimized for large, sparse graphs and provided in full as synthesizable VHDL code. An acceleration factor between 15 and 18 is obtained on a representative resting-state fMRI dataset, and maps of Euclidean path length reveal the anticipated heterogeneous cortical involvement in long-range integrative processing. These results enable high-resolution geodesic connectivity mapping for resting-state fMRI in patient populations and real-time geodesic mapping to support identification of imagined actions for fMRI-based brain-machine interfaces. Copyright © 2013 IPEM. Published by Elsevier Ltd. All rights reserved.

Design and evaluation of a foam-filled hat-stiffened panel concept for aircraft primary structural applications

NASA Technical Reports Server (NTRS)

Ambur, Damodar R.

1993-01-01

Geodesically stiffened structures are very efficient in carrying combined bending, torsion, and pressure loading that is typical of primary aircraft structures. They are also very damage tolerant since there are multiple load paths available to redistribute loads compared to prismatically stiffened structures. Geodesically stiffened structures utilize continuous filament composite materials which make them amenable to automated manufacturing processes to reduce cost. The current practice for geodesically stiffened structures is to use a solid blade construction for the stiffener. This stiffener configuration is not an efficient concept and there is a need to identify other stiffener configurations that are more efficient but utilize the same manufacturing process as the solid blade. This paper describes a foam-filled stiffener cross section that is more efficient than a solid-blade stiffener in the load range corresponding to primary aircraft structures. A prismatic hat-stiffener panel design is then selected for structural evaluation in uni-axial compression with and without impact damage. Experimental results for both single stiffener specimens and multi-stiffener panel specimens are presented. Finite element analysis results are presented that predict the buckling and postbuckling response of the test specimens. Analytical results for both the element and panel specimens are compared with experimental results.

Evaluation of five diffeomorphic image registration algorithms for mouse brain magnetic resonance microscopy.

PubMed

Fu, Zhenrong; Lin, Lan; Tian, Miao; Wang, Jingxuan; Zhang, Baiwen; Chu, Pingping; Li, Shaowu; Pathan, Muhammad Mohsin; Deng, Yulin; Wu, Shuicai

2017-11-01

The development of genetically engineered mouse models for neuronal diseases and behavioural disorders have generated a growing need for small animal imaging. High-resolution magnetic resonance microscopy (MRM) provides powerful capabilities for noninvasive studies of mouse brains, while avoiding some limits associated with the histological procedures. Quantitative comparison of structural images is a critical step in brain imaging analysis, which highly relies on the performance of image registration techniques. Nowadays, there is a mushrooming growth of human brain registration algorithms, while fine-tuning of those algorithms for mouse brain MRMs is rarely addressed. Because of their topology preservation property and outstanding performance in human studies, diffeomorphic transformations have become popular in computational anatomy. In this study, we specially tuned five diffeomorphic image registration algorithms [DARTEL, geodesic shooting, diffeo-demons, SyN (Greedy-SyN and geodesic-SyN)] for mouse brain MRMs and evaluated their performance using three measures [volume overlap percentage (VOP), residual intensity error (RIE) and surface concordance ratio (SCR)]. Geodesic-SyN performed significantly better than the other methods according to all three different measures. These findings are important for the studies on structural brain changes that may occur in wild-type and transgenic mouse brains. © 2017 The Authors Journal of Microscopy © 2017 Royal Microscopical Society.

YNOGK: A New Public Code for Calculating Null Geodesics in the Kerr Spacetime

NASA Astrophysics Data System (ADS)

Yang, Xiaolin; Wang, Jiancheng

2013-07-01

Following the work of Dexter & Agol, we present a new public code for the fast calculation of null geodesics in the Kerr spacetime. Using Weierstrass's and Jacobi's elliptic functions, we express all coordinates and affine parameters as analytical and numerical functions of a parameter p, which is an integral value along the geodesic. This is the main difference between our code and previous similar ones. The advantage of this treatment is that the information about the turning points does not need to be specified in advance by the user, and many applications such as imaging, the calculation of line profiles, and the observer-emitter problem, become root-finding problems. All elliptic integrations are computed by Carlson's elliptic integral method as in Dexter & Agol, which guarantees the fast computational speed of our code. The formulae to compute the constants of motion given by Cunningham & Bardeen have been extended, which allow one to readily handle situations in which the emitter or the observer has an arbitrary distance from, and motion state with respect to, the central compact object. The validation of the code has been extensively tested through applications to toy problems from the literature. The source FORTRAN code is freely available for download on our Web site http://www1.ynao.ac.cn/~yangxl/yxl.html.

Micromirror arrays using KOH:H[sub 2]O micromachining of silicon for lens templates, geodesic lenses, and other applications

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

Kendall, D.L.; Eaton, W.P.; Manginell, R.

Micromirrors having diameters from a few micrometers to several millimeters have been produced on (100) silicon by wet-chemical etching in KOH:H[sub 2]O. The f/[number sign]'s range from about 2.5 to at least 10. The microroughness of an etched mirror with diameter 550 [mu]m and 9.6-[mu]m sagitta is less than 5 nm and its surface figure is within 0.5 [mu]m of a perfect sphere. Data over a wide range of diameters are presented and a semiempirical model is developed to explain the behavior. The concordance of the normalized etched profiles for all diameter mirrors demonstrates that the etching is dominated bymore » surface reaction rather than diffusion limitation. Design and fabrication schemes are presented for making a wide range of mirror diameters and focal lengths, for both single micromirrors and arrays. The etched depressions can be used as templates for microlenses and as substrates for geodesic waveguide lenses and arrays. Chem-mechanical polishing on the etched structures reduces the edge curvature and produces oblate spheroidal surfaces, both of which should improve geodesic lens behavior. The etched structures can also be used as variable crystal orientation substrates for epitaxial nucleation and various surface analysis studies.« less

Micromirror arrays using KOH:H2O micromachining of silicon for lens templates, geodesic lenses, and other applications

NASA Astrophysics Data System (ADS)

Kendall, Don L.; Eaton, William P.; Manginell, Ronald P.; Digges, Thomas G.

1994-11-01

Micromirrors having diameters from a few micrometers to several millimeters have been produced on (100) silicon by wet-chemical etching in KOH:H2O. The f/#'s range from about 2.5 to at least 10. The microroughness of an etched mirror with diameter 550 micrometers and 9.6-micrometers sagitta is less than 5 nm and its surface figure is within 0.5 micrometers of a perfect sphere. Data over a wide range of diameters are presented and a semiempirical model is developed to explain the behavior. The concordance of the normalized etched profiles for all diameter mirrors demonstrates that the etching is dominated by surface reaction rather than diffusion limitation. Design and fabrication schemes are presented for making a wide range of mirror diameters and focal lengths, for both single micromirrors and arrays. The etched depressions can be used as templates for microlenses and as substrates for geodesic waveguide lenses and arrays. Chem-mechanical polishing on the etched structures reduces the edge curvature and produces oblate spheroidal surfaces, both of which should improve geodesic lens behavior. The etched structures can also be used as variable crystal orientation substrates for epitaxial nucleation and various surface analysis studies.

Structure of the effective potential for a spherical wormhole

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

Montelongo Garcia, N.; Zannias, T.

2008-09-15

The structure of the effective potential V describing causal geodesics near the throat of an arbitrary spherical wormhole is analyzed. Einstein's equations relative to a set of regular coordinates covering a vicinity of the throat imply that any spherical wormhole can be constructed from solutions of an effective initial value problem with the throat serving as an initial value surface. The initial data involve matter variables, the area A(0) of the throat, and the gradient {lambda}(0) of the redshift factor on the throat. Whenever {lambda}(0)=0, the effective potential V has a critical point on the throat. Conditions upon the datamore » are derived ensuring that the critical point is a local minimum (respectively maximum). For particular families of quasi-Schwarzschild wormholes, V exhibits a local minimum on the throat independently upon the energy E and angular momentum L{sup 2} of the test particles and thus such wormholes admit stable circular timelike and null geodesics on the throat. For families of Chaplygin wormholes, we show that such geodesics are unstable. Based on a suitable power series representation of the metric, properties of V away from the throat are obtained that are useful for the analysis of accretion disks and radiation processes near the throat of any spherical wormhole.« less

Event and Apparent Horizon Finders for 3 + 1 Numerical Relativity.

PubMed

Thornburg, Jonathan

2007-01-01

Event and apparent horizons are key diagnostics for the presence and properties of black holes. In this article I review numerical algorithms and codes for finding event and apparent horizons in numerically-computed spacetimes, focusing on calculations done using the 3 + 1 ADM formalism. The event horizon of an asymptotically-flat spacetime is the boundary between those events from which a future-pointing null geodesic can reach future null infinity and those events from which no such geodesic exists. The event horizon is a (continuous) null surface in spacetime. The event horizon is defined nonlocally in time : it is a global property of the entire spacetime and must be found in a separate post-processing phase after all (or at least the nonstationary part) of spacetime has been numerically computed. There are three basic algorithms for finding event horizons, based on integrating null geodesics forwards in time, integrating null geodesics backwards in time, and integrating null surfaces backwards in time. The last of these is generally the most efficient and accurate. In contrast to an event horizon, an apparent horizon is defined locally in time in a spacelike slice and depends only on data in that slice, so it can be (and usually is) found during the numerical computation of a spacetime. A marginally outer trapped surface (MOTS) in a slice is a smooth closed 2-surface whose future-pointing outgoing null geodesics have zero expansion Θ. An apparent horizon is then defined as a MOTS not contained in any other MOTS. The MOTS condition is a nonlinear elliptic partial differential equation (PDE) for the surface shape, containing the ADM 3-metric, its spatial derivatives, and the extrinsic curvature as coefficients. Most "apparent horizon" finders actually find MOTSs. There are a large number of apparent horizon finding algorithms, with differing trade-offs between speed, robustness, accuracy, and ease of programming. In axisymmetry, shooting algorithms work well and are fairly easy to program. In slices with no continuous symmetries, spectral integral-iteration algorithms and elliptic-PDE algorithms are fast and accurate, but require good initial guesses to converge. In many cases, Schnetter's "pretracking" algorithm can greatly improve an elliptic-PDE algorithm's robustness. Flow algorithms are generally quite slow but can be very robust in their convergence. Minimization methods are slow and relatively inaccurate in the context of a finite differencing simulation, but in a spectral code they can be relatively faster and more robust.

F.W. Bessel (1825): The calculation of longitude and latitude from geodesic measurements

NASA Astrophysics Data System (ADS)

Karney, C. F. F.; Deakin, R. E.

2010-08-01

Issue No. 86 (1825 October) of the Astronomische Nachrichten was largely devoted to a single paper by F. W. Bessel on the solution of the direct geodesic problem (see the first sentences of the paper). For the most part, the paper stands on its own and needs little introduction. However, a few words are in order to place this paper in its historical context. First of all, it should be no surprise that a paper on this subject appeared in an astronomical journal. At the time, the disciplines of astronomy, navigation, and surveying were inextricably linked -- the methods and, in many cases, the practitioners (in particular, Bessel) were the same. Prior to Bessel's paper, the solution of the geodesic problem had been the subject of several studies by Clairaut, Euler, du Séjour, Legendre, Oriani, and others. The interest in the subject was twofold. It combined several new fields of mathematics: the calculus of variations, the theory of elliptic functions, and the differential geometry of curved surfaces. It also addressed very practical needs: the determination of the figure of the earth, the requirements of large scale surveys, and the construction of map projections. With the papers of Legendre and of Oriani in 1806, the framework for the mathematical solution for an ellipsoid of revolution had been established. However, Bessel was firmly in the practical camp; he carried out the East Prussian survey that connected the West European and Russian triangulation networks and later he made the first accurate estimate of the figure of the Earth, the ``Bessel ellipsoid''. He lays out his goal for this paper in its first section: to simplify the numerical solution of the geodesic problem. In Sects. \\ref{sec2}--\\ref{sec4}, Bessel gives a clear and concise summary of the previous work on the problem. In the remaining sections, he develops series for the distance and longitude integrals and constructs the tables which allow geodesics to be calculated to an accuracy of about 3 cm over distances in excess of 1000 km (and the method remains accurate for geodesics that encircle the Earth). Despite the use of logarithms, Bessel's numerical methods are surprisingly up-to-date: he writes out his series in a form that allows them to be extended to any order and he carries out a rather detailed analysis of the numerical errors. Bessel's derivation and tables were extensively used throughout the nineteenth century and many twentieth century works continued to refer to ``Bessel's method''. However, over time, the attributions to Bessel have become diluted as authors cite more recent works. This trend accelerated with the introduction of electronic calculators when Bessel's algorithms were thought to be too complex and simpler less accurate ones were substituted (these approximate algorithms are still in widespread use). However, now that floating-point hardware is fast and accurate, it is these later algorithms that often seem outdated, while Bessel's are easily adapted for implementation on modern computers.

An integrated workflow for stress and flow modelling using outcrop-derived discrete fracture networks

NASA Astrophysics Data System (ADS)

Bisdom, K.; Nick, H. M.; Bertotti, G.

2017-06-01

Fluid flow in naturally fractured reservoirs is often controlled by subseismic-scale fracture networks. Although the fracture network can be partly sampled in the direct vicinity of wells, the inter-well scale network is poorly constrained in fractured reservoir models. Outcrop analogues can provide data for populating domains of the reservoir model where no direct measurements are available. However, extracting relevant statistics from large outcrops representative of inter-well scale fracture networks remains challenging. Recent advances in outcrop imaging provide high-resolution datasets that can cover areas of several hundred by several hundred meters, i.e. the domain between adjacent wells, but even then, data from the high-resolution models is often upscaled to reservoir flow grids, resulting in loss of accuracy. We present a workflow that uses photorealistic georeferenced outcrop models to construct geomechanical and fluid flow models containing thousands of discrete fractures covering sufficiently large areas, that does not require upscaling to model permeability. This workflow seamlessly integrates geomechanical Finite Element models with flow models that take into account stress-sensitive fracture permeability and matrix flow to determine the full permeability tensor. The applicability of this workflow is illustrated using an outcropping carbonate pavement in the Potiguar basin in Brazil, from which 1082 fractures are digitised. The permeability tensor for a range of matrix permeabilities shows that conventional upscaling to effective grid properties leads to potential underestimation of the true permeability and the orientation of principal permeabilities. The presented workflow yields the full permeability tensor model of discrete fracture networks with stress-induced apertures, instead of relying on effective properties as most conventional flow models do.

Analysis of Seismic Moment Tensor and Finite-Source Scaling During EGS Resource Development at The Geysers, CA

NASA Astrophysics Data System (ADS)

Boyd, O. S.; Dreger, D. S.; Gritto, R.

2015-12-01

Enhanced Geothermal Systems (EGS) resource development requires knowledge of subsurface physical parameters to quantify the evolution of fracture networks. We investigate seismicity in the vicinity of the EGS development at The Geysers Prati-32 injection well to determine moment magnitude, focal mechanism, and kinematic finite-source models with the goal of developing a rupture area scaling relationship for the Geysers and specifically for the Prati-32 EGS injection experiment. Thus far we have analyzed moment tensors of M ≥ 2 events, and are developing the capability to analyze the large numbers of events occurring as a result of the fluid injection and to push the analysis to smaller magnitude earthquakes. We have also determined finite-source models for five events ranging in magnitude from M 3.7 to 4.5. The scaling relationship between rupture area and moment magnitude of these events resembles that of a published empirical relationship derived for events from M 4.5 to 8.3. We plan to develop a scaling relationship in which moment magnitude and corner frequency are predictor variables for source rupture area constrained by the finite-source modeling. Inclusion of corner frequency in the empirical scaling relationship is proposed to account for possible variations in stress drop. If successful, we will use this relationship to extrapolate to the large numbers of events in the EGS seismicity cloud to estimate the coseismic fracture density. We will present the moment tensor and corner frequency results for the micro earthquakes, and for select events, finite-source models. Stress drop inferred from corner frequencies and from finite-source modeling will be compared.

Earthquake focal mechanism forecasting in Italy for PSHA purposes

NASA Astrophysics Data System (ADS)

Roselli, Pamela; Marzocchi, Warner; Mariucci, Maria Teresa; Montone, Paola

2018-01-01

In this paper, we put forward a procedure that aims to forecast focal mechanism of future earthquakes. One of the primary uses of such forecasts is in probabilistic seismic hazard analysis (PSHA); in fact, aiming at reducing the epistemic uncertainty, most of the newer ground motion prediction equations consider, besides the seismicity rates, the forecast of the focal mechanism of the next large earthquakes as input data. The data set used to this purpose is relative to focal mechanisms taken from the latest stress map release for Italy containing 392 well-constrained solutions of events, from 1908 to 2015, with Mw ≥ 4 and depths from 0 down to 40 km. The data set considers polarity focal mechanism solutions until to 1975 (23 events), whereas for 1976-2015, it takes into account only the Centroid Moment Tensor (CMT)-like earthquake focal solutions for data homogeneity. The forecasting model is rooted in the Total Weighted Moment Tensor concept that weighs information of past focal mechanisms evenly distributed in space, according to their distance from the spatial cells and magnitude. Specifically, for each cell of a regular 0.1° × 0.1° spatial grid, the model estimates the probability to observe a normal, reverse, or strike-slip fault plane solution for the next large earthquakes, the expected moment tensor and the related maximum horizontal stress orientation. These results will be available for the new PSHA model for Italy under development. Finally, to evaluate the reliability of the forecasts, we test them with an independent data set that consists of some of the strongest earthquakes with Mw ≥ 3.9 occurred during 2016 in different Italian tectonic provinces.

Three-dimensional seismic structure and moment tensors of non-double-couple earthquakes at the Hengill-Grensdalur volcanic complex, Iceland

USGS Publications Warehouse

Miller, A.D.; Julian, B.R.; Foulger, G.R.

1998-01-01

The volcanic and geothermal areas of Iceland are rich sources of non-double-couple (non-DC) earthquakes. A state-of-the-art digital seismometer network deployed at the Hengill-Grensdalur volcanic complex in 1991 recorded 4000 small earthquakes. We used the best recorded of these to determine 3-D VP and VP/VS structure tomographically and accurate earthquake moment tensors. The VP field is dominated by high seismic wave speed bodies interpreted as solidified intrusions. A widespread negative (-4 per cent) VP/VS anomaly in the upper 4 km correlates with the geothermal field, but is too strong to be caused solely by the effect of temperature upon liquid water or the presence of vapour, and requires in addition mineralogical or lithological differences between the geothermal reservoir and its surroundings. These may be caused by geothermal alteration. Well-constrained moment tensors were obtained for 70 of the best-recorded events by applying linear programming methods to P- and S-wave polarities and amplitude ratios. About 25 per cent of the mechanisms are, within observational error, consistent with DC mechanisms consistent with shear faulting. The other 75 per cent have significantly non-DC mechanisms. Many have substantial explosive components, one has a substantial implosive component, and the deviatoric component of many is strongly non-DC. Many of the non-DC mechanisms are consistent, within observational error, with simultaneous tensile and shear faulting. However, the mechanisms occupy a continuum in source-type parameter space and probably at least one additional source process is occurring. This may be fluid flow into newly formed cracks, causing partial compensation of the volumetric component. Studying non-shear earthquakes such as these has great potential for improving our understanding of geothermal processes and earthquake source processes in general.

Complementing the ground-based CMB-S4 experiment on large scales with the PIXIE satellite

NASA Astrophysics Data System (ADS)

Calabrese, Erminia; Alonso, David; Dunkley, Jo

2017-03-01

We present forecasts for cosmological parameters from future cosmic microwave background (CMB) data measured by the stage-4 (S4) generation of ground-based experiments in combination with large-scale anisotropy data from the PIXIE satellite. We demonstrate the complementarity of the two experiments and focus on science targets that benefit from their combination. We show that a cosmic-variance-limited measurement of the optical depth to reionization provided by PIXIE, with error σ (τ )=0.002 , is vital for enabling a 5 σ detection of the sum of the neutrino masses when combined with a CMB-S4 lensing measurement and with lower-redshift constraints on the growth of structure and the distance-redshift relation. Parameters characterizing the epoch of reionization will also be tightly constrained; PIXIE's τ constraint converts into σ (zre)=0.2 for the mean time of reionization, and a kinematic Sunyaev-Zel'dovich measurement from S4 gives σ (Δ zre)=0.03 for the duration of reionization. Both PIXIE and S4 will put strong constraints on primordial tensor fluctuations, vital for testing early-Universe models, and will do so at distinct angular scales. We forecast σ (r )≈5 ×10-4 for a signal with a tensor-to-scalar ratio r =10-3, after accounting for diffuse foreground removal and delensing. The wide and dense frequency coverage of PIXIE results in an expected foreground-degradation factor on r of only ≈25 %. By measuring large and small scales PIXIE and S4 will together better limit the energy injection at recombination from dark matter annihilation, with pann<0.09 ×10-6 m3/s /kg projected at 95% confidence. Cosmological parameters measured from the damping tail with S4 will be best constrained by polarization, which has the advantage of minimal contamination from extragalactic emission.

Constraining the parameters of the EAP sea ice rheology from satellite observations and discrete element model

NASA Astrophysics Data System (ADS)

Tsamados, Michel; Heorton, Harry; Feltham, Daniel; Muir, Alan; Baker, Steven

2016-04-01

The new elastic-plastic anisotropic (EAP) rheology that explicitly accounts for the sub-continuum anisotropy of the sea ice cover has been implemented into the latest version of the Los Alamos sea ice model CICE. The EAP rheology is widely used in the climate modeling scientific community (i.e. CPOM stand alone, RASM high resolution regional ice-ocean model, MetOffice fully coupled model). Early results from sensitivity studies (Tsamados et al, 2013) have shown the potential for an improved representation of the observed main sea ice characteristics with a substantial change of the spatial distribution of ice thickness and ice drift relative to model runs with the reference visco-plastic (VP) rheology. The model contains one new prognostic variable, the local structure tensor, which quantifies the degree of anisotropy of the sea ice, and two parameters that set the time scale of the evolution of this tensor. Observations from high resolution satellite SAR imagery as well as numerical simulation results from a discrete element model (DEM, see Wilchinsky, 2010) have shown that these individual floes can organize under external wind and thermal forcing to form an emergent isotropic sea ice state (via thermodynamic healing, thermal cracking) or an anisotropic sea ice state (via Coulombic failure lines due to shear rupture). In this work we use for the first time in the context of sea ice research a mathematical metric, the Tensorial Minkowski functionals (Schroeder-Turk, 2010), to measure quantitatively the degree of anisotropy and alignment of the sea ice at different scales. We apply the methodology on the GlobICE Envisat satellite deformation product (www.globice.info), on a prototype modified version of GlobICE applied on Sentinel-1 Synthetic Aperture Radar (SAR) imagery and on the DEM ice floe aggregates. By comparing these independent measurements of the sea ice anisotropy as well as its temporal evolution against the EAP model we are able to constrain the uncertain model parameters and functions in the EAP model.

Positive-entropy Hamiltonian systems on Nilmanifolds via scattering

NASA Astrophysics Data System (ADS)

Butler, Leo T.

2014-10-01

Let Σ be a compact quotient of T4, the Lie group of 4 × 4 upper triangular matrices with unity along the diagonal. The Lie algebra {\\mathfrak t}4 of T4 has the standard basis {Xij} of matrices with 0 everywhere but in the (i, j) entry, which is unity. Let g be the Carnot metric, a sub-Riemannian metric, on T4 for which Xi, i+1, (i = 1, 2, 3), is an orthonormal basis. Montgomery, Shapiro and Stolin showed that the geodesic flow of g is algebraically non-integrable. This paper proves that the geodesic flow of that Carnot metric on TΣ has positive topological entropy and its Euler field is real-analytically non-integrable. It extends earlier work by Butler and Gelfreich.

Boundary holographic Witten diagrams

DOE PAGES

Karch, Andreas; Sato, Yoshiki

2017-09-25

In this paper we discuss geodesic Witten diagrams in generic holographic conformal field theories with boundary or defect. Boundary CFTs allow two different de-compositions of two-point functions into conformal blocks: boundary channel and ambient channel. Building on earlier work, we derive a holographic dual of the boundary channel decomposition in terms of bulk-to-bulk propagators on lower dimensional AdS slices. In the situation in which we can treat the boundary or defect as a perturbation around pure AdS spacetime, we obtain the leading corrections to the two-point function both in boundary and ambient channel in terms of geodesic Witten diagrams whichmore » exactly reproduce the decomposition into corresponding conformal blocks on the field theory side.« less

Methods of Information Geometry to model complex shapes

NASA Astrophysics Data System (ADS)

De Sanctis, A.; Gattone, S. A.

2016-09-01

In this paper, a new statistical method to model patterns emerging in complex systems is proposed. A framework for shape analysis of 2- dimensional landmark data is introduced, in which each landmark is represented by a bivariate Gaussian distribution. From Information Geometry we know that Fisher-Rao metric endows the statistical manifold of parameters of a family of probability distributions with a Riemannian metric. Thus this approach allows to reconstruct the intermediate steps in the evolution between observed shapes by computing the geodesic, with respect to the Fisher-Rao metric, between the corresponding distributions. Furthermore, the geodesic path can be used for shape predictions. As application, we study the evolution of the rat skull shape. A future application in Ophthalmology is introduced.

On the heteroclinic connection problem for multi-well gradient systems

NASA Astrophysics Data System (ADS)

Zuniga, Andres; Sternberg, Peter

2016-10-01

We revisit the existence problem of heteroclinic connections in RN associated with Hamiltonian systems involving potentials W :RN → R having several global minima. Under very mild assumptions on W we present a simple variational approach to first find geodesics minimizing length of curves joining any two of the potential wells, where length is computed with respect to a degenerate metric having conformal factor √{ W}. Then we show that when such a minimizing geodesic avoids passing through other wells of the potential at intermediate times, it gives rise to a heteroclinic connection between the two wells. This work improves upon the approach of [22] and represents a more geometric alternative to the approaches of e.g. [5,10,14,17] for finding such connections.

Quantum frictionless trajectories versus geodesics

NASA Astrophysics Data System (ADS)

Barbado, Luis C.; Barceló, Carlos; Garay, Luis J.

2015-10-01

Moving particles outside a star will generally experience quantum friction caused by the Unruh radiation reaction. There exist however radial trajectories that lack this effect (in the outgoing radiation sector, and ignoring backscattering). Along these trajectories, observers perceive just stellar emission, without further contribution from the Unruh effect. They turn out to have the property that the variations of the Doppler and the gravitational shifts compensate each other. They are not geodesics, and their proper acceleration obeys an inverse square law, which means that it could in principle be generated by outgoing stellar radiation. In the case of a black hole emitting Hawking radiation, this may lead to a buoyancy scenario. The ingoing radiation sector has little effect and seems to slow down the fall even further.

Coordinate Families for the Schwarzschild Geometry Based on Radial Timelike Geodesics

NASA Technical Reports Server (NTRS)

Finch, Tehani K.

2015-01-01

We explore the connections between various coordinate systems associated with observersmoving inwardly along radial geodesics in the Schwarzschild geometry. Painleve-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from infinity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at infinity with non-zero initial inward velocity; Gautreau-Hoffmann time coordinates are adapted to observers dropped from rest from a finite distance from the black hole horizon.We construct from these an LMP family and a proper-time family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lemaître coordinates as well.

Vacuum solutions admitting a geodesic null congruence with shear proportional to expansion

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

Kupeli, A.H.

Algebraically general, nontwisting solutions for the vacuum to vacuum generalized Kerr--Schild (GKS) transformation are obtained. These solutions admit a geodesic null congruence with shear proportional to expansion. In the Newman--Penrose formalism, if l/sup ..mu../ is chosen to be the null vector of the GKS transformation, this property is stated as sigma = arho and Da = 0. It is assumed that a is a constant, and the background is chosen as a pp-wave solution. For generic values of a, the GKS metrics consist of the Kasner solutions. For a = +- (1 +- (2)/sup 1/2/), there are solutions with lessmore » symmetries including special cases of the Kota--Perjes and Lukacs solutions.« less

Calcium-43 chemical shift and electric field gradient tensor interplay: a sensitive probe of structure, polymorphism, and hydration.

PubMed

Widdifield, Cory M; Moudrakovski, Igor; Bryce, David L

2014-07-14

Calcium is the 5th most abundant element on earth, and is found in numerous biological tissues, proteins, materials, and increasingly in catalysts. However, due to a number of unfavourable nuclear properties, such as a low magnetogyric ratio, very low natural abundance, and its nuclear electric quadrupole moment, development of solid-state (43)Ca NMR has been constrained relative to similar nuclides. In this study, 12 commonly-available calcium compounds are analyzed via(43)Ca solid-state NMR and the information which may be obtained by the measurement of both the (43)Ca electric field gradient (EFG) and chemical shift tensors (the latter of which are extremely rare with only a handful of literature examples) is discussed. Combined with density functional theory (DFT) computations, this 'tensor interplay' is, for the first time for (43)Ca, illustrated to be diagnostic in distinguishing polymorphs (e.g., calcium formate), and the degree of hydration (e.g., CaCl2·2H2O and calcium tartrate tetrahydrate). For Ca(OH)2, we outline the first example of (1)H to (43)Ca cross-polarization on a sample at natural abundance in (43)Ca. Using prior knowledge of the relationship between the isotropic calcium chemical shift and the calcium quadrupolar coupling constant (CQ) with coordination number, we postulate the coordination number in a sample of calcium levulinate dihydrate, which does not have a known crystal structure. Natural samples of CaCO3 (aragonite polymorph) are used to show that the synthetic structure is present in nature. Gauge-including projector augmented-wave (GIPAW) DFT computations using accepted crystal structures for many of these systems generally result in calculated NMR tensor parameters which are in very good agreement with the experimental observations. This combination of (43)Ca NMR measurements with GIPAW DFT ultimately allows us to establish clear correlations between various solid-state (43)Ca NMR observables and selected structural parameters, such as unit cell dimensions and average Ca-O bond distances.

Simulation of Anisotropic Rock Damage for Geologic Fracturing

NASA Astrophysics Data System (ADS)

Busetti, S.; Xu, H.; Arson, C. F.

2014-12-01

A continuum damage model for differential stress-induced anisotropic crack formation and stiffness degradation is used to study geologic fracturing in rocks. The finite element-based model solves for deformation in the quasi-linear elastic domain and determines the six component damage tensor at each deformation increment. The model permits an isotropic or anisotropic intact or pre-damaged reference state, and the elasticity tensor evolves depending on the stress path. The damage variable, similar to Oda's fabric tensor, grows when the surface energy dissipated by three-dimensional opened cracks exceeds a threshold defined at the appropriate scale of the representative elementary volume (REV). At the laboratory or wellbore scale (<1m) brittle continuum damage reflects microcracking, grain boundary separation, grain crushing, or fine delamination, such as in shale. At outcrop (1m-100m), seismic (10m-1000m), and tectonic (>1000m) scales the damaged REV reflects early natural fracturing (background or tectonic fracturing) or shear strain localization (fault process zone, fault-tip damage, etc.). The numerical model was recently benchmarked against triaxial stress-strain data from laboratory rock mechanics tests. However, the utility of the model to predict geologic fabric such as natural fracturing in hydrocarbon reservoirs was not fully explored. To test the ability of the model to predict geological fracturing, finite element simulations (Abaqus) of common geologic scenarios with known fracture patterns (borehole pressurization, folding, faulting) are simulated and the modeled damage tensor is compared against physical fracture observations. Simulated damage anisotropy is similar to that derived using fractured rock-mass upscaling techniques for pre-determined fracture patterns. This suggests that if model parameters are constrained with local data (e.g., lab, wellbore, or reservoir domain), forward modeling could be used to predict mechanical fabric at the relevant REV scale. This reference fabric also can be used as the starting material property to pre-condition subsequent deformation or fluid flow. Continuing efforts are to expand the present damage model to couple damage evolution with plasticity and with permeability for more geologically realistic simulation.

Compact objects in relativistic theories of gravity

NASA Astrophysics Data System (ADS)

Okada da Silva, Hector

2017-05-01

In this dissertation we discuss several aspects of compact objects, i.e. neutron stars and black holes, in relativistic theories of gravity. We start by studying the role of nuclear physics (encoded in the so-called equation of state) in determining the properties of neutron stars in general relativity. We show that low-mass neutron stars are potentially useful astrophysical laboratories that can be used to constrain the properties of the equation of state. More specifically, we show that various bulk properties of these objects, such as their quadrupole moment and tidal deformability, are tightly correlated. Next, we develop a formalism that aims to capture how generic modifications from general relativity affect the structure of neutron stars, as predicted by a broad class of gravity theories, in the spirit of the parametrized post-Newtonian formalism (PPN). Our "post-Tolman-Oppenheimer-Volkoff" formalism provides a toolbox to study both stellar structure and the interior/exterior geometries of static, spherically symmetric relativistic stars. We also apply the formalism to parametrize deviations from general relativity in various astrophysical observables related with neutron stars, including surface redshift, apparent radius, Eddington luminosity. We then turn our attention to what is arguably the most well-motivated and well-investigated generalization of general relativity: scalar-tensor theory. We start by considering theories where gravity is mediated by a single extra scalar degree of freedom (in addition to the metric tensor). An interesting class of scalar-tensor theories passes all experimental tests in the weak-field regime of gravity, yet considerably deviates from general relativity in the strong-field regime in the presence of matter. A common assumption in modeling neutron stars is that the pressure within these object is spatially isotropic. We relax this assumption and examine how pressure anisotropy affects the mass, radius and moment of inertia of slowly rotating neutron stars, both in general relativity and in scalar-tensor gravity. We show that a sufficient amount of pressure anisotropy results in neutron star models whose properties in scalar-tensor theory deviate significantly from their general relativistic counterparts. Moreover, the presence of anisotropy allows these deviations to be considerable even for values of the theory's coupling parameter for which neutron stars in scalar-tensor theory would be otherwise indistinguishable from those in general relativity. Within scalar-tensor theory we also investigate the effects of the scalar field on the crustal torsional oscillations of neutron stars, which have been associated to quasi-periodic oscillations in the X-ray spectra in the aftermath of giant flares. We show that the presence of the scalar field has an influence on the thickness of the stellar crust, and investigate how it affects the oscillation frequencies. Deviations from the predictions of general relativity can be large for certain values of the theory's coupling parameter. However, the influence of the scalar field is degenerate with uncertainties in the equation of state of the star's crust and microphysics effects (electron screening) for values of the coupling allowed by binary pulsar observations. We also derive the stellar structure equations for slowly-rotating neutron stars in a broader class of scalar-tensor theories in which matter and scalar field are coupled through the so-called disformal coupling. We study in great detail how the disformal coupling affects the structure of neutron stars, and we investigate the existence of universal (equation of state-independent) relations connecting the stellar compactness and moment of inertia. In particular, we find that these universal relations can deviate considerably from the predictions of general relativity. (Abstract shortened by ProQuest.).

Structural Brain Connectivity Constrains within-a-Day Variability of Direct Functional Connectivity

PubMed Central

Park, Bumhee; Eo, Jinseok; Park, Hae-Jeong

2017-01-01

The idea that structural white matter connectivity constrains functional connectivity (interactions among brain regions) has widely been explored in studies of brain networks; studies have mostly focused on the “average” strength of functional connectivity. The question of how structural connectivity constrains the “variability” of functional connectivity remains unresolved. In this study, we investigated the variability of resting state functional connectivity that was acquired every 3 h within a single day from 12 participants (eight time sessions within a 24-h period, 165 scans per session). Three different types of functional connectivity (functional connectivity based on Pearson correlation, direct functional connectivity based on partial correlation, and the pseudo functional connectivity produced by their difference) were estimated from resting state functional magnetic resonance imaging data along with structural connectivity defined using fiber tractography of diffusion tensor imaging. Those types of functional connectivity were evaluated with regard to properties of structural connectivity (fiber streamline counts and lengths) and types of structural connectivity such as intra-/inter-hemispheric edges and topological edge types in the rich club organization. We observed that the structural connectivity constrained the variability of direct functional connectivity more than pseudo-functional connectivity and that the constraints depended strongly on structural connectivity types. The structural constraints were greater for intra-hemispheric and heterologous inter-hemispheric edges than homologous inter-hemispheric edges, and feeder and local edges than rich club edges in the rich club architecture. While each edge was highly variable, the multivariate patterns of edge involvement, especially the direct functional connectivity patterns among the rich club brain regions, showed low variability over time. This study suggests that structural connectivity not only constrains the strength of functional connectivity, but also the within-a-day variability of functional connectivity and connectivity patterns, particularly the direct functional connectivity among brain regions. PMID:28848416

Quantum mechanics of a constrained particle

NASA Astrophysics Data System (ADS)

da Costa, R. C. T.

1981-04-01

The motion of a particle rigidly bounded to a surface is discussed, considering the Schrödinger equation of a free particle constrained to move, by the action of an external potential, in an infinitely thin sheet of the ordinary three-dimensional space. Contrary to what seems to be the general belief expressed in the literature, this limiting process gives a perfectly well-defined result, provided that we take some simple precautions in the definition of the potentials and wave functions. It can then be shown that the wave function splits into two parts: the normal part, which contains the infinite energies required by the uncertainty principle, and a tangent part which contains "surface potentials" depending both on the Gaussian and mean curvatures. An immediate consequence of these results is the existence of different quantum mechanical properties for two isometric surfaces, as can be seen from the bound state which appears along the edge of a folded (but not stretched) plane. The fact that this surface potential is not a bending invariant (cannot be expressed as a function of the components of the metric tensor and their derivatives) is also interesting from the more general point of view of the quantum mechanics in curved spaces, since it can never be obtained from the classical Lagrangian of an a priori constrained particle without substantial modifications in the usual quantization procedures. Similar calculations are also presented for the case of a particle bounded to a curve. The properties of the constraining spatial potential, necessary to a meaningful limiting process, are discussed in some detail, and, as expected, the resulting Schrödinger equation contains a "linear potential" which is a function of the curvature.

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

Mohapi, N.; Hees, A.; Larena, J., E-mail: n.mohapi@gmail.com, E-mail: a.hees@ru.ac.za, E-mail: j.larena@ru.ac.za

The Einstein Equivalence Principle is a fundamental principle of the theory of General Relativity. While this principle has been thoroughly tested with standard matter, the question of its validity in the Dark sector remains open. In this paper, we consider a general tensor-scalar theory that allows to test the equivalence principle in the Dark sector by introducing two different conformal couplings to standard matter and to Dark matter. We constrain these couplings by considering galactic observations of strong lensing and of velocity dispersion. Our analysis shows that, in the case of a violation of the Einstein Equivalence Principle, data favourmore » violations through coupling strengths that are of opposite signs for ordinary and Dark matter. At the same time, our analysis does not show any significant deviations from General Relativity.« less

Fluids and vortex from constrained fluctuations around C-metric black holes

NASA Astrophysics Data System (ADS)

Hao, Xin; Wu, Bin; Zhao, Liu

2017-08-01

By foliating the four-dimensional C-metric black hole spacetime, we consider a kind of initial-value-like formulation of the vacuum Einstein's equation, the holographic initial data is a double consisting of the induced metric and the Brown-York energy momentum tensor on an arbitrary initial hypersurface. Then by perturbing the initial data that generates the background spacetime, it is shown that, in an appropriate limit, the fluctuation modes are governed by the continuity equation and the compressible Navier-Stokes equation which describe the momentum transport in non-relativistic viscous fluid on a flat Newtonian space. It turns out that the flat space fluid behaves as a pure vortex and the viscosity to entropy ratio is subjected to the black hole acceleration.

Review: Hamiltonian Linearization of the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge: A Radiation Gauge for Background-Independent Gravitational Waves in a Post-Minkowskian Einstein Spacetime

NASA Astrophysics Data System (ADS)

Agresti, Juri; De Pietri, Roberto; Lusanna, Luca; Martucci, Luca

2004-05-01

In the framework of the rest-frame instant form of tetrad gravity, where the Hamiltonian is the weak ADM energy {\\hat E}ADM, we define a special completely fixed 3-orthogonal Hamiltonian gauge, corresponding to a choice of non-harmonic 4-coordinates, in which the independent degrees of freedom of the gravitational field are described by two pairs of canonically conjugate Dirac observables (DO) r_{\\bar a}(\\tau ,\\vec \\sigma ), \\pi_{\\bar a}(\\tau ,\\vec \\sigma ), \\bar a = 1,2. We define a Hamiltonian linearization of the theory, i.e. gravitational waves, without introducing any background 4-metric, by retaining only the linear terms in the DO's in the super-hamiltonian constraint (the Lichnerowicz equation for the conformal factor of the 3-metric) and the quadratic terms in the DO's in {\\hat E}ADM. We solve all the constraints of the linearized theory: this amounts to work in a well defined post-Minkowskian Christodoulou-Klainermann space-time. The Hamilton equations imply the wave equation for the DO's r_{\\bar a}(\\tau ,\\vec \\sigma ), which replace the two polarizations of the TT harmonic gauge, and that linearized Einstein's equations are satisfied. Finally we study the geodesic equation, both for time-like and null geodesics, and the geodesic deviation equation.

Shell evolution above Z ,N =50 within Skyrme density functional theory: The impact of deformation and tensor interactions

NASA Astrophysics Data System (ADS)

Shi, Yue

2017-03-01

Background: Recent years have seen considerable effort in associating the shell evolution (SE) for a chain of isotones or isotopes with the underlying nuclear interactions. In particular, it has been fairly well established that the tensor part of the Skyrme interaction is indispensable for understanding certain SE above Z ,N =50 shell closures, as a function of nucleon numbers. Purpose: The purpose of the present work is twofold: (1) to study the effect of deformation due to blocking on the SE above Z ,N =50 shell closures and (2) to examine the optimal parametrizations in the tensor part which gives a proper description of the SE above Z ,N =50 shell closures. Methods: I use the Skyrme-Hartree-Fock-Bogoliubov (SHFB) method to compute the even-even vacua of the Z =50 isotopes and N =50 isotones. For Sb and odd-A Sn isotopes, I perform calculations with a blocking procedure which accounts for the polarization effects, including deformations. Results: The blocking SHFB calculations show that the light odd-A Sb isotopes, with only one valence proton occupying down-sloping Ω =11 /2- and Ω =7 /2+ Nilsson orbits, assume finite oblate deformations. This reduces the energy differences between 11 /2- and 7 /2+ states by about 500 keV for 51Sb56 -66 , bringing the energy-difference curve closer to the experimental one. With une2t1 energy density functional (EDF), which differs from unedf2 parametrization by tensor terms, a better description of the slope of Δ e (π 1 h11 /2-π 1 g7 /2) as a function of neutron number has been obtained. However, the trend of Δ e (π 1 g7 /2-π 2 d5 /2) curve is worse using une2t1 EDF. Δ e (ν 3 s1 /2-ν 2 d5 /2) and Δ e (ν 1 g7 /2-ν 2 d5 /2) curve for N =50 isotones using une2t1 seems to be consistent with experimental data. The neutron SE of Δ e (ν 1 h11 /2-ν 1 g7 /2) and Δ e (ν 1 g7 /2-ν 2 d5 /2) for Sn isotopes are shown to be sensive to αT tensor parameter. Conclusions: Within the Skyrme self-consistent mean-field model, the deformation degree of freedom has to be taken into account for Sb isotopes, N =51 isotones, and odd-A Sn isotopes when discussing variation of quantities like shell gap etc. The tensor terms are important for describing the strong variation of Δ E (Ωπ=11 /2--7 /2+) in Sb isotopes. The SE of 1 /2+ and 7 /2+ states in N =51 isotones may show signature for the existence of tensor interaction. The experimental excitation energies of 11 /2- and 7 /2+ states in odd-A Sn isotopes close to 132Sn give prospects for constraining the αT parameter.

Accelerated observers and the notion of singular spacetime

NASA Astrophysics Data System (ADS)

Olmo, Gonzalo J.; Rubiera-Garcia, Diego; Sanchez-Puente, Antonio

2018-03-01

Geodesic completeness is typically regarded as a basic criterion to determine whether a given spacetime is regular or singular. However, the principle of general covariance does not privilege any family of observers over the others and, therefore, observers with arbitrary motions should be able to provide a complete physical description of the world. This suggests that in a regular spacetime, all physically acceptable observers should have complete paths. In this work we explore this idea by studying the motion of accelerated observers in spherically symmetric spacetimes and illustrate it by considering two geodesically complete black hole spacetimes recently described in the literature. We show that for bound and locally unbound accelerations, the paths of accelerated test particles are complete, providing further support to the regularity of such spacetimes.

Coordinate Families for the Schwarzschild Geometry Based on Radial Timelike Geodesics

NASA Technical Reports Server (NTRS)

Finch, Tehani K.

2015-01-01

We explore the connections between various coordinate systems associated with observers moving inwardly along radial geodesics in the Schwarzschild geometry. Painleve-Gullstrand (PG) time is adapted to freely falling observers dropped from rest from in nity; Lake-Martel-Poisson (LMP) time coordinates are adapted to observers who start at in nity with non-zero initial inward velocity; Gautreau-Ho mann (GH) time coordinates are adapted to observers dropped from rest from a nite distance from the black hole horizon. We construct from these an LMP family and a propertime family of time coordinates, the intersection of which is PG time. We demonstrate that these coordinate families are distinct, but related, one-parameter generalizations of PG time, and show linkage to Lema^tre coordinates as well.

Light-cone observables and gauge-invariance in the geodesic light-cone formalism

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

Scaccabarozzi, Fulvio; Yoo, Jaiyul, E-mail: fulvio@physik.uzh.ch, E-mail: jyoo@physik.uzh.ch

The remarkable properties of the geodesic light-cone (GLC) coordinates allow analytic expressions for the light-cone observables, providing a new non-perturbative way for calculating the effects of inhomogeneities in our Universe. However, the gauge-invariance of these expressions in the GLC formalism has not been shown explicitly. Here we provide this missing part of the GLC formalism by proving the gauge-invariance of the GLC expressions for the light-cone observables, such as the observed redshift, the luminosity distance, and the physical area and volume of the observed sources. Our study provides a new insight on the properties of the GLC coordinates and itmore » complements the previous work by the GLC collaboration, leading to a comprehensive description of light propagation in the GLC representation.« less

Structural Analysis of Helios Filament-Wound Tanks Subjected to Internal Pressure and Cooling

NASA Technical Reports Server (NTRS)

Ko, William L

2005-01-01

A finite-element stress analysis is performed on Helios filament-wound hydrogen tanks to examine the stress field and effect of end dome geometry on the stress field. Each tank is composed of a central circular cylindrical section with either geodesic or hemispherical end domes, which have metallic polar bosses. The tanks are subjected to combined and separate internal pressure and temperature loading conditions, and the stress contributions of each loading component are examined. The tank-wall-polar-boss interfacial meridional tensile stress in the hemispherical dome is found to be approximately 27 percent lower than that in the geodesic dome. The effects of both material anisotropy and the aluminum lining on the intensities of tensile meridional stress at the tank-wall-polar-boss bonding interface are examined.

Scalar self-force on eccentric geodesics in Schwarzschild spacetime: A time-domain computation

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

Haas, Roland

2007-06-15

We calculate the self-force acting on a particle with scalar charge moving on a generic geodesic around a Schwarzschild black hole. This calculation requires an accurate computation of the retarded scalar field produced by the moving charge; this is done numerically with the help of a fourth-order convergent finite-difference scheme formulated in the time domain. The calculation also requires a regularization procedure, because the retarded field is singular on the particle's world line; this is handled mode-by-mode via the mode-sum regularization scheme first introduced by Barack and Ori. This paper presents the numerical method, various numerical tests, and a samplemore » of results for mildly eccentric orbits as well as ''zoom-whirl'' orbits.« less

Quantum Anosov flows: A new family of examples

NASA Astrophysics Data System (ADS)

Peter, Ingo J.; Emch, Gérard G.

1998-09-01

A quantum version is presented for the Anosov system defined by the time evolution implemented by the geodesic coflow on the cotangent bundle of any compact quotient manifold obtained from the Poincaré half-plane. While the canonical Weyl algebra does not close under time evolution, the symplectic structure of these classical systems can be exploited to produce objects akin to the CCR algebras encountered in quantum field theory. This construction allows one to lift both the geodesic and the horocyclic flows to a Weyl algebra describing the quantum dynamics corresponding to the systems under consideration. The Anosov relations as proposed in Ref. Reference 1 are found to be valid for these models. A quantum version of the classical ergodicity of these systems is discussed in the last section.

Adaptive form-finding method for form-fixed spatial network structures

NASA Astrophysics Data System (ADS)

Lan, Cheng; Tu, Xi; Xue, Junqing; Briseghella, Bruno; Zordan, Tobia

2018-02-01

An effective form-finding method for form-fixed spatial network structures is presented in this paper. The adaptive form-finding method is introduced along with the example of designing an ellipsoidal network dome with bar length variations being as small as possible. A typical spherical geodesic network is selected as an initial state, having bar lengths in a limit group number. Next, this network is transformed into the ellipsoidal shape as desired by applying compressions on bars according to the bar length variations caused by transformation. Afterwards, the dynamic relaxation method is employed to explicitly integrate the node positions by applying residual forces. During the form-finding process, the boundary condition of constraining nodes on the ellipsoid surface is innovatively considered as reactions on the normal direction of the surface at node positions, which are balanced with the components of the nodal forces in a reverse direction induced by compressions on bars. The node positions are also corrected according to the fixed-form condition in each explicit iteration step. In the serial results of time history, the optimal solution is found from a time history of states by properly choosing convergence criteria, and the presented form-finding procedure is proved to be applicable for form-fixed problems.

Linearized modified gravity theories with a cosmological term: advance of perihelion and deflection of light

NASA Astrophysics Data System (ADS)

Özer, Hatice; Delice, Özgür

2018-03-01

Two different ways of generalizing Einstein’s general theory of relativity with a cosmological constant to Brans–Dicke type scalar–tensor theories are investigated in the linearized field approximation. In the first case a cosmological constant term is coupled to a scalar field linearly whereas in the second case an arbitrary potential plays the role of a variable cosmological term. We see that the former configuration leads to a massless scalar field whereas the latter leads to a massive scalar field. General solutions of these linearized field equations for both cases are obtained corresponding to a static point mass. Geodesics of these solutions are also presented and solar system effects such as the advance of the perihelion, deflection of light rays and gravitational redshift were discussed. In general relativity a cosmological constant has no role in these phenomena. We see that for the Brans–Dicke theory, the cosmological constant also has no effect on these phenomena. This is because solar system observations require very large values of the Brans–Dicke parameter and the correction terms to these phenomena becomes identical to GR for these large values of this parameter. This result is also observed for the theory with arbitrary potential if the mass of the scalar field is very light. For a very heavy scalar field, however, there is no such limit on the value of this parameter and there are ranges of this parameter where these contributions may become relevant in these scales. Galactic and intergalactic dynamics is also discussed for these theories at the latter part of the paper with similar conclusions.

Integrability conditions for Killing-Yano tensors and conformal Killing-Yano tensors

NASA Astrophysics Data System (ADS)

Batista, Carlos

2015-01-01

The integrability conditions for the existence of a conformal Killing-Yano tensor of arbitrary order are worked out in all dimensions and expressed in terms of the Weyl tensor. As a consequence, the integrability conditions for the existence of a Killing-Yano tensor are also obtained. By means of such conditions, it is shown that in certain Einstein spaces one can use a conformal Killing-Yano tensor of order p to generate a Killing-Yano tensor of order (p -1 ) . Finally, it is proved that in maximally symmetric spaces the covariant derivative of a Killing-Yano tensor is a closed conformal Killing-Yano tensor and that every conformal Killing-Yano tensor is uniquely decomposed as the sum of a Killing-Yano tensor and a closed conformal Killing-Yano tensor.

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

Baleanu, Dumitru; Institute of Space Sciences, P.O. Box MG-6, Magurele-Bucharest

The geodesic motion of pseudo-classical spinning particles in extended Euclidean Taub-NUT space was analyzed. The non-generic symmetries of Taub-NUT was investigated. We found new non-generic symmetries in the presence of electromagnetic field like a monopole.

Calculating observables in inhomogeneous cosmologies. Part I: general framework

NASA Astrophysics Data System (ADS)

Hellaby, Charles; Walters, Anthony

2018-02-01

We lay out a general framework for calculating the variation of a set of cosmological observables, down the past null cone of an arbitrarily placed observer, in a given arbitrary inhomogeneous metric. The observables include redshift, proper motions, area distance and redshift-space density. Of particular interest are observables that are zero in the spherically symmetric case, such as proper motions. The algorithm is based on the null geodesic equation and the geodesic deviation equation, and it is tailored to creating a practical numerical implementation. The algorithm provides a method for tracking which light rays connect moving objects to the observer at successive times. Our algorithm is applied to the particular case of the Szekeres metric. A numerical implementation has been created and some results will be presented in a subsequent paper. Future work will explore the range of possibilities.

Geodesic Distance Algorithm for Extracting the Ascending Aorta from 3D CT Images

PubMed Central

Jang, Yeonggul; Jung, Ho Yub; Hong, Youngtaek; Cho, Iksung; Shim, Hackjoon; Chang, Hyuk-Jae

2016-01-01

This paper presents a method for the automatic 3D segmentation of the ascending aorta from coronary computed tomography angiography (CCTA). The segmentation is performed in three steps. First, the initial seed points are selected by minimizing a newly proposed energy function across the Hough circles. Second, the ascending aorta is segmented by geodesic distance transformation. Third, the seed points are effectively transferred through the next axial slice by a novel transfer function. Experiments are performed using a database composed of 10 patients' CCTA images. For the experiment, the ground truths are annotated manually on the axial image slices by a medical expert. A comparative evaluation with state-of-the-art commercial aorta segmentation algorithms shows that our approach is computationally more efficient and accurate under the DSC (Dice Similarity Coefficient) measurements. PMID:26904151

Projective flatness in the quantisation of bosons and fermions

NASA Astrophysics Data System (ADS)

Wu, Siye

2015-07-01

We compare the quantisation of linear systems of bosons and fermions. We recall the appearance of projectively flat connection and results on parallel transport in the quantisation of bosons. We then discuss pre-quantisation and quantisation of fermions using the calculus of fermionic variables. We define a natural connection on the bundle of Hilbert spaces and show that it is projectively flat. This identifies, up to a phase, equivalent spinor representations constructed by various polarisations. We introduce the concept of metaplectic correction for fermions and show that the bundle of corrected Hilbert spaces is naturally flat. We then show that the parallel transport in the bundle of Hilbert spaces along a geodesic is a rescaled projection provided that the geodesic lies within the complement of a cut locus. Finally, we study the bundle of Hilbert spaces when there is a symmetry.

Geodesics In A Spinning String Spacetime

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

Culetu, Hristu

2006-11-28

The geodesics equations for a rotating observer in a spinning string geometry are investigated using the Euler - Lagrange equations. For test particles with vanishing angular momentum, the radial equation of motion does not depend on the angular velocity {omega} but on the angular momentum of the string. A massless particle moves tachyonic but iteed tends asymptotically to unit velocity after a time of the order of few Planck time b. The spacetime has a horizon at r = 0, irrespective of the value of {omega} but its angular velocity is given by {omega} - 1/b. The Sagnac time delaymore » is computed proving to depend both on {omega} and the radius of the circular orbit. The velocity of an ingoing massive test particle approaches zero very close to the spinning string, as if it were rejected by it.« less

Global two-fluid simulations of geodesic acoustic modes in strongly shaped tight aspect ratio tokamak plasmas

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

Robinson, J. R.; Hnat, B.; Thyagaraja, A.

2013-05-15

Following recent observations suggesting the presence of the geodesic acoustic mode (GAM) in ohmically heated discharges in the Mega Amp Spherical Tokamak (MAST) [J. R. Robinson et al., Plasma Phys. Controlled Fusion 54, 105007 (2012)], the behaviour of the GAM is studied numerically using the two fluid, global code CENTORI [P. J. Knight et al. Comput. Phys. Commun. 183, 2346 (2012)]. We examine mode localisation and effects of magnetic geometry, given by aspect ratio, elongation, and safety factor, on the observed frequency of the mode. An excellent agreement between simulations and experimental data is found for simulation plasma parameters matchedmore » to those of MAST. Increasing aspect ratio yields good agreement between the GAM frequency found in the simulations and an analytical result obtained for elongated large aspect ratio plasmas.« less

On the Penrose inequality along null hypersurfaces

NASA Astrophysics Data System (ADS)

Mars, Marc; Soria, Alberto

2016-06-01

The null Penrose inequality, i.e. the Penrose inequality in terms of the Bondi energy, is studied by introducing a functional on surfaces and studying its properties along a null hypersurface Ω extending to past null infinity. We prove a general Penrose-type inequality which involves the limit at infinity of the Hawking energy along a specific class of geodesic foliations called Geodesic Asymptotically Bondi (GAB), which are shown to always exist. Whenever this foliation approaches large spheres, this inequality becomes the null Penrose inequality and we recover the results of Ludvigsen-Vickers (1983 J. Phys. A: Math. Gen. 16 3349-53) and Bergqvist (1997 Class. Quantum Grav. 14 2577-83). By exploiting further properties of the functional along general geodesic foliations, we introduce an approach to the null Penrose inequality called the Renormalized Area Method and find a set of two conditions which imply the validity of the null Penrose inequality. One of the conditions involves a limit at infinity and the other a restriction on the spacetime curvature along the flow. We investigate their range of applicability in two particular but interesting cases, namely the shear-free and vacuum case, where the null Penrose inequality is known to hold from the results by Sauter (2008 PhD Thesis Zürich ETH), and the case of null shells propagating in the Minkowski spacetime. Finally, a general inequality bounding the area of the quasi-local black hole in terms of an asymptotic quantity intrinsic of Ω is derived.

Critical phenomena at the threshold of immediate merger in binary black hole systems: The extreme mass ratio case

NASA Astrophysics Data System (ADS)

Gundlach, Carsten; Akcay, Sarp; Barack, Leor; Nagar, Alessandro

2012-10-01

In numerical simulations of black hole binaries, Pretorius and Khurana [Classical Quantum Gravity 24, S83 (2007)CQGRDG0264-938110.1088/0264-9381/24/12/S07] have observed critical behavior at the threshold between scattering and immediate merger. The number of orbits scales as n≃-γln⁡|p-p*| along any one-parameter family of initial data such that the threshold is at p=p*. Hence, they conjecture that in ultrarelativistic collisions almost all the kinetic energy can be converted into gravitational waves if the impact parameter is fine-tuned to the threshold. As a toy model for the binary, they consider the geodesic motion of a test particle in a Kerr black hole spacetime, where the unstable circular geodesics play the role of critical solutions, and calculate the critical exponent γ. Here, we incorporate radiation reaction into this model using the self-force approximation. The critical solution now evolves adiabatically along a sequence of unstable circular geodesic orbits under the effect of the self-force. We confirm that almost all the initial energy and angular momentum are radiated on the critical solution. Our calculation suggests that, even for infinite initial energy, this happens over a finite number of orbits given by n∞≃0.41/η, where η is the (small) mass ratio. We derive expressions for the time spent on the critical solution, number of orbits and radiated energy as functions of the initial energy and impact parameter.

Computing Diffeomorphic Paths for Large Motion Interpolation.

PubMed

Seo, Dohyung; Jeffrey, Ho; Vemuri, Baba C

2013-06-01

In this paper, we introduce a novel framework for computing a path of diffeomorphisms between a pair of input diffeomorphisms. Direct computation of a geodesic path on the space of diffeomorphisms Diff (Ω) is difficult, and it can be attributed mainly to the infinite dimensionality of Diff (Ω). Our proposed framework, to some degree, bypasses this difficulty using the quotient map of Diff (Ω) to the quotient space Diff ( M )/ Diff ( M ) μ obtained by quotienting out the subgroup of volume-preserving diffeomorphisms Diff ( M ) μ . This quotient space was recently identified as the unit sphere in a Hilbert space in mathematics literature, a space with well-known geometric properties. Our framework leverages this recent result by computing the diffeomorphic path in two stages. First, we project the given diffeomorphism pair onto this sphere and then compute the geodesic path between these projected points. Second, we lift the geodesic on the sphere back to the space of diffeomerphisms, by solving a quadratic programming problem with bilinear constraints using the augmented Lagrangian technique with penalty terms. In this way, we can estimate the path of diffeomorphisms, first, staying in the space of diffeomorphisms, and second, preserving shapes/volumes in the deformed images along the path as much as possible. We have applied our framework to interpolate intermediate frames of frame-sub-sampled video sequences. In the reported experiments, our approach compares favorably with the popular Large Deformation Diffeomorphic Metric Mapping framework (LDDMM).

Constraining some Horndeski gravity theories

NASA Astrophysics Data System (ADS)

Bhattacharya, Sourav; Chakraborty, Sumanta

2017-02-01

We discuss two spherically symmetric solutions admitted by the Horndeski (or scalar-tensor) theory in the context of Solar System and astrophysical scenarios. One of these solutions is derived for Einstein-Gauss-Bonnet gravity, while the other originates from the coupling of the Gauss-Bonnet invariant with a scalar field. Specifically, we discuss the perihelion precession and the bending angle of light for these two different spherically symmetric spacetimes derived in Maeda and Dadhich [Phys. Rev. D 75, 044007 (2007), 10.1103/PhysRevD.75.044007] and Sotiriou and Zhou [Phys. Rev. D 90, 124063 (2014), 10.1103/PhysRevD.90.124063], respectively. The latter, in particular, applies only to black-hole spacetimes. We further delineate on the numerical bounds of relevant parameters of these theories from such computations.

SPIDER: Probing the dawn of time from above the clouds

NASA Astrophysics Data System (ADS)

Moncelsi, Lorenzo; Spider Collaboration

2017-11-01

SPIDER is a balloon-borne microwave polarimeter designed to measure cosmological B-modes on degree angular scales in the presence of Galactic foregrounds. With six independent telescopes housing a total of 2000 detectors in the 90 GHz and 150 GHz frequency bands, SPIDER is the most instantaneously-sensitive CMB polarimeter deployed on the sky to date. SPIDER was successfully launched from McMurdo Station, Antarctica in January 2015 and acquired science data for 16 days. We cover the in-flight performance and present highlights from the ongoing data-analysis. After a successful recovery, the SPIDER team is planning the next flight, featuring one foreground-optimized channel at 280GHz, which will allow us constrain the primordial tensor-mode amplitude at the level of r < 0.03 (99% CL), in the presence of foregrounds.

Space-Based Gravitational-Wave Observations as Tools for Testing General Relativity

NASA Technical Reports Server (NTRS)

Will, Clifford M.

2004-01-01

We continued a project, to analyse the ways in which detection and study of gravitational waves could provide quantitative tests of general relativity, with particular emphasis on waves that would be detectable by space-based observatories, such as LISA. This work had three foci: 1) Tests of scalar-tensor theories of gravity that, could be done by analyzing gravitational waves from neutron stars inspiralling into massive black holes, as detectable by LISA; 2) Study of alternative theories of gravity in which the graviton could be massive, and of how gravitational-wave observations by space-based detectors, solar-system tests, and cosmological observations could constrain such theories; and 3) Study of gravitational-radiation back reaction of particles orbiting black holes in general relativity, with emphasis on the effects of spin.

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

Huang, Qing-Guo; Wang, Ke, E-mail: huangqg@itp.ac.cn, E-mail: wangke@itp.ac.cn

The early reionization (ERE) is supposed to be a physical process which happens after recombination, but before the instantaneous reionization caused by the first generation of stars. We investigate the effect of the ERE on the temperature and polarization power spectra of cosmic microwave background (CMB), and adopt principal components analysis (PCA) to model-independently reconstruct the ionization history during the ERE. In addition, we also discuss how the ERE affects the cosmological parameter estimates, and find that the ERE does not impose any significant influences on the tensor-to-scalar ratio r and the neutrino mass at the sensitivities of current experiments.more » The better CMB polarization data can be used to give a tighter constraint on the ERE and might be important for more precisely constraining cosmological parameters in the future.« less

A new Weyl-like tensor of geometric origin

NASA Astrophysics Data System (ADS)

Vishwakarma, Ram Gopal

2018-04-01

A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.

Parameterized post-Newtonian cosmology

NASA Astrophysics Data System (ADS)

Sanghai, Viraj A. A.; Clifton, Timothy

2017-03-01

Einstein’s theory of gravity has been extensively tested on solar system scales, and for isolated astrophysical systems, using the perturbative framework known as the parameterized post-Newtonian (PPN) formalism. This framework is designed for use in the weak-field and slow-motion limit of gravity, and can be used to constrain a large class of metric theories of gravity with data collected from the aforementioned systems. Given the potential of future surveys to probe cosmological scales to high precision, it is a topic of much contemporary interest to construct a similar framework to link Einstein’s theory of gravity and its alternatives to observations on cosmological scales. Our approach to this problem is to adapt and extend the existing PPN formalism for use in cosmology. We derive a set of equations that use the same parameters to consistently model both weak fields and cosmology. This allows us to parameterize a large class of modified theories of gravity and dark energy models on cosmological scales, using just four functions of time. These four functions can be directly linked to the background expansion of the universe, first-order cosmological perturbations, and the weak-field limit of the theory. They also reduce to the standard PPN parameters on solar system scales. We illustrate how dark energy models and scalar-tensor and vector-tensor theories of gravity fit into this framework, which we refer to as ‘parameterized post-Newtonian cosmology’ (PPNC).

Deciphering the role of fluids in early stage rifting from full moment tensor inversion of East African earthquakes

NASA Astrophysics Data System (ADS)

Oliva, S. J. C.; Ebinger, C. J.; Keir, D.; Shillington, D. J.; Chindandali, P. R. N.

2016-12-01

The East African Rift splits around the Archaean Tanzania craton into the magmatic Eastern branch and the mostly amagmatic Western branch, which continues south of the craton. Temporary seismic networks recently deployed in three rift sectors allow for comparison and insights into the early stages of rifting, including areas with lower crustal earthquakes. We analyze earthquakes with ML > 3.5 in the area recorded by CRAFTI (northern Tanzania/Kenya), TANGA (Tanganyika rift), and/or SEGMeNT (Malawi rift) networks. For events not well enclosed by these arrays, nearby permanent stations are used to improve azimuthal coverage when possible. We present source mechanisms as well as better-constrained source depth estimates from moment tensor inversion using Dreger and Ford TDMT algorithm (Dreger, 2003; Minson & Dreger, 2008). Data and synthetic waveforms are bandpass filtered between 0.02 to 0.10 Hz, or a narrower frequency band within this range, depending on lake noise, which can interfere strongly on the lower end of this frequency range. Results suggest local stress reorientations as well as significant dilatation components on some events within magmatic rift sectors. The implications of these results for crustal rheology and magmatic modification will be discussed in light of the growing complementary data sets from the three projects to inform our understanding of early rifting as a whole.

TASI Lectures on Cosmological Observables and String Theory

NASA Astrophysics Data System (ADS)

Silverstein, Eva

These lectures provide an updated pedagogical treatment of the theoretical structure and phenomenology of some basic mechanisms for inflation, along with an overview of the structure of cosmological uplifts of holographic duality. A full treatment of the problem requires `ultraviolet completion' because of the sensitivity of inflation to quantum gravity effects, including back reaction and non-adiabatic production of heavy degrees of freedom. Cosmological observations imply accelerated expansion of the late universe, and provide increasingly precise constraints and discovery potential on the amplitude and shape of primordial tensor and scalar perturbations, and some of their correlation functions. Most backgrounds of string theory have positive potential energy, with a rich but still highly constrained landscape of solutions. The theory contains novel mechanisms for inflation, some subject to significant observational tests, with highly UV-sensitive tensor mode measurements being a prime example along with certain shapes of primordial correlation functions. Although the detailed ultraviolet completion is not accessible experimentally, some of these mechanisms directly stimulate a more systematic analysis of the space of low energy theories and signatures relevant for analysis of data, which is sensitive to physics orders of magnitude above the energy scale of inflation as a result of long time evolution (dangerous irrelevance) and the substantial amount of data (allowing constraints on quantities with signal/noise. Portions of these lectures appeared previously in Les Houches 2013, "Post-Planck Cosmology".

Damped regional-scale stress inversions: Methodology and examples for southern California and the Coalinga aftershock sequence

USGS Publications Warehouse

Hardebeck, J.L.; Michael, A.J.

2006-01-01

We present a new focal mechanism stress inversion technique to produce regional-scale models of stress orientation containing the minimum complexity necessary to fit the data. Current practice is to divide a region into small subareas and to independently fit a stress tensor to the focal mechanisms of each subarea. This procedure may lead to apparent spatial variability that is actually an artifact of overfitting noisy data or nonuniquely fitting data that does not completely constrain the stress tensor. To remove these artifacts while retaining any stress variations that are strongly required by the data, we devise a damped inversion method to simultaneously invert for stress in all subareas while minimizing the difference in stress between adjacent subareas. This method is conceptually similar to other geophysical inverse techniques that incorporate damping, such as seismic tomography. In checkerboard tests, the damped inversion removes the stress rotation artifacts exhibited by an undamped inversion, while resolving sharper true stress rotations than a simple smoothed model or a moving-window inversion. We show an example of a spatially damped stress field for southern California. The methodology can also be used to study temporal stress changes, and an example for the Coalinga, California, aftershock sequence is shown. We recommend use of the damped inversion technique for any study examining spatial or temporal variations in the stress field.

Development of the Tensoral Computer Language

NASA Technical Reports Server (NTRS)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

Contraction coefficients for noisy quantum channels

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

Hiai, Fumio, E-mail: hiai.fumio@gmail.com; Ruskai, Mary Beth, E-mail: ruskai@member.ams.org

Generalized relative entropy, monotone Riemannian metrics, geodesic distance, and trace distance are all known to decrease under the action of quantum channels. We give some new bounds on, and relationships between, the maximal contraction for these quantities.

Databases post-processing in Tensoral

NASA Technical Reports Server (NTRS)

Dresselhaus, Eliot

1994-01-01

The Center for Turbulent Research (CTR) post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, introduced in this document and currently existing in prototype form, is the foundation of this effort. Tensoral provides a convenient and powerful protocol to connect users who wish to analyze fluids databases with the authors who generate them. In this document we introduce Tensoral and its prototype implementation in the form of a user's guide. This guide focuses on use of Tensoral for post-processing turbulence databases. The corresponding document - the Tensoral 'author's guide' - which focuses on how authors can make databases available to users via the Tensoral system - is currently unwritten. Section 1 of this user's guide defines Tensoral's basic notions: we explain the class of problems at hand and how Tensoral abstracts them. Section 2 defines Tensoral syntax for mathematical expressions. Section 3 shows how these expressions make up Tensoral statements. Section 4 shows how Tensoral statements and expressions are embedded into other computer languages (such as C or Vectoral) to make Tensoral programs. We conclude with a complete example program.

The 1/ N Expansion of Tensor Models with Two Symmetric Tensors

NASA Astrophysics Data System (ADS)

Gurau, Razvan

2018-06-01

It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.

The Weyl curvature tensor, Cotton-York tensor and gravitational waves: A covariant consideration

NASA Astrophysics Data System (ADS)

Osano, Bob

1 + 3 covariant approach to cosmological perturbation theory often employs the electric part (Eab), the magnetic part (Hab) of the Weyl tensor or the shear tensor (σab) in a phenomenological description of gravitational waves. The Cotton-York tensor is rarely mentioned in connection with gravitational waves in this approach. This tensor acts as a source for the magnetic part of the Weyl tensor which should not be neglected in studies of gravitational waves in the 1 + 3 formalism. The tensor is only mentioned in connection with studies of “silent model” but even there the connection with gravitational waves is not exhaustively explored. In this study, we demonstrate that the Cotton-York tensor encodes contributions from both electric and magnetic parts of the Weyl tensor and in directly from the shear tensor. In our opinion, this makes the Cotton-York tensor arguably the natural choice for linear gravitational waves in the 1 + 3 covariant formalism. The tensor is cumbersome to work with but that should negate its usefulness. It is conceivable that the tensor would equally be useful in the metric approach, although we have not demonstrated this in this study. We contend that the use of only one of the Weyl tensor or the shear tensor, although phenomenologically correct, leads to loss of information. Such information is vital particularly when examining the contribution of gravitational waves to the anisotropy of an almost-Friedmann-Lamitre-Robertson-Walker (FLRW) universe. The recourse to this loss is the use Cotton-York tensor.

Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.

PubMed

Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N

2017-05-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

NASA Astrophysics Data System (ADS)

Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.

2018-05-01

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

Focal mechanisms and tidal modulation for tectonic tremors in Taiwan

NASA Astrophysics Data System (ADS)

Ide, S.; Yabe, S.; Tai, H. J.; Chen, K. H.

2015-12-01

Tectonic tremors in Taiwan have been discovered beneath the southern Central Range, but their hosting structure has been unknown. Here we constrain the focal mechanism of underground deformation related to tremors, using moment tensor inversion in the very low frequency band and tidal stress analysis. Three types of seismic data are used for two analysis steps: detection of tremors and the moment tensor inversion. Short-period seismograms from CWBSN are used for tremor detection. Broadband seismograms from BATS and the TAIGER project are used for both steps. About 1000 tremors were detected using an envelope correlation method in the high frequency band (2-8 Hz). Broadband seismograms are stacked relative to the tremor timing, and inverted for a moment tensor in the low frequency band (0.02-0.05 Hz). The best solution was obtained at 32 km depth, as a double-couple consistent with a low-angle thrust fault dipping to the east-southeast, or a high-angle thrust with a south-southwest strike. Almost all tremors occur when tidal shear stress is positive and normal stress is negative (clamping). Since the clamping stress is high for a high-angle thrust fault, the low-angle thrust fault is more likely to be the fault plane. Tremor rate increases non-linearly with increasing shear stress, suggesting a velocity strengthening friction law. The high tidal sensitivity is inconsistent with horizontal slip motion suggested by previous studies, and normal faults that dominates regional shallow earthquakes. Our results favor thrust slip on a low-angle fault dipping to the east-southeast, consistent with the subduction of the Eurasian plate. The tremor region is characterized by a deep thermal anomaly with decrease normal stress. This region has also experienced enough subduction to produce metamorphic fluids. A large amount of fluid and low vertical stress may explain the high tidal sensitivity.

Moment tensor and location of seismic events in the 2017 DPRK test

NASA Astrophysics Data System (ADS)

Wei, S.; Shi, Q.; Chen, Q. F.; Wang, T.

2017-12-01

The main seismic event in the 2017 DPRK test was followed by a secondary event about eight minutes later. We conducted waveform analysis on the regional broadband waveform data to better constrain the moment tensor and location of these two events, to further understand their relations. In the first place, we applied the generalized Cut-And-Paste (gCAP) method to the regional data to invert the full moment tensor solutions of the two events. Our long period (0.02-0.08 Hz for Pnl, 0.02-0.055 Hz for surface waves) inversions show that the main event was composed of large positive ISO component ( 90% of the total moment) and has a moment magnitude of 5.4. In contrast, the second event shows large negative ISO component ( 50% of the total moment) with a moment magnitude of 4.5. Although there are trade-offs between the CLVD and the ISO component for the second event, chiefly caused by the coda waves from the first event, the result is more robust if we force a small CVLD component in the inversion. We also relocated the epicenter of the second event using P-wave first arrival picks, relative to the location of the first event, which has been accurately determined from the high-resolution geodetic data. The calibration from the first event allows us to precisely locate the second event, which shows an almost identical location to the first event. After a polarity correction, their high-frequency ( 0.25 - 0.9 Hz) regional surface waves also display high similarity, supporting the similar location but opposite ISO polarity of the two events. Our results suggest that the second event was likely to be caused by the collapsing after the main event, in agreement with the surface displacement derived from geodetic observation and modeling results.

Constraining Nonperturbative Strong-Field Effects in Scalar-Tensor Gravity by Combining Pulsar Timing and Laser-Interferometer Gravitational-Wave Detectors

NASA Astrophysics Data System (ADS)

Shao, Lijing; Sennett, Noah; Buonanno, Alessandra; Kramer, Michael; Wex, Norbert

2017-10-01

Pulsar timing and laser-interferometer gravitational-wave (GW) detectors are superb laboratories to study gravity theories in the strong-field regime. Here, we combine these tools to test the mono-scalar-tensor theory of Damour and Esposito-Farèse (DEF), which predicts nonperturbative scalarization phenomena for neutron stars (NSs). First, applying Markov-chain Monte Carlo techniques, we use the absence of dipolar radiation in the pulsar-timing observations of five binary systems composed of a NS and a white dwarf, and eleven equations of state (EOSs) for NSs, to derive the most stringent constraints on the two free parameters of the DEF scalar-tensor theory. Since the binary-pulsar bounds depend on the NS mass and the EOS, we find that current pulsar-timing observations leave scalarization windows, i.e., regions of parameter space where scalarization can still be prominent. Then, we investigate if these scalarization windows could be closed and if pulsar-timing constraints could be improved by laser-interferometer GW detectors, when spontaneous (or dynamical) scalarization sets in during the early (or late) stages of a binary NS (BNS) evolution. For the early inspiral of a BNS carrying constant scalar charge, we employ a Fisher-matrix analysis to show that Advanced LIGO can improve pulsar-timing constraints for some EOSs, and next-generation detectors, such as the Cosmic Explorer and Einstein Telescope, will be able to improve those bounds for all eleven EOSs. Using the late inspiral of a BNS, we estimate that for some of the EOSs under consideration, the onset of dynamical scalarization can happen early enough to improve the constraints on the DEF parameters obtained by combining the five binary pulsars. Thus, in the near future, the complementarity of pulsar timing and direct observations of GWs on the ground will be extremely valuable in probing gravity theories in the strong-field regime.

Old torsion Balance Observations - too old for modern Exploration?

NASA Astrophysics Data System (ADS)

Götze, H.-J.

2003-04-01

Gravity gradiometry is a new gravity measurement technology that could fundamentally change the game of subsurface modelling and enhance geological interpretations: at fully inertial stabilized platforms they provide observed components of the E&{uml;o}tv&{uml;o}s tensor for 3D interpretations in mining and oil exploration and other fields of pure and applied geophysics. Although gravity gradiometry was among the first geophysical methods used successfully in applied Geophysics (E&{uml;o}tv&{uml;o}s torsion balance), the technology fell from favour in the 1930s. From this time measurements, done by torsion balances (Drehwaagen), are presented here which were observed to detect salt domes in the Northwest German basin. The data were digitized from old copies, then reprocessed and recalculated to draw Bouguer anomaly maps. However, the second derivatives of the gravity potential provide also independent data which can be used to constrain forward modelling. 3D modelling of Vxz, Vyz and other components of the E&{uml;o}tv&{uml;o}s tensor provide better insight into the geometry of the salt dome structure than modelling of the Bouguer gravity field. In addition to this first example results from gravity data processing by applying curvature techniques and again 3D forward modelling of second derivatives of the potential of density domains in the uppermost crust in the area of the Dead Sea Transform (Jordan) is presented here. The 3D modelling is conducted by the program package IGMAS which supply possibilities to calculate potential, gravity, its components and the Eötvös tensor components. Based on results so far one can conclude that the knowledge of the "second derivatives of the potential" could fundamentally change the role of gravity field measurements in the process of underground investigations not only for resource exploration but for investigations along large faults systems.

Regional Moment Tensor Analysis of Earthquakes in Iran for 2010 to 2017 Using In-Country Data

NASA Astrophysics Data System (ADS)

Graybeal, D.; Braunmiller, J.

2017-12-01

Located in the middle of the Arabia-Eurasia continental collision, Iran is one of the most tectonically diverse and seismically active countries in the world. Until recently, however, seismic source parameter studies had to rely on teleseismic data or on data from temporary local arrays, which limited the scope of investigations. Relatively new broadband seismic networks operated by the Iranian Institute of Engineering Seismology (IIEES) and the Iranian Seismological Center (IRSC) currently consist of more than 100 stations and allow, for the first time, routine three-component full-waveform regional moment tensor analysis of the numerous M≥4.0 earthquakes that occur throughout the country. We use openly available, in-country data and include data from nearby permanent broadband stations available through IRIS and EIDA to improve azimuthal coverage for events in border regions. For the period from 2010 to 2017, we have obtained about 500 moment tensors for earthquakes ranging from Mw=3.6 to 7.8. The resulting database provides a unique, detailed view of deformation styles and earthquake depths in Iran. Overall, we find mainly thrust and strike-slip mechanisms as expected considering the convergent tectonic setting. Our magnitudes (Mw) are slightly smaller than ML and mb but comparable to Mw as reported in global catalogs (USGS ANSS). Event depths average about 3 km shallower than in global catalogs and are well constrained considering the capability of regional waveforms to resolve earthquake depth. Our dataset also contains several large magnitude main shock-aftershock sequences from different tectonic provinces, including the 2012 Ahar-Varzeghan (Mw=6.4), 2013 Kaki (Mw=6.5), and 2014 Murmuri (Mw=6.2) earthquakes. The most significant result in terms of seismogenesis and seismic hazard is that the vast majority of earthquakes occur at shallow depth, not in deeper basement. Our findings indicate that more than 80% of crustal seismicity in Iran likely occurs at depths of 12 km or less.

Constraining the Dynamic Rupture Properties with Moment Tensor Derived Vp/Vs Ratios.

NASA Astrophysics Data System (ADS)

Smith-Boughner, L.; Baig, A. M.; Urbancic, T.; Viegas, G. F.

2014-12-01

The goal of hydraulic fracturing is to increase the permeability of rocks to extract hydrocarbons from "tight" formations. This process stimulates fluid-driven fractures which induce microseismic events. Successfully treating the formations, stimulating large volumes of the reservoir, depends on targeting parts of the formation with more "brittleness", a property which is frequently characterized from the mechanical properties of the rock. Typically, these properties are constrained using well-logs, vertical seismic profiles and 3-D seismic surveys. Such tools provide a static view of the reservoir on very large or very small scales. While lithology controls the average rock strength within a unit, the content (gas or fluid filled), the shape of the pore space and the concentration of micro-fractures alters the mechanical properties of the reservoir. Seismic moment tensor inversion of the events generated during these stimulations reveals that they are significantly non-double-couple, and are described by a tensile angle and a Poisson's ratio (or, equivalently, ratio of shear to compressional velocities, Vp/Vs) of the rock-fracture system. Following Vavryčuk (2011), the mechanical properties of the reservoir (i.e. Vp/Vs ratio) are estimated as the hydraulic fracture progresses from an extensive catalog of microseismic events spanning magnitudes of -1.5 to 0.8 in the Horn-River Basin, Canada. Studying several fracture stages in the reservoir reveals temporal and spatial variations in the rock strength within a unit as hydraulic fracturing proceeds. Initially, the estimated values of Vp/Vs are quite close to those determined from 3-D seismic surveys. As the stage progresses, previously fractured regions have lower Vp/Vs values. At the onset of maximum treating pressure, regions have anomalously high Vp/Vs values, which could reflect short-term local concentrations of high pore pressures or other interactions of the treatment with the formation. The relationship between source parameters and variations in Vp/Vs are also examined. This technique has the potential to provide a unique and dynamic view of variations in the reservoir both spatially and temporally.

Estimating Stresses, Fault Friction and Fluid Pressure from Topography and Coseismic Slip Models

NASA Astrophysics Data System (ADS)

Styron, R. H.; Hetland, E. A.

2014-12-01

Stress is a first-order control on the deformation state of the earth. However, stress is notoriously hard to measure, and researchers typically only estimate the directions and relative magnitudes of principal stresses, with little quantification of the uncertainties or absolute magnitude. To improve upon this, we have developed methods to constrain the full stress tensor field in a region surrounding a fault, including tectonic, topographic, and lithostatic components, as well as static friction and pore fluid pressure on the fault. Our methods are based on elastic halfspace techniques for estimating topographic stresses from a DEM, and we use a Bayesian approach to estimate accumulated tectonic stress, fluid pressure, and friction from fault geometry and slip rake, assuming Mohr-Coulomb fault mechanics. The nature of the tectonic stress inversion is such that either the stress maximum or minimum is better constrained, depending on the topography and fault deformation style. Our results from the 2008 Wenchuan event yield shear stresses from topography up to 20 MPa (normal-sinistral shear sense) and topographic normal stresses up to 80 MPa on the faults; tectonic stress had to be large enough to overcome topography to produce the observed reverse-dextral slip. Maximum tectonic stress is constrained to be >0.3 * lithostatic stress (depth-increasing), with a most likely value around 0.8, trending 90-110°E. Minimum tectonic stress is about half of maximum. Static fault friction is constrained at 0.1-0.4, and fluid pressure at 0-0.6 * total pressure on the fault. Additionally, the patterns of topographic stress and slip suggest that topographic normal stress may limit fault slip once failure has occurred. Preliminary results from the 2013 Balochistan earthquake are similar, but yield stronger constraints on the upper limits of maximum tectonic stress, as well as tight constraints on the magnitude of minimum tectonic stress and stress orientation. Work in progress on the Wasatch fault suggests that maximum tectonic stress may also be able to be constrained, and that some of the shallow rupture segmentation may be due in part to localized topographic loading. Future directions of this work include regions where high relief influences fault kinematics (such as Tibet).

Tensor Algebra Library for NVidia Graphics Processing Units

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

Liakh, Dmitry

This is a general purpose math library implementing basic tensor algebra operations on NVidia GPU accelerators. This software is a tensor algebra library that can perform basic tensor algebra operations, including tensor contractions, tensor products, tensor additions, etc., on NVidia GPU accelerators, asynchronously with respect to the CPU host. It supports a simultaneous use of multiple NVidia GPUs. Each asynchronous API function returns a handle which can later be used for querying the completion of the corresponding tensor algebra operation on a specific GPU. The tensors participating in a particular tensor operation are assumed to be stored in local RAMmore » of a node or GPU RAM. The main research area where this library can be utilized is the quantum many-body theory (e.g., in electronic structure theory).« less

Retrospective Correction of Physiological Noise in DTI Using an Extended Tensor Model and Peripheral Measurements

PubMed Central

Mohammadi, Siawoosh; Hutton, Chloe; Nagy, Zoltan; Josephs, Oliver; Weiskopf, Nikolaus

2013-01-01

Diffusion tensor imaging is widely used in research and clinical applications, but this modality is highly sensitive to artefacts. We developed an easy-to-implement extension of the original diffusion tensor model to account for physiological noise in diffusion tensor imaging using measures of peripheral physiology (pulse and respiration), the so-called extended tensor model. Within the framework of the extended tensor model two types of regressors, which respectively modeled small (linear) and strong (nonlinear) variations in the diffusion signal, were derived from peripheral measures. We tested the performance of four extended tensor models with different physiological noise regressors on nongated and gated diffusion tensor imaging data, and compared it to an established data-driven robust fitting method. In the brainstem and cerebellum the extended tensor models reduced the noise in the tensor-fit by up to 23% in accordance with previous studies on physiological noise. The extended tensor model addresses both large-amplitude outliers and small-amplitude signal-changes. The framework of the extended tensor model also facilitates further investigation into physiological noise in diffusion tensor imaging. The proposed extended tensor model can be readily combined with other artefact correction methods such as robust fitting and eddy current correction. PMID:22936599

Testing for a cosmological influence on local physics using atomic and gravitational clocks

NASA Technical Reports Server (NTRS)

Adams, P. J.; Hellings, R. W.; Canuto, V. M.; Goldman, I.

1983-01-01

The existence of a possible influence of the large-scale structure of the universe on local physics is discussed. A particular realization of such an influence is discussed in terms of the behavior in time of atomic and gravitational clocks. Two natural categories of metric theories embodying a cosmic infuence exist. The first category has geodesic equations of motion in atomic units, while the second category has geodesic equations of motion in gravitational units. Equations of motion for test bodies are derived for both categories of theories in the appropriate parametrized post-Newtonian limit and are applied to the Solar System. Ranging data to the Viking lander on Mars are of sufficient precision to reveal (1) if such a cosmological influence exists at the level of Hubble's constant, and (2) which category of theories is appropriate for a descripton of the phenomenon.

Saturation of energetic-particle-driven geodesic acoustic modes due to wave-particle nonlinearity

NASA Astrophysics Data System (ADS)

Biancalani, A.; Chavdarovski, I.; Qiu, Z.; Bottino, A.; Del Sarto, D.; Ghizzo, A.; Gürcan, Ö.; Morel, P.; Novikau, I.

2017-12-01

The nonlinear dynamics of energetic-particle (EP) driven geodesic acoustic modes (EGAM) is investigated here. A numerical analysis with the global gyrokinetic particle-in-cell code ORB5 is performed, and the results are interpreted with the analytical theory, in close comparison with the theory of the beam-plasma instability. Only axisymmetric modes are considered, with a nonlinear dynamics determined by wave-particle interaction. Quadratic scalings of the saturated electric field with respect to the linear growth rate are found for the case of interest. As a main result, the formula for the saturation level is provided. Near the saturation, we observe a transition from adiabatic to non-adiabatic dynamics, i.e. the frequency chirping rate becomes comparable to the resonant EP bounce frequency. The numerical analysis is performed here with electrostatic simulations with circular flux surfaces, and kinetic effects of the electrons are neglected.

Minimal conditions for the existence of a Hawking-like flux

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

Barcelo, Carlos; Liberati, Stefano; Sonego, Sebastiano

2011-02-15

We investigate the minimal conditions that an asymptotically flat general relativistic spacetime must satisfy in order for a Hawking-like Planckian flux of particles to arrive at future null infinity. We demonstrate that there is no requirement that any sort of horizon form anywhere in the spacetime. We find that the irreducible core requirement is encoded in an approximately exponential 'peeling' relationship between affine coordinates on past and future null infinity. As long as a suitable adiabaticity condition holds, then a Planck-distributed Hawking-like flux will arrive at future null infinity with temperature determined by the e-folding properties of the outgoing nullmore » geodesics. The temperature of the Hawking-like flux can slowly evolve as a function of time. We also show that the notion of peeling of null geodesics is distinct from the usual notion of 'inaffinity' used in Hawking's definition of surface gravity.« less

Hawking Radiation of the Charged Particle Via Tunneling from the Reissner-Nordström Black Hole

NASA Astrophysics Data System (ADS)

Pu, Jin; Han, Yan

2017-08-01

Since Parikh and Wilczek proposed a semiclassical tunneling method to investigate the Hawking radiation of static and spherically symmetric black holes, the method has been extensively developed to study various black holes. However, in almost all of the subsequent papers, there exists a important shortcoming that the geodesic equation of the massive particle is defined inconsistently with that of the massless particle. In this paper, we propose a new idea to reinvestigate the tunneling radiation from the event horizon of the Reissner-Nordström black hole. In our treatment, by starting from the Lagrangian analysis on the action, we redefine the geodesic equation of the massive and massless particle via tunneling from the event horizon of the Reissner-Nordström black hole, which overcomes the shortcoming mentioned above. The highlight of our work is a new and important development for the Parikh-Wilczek's semiclassical tunneling method.

Chirping and Sudden Excitation of Energetic-Particle-Driven Geodesic Acoustic Modes in a Large Helical Device Experiment

NASA Astrophysics Data System (ADS)

Wang, Hao; Todo, Yasushi; Ido, Takeshi; Suzuki, Yasuhiro

2018-04-01

Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.

Chirping and Sudden Excitation of Energetic-Particle-Driven Geodesic Acoustic Modes in a Large Helical Device Experiment.

PubMed

Wang, Hao; Todo, Yasushi; Ido, Takeshi; Suzuki, Yasuhiro

2018-04-27

Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.

Comprehensive comparisons of geodesic acoustic mode characteristics and dynamics between Tore Supra experiments and gyrokinetic simulations

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

Storelli, A., E-mail: alexandre.storelli@lpp.polytechnique.fr; Vermare, L.; Hennequin, P.

2015-06-15

In a dedicated collisionality scan in Tore Supra, the geodesic acoustic mode (GAM) is detected and identified with the Doppler backscattering technique. Observations are compared to the results of a simulation with the gyrokinetic code GYSELA. We found that the GAM frequency in experiments is lower than predicted by simulation and theory. Moreover, the disagreement is higher in the low collisionality scenario. Bursts of non harmonic GAM oscillations have been characterized with filtering techniques, such as the Hilbert-Huang transform. When comparing this dynamical behaviour between experiments and simulation, the probability density function of GAM amplitude and the burst autocorrelation timemore » are found to be remarkably similar. In the simulation, where the radial profile of GAM frequency is continuous, we observed a phenomenon of radial phase mixing of the GAM oscillations, which could influence the burst autocorrelation time.« less

Low-Dimensional Statistics of Anatomical Variability via Compact Representation of Image Deformations.

PubMed

Zhang, Miaomiao; Wells, William M; Golland, Polina

2016-10-01

Using image-based descriptors to investigate clinical hypotheses and therapeutic implications is challenging due to the notorious "curse of dimensionality" coupled with a small sample size. In this paper, we present a low-dimensional analysis of anatomical shape variability in the space of diffeomorphisms and demonstrate its benefits for clinical studies. To combat the high dimensionality of the deformation descriptors, we develop a probabilistic model of principal geodesic analysis in a bandlimited low-dimensional space that still captures the underlying variability of image data. We demonstrate the performance of our model on a set of 3D brain MRI scans from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database. Our model yields a more compact representation of group variation at substantially lower computational cost than models based on the high-dimensional state-of-the-art approaches such as tangent space PCA (TPCA) and probabilistic principal geodesic analysis (PPGA).

A Time-Space Symmetry Based Cylindrical Model for Quantum Mechanical Interpretations

NASA Astrophysics Data System (ADS)

Vo Van, Thuan

2017-12-01

Following a bi-cylindrical model of geometrical dynamics, our study shows that a 6D-gravitational equation leads to geodesic description in an extended symmetrical time-space, which fits Hubble-like expansion on a microscopic scale. As a duality, the geodesic solution is mathematically equivalent to the basic Klein-Gordon-Fock equations of free massive elementary particles, in particular, the squared Dirac equations of leptons. The quantum indeterminism is proved to have originated from space-time curvatures. Interpretation of some important issues of quantum mechanical reality is carried out in comparison with the 5D space-time-matter theory. A solution of lepton mass hierarchy is proposed by extending to higher dimensional curvatures of time-like hyper-spherical surfaces than one of the cylindrical dynamical geometry. In a result, the reasonable charged lepton mass ratios have been calculated, which would be tested experimentally.

Fullerene-like chemistry at the interior carbon atoms of an alkene-centered C26H12 geodesic polyarene.

PubMed

Bronstein, Hindy E; Scott, Lawrence T

2008-01-04

The title compound (1) undergoes 1,2-addition reactions of both electrophilic and nucleophilic reagents preferentially at the "interior" carbon atoms of the central 6:6-bond to give fullerene-type adducts 2, 3, 4, and 5. Such fullerene-like chemistry is unprecedented for a topologically 2-dimensional polycyclic aromatic hydrocarbon and qualifies this geodesic polyarene as a "bridge" between the old flat world of polycyclic aromatic hydrocarbons (PAHs) and the new round world of fullerenes. The relief of pyramidalization strain, as in the addition reactions of fullerenes, presumably contributes to the atypical mode of reactivity seen in 1. Molecular orbital calculations, however, reveal features of the nonalternant pi system in 1 that may also play an important role. Thus, the fullerene-like chemistry of 1 may be driven by two or more factors, the relative importances of which are difficult to discern.

A Review of Depth and Normal Fusion Algorithms

PubMed Central

Štolc, Svorad; Pock, Thomas

2018-01-01

Geometric surface information such as depth maps and surface normals can be acquired by various methods such as stereo light fields, shape from shading and photometric stereo techniques. We compare several algorithms which deal with the combination of depth with surface normal information in order to reconstruct a refined depth map. The reasons for performance differences are examined from the perspective of alternative formulations of surface normals for depth reconstruction. We review and analyze methods in a systematic way. Based on our findings, we introduce a new generalized fusion method, which is formulated as a least squares problem and outperforms previous methods in the depth error domain by introducing a novel normal weighting that performs closer to the geodesic distance measure. Furthermore, a novel method is introduced based on Total Generalized Variation (TGV) which further outperforms previous approaches in terms of the geodesic normal distance error and maintains comparable quality in the depth error domain. PMID:29389903

Holographic definition of points and distances

NASA Astrophysics Data System (ADS)

Czech, Bartłomiej; Lamprou, Lampros

2014-11-01

We discuss the way in which field theory quantities assemble the spatial geometry of three-dimensional anti-de Sitter space (AdS3). The field theory ingredients are the entanglement entropies of boundary intervals. A point in AdS3 corresponds to a collection of boundary intervals which is selected by a variational principle we discuss. Coordinates in AdS3 are integration constants of the resulting equation of motion. We propose a distance function for this collection of points, which obeys the triangle inequality as a consequence of the strong subadditivity of entropy. Our construction correctly reproduces the static slice of AdS3 and the Ryu-Takayanagi relation between geodesics and entanglement entropies. We discuss how these results extend to quotients of AdS3 —the conical defect and the BTZ geometries. In these cases, the set of entanglement entropies must be supplemented by other field theory quantities, which can carry the information about lengths of nonminimal geodesics.

Indirect (source-free) integration method. I. Wave-forms from geodesic generic orbits of EMRIs

NASA Astrophysics Data System (ADS)

Ritter, Patxi; Aoudia, Sofiane; Spallicci, Alessandro D. A. M.; Cordier, Stéphane

2016-12-01

The Regge-Wheeler-Zerilli (RWZ) wave-equation describes Schwarzschild-Droste black hole perturbations. The source term contains a Dirac distribution and its derivative. We have previously designed a method of integration in time domain. It consists of a finite difference scheme where analytic expressions, dealing with the wave-function discontinuity through the jump conditions, replace the direct integration of the source and the potential. Herein, we successfully apply the same method to the geodesic generic orbits of EMRI (Extreme Mass Ratio Inspiral) sources, at second order. An EMRI is a Compact Star (CS) captured by a Super-Massive Black Hole (SMBH). These are considered the best probes for testing gravitation in strong regime. The gravitational wave-forms, the radiated energy and angular momentum at infinity are computed and extensively compared with other methods, for different orbits (circular, elliptic, parabolic, including zoom-whirl).

Site-selective covalent functionalization at interior carbon atoms and on the rim of circumtrindene, a C36H12 open geodesic polyarene

PubMed Central

Cho, Hee Yeon; Ansems, Ronald B M

2014-01-01

Summary Circumtrindene (6, C36H12), one of the largest open geodesic polyarenes ever reported, exhibits fullerene-like reactivity at its interior carbon atoms, whereas its edge carbons react like those of planar polycyclic aromatic hydrocarbons (PAHs). The Bingel–Hirsch and Prato reactions – two traditional methods for fullerene functionalization – afford derivatives of circumtrindene with one of the interior 6:6 C=C bonds modified. On the other hand, functionalization on the rim of circumtrindene can be achieved by normal electrophilic aromatic substitution, the most common reaction of planar PAHs. This peripheral functionalization has been used to extend the π-system of the polyarene by subsequent coupling reactions and to probe the magnetic environment of the concave/convex space around the hydrocarbon bowl. For both classes of functionalization, computational results are reported to complement the experimental observations. PMID:24991245

Inside out: meet the operators inside the horizon. On bulk reconstruction behind causal horizons

NASA Astrophysics Data System (ADS)

Almheiri, Ahmed; Anous, Tarek; Lewkowycz, Aitor

2018-01-01

Based on the work of Heemskerk, Marolf, Polchinski and Sully (HMPS), we study the reconstruction of operators behind causal horizons in time dependent geometries obtained by acting with shockwaves on pure states or thermal states. These geometries admit a natural basis of gauge invariant operators, namely those geodesically dressed to the boundary along geodesics which emanate from the bifurcate horizon at constant Rindler time. We outline a procedure for obtaining operators behind the causal horizon but inside the entanglement wedge by exploiting the equality between bulk and boundary time evolution, as well as the freedom to consider the operators evolved by distinct Hamiltonians. This requires we carefully keep track of how the operators are gravitationally dressed and that we address issues regarding background dependence. We compare this procedure to reconstruction using modular flow, and illustrate some formal points in simple cases such as AdS2 and AdS3.

[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].

PubMed

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.

C%2B%2B tensor toolbox user manual.

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

Plantenga, Todd D.; Kolda, Tamara Gibson

2012-04-01

The C++ Tensor Toolbox is a software package for computing tensor decompositions. It is based on the Matlab Tensor Toolbox, and is particularly optimized for sparse data sets. This user manual briefly overviews tensor decomposition mathematics, software capabilities, and installation of the package. Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors in C++. The Toolbox compiles into libraries and is intended for use with custom applications written by users.

Tensor Factorization for Low-Rank Tensor Completion.

PubMed

Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao

2018-03-01

Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.

Similar Tensor Arrays - A Framework for Storage of Tensor Array Data

NASA Astrophysics Data System (ADS)

Brun, Anders; Martin-Fernandez, Marcos; Acar, Burak; Munoz-Moreno, Emma; Cammoun, Leila; Sigfridsson, Andreas; Sosa-Cabrera, Dario; Svensson, Björn; Herberthson, Magnus; Knutsson, Hans

This chapter describes a framework for storage of tensor array data, useful to describe regularly sampled tensor fields. The main component of the framework, called Similar Tensor Array Core (STAC), is the result of a collaboration between research groups within the SIMILAR network of excellence. It aims to capture the essence of regularly sampled tensor fields using a minimal set of attributes and can therefore be used as a “greatest common divisor” and interface between tensor array processing algorithms. This is potentially useful in applied fields like medical image analysis, in particular in Diffusion Tensor MRI, where misinterpretation of tensor array data is a common source of errors. By promoting a strictly geometric perspective on tensor arrays, with a close resemblance to the terminology used in differential geometry, (STAC) removes ambiguities and guides the user to define all necessary information. In contrast to existing tensor array file formats, it is minimalistic and based on an intrinsic and geometric interpretation of the array itself, without references to other coordinate systems.

Electromagnetic stress tensor for an amorphous metamaterial medium

NASA Astrophysics Data System (ADS)

Wang, Neng; Wang, Shubo; Ng, Jack

2018-03-01

We analytically and numerically investigated the internal optical forces exerted by an electromagnetic wave inside an amorphous metamaterial medium. We derived, by using the principle of virtual work, the Helmholtz stress tensor, which takes into account the electrostriction effect. Several examples of amorphous media are considered, and different electromagnetic stress tensors, such as the Einstein-Laub tensor and Minkowski tensor, are also compared. It is concluded that the Helmholtz stress tensor is the appropriate tensor for such systems.

Unsupervised Classification of PolSAR Data Using a Scattering Similarity Measure Derived From a Geodesic Distance

NASA Astrophysics Data System (ADS)

Ratha, Debanshu; Bhattacharya, Avik; Frery, Alejandro C.

2018-01-01

In this letter, we propose a novel technique for obtaining scattering components from Polarimetric Synthetic Aperture Radar (PolSAR) data using the geodesic distance on the unit sphere. This geodesic distance is obtained between an elementary target and the observed Kennaugh matrix, and it is further utilized to compute a similarity measure between scattering mechanisms. The normalized similarity measure for each elementary target is then modulated with the total scattering power (Span). This measure is used to categorize pixels into three categories i.e. odd-bounce, double-bounce and volume, depending on which of the above scattering mechanisms dominate. Then the maximum likelihood classifier of [J.-S. Lee, M. R. Grunes, E. Pottier, and L. Ferro-Famil, Unsupervised terrain classification preserving polarimetric scattering characteristics, IEEE Trans. Geos. Rem. Sens., vol. 42, no. 4, pp. 722731, April 2004.] based on the complex Wishart distribution is iteratively used for each category. Dominant scattering mechanisms are thus preserved in this classification scheme. We show results for L-band AIRSAR and ALOS-2 datasets acquired over San Francisco and Mumbai, respectively. The scattering mechanisms are better preserved using the proposed methodology than the unsupervised classification results using the Freeman-Durden scattering powers on an orientation angle (OA) corrected PolSAR image. Furthermore, (1) the scattering similarity is a completely non-negative quantity unlike the negative powers that might occur in double- bounce and odd-bounce scattering component under Freeman Durden decomposition (FDD), and (2) the methodology can be extended to more canonical targets as well as for bistatic scattering.

Probing the Higgs with angular observables at future e +e – colliders

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

Liu, Zhen

In this paper, I summarize our recent works on using differential observables to explore the physics potential of future e +e – colliders in the framework of Higgs effective field theory. This proceeding is based upon Refs. 1 and 2. We study angular observables in the e +e – → ZHℓ +ℓ –bmore » $$\\bar{b}$$ channel at future circular e +e – colliders such as CEPC and FCC-ee. Taking into account the impact of realistic cut acceptance and detector effects, we forecast the precision of six angular asymmetries at CEPC (FCC-ee) with center-of-mass energy √s = 240 GeV and 5 (30) ab –1 integrated luminosity. We then determine the projected sensitivity to a range of operators relevant for the Higgsstrahlung process in the dimension-6 Higgs EFT. Our results show that angular observables provide complementary sensitivity to rate measurements when constraining various tensor structures arising from new physics. We further find that angular asymmetries provide a novel means of constraining the “blind spot” in indirect limits on supersymmetric scalar top partners. Finally, we also discuss the possibility of using ZZ-fusion at e +e – machines at different energies to probe new operators.« less

A predictive parameter estimation approach for the thermodynamically constrained averaging theory applied to diffusion in porous media

NASA Astrophysics Data System (ADS)

Valdes-Parada, F. J.; Ostvar, S.; Wood, B. D.; Miller, C. T.

2017-12-01

Modeling of hierarchical systems such as porous media can be performed by different approaches that bridge microscale physics to the macroscale. Among the several alternatives available in the literature, the thermodynamically constrained averaging theory (TCAT) has emerged as a robust modeling approach that provides macroscale models that are consistent across scales. For specific closure relation forms, TCAT models are expressed in terms of parameters that depend upon the physical system under study. These parameters are usually obtained from inverse modeling based upon either experimental data or direct numerical simulation at the pore scale. Other upscaling approaches, such as the method of volume averaging, involve an a priori scheme for parameter estimation for certain microscale and transport conditions. In this work, we show how such a predictive scheme can be implemented in TCAT by studying the simple problem of single-phase passive diffusion in rigid and homogeneous porous media. The components of the effective diffusivity tensor are predicted for several porous media by solving ancillary boundary-value problems in periodic unit cells. The results are validated through a comparison with data from direct numerical simulation. This extension of TCAT constitutes a useful advance for certain classes of problems amenable to this estimation approach.

Probing the Higgs with angular observables at future e +e – colliders

DOE PAGES

Liu, Zhen

2016-10-24

In this paper, I summarize our recent works on using differential observables to explore the physics potential of future e +e – colliders in the framework of Higgs effective field theory. This proceeding is based upon Refs. 1 and 2. We study angular observables in the e +e – → ZHℓ +ℓ –bmore » $$\\bar{b}$$ channel at future circular e +e – colliders such as CEPC and FCC-ee. Taking into account the impact of realistic cut acceptance and detector effects, we forecast the precision of six angular asymmetries at CEPC (FCC-ee) with center-of-mass energy √s = 240 GeV and 5 (30) ab –1 integrated luminosity. We then determine the projected sensitivity to a range of operators relevant for the Higgsstrahlung process in the dimension-6 Higgs EFT. Our results show that angular observables provide complementary sensitivity to rate measurements when constraining various tensor structures arising from new physics. We further find that angular asymmetries provide a novel means of constraining the “blind spot” in indirect limits on supersymmetric scalar top partners. Finally, we also discuss the possibility of using ZZ-fusion at e +e – machines at different energies to probe new operators.« less

Tensor Toolbox for MATLAB v. 3.0

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

Kola, Tamara; Bader, Brett W.; Acar Ataman, Evrim NMN

Tensors (also known as multidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to network analysis. The Tensor Toolbox provides classes for manipulating dense, sparse, and structured tensors using MATLAB's object-oriented features. It also provides algorithms for tensor decomposition and factorization, algorithms for computing tensor eigenvalues, and methods for visualization of results.

Reconstructing the microstructure of polyimide-silicalite mixed-matrix membranes and their particle connectivity using FIB-SEM tomography.

PubMed

Diblíková, P; Veselý, M; Sysel, P; Čapek, P

2018-03-01

Properties of a composite material made of a continuous matrix and particles often depend on microscopic details, such as contacts between particles. Focusing on processing raw focused-ion beam scanning electron microscope (FIB-SEM) tomography data, we reconstructed three mixed-matrix membrane samples made of 6FDA-ODA polyimide and silicalite-1 particles. In the first step of image processing, backscattered electron (BSE) and secondary electron (SE) signals were mixed in a ratio that was expected to obtain a segmented 3D image with a realistic volume fraction of silicalite-1. Second, after spatial alignment of the stacked FIB-SEM data, the 3D image was smoothed using adaptive median and anisotropic nonlinear diffusion filters. Third, the image was segmented using the power watershed method coupled with a seeding algorithm based on geodesic reconstruction from the markers. If the resulting volume fraction did not match the target value quantified by chemical analysis of the sample, the BSE and SE signals were mixed in another ratio and the procedure was repeated until the target volume fraction was achieved. Otherwise, the segmented 3D image (replica) was accepted and its microstructure was thoroughly characterized with special attention paid to connectivity of the silicalite phase. In terms of the phase connectivity, Monte Carlo simulations based on the pure-phase permeability values enabled us to calculate the effective permeability tensor, the main diagonal elements of which were compared with the experimental permeability. In line with the hypothesis proposed in our recent paper (Čapek, P. et al. (2014) Comput. Mater. Sci. 89, 142-156), the results confirmed that the existence of particle clusters was a key microstructural feature determining effective permeability. © 2017 The Authors Journal of Microscopy © 2017 Royal Microscopical Society.

Spherical Tensor Calculus for Local Adaptive Filtering

NASA Astrophysics Data System (ADS)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Recruitment and Recommendation of College Students: North Korea.

DTIC Science & Technology

1960-09-14

Journalism, Chinese Literat- ure, Library Science , Russian Language and Literature, Geology, Geodesic Chart Science (Ch’ukchi Chldohak), Planning...History, Philosophy, Library Science , Politi- cal Economy, and Meteorological ^um.unhak/. (f) The Preparatory School for Honor Soldiers. 2. Kim

High-resolution observations of core and suprathermal ions in the auroral ionosphere: Techniques and results from the GEODESIC sounding rocket

NASA Astrophysics Data System (ADS)

Burchill, Johnathan Kerr

Low-energy (Ek ˜ 10-1--10 1 eV) ions comprise the bulk of Earth's ionosphere, and represent the initial stages of ion heating and outflow from Earth's auroral regions. The suprathermal ion imager (SII) is a fast (˜93 images/sec), compact, two-dimensional ion energy (0 < Ek < 20 eV) and direction-of-arrival analyzer designed to observe the energy distributions of these ions in detail, with emphasis on exploring small-scale (˜10--100 m) structure in the ionosphere. The SII was flown into an auroral substorm on the GEODESIC sounding rocket from Poker Flat, Alaska, on 26 February 2000. The technical element of this thesis deals with the development of a computer model of the SII, and techniques for extracting and interpreting physical quantities from the SII observations. Laboratory and in-flight calibrations demonstrate that the analyzer imaging capability departs from the ideal model. Nevertheless, the SII represents a technological step forward, and has yielded new scientific results. The scientific element of this thesis focuses on simultaneous observations of ion energy distributions and low-frequency plasma waves in the topside (500--1000 km) auroral ionosphere. GEODESIC encountered three types of plasma wave which have previously been associated with ion heating. However, heated ions were only observed in association with localized density depletions and wave enhancements known as lower-hybrid solitary structures (LHSS). Approximately 90% of the LHSS ion number density is comprised of the ambient isotropic sub-eV core population. The remaining 10% corresponds to transverse acceleration of ions (TAI) to within 5° transverse to the geomagnetic field and to mean energies up to 5--10 eV, consistent with previous findings. Contrary to previously published observations, the GEODESIC TAI is consistent with localized bulk heating of some of the ambient core. Ion heating was not observed in association with large-scale (>1 km) broadband extremely low frequency (BB ELF) wave enhancements. Similarly, no ion heating was detected in the presence of large amplitude, short perpendicular wavelength Alfven waves. Differences between low-frequency ion flow fluctuations and convection drift fluctuations can be explained only partially by ion polarization drift physics.

Map Projection Induced Variations in Locations of Polygon Geofence Edges

NASA Technical Reports Server (NTRS)

Neeley, Paula; Narkawicz, Anthony

2017-01-01

This Paper under-estimates answers to the following question under various constraints: If a geofencing algorithm uses a map projection to determine whether a position is inside/outside a polygon region, how far outside/inside the polygon can the point be and the algorithm determine that it is inside/outside (the opposite and therefore incorrect answer)? Geofencing systems for unmanned aircraft systems (UAS) often model stay-in and stay-out regions using 2D polygons with minimum and maximum altitudes. The vertices of the polygons are typically input as latitude-longitude pairs, and the edges as paths between adjacent vertices. There are numerous ways to generate these paths, resulting in numerous potential locations for the edges of stay-in and stay-out regions. These paths may be geodesics on a spherical model of the earth or geodesics on the WGS84 reference ellipsoid. In geofencing applications that use map projections, these paths are inverse images of straight lines in the projected plane. This projected plane may be a projection of a spherical earth model onto a tangent plane, called an orthographic projection. Alternatively, it may be a projection where the straight lines in the projected plane correspond to straight lines in the latitudelongitude coordinate system, also called a Plate Carr´ee projection. This paper estimates distances between different edge paths and an oracle path, which is a geodesic on either the spherical earth or the WGS84 ellipsoidal earth. This paper therefore estimates how far apart different edge paths can be rather than comparing their path lengths, which are not considered. Rather, the comparision is between the actual locations of the edges between vertices. For edges drawn using orthographic projections, this maximum distance increases as the distance from the polygon vertices to the projection point increases. For edges drawn using Plate Carr´ee projections, this maximum distance increases as the vertices become further from the equator. Distances between geodesics on a spherical earth and a WGS84 ellipsoidal earth are also analyzed, using the WGS84 ellipsoid as the oracle. Bounds on the 2D distance between a straight line and a great circle path, in an orthographically projected plane rather than on the surface of the earth, have been formally verified in the PVS theorem prover, meaning that they are mathematically correct in the absence of floating point errors.

COMPARISON OF VOLUMETRIC REGISTRATION ALGORITHMS FOR TENSOR-BASED MORPHOMETRY

PubMed Central

Villalon, Julio; Joshi, Anand A.; Toga, Arthur W.; Thompson, Paul M.

2015-01-01

Nonlinear registration of brain MRI scans is often used to quantify morphological differences associated with disease or genetic factors. Recently, surface-guided fully 3D volumetric registrations have been developed that combine intensity-guided volume registrations with cortical surface constraints. In this paper, we compare one such algorithm to two popular high-dimensional volumetric registration methods: large-deformation viscous fluid registration, formulated in a Riemannian framework, and the diffeomorphic “Demons” algorithm. We performed an objective morphometric comparison, by using a large MRI dataset from 340 young adult twin subjects to examine 3D patterns of correlations in anatomical volumes. Surface-constrained volume registration gave greater effect sizes for detecting morphometric associations near the cortex, while the other two approaches gave greater effects sizes subcortically. These findings suggest novel ways to combine the advantages of multiple methods in the future. PMID:26925198

Constant-roll (quasi-)linear inflation

NASA Astrophysics Data System (ADS)

Karam, A.; Marzola, L.; Pappas, T.; Racioppi, A.; Tamvakis, K.

2018-05-01

In constant-roll inflation, the scalar field that drives the accelerated expansion of the Universe is rolling down its potential at a constant rate. Within this framework, we highlight the relations between the Hubble slow-roll parameters and the potential ones, studying in detail the case of a single-field Coleman-Weinberg model characterised by a non-minimal coupling of the inflaton to gravity. With respect to the exact constant-roll predictions, we find that assuming an approximate slow-roll behaviour yields a difference of Δ r = 0.001 in the tensor-to-scalar ratio prediction. Such a discrepancy is in principle testable by future satellite missions. As for the scalar spectral index ns, we find that the existing 2-σ bound constrains the value of the non-minimal coupling to ξphi ~ 0.29–0.31 in the model under consideration.

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

Bellomo, Nicola; Bellini, Emilio; Hu, Bin

Cosmological observables show a dependence with the neutrino mass, which is partially degenerate with parameters of extended models of gravity. We study and explore this degeneracy in Horndeski generalized scalar-tensor theories of gravity. Using forecasted cosmic microwave background and galaxy power spectrum datasets, we find that a single parameter in the linear regime of the effective theory dominates the correlation with the total neutrino mass. For any given mass, a particular value of this parameter approximately cancels the power suppression due to the neutrino mass at a given redshift. The extent of the cancellation of this degeneracy depends on themore » cosmological large-scale structure data used at different redshifts. We constrain the parameters and functions of the effective gravity theory and determine the influence of gravity on the determination of the neutrino mass from present and future surveys.« less

Detecting Lorentz Violations with Gravitational Waves From Black Hole Binaries

NASA Astrophysics Data System (ADS)

Sotiriou, Thomas P.

2018-01-01

Gravitational wave observations have been used to test Lorentz symmetry by looking for dispersive effects that are caused by higher order corrections to the dispersion relation. In this Letter I argue on general grounds that, when such corrections are present, there will also be a scalar excitation. Hence, a smoking-gun observation of Lorentz symmetry breaking would be the direct detection of scalar waves that travel at a speed other than the speed of the standard gravitational wave polarizations or the speed of light. Interestingly, in known Lorentz-breaking gravity theories the difference between the speeds of scalar and tensor waves is virtually unconstrained, whereas the difference between the latter and the speed of light is already severely constrained by the coincident detection of gravitational waves and gamma rays from a binary neutron star merger.

Bounds on isocurvature perturbations from cosmic microwave background and large scale structure data.

PubMed

Crotty, Patrick; García-Bellido, Juan; Lesgourgues, Julien; Riazuelo, Alain

2003-10-24

We obtain very stringent bounds on the possible cold dark matter, baryon, and neutrino isocurvature contributions to the primordial fluctuations in the Universe, using recent cosmic microwave background and large scale structure data. Neglecting the possible effects of spatial curvature, tensor perturbations, and reionization, we perform a Bayesian likelihood analysis with nine free parameters, and find that the amplitude of the isocurvature component cannot be larger than about 31% for the cold dark matter mode, 91% for the baryon mode, 76% for the neutrino density mode, and 60% for the neutrino velocity mode, at 2sigma, for uncorrelated models. For correlated adiabatic and isocurvature components, the fraction could be slightly larger. However, the cross-correlation coefficient is strongly constrained, and maximally correlated/anticorrelated models are disfavored. This puts strong bounds on the curvaton model.