Triangulated loop quantum cosmology: Bianchi IX universe and inhomogeneous perturbations
Battisti, Marco Valerio; Marciano, Antonino; Rovelli, Carlo
2010-03-15
We develop the triangulated version of loop quantum cosmology, recently introduced in the literature. We focus on the dipole cosmology, where space is a three-sphere and the triangulation is formed by two tetrahedra. We show that the discrete fiducial connection has a simple and appealing geometrical interpretation and we correct the ansatz on the relation between the model variables and the Friedmann-Robertson-Walker scale factor. The modified ansatz leads to the convergence of the Hamiltonian constraint to the continuum one. We then ask which degrees of freedom are captured by this model. We show that the model is rich enough to describe the (anisotropic) Bianchi IX universe, and give the explicit relation between the Bianchi IX variables and the variables of the model. We discuss the possibility of using this path in order to define the quantization of the Bianchi IX universe. The model contains more degrees of freedom than Bianchi IX, and therefore captures some inhomogeneous degrees of freedom as well. Inhomogeneous degrees of freedom can be expanded in representations of the SU(2) Bianchi IX isometry group, and the dipole model captures the lowest integer representation of these, connected to hyperspherical harmonic of angular momentum j=1.
Asymptotic dynamics of the exceptional Bianchi cosmologies
NASA Astrophysics Data System (ADS)
Hewitt, C. G.; Horwood, J. T.; Wainwright, J.
2003-05-01
In this paper we give, for the first time, a qualitative description of the asymptotic dynamics of a class of non-tilted spatially homogeneous (SH) cosmologies, the so-called exceptional Bianchi cosmologies, which are of Bianchi type VI$_{-1/9}$. This class is of interest for two reasons. Firstly, it is generic within the class of non-tilted SH cosmologies, being of the same generality as the models of Bianchi types VIII and IX. Secondly, it is the SH limit of a generic class of spatially inhomogeneous $G_{2}$ cosmologies. Using the orthonormal frame formalism and Hubble-normalized variables, we show that the exceptional Bianchi cosmologies differ from the non-exceptional Bianchi cosmologies of type VI$_{h}$ in two significant ways. Firstly, the models exhibit an oscillatory approach to the initial singularity and hence are not asymptotically self-similar. Secondly, at late times, although the models are asymptotically self-similar, the future attractor for the vacuum-dominated models is the so-called Robinson-Trautman SH model instead of the vacuum SH plane wave models.
Inhomogeneous cosmology: Gravitational radiation in Bianchi backgrounds
Adams, P.J.; Hellings, R.W.; Zimmerman, R.L.; Farhoosh, H.; Levine, D.I.; Zeldich, S.
1982-02-01
An exact formalism is developed for describing cosmological models with strong, long wavelength gravitational waves of general polarization propagating over backgrounds corresponding to Bianchi types I through VII. We introduce and discuss a new metric which exhibits the appropriate symmetries of two equivalent independent polarizations of gravitational waves. The formalism is applied to an empty type I cosmology, and it is shown how the original z-dependent chaotic singularity structure transforms itself into gravitational radiation propagating along the z-axis in a Bianchi I background.
Inhomogeneous cosmology - Gravitational radiation in Bianchi backgrounds
NASA Technical Reports Server (NTRS)
Adams, P. J.; Hellings, R. W.; Zimmerman, R. L.; Farhoosh, H.; Levine, D. I.; Zeldich, S.
1982-01-01
An exact formalism is developed for describing cosmological models with strong, long wavelength gravitational waves of general polarization, propagating over backgrounds corresponding to Bianchi types I through VII. A new metric which exhibits the appropriate symmetries of two equivalent independent polarizations of gravitational waves is introduced and discussed. The formalism is applied to an empty type I cosmology, and it is shown how the original z-dependent chaotic singularity structure transforms itself into gravitational radiation propagating along the z-axis in a Bianchi I background.
Quantum supersymmetric Bianchi IX cosmology
NASA Astrophysics Data System (ADS)
Damour, Thibault; Spindel, Philippe
2014-11-01
We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D =4 simple supergravity for a S U (2 ) -homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. After imposition of the diffeomorphism constraints, the wave function of the Universe becomes a 64-component spinor of spin(8,4) depending on the three squashing parameters, which satisfies Dirac-like, and Klein-Gordon-like, wave equations describing the propagation of a "quantum spinning particle" reflecting off spin-dependent potential walls. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact subalgebra of the rank-3 hyperbolic Kac-Moody algebra A E3 . The (quartic-in-fermions) squared-mass term μ^ 2 entering the Klein-Gordon-like equation has several remarkable properties: (i) it commutes with all the other (Kac-Moody-related) building blocks of the Hamiltonian; (ii) it is a quadratic function of the fermion number NF; and (iii) it is negative in most of the Hilbert space. The latter property leads to a possible quantum avoidance of the singularity ("cosmological bounce"), and suggests imposing the boundary condition that the wave function of the Universe vanish when the volume of space tends to zero (a type of boundary condition which looks like a final-state condition when considering the big crunch inside a black hole). The space of solutions is a mixture of "discrete-spectrum states" (parametrized by a few constant parameters, and known in explicit form) and of continuous-spectrum states (parametrized by arbitrary functions entering some initial-value problem). The predominantly negative values of the squared-mass term lead to a "bottle
Higher-dimensional Bianchi type-VIh cosmologies
NASA Astrophysics Data System (ADS)
Lorenz-Petzold, D.
1985-09-01
The higher-dimensional perfect fluid equations of a generalization of the (1 + 3)-dimensional Bianchi type-VIh space-time are discussed. Bianchi type-V and Bianchi type-III space-times are also included as special cases. It is shown that the Chodos-Detweiler (1980) mechanism of cosmological dimensional-reduction is possible in these cases.
Bianchi Type V Cosmological Models with Varying Cosmological Term
NASA Astrophysics Data System (ADS)
Tiwari, R. K.; Singh, Rameshwar
2015-05-01
We have analyzed a new class of spatially homogeneous and anisotropic Bianchi type-V cosmological models with perfect fluid distribution in presence of time varying cosmological and gravitational constants in the framework of general relativity. Exact solutions of Einstein's field equations are obtained for two types of cosmologies viz. m ≠ 3 and m = 3 respectively. We propose an alternate variation law in which the anisotropy ( σ/ 𝜃) per unit expansion scalar ( 𝜃) is proportional to a function of scale factor R i.e. (where σ is a shear scalar) Tiwari (The African Review of Physics, 8, 437-447 2013). Physical properties of the models are discussed in detail. The models isotropize at late times. Some cosmological distance parameters for both the models have also been presented. We also discussed state finder parameters and observe that our solutions favor Λ C D M model.
Anisotropic Bianchi types VIII and IX locally rotationally symmetric cosmologies
Assad, M.J.D.; Soares, I.D.
1983-10-15
We present a class of exact cosmological solutions of Einstein-Maxwell equations, which are anisotropic and spatially homogeneous of Bianchi types VIII and IX, and class IIIb in the Stewart-Ellis classification of locally rotationally symmetric models. If we take the electromagnetic field equal to zero, a class of Bianchi types VIII/IX spatially homogeneous anisotropic cosmological solutions with perfect fluid is obtained.
Loop quantization of vacuum Bianchi I cosmology
Martin-Benito, M.; Mena Marugan, G. A.; Pawlowski, T.
2008-09-15
We analyze the loop quantization of the family of vacuum Bianchi I spacetimes, a gravitational system of which classical solutions describe homogeneous anisotropic cosmologies. We rigorously construct the operator that represents the Hamiltonian constraint, showing that the states of zero volume completely decouple from the rest of quantum states. This fact ensures that the classical cosmological singularity is resolved in the quantum theory. In addition, this allows us to adopt an equivalent quantum description in terms of a well-defined densitized Hamiltonian constraint. This latter constraint can be regarded in a certain sense as a difference evolution equation in an internal time provided by one of the triad components, which is polymerically quantized. Generically, this evolution equation is a relation between the projection of the quantum states in three different sections of constant internal time. Nevertheless, around the initial singularity the equation involves only the two closest sections with the same orientation of the triad. This has a double effect: on the one hand, physical states are determined just by the data on one section, on the other hand, the evolution defined in this way never crosses the singularity, without the need of any special boundary condition. Finally, we determine the inner product and the physical Hilbert space employing group averaging techniques, and we specify a complete algebra of Dirac observables. This completes the quantization program.
Loop quantum cosmology of Bianchi type IX models
Wilson-Ewing, Edward
2010-08-15
The loop quantum cosmology 'improved dynamics' of the Bianchi type IX model are studied. The action of the Hamiltonian constraint operator is obtained via techniques developed for the Bianchi type I and type II models, no new input is required. It is shown that the big bang and big crunch singularities are resolved by quantum gravity effects. We also present effective equations which provide quantum geometry corrections to the classical equations of motion.
Loop quantum cosmology of Bianchi type I models
NASA Astrophysics Data System (ADS)
Ashtekar, Abhay; Wilson-Ewing, Edward
2009-04-01
The “improved dynamics” of loop quantum cosmology is extended to include anisotropies of the Bianchi type I model. As in the isotropic case, a massless scalar field serves as a relational time parameter. However, the extension is nontrivial because one has to face several conceptual subtleties as well as technical difficulties. These include a better understanding of the relation between loop quantum gravity and loop quantum cosmology, handling novel features associated with the nonlocal field strength operator in presence of anisotropies, and finding dynamical variables that make the action of the Hamiltonian constraint manageable. Our analysis provides a conceptually complete description that overcomes limitations of earlier works. We again find that the big-bang singularity is resolved by quantum geometry effects but, because of the presence of Weyl curvature, Planck scale physics is now much richer than in the isotropic case. Since the Bianchi I models play a key role in the Belinskii, Khalatnikov, Lifshitz conjecture on the nature of generic spacelike singularities in general relativity, the quantum dynamics of Bianchi I cosmologies is likely to provide considerable intuition about the fate of generic spacelike singularities in quantum gravity. Finally, we show that the quantum dynamics of Bianchi I cosmologies projects down exactly to that of the Friedmann model. This opens a new avenue to relate more complicated models to simpler ones, thereby providing a new tool to relate the quantum dynamics of loop quantum gravity to that of loop quantum cosmology.
Loop quantum cosmology of Bianchi type I models
Ashtekar, Abhay; Wilson-Ewing, Edward
2009-04-15
The ''improved dynamics'' of loop quantum cosmology is extended to include anisotropies of the Bianchi type I model. As in the isotropic case, a massless scalar field serves as a relational time parameter. However, the extension is nontrivial because one has to face several conceptual subtleties as well as technical difficulties. These include a better understanding of the relation between loop quantum gravity and loop quantum cosmology, handling novel features associated with the nonlocal field strength operator in presence of anisotropies, and finding dynamical variables that make the action of the Hamiltonian constraint manageable. Our analysis provides a conceptually complete description that overcomes limitations of earlier works. We again find that the big-bang singularity is resolved by quantum geometry effects but, because of the presence of Weyl curvature, Planck scale physics is now much richer than in the isotropic case. Since the Bianchi I models play a key role in the Belinskii, Khalatnikov, Lifshitz conjecture on the nature of generic spacelike singularities in general relativity, the quantum dynamics of Bianchi I cosmologies is likely to provide considerable intuition about the fate of generic spacelike singularities in quantum gravity. Finally, we show that the quantum dynamics of Bianchi I cosmologies projects down exactly to that of the Friedmann model. This opens a new avenue to relate more complicated models to simpler ones, thereby providing a new tool to relate the quantum dynamics of loop quantum gravity to that of loop quantum cosmology.
Effective dynamics in Bianchi type II loop quantum cosmology
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Montoya, Edison
2012-05-01
We numerically investigate the solutions to the effective equations of the Bianchi II model within the “improved” loop quantum cosmology dynamics. The matter source is a massless scalar field. We perform a systematic study of the space of solutions, and focus on the behavior of several geometrical observables. We show that the big bang singularity is replaced by a bounce and the pointlike singularities do not saturate the energy density bound. There are up to three directional bounces in the scale factors, one global bounce in the expansion, the shear presents up to four local maxima and can be zero at the bounce. This allows for solutions with density larger than the maximal density for the isotropic and Bianchi I cases. The asymptotic behavior is shown to behave like that of a Bianchi I model, and the effective solutions connect anisotropic solutions even when the shear is zero at the bounce. All known facts of Bianchi I are reproduced. In the “vacuum limit,” solutions are such that almost all the dynamics is due to the anisotropies. Since Bianchi II plays an important role in the Bianchi IX model and the Belinskii, Khalatnikov, Lifshitz conjecture, our results can provide an intuitive understanding of the behavior in the vicinity of general spacelike singularities, when loop-geometric corrections are present.
Bianchi Type V Viscous Fluid Cosmological Models with Varying Cosmological Term
NASA Astrophysics Data System (ADS)
Singh, J. P.; Baghel, P. S.; Singh, A.
2015-08-01
Bianchi type V viscous fluid cosmological models with varying cosmological term Λ are investigated. We have examined a cosmological scenario proposing expansion anisotropy σ/ θ to be suitable function of average scale factor S in the background of homogeneous, anisotropic Bianchi type V space-time. The models isotropize asymptotically and the presence of shear viscosity accelerates the isotropization. Our models describe a unified expansion history of the universe indicating initial decelerating expansion and late time accelerating phase consistent with observations. Physical and kinematical parameters of the models are discussed.
Spectral action for Bianchi type-IX cosmological models
NASA Astrophysics Data System (ADS)
Fan, Wentao; Fathizadeh, Farzad; Marcolli, Matilde
2015-10-01
A rationality result previously proved for Robertson-Walker metrics is extended to a homogeneous anisotropic cosmological model, namely the Bianchi type-IX minisuperspace. It is shown that the Seeley-de Witt coefficients appearing in the expansion of the spectral action for the Bianchi type-IX geometry are expressed in terms of polynomials with rational coefficients in the cosmic evolution factors w 1( t) , w 2( t) , w 3( t) , and their higher derivates with respect to time. We begin with the computation of the Dirac operator of this geometry and calculate the coefficients a 0 ,a 2 ,a 4 of the spectral action by using heat kernel methods and parametric pseudodifferential calculus. An efficient method is devised for computing the Seeley-de Witt coefficients of a geometry by making use of Wodzicki's noncommutative residue, and it is confirmed that the method checks out for the cosmological model studied in this article. The advantages of the new method are discussed, which combined with symmetries of the Bianchi type-IX metric, yield an elegant proof of the rationality result.
The general solution of Bianchi type III vacuum cosmology
NASA Astrophysics Data System (ADS)
Christodoulakis, T.; Terzis, Petros A.
2007-02-01
The second-order ordinary differential equation which describes the unknown part of the solution space of some vacuum Bianchi cosmologies is completely integrated for type III, thus obtaining the general solution to Einstein's field equations for this case, with the aid of the sixth Painlevé transcendent PVI. For particular representations of PVI we obtain the known Kinnersley two-parameter spacetime and a solution of Euclidean signature. The imposition of the spacetime generalization of a 'hidden' symmetry of the generic type III spatial slice enables us to retrieve the two-parameter subfamily without considering the Painlevé transcendent.
Generalized uncertainty principle in Bianchi type I quantum cosmology
NASA Astrophysics Data System (ADS)
Vakili, B.; Sepangi, H. R.
2007-07-01
We study a quantum Bianchi type I model in which the dynamical variables of the corresponding minisuperspace obey the generalized Heisenberg algebra. Such a generalized uncertainty principle has its origin in the existence of a minimal length suggested by quantum gravity and sting theory. We present approximate analytical solutions to the corresponding Wheeler DeWitt equation in the limit where the scale factor of the universe is small and compare the results with the standard commutative and noncommutative quantum cosmology. Similarities and differences of these solutions are also discussed.
Anisotropic cosmology and inflation from a tilted Bianchi IX model
NASA Astrophysics Data System (ADS)
Sundell, P.; Koivisto, T.
2015-12-01
The dynamics of the tilted axisymmetric Bianchi IX cosmological models are explored allowing energy flux in the source fluid. The Einstein equations and the continuity equation are presented treating the equation of state w and the tilt angle of the fluid λ as time-dependent functions, but when analyzing the phase space w and λ are considered free parameters and the shear, the vorticity and the curvature of the spacetime span a three-dimensional phase space that contains seven fixed points. One of them is an attractor that inflates the universe anisotropically, thus providing a counterexample to the cosmic no-hair conjecture. Also, examples of realistic though fine-tuned cosmologies are presented wherein the rotation can become significant towards the present epoch but the shear stays within the observational bounds. The examples suggest that the model used here can explain the parity-violating anomalies of the cosmic microwave background. The result significantly differs from an earlier study, where a nonaxisymmetric Bianchi IX type model with a tilted perfect dust source was found to induce too much shear for observationally significant vorticity.
NASA Astrophysics Data System (ADS)
Roy, S. R.; Banerjee, S. K.
1992-11-01
A homogeneous Bianchi type VIh cosmological model filled with perfect fluid, null electromagnetic field and streaming neutrinos is obtained for which the free gravitational field is of the electric type. The barotropic equation of statep = (γ-1)ɛ is imposed in the particular case of Bianchi VI0 string models. Various physical and kinematical properties of the models are discussed.
Quantum Bianchi Type IX Cosmology in K-Essence Theory
NASA Astrophysics Data System (ADS)
Espinoza-García, Abraham; Socorro, J.; Pimentel, Luis O.
2014-09-01
We use one of the simplest forms of the K-essence theory and apply it to the anisotropic Bianchi type IX cosmological model, with a barotropic perfect fluid modeling the usual matter content. We show that the most important contribution of the scalar field occurs during a stiff matter phase. Also, we present a canonical quantization procedure of the theory which can be simplified by reinterpreting the scalar field as an exotic part of the total matter content. The solutions to the Wheeler-DeWitt equation were found using the Bohmian formulation Bohm (Phys. Rev. 85(2):166, 1952) of quantum mechanics, employing the amplitude-real-phase approach Moncrief and Ryan (Phys. Rev. D 44:2375, 1991), where the ansatz for the wave function is of the form Ψ( ℓ μ )= χ( ϕ) W( ℓ μ ), where S is the superpotential function, which plays an important role in solving the Hamilton-Jacobi equation.
Gravitational radiation in Bianchi Type V cosmological models
Hogan, P.A.
1988-01-01
This paper is concerned with the development of the theory of embedding gravitational radiation fields in expanding universes pioneered by Hawking. The problem of embedding such fields in the expanding Friedmann-Lemaitre-Robertson-Walker dust-filled universe, considered by Hawking, is reexamined in a new formalism which permits an easy analysis, in particular, of the relationship between the boundary conditions and the satisfaction, by the Weyl tensor, of the conventional peeling-off behavior. Since gravity wave detectors are expected to pick up plane-fronted gravitational waves, the main thrust of this paper concerns the development of a formulation of Bianchi Type V cosmological models which enables the embedding of such plane-fronted waves to be carried out. This is worked out explicitly in the case of a perfect fluid, with pressure proportional to energy density, and with the histories of the fluid particles orthogonal to the surfaces of homogeneity. 18 references.
Loop quantum cosmology in Bianchi type I models: Analytical investigation
Chiou, D.-W.
2007-01-15
The comprehensive formulation for loop quantum cosmology in the spatially flat, isotropic model was recently constructed. In this paper, the methods are extended to the anisotropic Bianchi I cosmology. Both the precursor and the improved strategies are applied and the expected results are established: (i) the scalar field again serves as an internal clock and is treated as emergent time; (ii) the total Hamiltonian constraint is derived by imposing the fundamental discreteness and gives the evolution as a difference equation; and (iii) the physical Hilbert space, Dirac observables, and semiclassical states are constructed rigorously. It is also shown that the state in the kinematical Hilbert space associated with the classical singularity is decoupled in the difference evolution equation, indicating that the big bounce may take place when any of the area scales undergoes the vanishing behavior. The investigation affirms the robustness of the framework used in the isotropic model by enlarging its domain of validity and provides foundations to conduct the detailed numerical analysis.
Bianchi I in scalar and scalar-tensor cosmologies
NASA Astrophysics Data System (ADS)
Belinchón, José
2012-08-01
We study how the constants G and Λ may vary in different theoretical models (general relativity (GR) with a perfect fluid, scalar cosmological models (SM) ("quintessence") with and without interacting scalar and matter fields and three scalar-tensor theories (STT) with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study the Bianchi I models, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we conclude that the solutions are isotropic and noninflationary. We also arrive at the conclusion that in the GR model with time-varying constants, Λ vanishes while G is constant. In the SM all the solutions are massless i.e. the potential vanishes and all the interacting models are inconsistent from the thermodynamical point of view. The solutions obtained in the STT collapse to the perfect fluid one obtained in the GR model where G is a true constant and Λ vanishes as in the GR and SM frameworks.
Bianchi type-I cosmological model with quadratic equation of state
NASA Astrophysics Data System (ADS)
Reddy, D. R. K.; Adhav, K. S.; Purandare, M. A.
2015-05-01
Bianchi type-I cosmological model containing perfect fluid with quadratic equation of state has been studied in general theory of relativity. The general solutions of the Einstein's field equations for Bianchi type-I space-time have been obtained under the assumption of quadratic equation of state (EoS) p= αρ 2- ρ, where α is constant and strictly α≠0. The physical and geometrical aspects of the model are discussed.
Loop quantum cosmology of Bianchi IX: Inclusion of inverse triad corrections
NASA Astrophysics Data System (ADS)
Corichi, Alejandro; Karami, Asieh
2016-06-01
We consider the loop quantization of the (diagonal) Bianchi type IX cosmological model. We explore different quantization prescriptions that extend the work of Wilson-Ewing and Singh. In particular, we study two different ways of implementing the so-called inverse triad corrections. We construct the corresponding Hamiltonian constraint operators and show that the singularity is formally resolved. We find the effective equations associated with the different quantization prescriptions, and study the relation with the isotropic k = 1 model that, classically, is contained within the Bianchi IX model. Somewhat surprisingly, we find the most natural quantization does not reduce to the k = 1 model. We use geometrically defined scalar observables to explore the physical implications of each of these theories. This is the first part in a series of papers analyzing different aspects of the Bianchi IX model, with inverse corrections, within loop quantum cosmology (LQC).
Bianchi type-I magnetized radiating cosmological model in self creation theory of gravitation
NASA Astrophysics Data System (ADS)
Jain, Vimal Chand; Jain, Nikhil
2015-06-01
We have investigated Bianchi type-I cosmological model in the presence of magnetized field with disordered radiation in Barber's second self-creation theory of gravitation. To obtain exact solution we assume that the component of shear tensor is proportional to expansion ( θ). Some geometrical and physical properties of the model have also been discussed.
Tilted Bianchi Type III Wet Dark Fluid Cosmological Model in Saez and Ballester Theory
NASA Astrophysics Data System (ADS)
Sahu, Subrata Kumar; Kantila, Endale Nigatu; Gebru, Dawit Melese
2016-01-01
Tilted Bianchi-III wet dark fluid cosmological model is investigated in the frame work of Saez and Ballester theory (Phys. Lett. A. 113:467, 1986). Exact solutions to the field equations are derived when the metric potentials are functions of cosmic time only. Some physical and geometrical properties of the solutions are also discussed.
NASA Astrophysics Data System (ADS)
Körpinar, Talat; Turhan, Essin
2015-05-01
In this paper, we study energy of time involute particles of biharmonic particles in Bianchi type-I (B-I) cosmological model spacetime. We give a geometrical description of energy for a Frenet vector fields of timelike biharmonic particle. Finally, using the Frenet frame of the given particle, we obtain different cases for this particles and give important characterizations about them in Bianchi type-I (B-I) cosmological model spacetime.
Wheeler-DeWitt equation and Lie symmetries in Bianchi scalar-field cosmology
NASA Astrophysics Data System (ADS)
Paliathanasis, A.; Karpathopoulos, L.; Wojnar, A.; Capozziello, S.
2016-04-01
Lie symmetries are discussed for the Wheeler-De Witt equation in Bianchi Class A cosmologies. In particular, we consider general relativity, minimally coupled scalar-field gravity and hybrid gravity as paradigmatic examples of the approach. Several invariant solutions are determined and classified according to the form of the scalar-field potential. The approach gives rise to a suitable method to select classical solutions and it is based on the first principle of the existence of symmetries.
LRS Bianchi type-I string cosmological models in f (R, T) gravity
NASA Astrophysics Data System (ADS)
Kanakavalli, T.; Ananda Rao, G.
2016-07-01
Spatially homogeneous and anisotropic LRS Bianchi type-I space time is investigated in the presence of cosmic string source in a modified theory of gravitation formulated by Harko et al. (Phys. Rev. D 84:024020, 2011). We have solved the field equations using the equations of state for strings and presented cosmological models which describe geometric string, Takabayasi string and Reddy string in this particular theory. Some physical and kinematical parameters of the models are computed and discussed their physical significance.
Big-bounce cosmology from quantum gravity: The case of a cyclical Bianchi I universe
NASA Astrophysics Data System (ADS)
Moriconi, Riccardo; Montani, Giovanni; Capozziello, Salvatore
2016-07-01
We analyze the classical and quantum dynamics of a Bianchi I model in the presence of a small negative cosmological constant characterizing its evolution in term of the dust-time dualism. We demonstrate that in a canonical metric approach, the cosmological singularity is removed in correspondence to a positive defined value of the dust energy density. Furthermore, the quantum big bounce is connected to the Universe's turning point via a well-defined semiclassical limit. Then we can reliably infer that the proposed scenario is compatible with a cyclical universe picture. We also show how, when the contribution of the dust energy density is sufficiently high, the proposed scenario can be extended to the Bianchi IX cosmology and therefore how it can be regarded as a paradigm for the generic cosmological model. Finally, we investigate the origin of the observed cutoff on the cosmological dynamics, demonstrating how the big-bounce evolution can be mimicked by the same semiclassical scenario, where the negative cosmological constant is replaced via a polymer discretization of the Universe's volume. A direct proportionality law between these two parameters is then established.
General features of Bianchi-I cosmological models in Lovelock gravity
Pavluchenko, S. A.
2009-11-15
We derived equations of motion corresponding to Bianchi-I cosmological models in the Lovelock gravity. Equations derived in the general case, without any specific ansatz for any number of spatial dimensions and any order of the Lovelock correction. We also analyzed the equations of motion solely taking into account the highest-order correction and described the drastic difference between the cases with odd and even numbers of spatial dimensions. For power-law ansatz we derived conditions for Kasner and generalized Milne regimes for the model considered. Finally, we discuss the possible influence of matter in the form of perfect fluid on the solutions obtained.
General features of Bianchi-I cosmological models in Lovelock gravity
NASA Astrophysics Data System (ADS)
Pavluchenko, S. A.
2009-11-01
We derived equations of motion corresponding to Bianchi-I cosmological models in the Lovelock gravity. Equations derived in the general case, without any specific ansatz for any number of spatial dimensions and any order of the Lovelock correction. We also analyzed the equations of motion solely taking into account the highest-order correction and described the drastic difference between the cases with odd and even numbers of spatial dimensions. For power-law ansatz we derived conditions for Kasner and generalized Milne regimes for the model considered. Finally, we discuss the possible influence of matter in the form of perfect fluid on the solutions obtained.
Bianchi type-VIh string cloud cosmological models with bulk viscosity
NASA Astrophysics Data System (ADS)
Tripathy, Sunil K.; Behera, Dipanjali
2010-11-01
String cloud cosmological models are studied using spatially homogeneous and anisotropic Bianchi type VIh metric in the frame work of general relativity. The field equations are solved for massive string cloud in presence of bulk viscosity. A general linear equation of state of the cosmic string tension density with the proper energy density of the universe is considered. The physical and kinematical properties of the models have been discussed in detail and the limits of the anisotropic parameter responsible for different phases of the universe are explored.
Behavior of nonlinear anisotropies in bouncing Bianchi I models of loop quantum cosmology
Chiou, D.-W.; Vandersloot, Kevin
2007-10-15
In homogeneous and isotropic loop quantum cosmology, gravity can behave repulsively at Planckian energy densities leading to the replacement of the big bang singularity with a big bounce. Yet in any bouncing scenario it is important to include nonlinear effects from anisotropies which typically grow during the collapsing phase. We investigate the dynamics of a Bianchi I anisotropic model within the framework of loop quantum cosmology. Using effective semiclassical equations of motion to study the dynamics, we show that the big bounce is still predicted with only differences in detail arising from the inclusion of anisotropies. We show that the anisotropic shear term grows during the collapsing phase, but remains finite through the bounce. Immediately following the bounce, the anisotropies decay and with the inclusion of matter with equation of state w<+1, the universe isotropizes in the expanding phase.
The general class of Bianchi cosmological models with varying EoS parameter
NASA Astrophysics Data System (ADS)
Chaubey, R.; Shukla, A. K.
2015-03-01
This paper deals with the general class of Bianchi cosmological models with varying equation of state (EoS) parameter. We have discussed three different types of physically viable cosmological solutions of average scale factor by using a special law for deceleration parameter which is linear in time with a negative slope. The exact solutions to the corresponding field equations are obtained for three different physical viable cosmologies. The EoS parameter for deceleration parameter as well as dark energy is found to be the time varying function. We have using the latest observational data to draw a qualitative picture of the evaluation of the universe. In our constructed model, the equation of state parameter of dark energy is obtained as time varying and it is evolving with negative sign which is consistent with recent observation. We also shows that, at the early stage, the equation of state (EoS) parameter ( γ) is positive i.e. the universe was matter dominated but at large time, the universe evolving with negative values i.e. the present epoch. All physical parameters are calculated and discussed in each physical viable cosmological model.
Anisotropic matter in cosmology: locally rotationally symmetric Bianchi I and VII o models
NASA Astrophysics Data System (ADS)
Sloan, David
2016-05-01
We examine the behaviour of homogeneous, anisotropic space-times, specifically the locally rotationally symmetric Bianchi types I and VII o in the presence of anisotropic matter. By finding an appropriate constant of the motion, and transforming the equations of motion we are able to provide exact solutions in the presence of perfect fluids with anisotropic pressures. The solution space covers matter consisting of a single perfect fluid which satisfies the weak energy condition and is rich enough to contain solutions which exhibit behaviour which is qualitatively distinct from the isotropic sector. Thus we find that there is more ‘matter that matters’ close to a homogeneous singularity than the usual stiff fluid. Example metrics are given for cosmologies whose matter sources are magnetic fields, relativistic particles, cosmic strings and domain walls.
Wave-like solutions for Bianchi type I cosmologies in 5D
NASA Astrophysics Data System (ADS)
Ponce de Leon, J.
2008-10-01
We derive exact solutions to the vacuum Einstein field equations in 5D, under the assumption that (i) the line element in 5D possesses self-similar symmetry, in the classical understanding of Sedov, Taub and Zeldovich, and that (ii) the metric tensor is diagonal and independent of the coordinates for ordinary 3D space. These assumptions lead to three different types of self-similarity in 5D: homothetic, conformal and 'wave-like'. In this work we present the most general wave-like solutions to the 5D field equations. Using the standard technique based on Campbell's theorem, they generate a large number of anisotropic cosmological models of Bianchi type I, which can be applied to our universe after the big bang, when anisotropies could have played an important role. We present a complete review of all possible cases of self-similar anisotropic cosmologies in 5D. Our analysis extends a number of previous studies on wave-like solutions in 5D with spatial spherical symmetry.
Effective dynamics, big bounces, and scaling symmetry in Bianchi type I loop quantum cosmology
Chiou, D.-W.
2007-12-15
The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to 3 times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale.
Bianchi IX dynamics in bouncing cosmologies: homoclinic chaos and the BKL conjecture
NASA Astrophysics Data System (ADS)
Maier, Rodrigo; Damião Soares, Ivano; Valentino Tonini, Eduardo
2015-12-01
We examine the dynamics of a Bianchi IX model with three scale factors on a 4-dim Lorentzian brane embedded in a 5-dim conformally flat empty bulk with a timelike extra dimension. The matter content is a pressureless perfect fluid restricted to the brane, with the embedding consistently satisfying the Gauss-Codazzi equations. The 4-dim Einstein equations on the brane reduce to a 6-dim Hamiltonian dynamical system with additional terms (due to the bulk-brane interaction) that avoid the singularity and implement nonsingular bounces in the model. We examine the complex Bianchi IX dynamics in its approach to the neighborhood of the bounce which replaces the cosmological singularity of general relativity. The phase space of the model presents (i) two critical points (a saddle-center-center and a center-center-center) in a finite region of phase space, (ii) two asymptotic de Sitter critical points at infinity, one acting as an attractor to late-time acceleration and (iii) a 2-dim invariant plane, which together organize the dynamics of the phase space. The saddle-center-center engenders in the phase space the topology of stable and unstable 4-dim cylinders R × S 3, where R is a saddle direction and S 3 is the center manifold of unstable periodic orbits, the latter being the nonlinear extension of the center-center sector. By a proper canonical transformation the degrees of freedom of the dynamics are separated into one degree connected with the expansion/contraction of the scales of the model, and two rotational degrees of freedom associated with the center manifold S 3. The typical dynamical flow is thus an oscillatory mode about the orbits of the invariant plane. The stable and unstable cylinders are spanned by oscillatory orbits about the separatrix towards the bounce, leading to the homoclinic transversal intersection of the cylinders, as shown numerically in two distinct simulations. The homoclinic intersection manifold has the topology of R × S 2 consisting of
NASA Astrophysics Data System (ADS)
Ayissi, Raoul Domingo; Noutchegueme, Norbert
2015-01-01
Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the
Ayissi, Raoul Domingo Noutchegueme, Norbert
2015-01-15
Global solutions regular for the Einstein-Boltzmann equation on a magnetized Bianchi type-I cosmological model with the cosmological constant are investigated. We suppose that the metric is locally rotationally symmetric. The Einstein-Boltzmann equation has been already considered by some authors. But, in general Bancel and Choquet-Bruhat [Ann. Henri Poincaré XVIII(3), 263 (1973); Commun. Math. Phys. 33, 83 (1973)], they proved only the local existence, and in the case of the nonrelativistic Boltzmann equation. Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] obtained a global existence result, for the relativistic Boltzmann equation coupled with the Einstein equations and using the Yosida operator, but confusing unfortunately with the nonrelativistic case. Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)] and Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], have obtained a global solution in time, but still using the Yosida operator and considering only the uncharged case. Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)] also proved a global existence of solutions to the Maxwell-Boltzmann system using the characteristic method. In this paper, we obtain using a method totally different from those used in the works of Noutchegueme and Dongho [Classical Quantum Gravity 23, 2979 (2006)], Noutchegueme, Dongho, and Takou [Gen. Relativ. Gravitation 37, 2047 (2005)], Noutchegueme and Ayissi [Adv. Stud. Theor. Phys. 4, 855 (2010)], and Mucha [Global existence of solutions of the Einstein-Boltzmann equation in the spatially homogeneous case. Evolution equation, existence, regularity and singularities (Banach Center Publications, Institute of Mathematics, Polish Academy of Science, 2000), Vol. 52] the
Bianchi Type VI1 Viscous Fluid Cosmological Model in Wesson´s Theory of Gravitation
NASA Astrophysics Data System (ADS)
Khadekar, G. S.; Avachar, G. R.
2007-03-01
Field equations of a scale invariant theory of gravitation proposed by Wesson [1, 2] are obtained in the presence of viscous fluid with the aid of Bianchi type VIh space-time with the time dependent gauge function (Dirac gauge). It is found that Bianchi type VIh (h = 1) space-time with viscous fluid is feasible in this theory, whereas Bianchi type VIh (h = -1, 0) space-times are not feasible in this theory, even in the presence of viscosity. For the feasible case, by assuming a relation connecting viscosity and metric coefficient, we have obtained a nonsingular-radiating model. We have discussed some physical and kinematical properties of the models.
Physical aspects of unitary evolution of Bianchi-I quantum cosmological model
NASA Astrophysics Data System (ADS)
Pal, Sridip
2016-02-01
In this study, we examine some physical aspects of unitary evolution of the Bianchi-I model. In particular, we investigate the behavior of the volume and the scale factor as a function of time for the Bianchi-I universe with ultra-relativistic fluid (α = 1). The expectation value of volume is shown not to hit any singularity. We elucidate on the anisotropic nature of the solution and physically interpret the wavefunction as a superposition of collapsing universe and expanding universe mimicking Hartle-Hawking type wavefunction. The same analysis has been done for α \
Inhomogeneous generalization of some Bianchi models
NASA Astrophysics Data System (ADS)
Carmeli, M.; Charach, Ch.
1980-02-01
Vacuum Bianchi models which can be transformed to the Einstein-Rosen metric are considered. The models are used in order to construct new inhomogeneous universes, which are generalizations of Bianchi cosmologies of types III, V and VIh. Recent generalizations of these Bianchi models, considered by Wainwright et al., are also discussed.
Anisotropic Bianchi-III cosmological model in f (R, T) gravity
NASA Astrophysics Data System (ADS)
Sahoo, P. K.; Sahu, S. K.; Nath, A.
2016-01-01
An anisotropic Bianchi type-III universe is investigated in the presence of a perfect fluid within the framework of f(R,T) gravity, where R is the Ricci scalar and T is the trace of the source of matter. Here we have considered the first two cases of the f(R,T) model, i.e. f(R,T)=R+2f(T) and f(R,T)=f1(R)+f2(T). We have shown that the field equations of f(R,T) gravity are solvable for any arbitrary function of a scale factor. To get a physically realistic model of the universe, we have assumed a simple power-law form of a scale factor. The exact solutions of the field equations are obtained, which represent an expanding model of the universe which starts expanding with a big bang at t = 0 . The physical behaviours of the model are discussed.
Camci, Ugur; Kucukakca, Yusuf
2007-10-15
We consider some scalar-coupled theories of gravity, including induced gravity, and study the Noether symmetries of Bianchi I, Bianchi III, and Kantowski-Sachs cosmological models for this theory. For various forms of coupling of the scalar field with gravity, some potentials are found in these cosmological models under the assumption that the Lagrangian admits Noether symmetry. The solutions of the field equations for the considered models are presented by using the results obtained from the Noether symmetry. We also find the explicit form of the scalar field in terms of the conformal time for Bianchi I, III, and Kantowski-Sachs models.
NASA Astrophysics Data System (ADS)
Montani, Giovanni
1. Historical picture. 1.1. The concept of universe through the centuries. 1.2. The XIX century knowledge. 1.3. Birth of scientific cosmology. 1.4. The genesis of the hot big bang model. 1.5. Guidelines to the literature -- 2. Fundamental tools. 2.1. Einstein equations. 2.2. Matter fields. 2.3. Hamiltonian formulation of the dynamics. 2.4. Synchronous reference system. 2.5. Tetradic formalism. 2.6. Gauge-like formulation of GR. 2.7. Singularity theorems. 2.8. Guidelines to the literature -- 3. The structure and dynamics of the isotropic universe. 3.1. The RW geometry. 3.2. The FRW cosmology. 3.3. Dissipative cosmologies. 3.4. Inhomogeneous fluctuations in the universe. 3.5. General relativistic perturbation theory. 3.6. The Lemaitre-Tolmann-Bondi spherical solution. 3.7. Guidelines to the literature -- 4. Features of the observed universe. 4.1. Current status: The concordance model. 4.2. The large-scale structure. 4.3. The acceleration of the universe. 4.4. The cosmic microwave background. 4.5. Guidelines to the literature -- 5. The theory of inflation. 5.1. The shortcomings of the standard cosmology. 5.2. The inflationary paradigm. 5.3. Presence of a self-interacting scalar field. 5.4. Inflationary dynamics. 5.5. Solution to the shortcomings of the standard cosmology. 5.6. General features. 5.7. Possible explanations for the present acceleration of the universe. 5.8. Guidelines to the literature -- 6. Inhomogeneous quasi-isotropic cosmologies. 6.1. Quasi-isotropic solution. 6.2. The presence of ultrarelativistic matter. 6.3. The role of a massless scalar field. 6.4. The role of an electromagnetic field. 6.5. Quasi-isotropic inflation. 6.6. Quasi-isotropic viscous solution. 6.7. Guidelines to the literature -- 7. Homogeneous universes. 7.1. Homogeneous cosmological models. 7.2. Kasner solution. 7.3. The dynamics of the Bianchi models. 7.4. Bianchi types VIII and IX models. 7.5. Dynamical systems approach. 7.6. Multidimensional homogeneous universes. 7.7. Guidelines
Non-existence of perfect dark energy fluid in Bianchi type-IV space time
NASA Astrophysics Data System (ADS)
Mishra, B.; Sahoo, P. K.; Suresh, Srikanth
2015-07-01
In this paper, non-diagonal Bianchi type-IV space-time is investigated in Einstein general theory of relativity. The matter field is considered in the form of perfect dark energy fluid. It is interesting to observe that in this case, Bianchi type IV perfect dark energy fluid cosmological model does not exist. The space-time reduces to Minkowskian geometry.
A dynamical systems approach to the tilted Bianchi models of solvable type
NASA Astrophysics Data System (ADS)
Coley, Alan; Hervik, Sigbjørn
2005-02-01
We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VIh and VIIh) with a perfect fluid and a linear barotropic γ-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi type VII0 models. We prove the important result that for non-inflationary Bianchi type VIIh models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VIIh invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exist closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VIIh models there is a bifurcation in which a set of equilibrium points turns into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VIIh models in this region the solution curves approach a compact surface which is topologically a torus.
A Class of Homogeneous Scalar Tensor Cosmologies with a Radiation Fluid
NASA Astrophysics Data System (ADS)
Yazadjiev, Stoytcho S.
We present a new class of exact homogeneous cosmological solutions with a radiation fluid for all scalar tensor theories. The solutions belong to Bianchi type VIh cosmologies. Explicit examples of nonsingular homogeneous scalar tensor cosmologies are also given.
Planimetric Martian triangulations
Arthur, D.W.G.; McMacken, D.K.
1977-01-01
Narrow-angle photographs, which have severe drawbacks for stereophotogrammetry, have advantages for simple plane triangulations. Rectified narrow-angle pictures corrected for map projection effects can be combined in the map plane in relatively accurate planimetric triangulations. Provided the strict precepts of least squares are not followed, these triangulations can incorporate considerable overdetermination without increase in the labor of solving the equations. These plane triangulations have been used successfully in the cartography of Mars and are illustrated here by a triangulation of the environs of the prime Martian landing site.
Spin precession in anisotropic cosmologies
NASA Astrophysics Data System (ADS)
Kamenshchik, A. Yu.; Teryaev, O. V.
2016-05-01
We consider the precession of a Dirac particle spin in some anisotropic Bianchi universes. This effect is present already in the Bianchi-I universe. We discuss in some detail the geodesics and the spin precession for both the Kasner and the Heckmann-Schucking solutions. In the Bianchi-IX universe the spin precession acquires the chaotic character due to the stochasticity of the oscillatory approach to the cosmological singularity. The related helicity flip of fermions in the very early universe may produce the sterile particles contributing to dark matter.
Effective action for noncommutative Bianchi I model
NASA Astrophysics Data System (ADS)
Rosenbaum, M.; Vergara, J. D.; Minzoni, A. A.
2013-06-01
Quantum Mechanics, as a mini-superspace of Field Theory has been assumed to provide physically relevant information on quantum processes in Field Theory. In the case of Quantum Gravity this would imply using Cosmological models to investigate quantum processes at distances of the order of the Planck scale. However because of the Stone-von Neuman Theorem, it is well known that quantization of Cosmological models by the Wheeler-DeWitt procedure in the context of a Heisenberg-Weyl group with piecewise continuous parameters leads irremediably to a volume singularity. In order to avoid this information catastrophe it has been suggested recently the need to introduce in an effective theory of the quantization some form of reticulation in 3-space. On the other hand, since in the geometry of the General Relativistic formulation of Gravitation space can not be visualized as some underlying static manifold in which the physical system evolves, it would be interesting to investigate whether the effective reticulation which removes the singularity in such simple cosmologies as the Bianchi models has a dynamical origin manifested by a noncommutativity of the generators of the Heisenberg-Weyl algebra, as would be expected from an operational point of view at the Planck length scale.
Effective action for noncommutative Bianchi I model
Rosenbaum, M.; Vergara, J. D.; Minzoni, A. A.
2013-06-12
Quantum Mechanics, as a mini-superspace of Field Theory has been assumed to provide physically relevant information on quantum processes in Field Theory. In the case of Quantum Gravity this would imply using Cosmological models to investigate quantum processes at distances of the order of the Planck scale. However because of the Stone-von Neuman Theorem, it is well known that quantization of Cosmological models by the Wheeler-DeWitt procedure in the context of a Heisenberg-Weyl group with piecewise continuous parameters leads irremediably to a volume singularity. In order to avoid this information catastrophe it has been suggested recently the need to introduce in an effective theory of the quantization some form of reticulation in 3-space. On the other hand, since in the geometry of the General Relativistic formulation of Gravitation space can not be visualized as some underlying static manifold in which the physical system evolves, it would be interesting to investigate whether the effective reticulation which removes the singularity in such simple cosmologies as the Bianchi models has a dynamical origin manifested by a noncommutativity of the generators of the Heisenberg-Weyl algebra, as would be expected from an operational point of view at the Planck length scale.
Quantum gravitational Kasner transitions in Bianchi-I spacetime
NASA Astrophysics Data System (ADS)
Gupt, Brajesh; Singh, Parampreet
2012-07-01
Because of nonperturbative quantum gravitational effects, the classical big bang singularity is replaced by a quantum big bounce of the mean scale factor in loop quantization of Bianchi-I spacetime. An important issue is to understand the various differences in the physical properties of the spacetime across the bounce. We investigate this issue in the context of various geometrical structures, identified by the Kasner exponents of the metric, which arise on approach to the singularity in the classical theory. Using an effective spacetime description of the Bianchi-I model in loop quantum cosmology with dust, radiation and stiff matter, we find that as in the classical theory, geometrical structures such as a cigar or a pancake form, but they are finite and nonsingular. Depending on the initial conditions of the matter and anisotropies, different geometric structures are possible in the pre- and post-bounce phases in physical evolution. Thus, quantum gravitational effects can cause a Kasner transition in Bianchi-I spacetime, which is not possible at the classical level. Interestingly, we find that not all transitions are allowed at the level of effective dynamics in loop quantum cosmology. We find the selection rules and underlying conditions for all allowed and forbidden transitions. The selection rules suggest that for a given set of initial conditions on anisotropies, the occurrence of Kasner transitions follows a distinct pattern, and certain transitions are more favored than others.
ERIC Educational Resources Information Center
Denzin, Norman K.
2012-01-01
The author's thesis is simple and direct. Those in the mixed methods qualitative inquiry community need a new story line, one that does not confuse pragmatism for triangulation, and triangulation for mixed methods research (MMR). A different third way is required, one that inspires generative politics and dialogic democracy and helps shape…
NASA Astrophysics Data System (ADS)
Camci, U.; Yildirim, A.; Basaran Oz, I.
2016-03-01
The Noether symmetry approach is useful tool to restrict the arbitrariness in a gravity theory when the equations of motion are underdetermined due to the high number of functions to be determined in the ansatz. We consider two scalar-coupled theories of gravity, one motivated by induced gravity, the other more standard; in Bianchi I, Bianchi III and Kantowski-Sachs cosmological models. For these models, we present a full set of Noether gauge symmetries, which are more general than those obtained by the strict Noether symmetry approach in our recent work. Some exact solutions are derived using the first integrals corresponding to the obtained Noether gauge symmetries.
Bianchi Type-IX Dust Filled Universe with Ideal Fluid Distribution in Creation Field
NASA Astrophysics Data System (ADS)
Patil, V. R.; Bolke, P. A.; Bayaskar, N. S.
2014-12-01
We have investigated Bianchi type-IX dust filled universe for ideal fluid distribution in creation field in which creation field is a function of time t only. To get deterministic cosmological model, we have assumed a supplementary condition a = b n , where a and b are metric potential and n is constant. Also, we have study the physical and geometrical parameters of the said cosmological model.
Triangulation of NURBS Surfaces
NASA Technical Reports Server (NTRS)
Samareh-Abolhassani, Jamshid
1994-01-01
A technique is presented for triangulation of NURBS surfaces. This technique is built upon an advancing front technique combined with grid point projection. This combined approach has been successfully implemented for structured and unstructured grids.
NASA Astrophysics Data System (ADS)
Clancy, Dominic; Feinstein, Alexander; Lidsey, James E.; Tavakol, Reza
1999-04-01
Global symmetries of the string effective action are employed to generate tilted, homogeneous Bianchi type VIh string cosmologies from a previously known stiff perfect fluid solution to Einstein gravity. The dilaton field is not constant on the surfaces of homogeneity. The future asymptotic state of the models is interpreted as a plane wave and is itself an exact solution to the string equations of motion to all orders in the inverse string tension. An inhomogeneous generalization of the Bianchi type III model is also found.
Bianchi type-I, type-III and Kantowski-Sachs solutions in f( T) gravity
NASA Astrophysics Data System (ADS)
Rodrigues, M. E.; Kpadonou, A. V.; Rahaman, F.; Oliveira, P. J.; Houndjo, M. J. S.
2015-06-01
In the context of modified tele-parallel theory of gravity, we undertake cosmological anisotropic models and search for their solutions. Within a suitable choice of non-diagonal tetrads, the decoupled equations of motion are obtained for Bianchi-I, Bianchi-III and Kantowski-Sachs models, from which we obtain the correspondent solutions. By the way, energy density and pressures are also obtained, showing, as an important result, that our universe may live a quintessence like universe even while anisotropic models are considered.
Geodesic-light-cone coordinates and the Bianchi I spacetime
NASA Astrophysics Data System (ADS)
Fleury, Pierre; Nugier, Fabien; Fanizza, Giuseppe
2016-06-01
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; and (ii) offers a glimpse into new ways to constrain cosmic isotropy from the Hubble diagram.
Late-time behaviour of the tilted Bianchi type VIh models
NASA Astrophysics Data System (ADS)
Hervik, S.; van den Hoogen, R. J.; Lim, W. C.; Coley, A. A.
2007-08-01
We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VIh using dynamical systems methods and numerical experimentation, with an emphasis on their future asymptotic evolution. We determine all of the equilibrium points of the type VIh state space (which correspond to exact self-similar solutions of the Einstein equations, some of which are new), and their stability is investigated. We find that there are vacuum plane-wave solutions that act as future attractors. In the parameter space, a 'loophole' is shown to exist in which there are no stable equilibrium points. We then show that a Hopf-bifurcation can occur resulting in a stable closed orbit (which we refer to as the Mussel attractor) corresponding to points both inside the loophole and points just outside the loophole; in the former case the closed curves act as late-time attractors while in the latter case these attracting curves will co-exist with attracting equilibrium points. In the special Bianchi type III case, centre manifold theory is required to determine the future attractors. Comprehensive numerical experiments are carried out to complement and confirm the analytical results presented. We note that the Bianchi type VIh case is of particular interest in that it contains many different subcases which exhibit many of the different possible future asymptotic behaviours of Bianchi cosmological models.
NASA Astrophysics Data System (ADS)
Socorro, J.; Toledo Sesma, L.
2016-03-01
In this work we construct an effective four-dimensional model by compactifying a ten-dimensional theory of gravity coupled with a real scalar dilaton field on a time-dependent torus without the contributions of fluxes as first approximation. This approach is applied to anisotropic cosmological Bianchi type II model for which we study the classical coupling of the anisotropic scale factors with the two real scalar moduli produced by the compactification process. Also, we present some solutions to the corresponding Wheeler-DeWitt (WDW) equation in the context of Standard Quantum Cosmology and we claim that these quantum solution are generic in the moduli scalar field for all Bianchi Class A models. Also we give the relation to these solutions for asymptotic behavior to large argument in the corresponding quantum solution in the gravitational variables and compare with Bohm's solutions, finding that this corresponds to the lowest-order WKB approximation.
Unified Description of Bianchi Type-I Universe in f (R) Gravity
NASA Astrophysics Data System (ADS)
Katore, S. D.; Hatkar, S. P.; Baxi, R. J.
2016-04-01
The present study explores the Bianchi type I universe in the frame work of f( R) theory of gravity by considering strange quark matter attached to string cloud and domain walls in the presence and absence of magnetism. Field equations are solved by choosing a constant curvature method. It is found that obtained cosmological models are relevant to the early era of evolution of the universe. The strange quark matter may be a source of string cloud and domain walls.
Blocking Delaunay triangulations.
Aichholzer, Oswin; Fabila-Monroy, Ruy; Hackl, Thomas; van Kreveld, Marc; Pilz, Alexander; Ramos, Pedro; Vogtenhuber, Birgit
2013-02-01
Given a set B of n black points in general position, we say that a set of white points W blocks B if in the Delaunay triangulation of [Formula: see text] there is no edge connecting two black points. We give the following bounds for the size of the smallest set W blocking B: (i) [Formula: see text] white points are always sufficient to block a set of n black points, (ii) if B is in convex position, [Formula: see text] white points are always sufficient to block it, and (iii) at least [Formula: see text] white points are always necessary to block a set of n black points. PMID:23483043
Blocking Delaunay triangulations
Aichholzer, Oswin; Fabila-Monroy, Ruy; Hackl, Thomas; van Kreveld, Marc; Pilz, Alexander; Ramos, Pedro; Vogtenhuber, Birgit
2013-01-01
Given a set B of n black points in general position, we say that a set of white points W blocks B if in the Delaunay triangulation of B∪W there is no edge connecting two black points. We give the following bounds for the size of the smallest set W blocking B: (i) 3n/2 white points are always sufficient to block a set of n black points, (ii) if B is in convex position, 5n/4 white points are always sufficient to block it, and (iii) at least n−1 white points are always necessary to block a set of n black points. PMID:23483043
Bianchi class A models in Sàez-Ballester's theory
NASA Astrophysics Data System (ADS)
Socorro, J.; Espinoza-García, Abraham
2012-08-01
We apply the Sàez-Ballester (SB) theory to Bianchi class A models, with a barotropic perfect fluid in a stiff matter epoch. We obtain exact classical solutions à la Hamilton for Bianchi type I, II and VIh=-1 models. We also find exact quantum solutions to all Bianchi Class A models employing a particular ansatz for the wave function of the universe.
Lindstrom, P
2009-12-23
We describe a simple and efficient algorithm for two-view triangulation of 3D points from approximate 2D matches based on minimizing the L2 reprojection error. Our iterative algorithm improves on the one by Kanatani et al. by ensuring that in each iteration the epipolar constraint is satisfied. In the case where the two cameras are pointed in the same direction, the method provably converges to an optimal solution in exactly two iterations. For more general camera poses, two iterations are sufficient to achieve convergence to machine precision, which we exploit to devise a fast, non-iterative method. The resulting algorithm amounts to little more than solving a quadratic equation, and involves a fixed, small number of simple matrixvector operations and no conditional branches. We demonstrate that the method computes solutions that agree to very high precision with those of Hartley and Sturm's original polynomial method, though achieves higher numerical stability and 1-4 orders of magnitude greater speed.
Entropy of unimodular lattice triangulations
NASA Astrophysics Data System (ADS)
Knauf, Johannes F.; Krüger, Benedikt; Mecke, Klaus
2015-02-01
Triangulations are important objects of study in combinatorics, finite element simulations and quantum gravity, where their entropy is crucial for many physical properties. Due to their inherent complex topological structure even the number of possible triangulations is unknown for large systems. We present a novel algorithm for an approximate enumeration which is based on calculations of the density of states using the Wang-Landau flat histogram sampling. For triangulations on two-dimensional integer lattices we achieve excellent agreement with known exact numbers of small triangulations as well as an improvement of analytical calculated asymptotics. The entropy density is C=2.196(3) consistent with rigorous upper and lower bounds. The presented numerical scheme can easily be applied to other counting and optimization problems.
Braneworld cosmological models with anisotropy
NASA Astrophysics Data System (ADS)
Campos, Antonio; Maartens, Roy; Matravers, David; Sopuerta, Carlos F.
2003-11-01
For a cosmological Randall-Sundrum braneworld with anisotropy, i.e., of Bianchi type, the modified Einstein equations on the brane include components of the five-dimensional Weyl tensor for which there are no evolution equations on the brane. If the bulk field equations are not solved, this Weyl term remains unknown, and many previous studies have simply prescribed it as ad hoc. We construct a family of Bianchi braneworlds with anisotropy by solving the five-dimensional field equations in the bulk. We analyze the cosmological dynamics on the brane, including the Weyl term, and shed light on the relation between anisotropy on the brane and the Weyl curvature in the bulk. In these models, it is not possible to achieve geometric anisotropy for a perfect fluid or scalar field—the junction conditions require anisotropic stress on the brane. But the solutions can isotropize and approach a Friedmann brane in an anti de Sitter bulk.
Introduction to Causal Dynamical Triangulations
NASA Astrophysics Data System (ADS)
Görlich, Andrzej
The method of causal dynamical triangulations is a non-perturbative and background-independent approach to quantum theory of gravity. In this review we present recent results obtained within the four dimensional model of causal dynamical triangulations. We describe the phase structure of the model and demonstrate how a macroscopic four-dimensional de Sitter universe emerges dynamically from the full gravitational path integral. We show how to reconstruct the effective action describing scale factor fluctuations from Monte Carlo data.
Inhomogeneous Einstein-Rosen string cosmology
NASA Astrophysics Data System (ADS)
Clancy, Dominic; Feinstein, Alexander; Lidsey, James E.; Tavakol, Reza
1999-08-01
Families of anisotropic and inhomogeneous string cosmologies containing non-trivial dilaton and axion fields are derived by applying the global symmetries of the string effective action to a generalized Einstein-Rosen metric. The models exhibit a two-dimensional group of Abelian isometries. In particular, two classes of exact solutions are found that represent inhomogeneous generalizations of the Bianchi type VIh cosmology. The asymptotic behavior of the solutions is investigated and further applications are briefly discussed.
Vector fields and Loop Quantum Cosmology
Artymowski, Michał; Lalak, Zygmunt E-mail: Zygmunt.Lalak@fuw.edu.pl
2011-09-01
In the context of the Loop Quantum Cosmology we have analysed the holonomy correction to the classical evolution of the simplified Bianchi I model in the presence of vector fields. For the Universe dominated by a massive vector field or by a combination of a scalar field and a vector field a smooth transition between Kasner-like and Kasner-unlike solutions for a Bianchi I model has been demonstrated. In this case a lack of initial curvature singularity and a finite maximal energy density appear already at the level of General Relativity, which simulates a classical Big Bounce.
Quasi-greedy triangulations approximating the minimum weight triangulation
Levcopoulos, C.; Krznaric, D.
1996-12-31
This paper settles the following two open problems: (1) What is the worst-case approximation ratio between the greedy and the minimum weight triangulation? (2) Is there a polynomial time algorithm that always pro- duces a triangulation whose length is within a constant factor from the minimum? The answer to the first question is that the known {Omega}({radical}n) lower bound is tight. The second question is answered in the affirmative by using a slight modification of an O(n log n) algorithm for the greedy triangulation. We also derive some other interesting results. For example, we show that a constant-factor approximation of the minimum weight convex partition can be obtained within the same time bounds.
Anisotropic spinfoam cosmology
NASA Astrophysics Data System (ADS)
Rennert, Julian; Sloan, David
2014-01-01
The dynamics of a homogeneous, anisotropic universe are investigated within the context of spinfoam cosmology. Transition amplitudes are calculated for a graph consisting of a single node and three links—the ‘Daisy graph’—probing the behaviour a classical Bianchi I spacetime. It is shown further how the use of such single node graphs gives rise to a simplification of states such that all orders in the spin expansion can be calculated, indicating that it is the vertex expansion that contains information about quantum dynamics.
Unstable anisotropic loop quantum cosmology
Nelson, William; Sakellariadou, Mairi
2009-09-15
We study stability conditions of the full Hamiltonian constraint equation describing the quantum dynamics of the diagonal Bianchi I model in the context of loop quantum cosmology. Our analysis has shown robust evidence of an instability in the explicit implementation of the difference equation, implying important consequences for the correspondence between the full loop quantum gravity theory and loop quantum cosmology. As a result, one may question the choice of the quantization approach, the model of lattice refinement, and/or the role of the ambiguity parameters; all these should, in principle, be dictated by the full loop quantum gravity theory.
Dynamics of Anisotropic Bianchi Type-III Bulk Viscous String Model with Magnetic Field
NASA Astrophysics Data System (ADS)
Singh, M. K.; Ram, Shri
2014-07-01
In this paper, we discuss the dynamics of spatially homogeneous and anisotropic Bianchi type-III string cosmological model in presence of bulk viscous fluid and electromagnetic field. Exact solutions of Einstein's field equations are obtained by assuming (i) a special form of the deceleration parameter and (ii) the component of the shear scalar tensor is proportional to mean Hubble parameter. The source of magnetic field is due to an electric current produced along z-axis. The role of bulk viscosity and magnetic field in establishing string phase of universe is presented. The physical and kinematical features of solutions are also discussed in detail.
Exact self-similar Bianchi II solutions for some scalar-tensor theories
NASA Astrophysics Data System (ADS)
Belinchón, J. A.
2013-06-01
We study how may behave the gravitational and the cosmological "constants", ( G and Λ) in several scalar-tensor theories with Bianchi II symmetries. By working under the hypothesis of self-similarity we find exact solutions for three different theoretical models, which are: the Jordan-Brans-Dicke (JBD) with Λ( ϕ), the usual JBD model with potential U( ϕ) (that mimics the behavior of Λ( ϕ)) and the induced gravity (IG) model proposed by Sakharov and Zee. After a careful study of the obtained solutions we may conclude that the solutions are quite similar although the IG model shows some peculiarities.
Spinor fields in Bianchi type-I universe
NASA Astrophysics Data System (ADS)
Saha, B.
2006-12-01
A system of minimally coupled nonlinear spinor and scalar fields within the scope of a Bianchi type-I (BI) cosmological model in the presence of a perfect fluid and a cosmological constant (Λ term) is studied, and solutions to the corresponding field equations are obtained. The problem of initial singularity and the asymptotical isotropization process of the Universe are thoroughly studied. The effect of the Λ term on the character of evolution is analyzed. It is shown that some special choice of spinor field nonlinearity generates a regular solution, but the absence of singularity results in violating the dominant energy condition in the Hawking-Penrose theorem. It is also shown that a positive Λ, which denotes an additional gravitational force in our case, gives rise to an oscillatory or a non-periodic mode of expansion of the Universe depending on the choice of problem parameter. The regular oscillatory mode of expansion violets the dominant energy condition if the spinor field nonlinearity occurs as a result of self-action, whereas, in the case of a linear spinor field or nonlinear one that occurs due to interaction with a scalar field, the dominant condition remains unbroken. A system with time-varying gravitational (G) and cosmological (Λ) constants is also studied to some extent. The introduction of magneto-fluid in the system generates nonhomogeneity in the energy-momentum tensor and can be exactly solved only under some additional condition. Though in this case, we indeed deal with all four known fields, i.e., spinor, scalar, electromagnetic, and gravitational, the over-all picture of evolution remains unchanged.
Conformal Killing Vectors in LRS Bianchi Type V Spacetimes
NASA Astrophysics Data System (ADS)
Suhail, Khan; Tahir, Hussain; Ashfaque, H. Bokhari; Gulzar, Ali Khan
2016-03-01
In this note, we investigate conformal Killing vectors (CKVs) of locally rotationally symmetric (LRS) Bianchi type V spacetimes. Subject to some integrability conditions, CKVs up to implicit functions of (t,x) are obtained. Solving these integrability conditions in some particular cases, the CKVs are completely determined, obtaining a classification of LRS Bianchi type V spacetimes. The inheriting conformal Killing vectors of LRS Bianchi type V spacetimes are also discussed.
Evolution in bouncing quantum cosmology
NASA Astrophysics Data System (ADS)
Mielczarek, Jakub; Piechocki, Włodzimierz
2012-03-01
We present the method of describing an evolution in quantum cosmology in the framework of the reduced phase space quantization of loop cosmology. We apply our method to the flat Friedmann-Robertson-Walker model coupled to a massless scalar field. We identify the physical quantum Hamiltonian that is positive-definite and generates globally a unitary evolution of the considered quantum system. We examine the properties of expectation values of physical observables in the process of the quantum big bounce transition. The dispersion of evolved observables is studied for the Gaussian state. Calculated relative fluctuations enable an examination of the semi-classicality conditions and possible occurrence of the cosmic forgetfulness. Preliminary estimations based on the cosmological data suggest that there was no cosmic amnesia. Presented results are analytical, and numerical computations are only used for the visualization purposes. Our method may be generalized to sophisticated cosmological models including the Bianchi-type universes.
LRS Bianchi Type-II Inflationary Universe with Massless Scalar Field and Time Varying Λ
NASA Astrophysics Data System (ADS)
Raj, Bali; Swati
2012-08-01
The locally rotationally symmetric (LRS) Bianchi type-II inflationary cosmological model is investigated for massless scalar field with flat potential and time varying Λ. To obtain the deterministic solution, it is assumed that scale factor is a(t)~eHt as we considered previously for Bianchi type-I spacetime and Λ~a-2 as considered by Chen and Wu, where H is the Hubble constant and effective potential V(phi)=const; phi Higg's field. It is shown that such a time varying Λ leads to no conflict with existing observations. However, it does change the predictions of standard cosmology in the matter-dominated phase and alleviates some problems in reconciling observations with the inflationary scenario. The model represents anisotropic spacetime in general. However, the model isotropizes for large values of t and β = 3H2, where β is constant. The physical and geometrical aspects of the model in the context of an inflationary scenario is also discussed.
Some properties of n-dimensional triangulations
NASA Technical Reports Server (NTRS)
Lawson, C. L.
1985-01-01
A number of mathematical results relevant to the problem of constructing a triangulation, i.e., a simplicial tessellation, of the convex hull of an arbitrary finite set of points in n-space are described. The principal results achieved are: (1) a set of n+2 points in n-space may be triangulated in at most 2 different ways; (2) the sphere test defined in this report selects a preferred one of these two triangulations; (3) a set of parameters is defined that permits the characterization and enumeration of all sets of n+2 points in n-space that are significantly different from the point of view of their possible triangulation; (4) the local sphere test induces a global sphere test property for a triangulation; and (5) a triangulation satisfying the global sphere property is dual to the n-dimensional Dirichlet tesselation, i.e., it is a Delaunay triangulation.
Inhomogeneous generalizations of Bianchi type VIh models with perfect fluid
NASA Astrophysics Data System (ADS)
Roy, S. R.; Prasad, A.
1991-07-01
Inhomogeneous universes admitting an Abelian G2 of isometry and filled with perfect fluid have been derived. These contain as special cases exact homogeneous universes of Bianchi type VIh. Many of these universes asymptotically tend to homogeneous Bianchi VIh universes. The models have been discussed for their physical and kinematical behaviors.
Dynamical analysis of anisotropic cosmological model with quintessence
NASA Astrophysics Data System (ADS)
Chaubey, R.; Raushan, Rakesh
2016-07-01
The present work is a phase-plane analysis of LRS Bianchi type I cosmological model with a scalar field and exponential potential. The evolution equations are reduced to an autonomous system of ordinary equations by suitable transformation of variables. We also analyse the evolution of the effective equation of state parameter for different values of curvature. The nature of critical points is analysed and stable attractors are examined from the point of view of cosmology.
NASA Astrophysics Data System (ADS)
Barrow, John D.; Ganguly, Chandrima
2016-06-01
We study the behaviour of Bianchi class A universes containing an ultra-stiff isotropic ghost field and a fluid with anisotropic pressures which is also ultra-stiff on the average. This allows us to investigate whether cyclic universe scenarios, like the ekpyrotic model, do indeed lead to isotropization on approach to a singularity (or bounce) in the presence of dominant ultra-stiff pressure anisotropies. We specialize to consider the closed Bianchi type IX universe, and show that when the anisotropic pressures are stiffer on average than any isotropic ultra-stiff fluid then, if they dominate on approach to the singularity, it will be anisotropic. We include an isotropic ultra-stiff ghost fluid with negative energy density in order to create a cosmological bounce at finite volume in the absence of the anisotropic fluid. When the dominant anisotropic fluid is present it leads to an anisotropic cosmological singularity rather than an isotropic bounce. The inclusion of anisotropic stresses generated by collisionless particles in an anisotropically expanding universe is therefore essential for a full analysis of the consequences of a cosmological bounce or singularity in cyclic universes.
Helical phase of chiral nematic liquid crystals as the Bianchi VII0 group manifold.
Gibbons, G W; Warnick, C M
2011-09-01
We show that the optical structure of the helical phase of a chiral nematic is naturally associated with the Bianchi VII(0) group manifold, of which we give a full account. The Joets-Ribotta metric governing propagation of the extraordinary rays is invariant under the simply transitive action of the universal cover E(2) of the three-dimensional Euclidean group of two dimensions. Thus extraordinary light rays are geodesics of a left-invariant metric on this Bianchi type VII(0) group. We are able to solve, by separation of variables, both the wave equation and the Hamilton-Jacobi equation for this metric. The former reduces to Mathieu's equation, and the latter to the quadrantal pendulum equation. We discuss Maxwell's equations for uniaxial optical materials where the configuration is invariant under a group action and develop a formalism to take advantage of these symmetries. The material is not assumed to be impedance matched, thus going beyond the usual scope of transformation optics. We show that for a chiral nematic in its helical phase Maxwell's equations reduce to a generalized Mathieu equation. Our results may also be relevant to helical phases of some magnetic materials and to light propagation in certain cosmological models. PMID:22060392
Triangulation of cubic panorama for view synthesis.
Zhang, Chunxiao; Zhao, Yan; Wu, Falin
2011-08-01
An unstructured triangulation approach, new to our knowledge, is proposed to apply triangular meshes for representing and rendering a scene on a cubic panorama (CP). It sophisticatedly converts a complicated three-dimensional triangulation into a simple three-step triangulation. First, a two-dimensional Delaunay triangulation is individually carried out on each face. Second, an improved polygonal triangulation is implemented in the intermediate regions of each of two faces. Third, a cobweblike triangulation is designed for the remaining intermediate regions after unfolding four faces to the top/bottom face. Since the last two steps well solve the boundary problem arising from cube edges, the triangulation with irregular-distribution feature points is implemented in a CP as a whole. The triangular meshes can be warped from multiple reference CPs onto an arbitrary viewpoint by face-to-face homography transformations. The experiments indicate that the proposed triangulation approach provides a good modeling for the scene with photorealistic rendered CPs. PMID:21833101
Making the Case for Causal Dynamical Triangulations
NASA Astrophysics Data System (ADS)
Cooperman, Joshua H.
2015-11-01
The aim of the causal dynamical triangulations approach is to define nonperturbatively a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. My aim in this paper is to give a concise yet comprehensive, impartial yet personal presentation of the causal dynamical triangulations approach.
Mixed Methods, Triangulation, and Causal Explanation
ERIC Educational Resources Information Center
Howe, Kenneth R.
2012-01-01
This article distinguishes a disjunctive conception of mixed methods/triangulation, which brings different methods to bear on different questions, from a conjunctive conception, which brings different methods to bear on the same question. It then examines a more inclusive, holistic conception of mixed methods/triangulation that accommodates…
Linear-size nonobtuse triangulation of polygons
Bern, M.; Mitchell, S.; Ruppert, J.
1994-05-01
We give an algorithm for triangulating n-vertex polygonal regions (with holes) so that no angle in the final triangulation measures more than {pi}/2. The number of triangles in the triangulation is only 0(n), improving a previous bound of 0(n{sup 2}), and the worst-case running time is 0(n log{sup 2} n). The basic technique used in the algorithm, recursive subdivision by disks, is new and may have wider application in mesh generation. We also report on an implementation of our algorithm.
Uav Photogrammetry: Block Triangulation Comparisons
NASA Astrophysics Data System (ADS)
Gini, R.; Pagliari, D.; Passoni, D.; Pinto, L.; Sona, G.; Dosso, P.
2013-08-01
UAVs systems represent a flexible technology able to collect a big amount of high resolution information, both for metric and interpretation uses. In the frame of experimental tests carried out at Dept. ICA of Politecnico di Milano to validate vector-sensor systems and to assess metric accuracies of images acquired by UAVs, a block of photos taken by a fixed wing system is triangulated with several software. The test field is a rural area included in an Italian Park ("Parco Adda Nord"), useful to study flight and imagery performances on buildings, roads, cultivated and uncultivated vegetation. The UAV SenseFly, equipped with a camera Canon Ixus 220HS, flew autonomously over the area at a height of 130 m yielding a block of 49 images divided in 5 strips. Sixteen pre-signalized Ground Control Points, surveyed in the area through GPS (NRTK survey), allowed the referencing of the block and accuracy analyses. Approximate values for exterior orientation parameters (positions and attitudes) were recorded by the flight control system. The block was processed with several software: Erdas-LPS, EyeDEA (Univ. of Parma), Agisoft Photoscan, Pix4UAV, in assisted or automatic way. Results comparisons are given in terms of differences among digital surface models, differences in orientation parameters and accuracies, when available. Moreover, image and ground point coordinates obtained by the various software were independently used as initial values in a comparative adjustment made by scientific in-house software, which can apply constraints to evaluate the effectiveness of different methods of point extraction and accuracies on ground check points.
Stability of the anisotropically inflating Bianchi type VI expanding solutions
Kao, W. F.; Lin, Ing-Chen
2011-03-15
A special class of the Bianchi type VI expanding solutions was speculated to break the cosmic no-hair theorem that will not approach the late-time de Sitter solution. We will show that an unstable mode always exists when the perturbation of the field equations is applied to the system. In addition to a model-independent perturbation formula, a simplification is also achieved by the introduction of a {delta}R=0 solution good for quadratic models in all Bianchi spaces. The result shows that this special class of anisotropically expanding solutions is unstable.
Stability conditions for the Bianchi type II anisotropically inflating universes
Kao, W.F.; Lin, Ing-Chen E-mail: g9522528@oz.nthu.edu.tw
2009-01-15
Stability conditions for a class of anisotropically inflating solutions in the Bianchi type II background space are shown explicitly in this paper. These inflating solutions were known to break the cosmic no-hair theorem such that they do not approach the de Sitter universe at large times. It can be shown that unstable modes of the anisotropic perturbations always exist for this class of expanding solutions. As a result, we show that these set of anisotropically expanding solutions are unstable against anisotropic perturbations in the Bianchi type II space.
Ricci inheritance collineations in Bianchi type II spacetime
NASA Astrophysics Data System (ADS)
Hussain, Tahir; Akhtar, Sumaira Saleem; Bokhari, Ashfaque H.; Khan, Suhail
2016-06-01
In this paper, we present a complete classification of Bianchi type II spacetime according to Ricci inheritance collineations (RICs). The RICs are classified considering cases when the Ricci tensor is both degenerate as well as non-degenerate. In case of non-degenerate Ricci tensor, it is found that Bianchi type II spacetime admits 4-, 5-, 6- or 7-dimensional Lie algebra of RICs. In the case when the Ricci tensor is degenerate, majority cases give rise to infinitely many RICs, while remaining cases admit finite RICs given by 4, 5 or 6.
A study of positive energy condition in Bianchi V spacetimes via Noether symmetries
NASA Astrophysics Data System (ADS)
Ali, Sajid; Hussain, Ibrar
2016-02-01
In this paper we use Noether symmetries of the geodesic Lagrangian in Bianchi V spacetimes to study various cosmological solutions of Einstein's field equations. Our first result is the identification of the subalgebras of Noether symmetries of the equations of motion in such spacetimes with dimension 4, 5, 6, 7, 9 or 10 of the maximal algebra of Lie point symmetries of dimension 13. Second, we give a physical interpretation of new cosmological solutions which satisfy the positive energy condition and yield critical bounds on the expansion coefficient α , in which the underlying non-flat spacetimes have interesting physical properties. Specifically the energy density behaves in one of the following ways. (i) It is positive and constant for all time. (ii) It varies with time and attains a global maximum after some time and then asymptotically converges to zero. (iii) It increases for all time and attains a maximum value at the asymptotic limit t→ ∞. In particular a non-flat spacetime is obtained that mimics the expansion in a flat FRW universe dominated by vacuum energy such that the expansion factor has the same form in both. However, the energy density is dynamical in the former.
Bianchi type-II models in the presence of perfect fluid and anisotropic dark energy
NASA Astrophysics Data System (ADS)
Kumar, Suresh; Akarsu, Özgür
2012-06-01
The spatially homogeneous but totally anisotropic and non-flat Bianchi type-II cosmological model has been studied in general relativity in the presence of two minimally interacting fluids; a perfect fluid as the matter fluid and a hypothetical anisotropic fluid as the dark energy fluid. The Einstein field equations have been solved by applying two kinematical Ansätze: we have assumed the variation law for the mean Hubble parameter that yields a constant value of the deceleration parameter, and one of the components of the shear tensor has been considered proportional to the mean Hubble parameter. We have particularly dwelled on the accelerating models with non-divergent expansion anisotropy as the Universe evolves. Yielding the anisotropic pressure, the fluid we consider in the context of dark energy can produce results that can be produced in the presence of isotropic fluid in accordance with the ΛCDM cosmology. However, the derived model gives additional opportunities by being able to allow kinematics that cannot be produced in the presence of fluids that yield only isotropic pressure. We have obtained well-behaving cases where the anisotropy of the expansion and the anisotropy of the fluid converge to finite values (include zero) in the late Universe. We have also showed that, although the metric we consider is totally anisotropic, the anisotropy of the dark energy is constrained to be axially symmetric, as long as the overall energy momentum tensor possesses zero shear stress.
Inflation in a renormalizable cosmological model and the cosmic no hair conjecture
NASA Technical Reports Server (NTRS)
Maeda, Kei-Ichi; Stein-Schabes, Jaime A.; Futamase, Toshifumi
1988-01-01
The possibility of having inflation in a renormalizable cosmological model is investigated. The Cosmic No Hair Conjecture is proved to hold for all Bianchi types except Bianchi IX. By the use of a conformal transformation on the metric it is shown that these models are equivalent to the ones described by the Einstein-Hilbert action for gravity minimally coupled to a set of scalar fields with inflationary potentials. Henceforth, it is proven that inflationary solutions behave as attractors in solution space, making it a natural event in the evolution of such models.
Can cosmic parallax distinguish between anisotropic cosmologies?
Fontanini, Michele; West, Eric J.; Trodden, Mark
2009-12-15
In an anisotropic universe, observers not positioned at a point of special symmetry should observe cosmic parallax--the relative angular motion of test galaxies over cosmic time. It was recently argued that the nonobservance of this effect in upcoming precision astrometry missions such as GAIA may be used to place strong bounds on the position of off-center observers in a void-model universe described by the Lemaitre-Tolman-Bondi metric. We consider the analogous effect in anisotropic cosmological models described by an axisymmetric homogeneous Bianchi type I metric and discuss whether any observation of cosmic parallax would distinguish between different anisotropic evolutions.
NASA Astrophysics Data System (ADS)
Dymnikova, Irina
2003-06-01
In the spherically symmetric case the dominant energy condition, together with the requirement of regularity of a density and finiteness of the mass, defines the family of asymptotically flat globally regular solutions to the Einstein minimally coupled equations which includes the class of metrics asymptotically de Sitter as r --> 0 and asymptotically Schwarzschild as r --> ∞. A source term connects smoothly de Sitter vacuum in the origin with the Minkowski vacuum at infinity and corresponds to anisotropic vacuum defined macroscopically by the algebraic structure of its stress-energy tensor invariant under boosts in the radial direction. Dependently on parameters, geometry describes vacuum nonsingular black and white holes, and self-gravitating particle-like structures. ADM mass for this class is related to both de Sitter vacuum trapped inside an object and to breaking of space-time symmetry. This class of metrics is easily extended to the case of nonzero cosmological constant at infinity. The source term connects then smoothly two de Sitter vacua and corresponds to extension of the Einstein cosmological term Λgμν to an r-dependent cosmological term Λμν. In this approach a constant scalar Λ associated with a vacuum density Λ = 8πGρvac, becomes a tensor component Λtt associated explicitly with a density component of a perfect fluid tensor whose vacuum properties follow from its symmetry and whose variability follows from the Bianchi identities. In this review we outline and discuss Λμν geometry and its applications.
Triangulation technique in optical fiber sensing
NASA Astrophysics Data System (ADS)
Brenci, Massimo; Mencaglia, Andrea A.; Mignani, Anna G.
1990-08-01
Optical triangulation is a very well-known classical technique which can be advantageously performed by optical fibers, taking profit from their geometrical versatility, intrinsic safety and good transmission properties. The exploitation of different optical architectures provides spatial information over single or multiple sensing zones, so that a wide class of intensity-modulated optical fiber sensors can be achieved.
Spectral Properties of Unimodular Lattice Triangulations
NASA Astrophysics Data System (ADS)
Krüger, Benedikt; Schmidt, Ella M.; Mecke, Klaus
2016-05-01
Random unimodular lattice triangulations have been recently used as an embedded random graph model, which exhibit a crossover behavior between an ordered, large-world and a disordered, small-world behavior. Using the ergodic Pachner flips that transform such triangulations into another and an energy functional that corresponds to the degree distribution variance, Markov chain Monte Carlo simulations can be applied to study these graphs. Here, we consider the spectra of the adjacency and the Laplacian matrix as well as the algebraic connectivity and the spectral radius. Power law dependencies on the system size can clearly be identified and compared to analytical solutions for periodic ground states. For random triangulations we find a qualitative agreement of the spectral properties with well-known random graph models. In the microcanonical ensemble analytical approximations agree with numerical simulations. In the canonical ensemble a crossover behavior can be found for the algebraic connectivity and the spectral radius, thus combining large-world and small-world behavior in one model. The considered spectral properties can be applied to transport problems on triangulation graphs and the crossover behavior allows a tuning of important transport quantities.
Triangulation using synthetic aperture radar images
NASA Technical Reports Server (NTRS)
Wu, Sherman S. C.; Howington-Kraus, Annie E.
1991-01-01
For the extraction of topographic information about Venus from stereoradar images obtained from the Magellan Mission, a Synthetic Aperture Radar (SAR) compilation system was developed on analytical stereoplotters. The system software was extensively tested by using stereoradar images from various spacecraft and airborne radar systems, including Seasat, SIR-B, ERIM XCL, and STAR-1. Stereomodeling from radar images was proven feasible, and development is on a correct approach. During testing, the software was enhanced and modified to obtain more flexibility and better precision. Triangulation software for establishing control points by using SAR images was also developed through a joint effort with the Defense Mapping Agency. The SAR triangulation system comprises four main programs, TRIDATA, MODDATA, TRISAR, and SHEAR. The first two programs are used to sort and update the data; the third program, the main one, performs iterative statistical adjustment; and the fourth program analyzes the results. Also, input are flight data and data from the Global Positioning System and Inertial System (navigation information). The SAR triangulation system was tested with six strips of STAR-1 radar images on a VAX-750 computer. Each strip contains images of 10 minutes flight time (equivalent to a ground distance of 73.5 km); the images cover a ground width of 22.5 km. All images were collected from the same side. With an input of 44 primary control points, 441 ground control points were produced. The adjustment process converged after eight iterations. With a 6-m/pixel resolution of the radar images, the triangulation adjustment has an average standard elevation error of 81 m. Development of Magellan radargrammetry will be continued to convert both SAR compilation and triangulation systems into digital form.
Cho, Y.M. Department of Physics, Seoul National University, Seoul )
1990-04-15
Recently a unified cosmology was proposed as a higher-dimensional generalization of the standard big-bang cosmology. In this paper we discuss its foundation, characteristics, and possible cosmological solutions in detail. In particular we discuss how the missing-mass problem, the horizon problem, and the flatness problem of the standard model can be resolved within the context of this unified cosmology.
Statistical properties of cosmological billiards
NASA Astrophysics Data System (ADS)
Damour, Thibault; Lecian, Orchidea Maria
2011-02-01
Belinski, Khalatnikov, and Lifshitz pioneered the study of the statistical properties of the never-ending oscillatory behavior (among successive Kasner epochs) of the geometry near a spacelike singularity. We show how the use of a “cosmological billiard” description allows one to refine and deepen the understanding of these statistical properties. Contrary to previous treatments, we do not quotient the dynamics by its discrete symmetry group (of order 6), thereby uncovering new phenomena, such as correlations between the successive billiard corners in which the oscillations take place. Starting from the general integral invariants of Hamiltonian systems, we show how to construct invariant measures for various projections of the cosmological-billiard dynamics. In particular, we exhibit, for the first time, a (non-normalizable) invariant measure on the “Kasner circle” which parametrizes the exponents of successive Kasner epochs. Finally, we discuss the relation between: (i) the unquotiented dynamics of the Bianchi-IX (a, b, c or mixmaster) model; (ii) its quotienting by the group of permutations of (a, b, c); and (iii) the billiard dynamics that arose in recent studies suggesting the hidden presence of Kac-Moody symmetries in cosmological billiards.
Chaotic Inflationary Scenario in Bianchi Type i Spacetime
NASA Astrophysics Data System (ADS)
Bali, Raj
2012-03-01
Chaotic inflationary model of the early universe proposed by Linde7 is investigated in the frame work of Bianchi type I spacetime. To determine inflationary scenario, we assume that scale factor R3 = ABC ˜ e3Ht, V(φ ) = (1)/(2)m2φ ^2+(λ )/(n)φ ^n, λ being a constant, m the mass, V(ϕ) the potential energy density. It is shown that chaotic model leads to an inflationary phase which also helps in isotropization process. The Higg's field (ϕ) is initially large but decreases due to lapse of time in both cases. The assumption R3 = ABC e3Ht does not lead to FRW model immediately but for large values of t, it reduces to FRW model since shear σ = 0 in FRW model and shear σ ≠ 0 in Bianchi type I model. The physical aspects of the model are also discussed.
Diffeomorphism invariant cosmological symmetry in full quantum gravity
NASA Astrophysics Data System (ADS)
Beetle, Christopher; Engle, Jonathan S.; Hogan, Matthew E.; Mendonça, Phillip
2016-06-01
This paper summarizes a new proposal to define rigorously a sector of loop quantum gravity at the diffeomorphism invariant level corresponding to homogeneous and isotropic cosmologies, thereby enabling a detailed comparison of results in loop quantum gravity and loop quantum cosmology. The key technical steps we have completed are (a) to formulate conditions for homogeneity and isotropy in a diffeomorphism covariant way on the classical phase-space of general relativity, and (b) to translate these conditions consistently using well-understood techniques to loop quantum gravity. Some additional steps, such as constructing a specific embedding of the Hilbert space of loop quantum cosmology into a space of (distributional) states in the full theory, remain incomplete. However, we also describe, as a proof of concept, a complete analysis of an analogous embedding of homogeneous and isotropic loop quantum cosmology into the quantum Bianchi I model of Ashtekar and Wilson-Ewing. Details will appear in a pair of forthcoming papers.
The Newtonian approximation in Causal Dynamical Triangulations
NASA Astrophysics Data System (ADS)
Getchell, Adam
2015-04-01
I review how to derive Newton's law of universal gravitation from the Weyl strut between two Chazy-Curzon particles. I also briefly review Causal Dynamical Triangulations (CDT), a method for evaluating the path integral from canonical quantum gravity using Regge calculus and restrictions of the class of simplicial manifolds evaluated to those with a defined time foliation, thus enforcing a causal structure. I then discuss how to apply this approach to Causal Dynamical Triangulations, in particular modifying the algorithm to keep two simplicial submanifolds with curvature (i.e. mass) a fixed distance from each other, modulo regularized deviations and across all time slices. I then discuss how to determine if CDT produces an equivalent Weyl strut, which can then be used to obtain the Newtonian limit. I wrap up with a brief discussion of computational methods and code development.
Roaming moduli space using dynamical triangulations
NASA Astrophysics Data System (ADS)
Ambjørn, J.; Barkley, J.; Budd, T. G.
2012-05-01
In critical as well as in non-critical string theory the partition function reduces to an integral over moduli space after integration over matter fields. For non-critical string theory this moduli integrand is known for genus one surfaces. The formalism of dynamical triangulations provides us with a regularization of non-critical string theory. We show how to assign in a simple and geometrical way a moduli parameter to each triangulation. After integrating over possible matter fields we can thus construct the moduli integrand. We show numerically for c=0 and c=-2 non-critical strings that the moduli integrand converges to the known continuum expression when the number of triangles goes to infinity.
Extending particle tracking capability with Delaunay triangulation.
Chen, Kejia; Anthony, Stephen M; Granick, Steve
2014-04-29
Particle tracking, the analysis of individual moving elements in time series of microscopic images, enables burgeoning new applications, but there is need to better resolve conformation and dynamics. Here we describe the advantages of Delaunay triangulation to extend the capabilities of particle tracking in three areas: (1) discriminating irregularly shaped objects, which allows one to track items other than point features; (2) combining time and space to better connect missing frames in trajectories; and (3) identifying shape backbone. To demonstrate the method, specific examples are given, involving analyzing the time-dependent molecular conformations of actin filaments and λ-DNA. The main limitation of this method, shared by all other clustering techniques, is the difficulty to separate objects when they are very close. This can be mitigated by inspecting locally to remove edges that are longer than their neighbors and also edges that link two objects, using methods described here, so that the combination of Delaunay triangulation with edge removal can be robustly applied to processing large data sets. As common software packages, both commercial and open source, can construct Delaunay triangulation on command, the methods described in this paper are both computationally efficient and easy to implement. PMID:24734998
Sprite initiation altitude measured by triangulation
NASA Astrophysics Data System (ADS)
Stenbaek-Nielsen, H. C.; Haaland, R.; McHarg, M. G.; Hensley, B. A.; Kanmae, T.
2010-03-01
High time resolution (10,000 frames per second) images of sprites combined with multistation concurrent video recordings have provided data for triangulation of the altitude of the initial sprite onset. The high-speed images were obtained from the Langmuir Laboratory, New Mexico, during summer campaigns in 2007 and 2008 with video observations from sites at Portales, New Mexico, and Las Vegas, New Mexico. Sprites start with one or more downward-propagating streamer heads. The triangulated onset altitudes of this initial downward streamer vary between 66 and 89 km. In some sprites the downward streamers are followed a little later by upward-propagating streamers. The upward streamers start from a lower altitude and existing luminous sprite structures and their triangulated altitudes vary from 64 to 78 km. The downward streamers create C sprite characteristics, while the upward streamers form the broad diffuse tops of carrot sprites. In the sprites analyzed the higher onset altitudes for the downward-propagating initial streamers were associated with C sprites and the lower with carrot sprites, but our larger data set indicates that this is not generally the case. It appears that the dominant sprite types vary from year to year, indicating that some longer-lasting environmental parameter, such as mesospheric conductivity and composition or thunderstorm cloud dynamics, may play an important role in determining the types of sprites observed.
Coefficient adaptive triangulation for strongly anisotropic problems
D`Azevedo, E.F.; Romine, C.H.; Donato, J.M.
1996-01-01
Second order elliptic partial differential equations arise in many important applications, including flow through porous media, heat conduction, the distribution of electrical or magnetic potential. The prototype is the Laplace problem, which in discrete form produces a coefficient matrix that is relatively easy to solve in a regular domain. However, the presence of anisotropy produces a matrix whose condition number is increased, making the resulting linear system more difficult to solve. In this work, we take the anisotropy into account in the discretization by mapping each anisotropic region into a ``stretched`` coordinate space in which the anisotropy is removed. The region is then uniformly triangulated, and the resulting triangulation mapped back to the original space. The effect is to generate long slender triangles that are oriented in the direction of ``preferred flow.`` Slender triangles are generally regarded as numerically undesirable since they tend to cause poor conditioning; however, our triangulation has the effect of producing effective isotropy, thus improving the condition number of the resulting coefficient matrix.
The simplest possible bouncing quantum cosmological model
NASA Astrophysics Data System (ADS)
Peter, Patrick; Vitenti, Sandro D. P.
2016-06-01
We present and expand the simplest possible quantum cosmological bouncing model already discussed in previous works: the trajectory formulation of quantum mechanics applied to cosmology (through the Wheeler-De Witt equation) in the Friedmann-Lemaître-Robertson-Walker (FLRW) minisuperspace without spatial curvature. The initial conditions that were previously assumed were such that the wave function would not change its functional form but instead provide a dynamics to its parameters. Here, we consider a more general situation, in practice consisting of modified Gaussian wave functions, aiming at obtaining a nonsingular bounce from a contracting phase. Whereas previous works consistently obtain very symmetric bounces, we find that it is possible to produce highly non-symmetric solutions, and even cases for which multiple bounces naturally occur. We also introduce a means of treating the shear in this category of models by quantizing in the Bianchi I minisuperspace.
Some Bianchi type generalized ghost piligrim dark energy models in general relativity
NASA Astrophysics Data System (ADS)
Santhi, M. Vijaya; Aditya, Y.; Rao, V. U. M.
2016-04-01
In this paper, we consider Bianchi type-III, V and VI0 space-times filled with generalized ghost pilgrim dark energy (GGPDE) in general relativity. Here we assume the anisotropic distribution of GGPDE by introducing skewness parameters. To get deterministic solutions, we consider the scale factor a(t)=(tnet)^{ 1/k}, so called hybrid expansion, which yields a time dependent deceleration parameter, and exhibits a transition of the Universe from early decelerated phase to the recent accelerating phase. To describe the behavior of the obtained models we construct equation of state (ω_{Λ}), squared sound speed (vs2) parameters and ω_{Λ}-dot{ω }_{Λ}, r-s planes. It is worth mentioning here that the analysis of evolution parameters supports the concept of pilgrim dark energy (PDE). Also, these models remain stable for PDE parameter β =-0.5. Moreover, the cosmological planes correspond to Λ CDM limit as well as different well-known dark energy models.
A first look at transition amplitudes in (2 + 1)-dimensional causal dynamical triangulations
NASA Astrophysics Data System (ADS)
Cooperman, Joshua H.; Miller, Jonah M.
2014-02-01
We study a lattice regularization of the gravitational path integral—causal dynamical triangulations—for (2 + 1)-dimensional Einstein gravity with positive cosmological constant in the presence of past and future spacelike boundaries of fixed intrinsic geometries. For spatial topology of a 2-sphere, we determine the form of the Einstein-Hilbert action supplemented by the Gibbons-Hawking-York boundary terms within the Regge calculus of causal triangulations. Employing this action we numerically simulate a variety of transition amplitudes from the past boundary to the future boundary. To the extent that we have so far investigated them, these transition amplitudes appear consistent with the gravitational effective action previously found to characterize the ground state of quantum spacetime geometry within the Euclidean de Sitter-like phase. Certain of these transition amplitudes convincingly demonstrate that the so-called stalks present in this phase are numerical artifacts of the lattice regularization, seemingly indicate that the quantization technique of causal dynamical triangulations differs in detail from that of the no-boundary proposal of Hartle and Hawking, and possibly represent the first numerical simulations of portions of temporally unbounded quantum spacetime geometry within the causal dynamical triangulations approach. We also uncover tantalizing evidence suggesting that Lorentzian not Euclidean de Sitter spacetime dominates the ground state on sufficiently large scales.
Quantization ambiguities and bounds on geometric scalars in anisotropic loop quantum cosmology
NASA Astrophysics Data System (ADS)
Singh, Parampreet; Wilson-Ewing, Edward
2014-02-01
We study quantization ambiguities in loop quantum cosmology that arise for space-times with non-zero spatial curvature and anisotropies. Motivated by lessons from different possible loop quantizations of the closed Friedmann-Lemaître-Robertson-Walker cosmology, we find that using open holonomies of the extrinsic curvature, which due to gauge-fixing can be treated as a connection, leads to the same quantum geometry effects that are found in spatially flat cosmologies. More specifically, in contrast to the quantization based on open holonomies of the Ashtekar-Barbero connection, the expansion and shear scalars in the effective theories of the Bianchi type II and Bianchi type IX models have upper bounds, and these are in exact agreement with the bounds found in the effective theories of the Friedmann-Lemaître-Robertson-Walker and Bianchi type I models in loop quantum cosmology. We also comment on some ambiguities present in the definition of inverse triad operators and their role.
Strategies for nonobtuse boundary Delaunay triangulations
Murphy, M. |; Gable, C.W.
1998-12-31
Delaunay Triangulations with nonobtuse triangles at the boundaries satisfy a minimal requirement for Control Volume meshes. They motivate this quality requirement, discuss it in context with others that have been proposed, and give point placement strategies that generate the fewest or close to the fewest number of Steiner points needed to satisfy it for a particular problem instance. The advantage is that this strategy places a number of Steiner points proportional to the combinatorial size of the input rather than the local feature size, resulting in far fewer points in many cases.
Phenomenological dynamics of loop quantum cosmology in Kantowski-Sachs spacetime
Chiou, D.-W.
2008-08-15
The fundamental theory and the semiclassical description of loop quantum cosmology (LQC) have been studied in the Friedmann-Robertson-Walker and Bianchi I models. As an extension to include both anisotropy and intrinsic curvature, this paper investigates the cosmological model of Kantowski-Sachs spacetime with a free massless scalar field at the level of phenomenological dynamics with the LQC discreteness corrections. The LQC corrections are implemented in two different improved quantization schemes. In both schemes, the big bang and big crunch singularities of the classical solution are resolved and replaced by the big bounces when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. Symmetries of scaling are also noted and suggest that the fundamental spatial scale (area gap) may give rise to a temporal scale. The bouncing scenarios are in an analogous fashion of the Bianchi I model, naturally extending the observations obtained previously.
Stochastic eternal inflation in a Bianchi type I universe
NASA Astrophysics Data System (ADS)
Kohli, Ikjyot Singh; Haslam, Michael C.
2016-01-01
The phenomenon of stochastic eternal inflation is studied for a chaotic inflation potential in a Bianchi type I spacetime background. After deriving the appropriate stochastic Klein-Gordon equation, we give details on the conditions for eternal inflation. It is shown that for eternal inflation to occur, the amount of anisotropy must be small. In fact, it is shown that eternal inflation will only take place if the shear anisotropy variables take on values within a small region of the interior of the Kasner circle. We then calculate the probability of eternal inflation occurring based on techniques from stochastic calculus.
Finding a covering triangulation whose maximum angle is provably small
Mitchell, S.A.; Park, J.K.
1993-03-03
Given a planar straight-line graph, we find a covering triangulation whose maximum angle is as small as possible. A covering triangulation is a triangulation whose vertex set contains the input vertex set and whose edge set contains the input edge set. Such a triangulation differs from the usual Steiner triangulation in that we may not add a Steiner vertex on any input edge. Covering triangulations provide a convenient method for triangulating multiple regions sharing a common boundary, as each region can be triangulated independently. As it is possible that no finite covering triangulation is optimal in terms of its maximum angle, we propose an approximation algorithm. Our algorithm produces a covering triangulation whose maximum angle {gamma} is probably close to {gamma}{sub opt}, a lower bound on the maximum angle in any covering triangulation of the input graph. Note that we must have {gamma} {le} 3{gamma}{sub opt}, since we always have {gamma}{sub opt} {ge} {pi}/3 and no triangulation can contain an angle of size greater than {pi}. We prove something significantly stronger. We show that {pi} {minus} {gamma} {ge} ({pi} {minus} {gamma}{sub opt})/6, i.e., our {gamma} is not much closer to {pi} than is {gamma}{sub opt}. This result represents the first nontrivial bound on a covering triangulation`s maximum angle. We require a subroutine for the following problem: Given a polygon with holes, find a Steiner triangulation whose maximum angle is bounded away from {pi}. No angle larger than 8{pi}/9 is sufficient for the bound on {gamma} claimed above. The number of Steiner vertices added by our algorithm and its running time are highly dependent on the corresponding bounds for the subroutine. Given an n-vertex planar straight-line graph, we require O(n + S(n)) Steiner vertices and O(n log n + T(n)) time, where S(n) is the number of Steiner vertices added by the subroutine and T(n) is its running time for an O(n)-vertex polygon with holes.
NASA Astrophysics Data System (ADS)
Sanders, Robert H.
I discuss the classical cosmological tests, i.e., angular size-redshift, flux-redshift, and galaxy number counts, in the light of the cosmology prescribed by the interpretation of the CMB anisotropies. The discussion is somewhat of a primer for physicists, with emphasis upon the possible systematic uncertainties in the observations and their interpretation. Given the curious composition of the Universe inherent in the emerging cosmological model, I stress the value of searching for inconsistencies rather than concordance, and suggest that the prevailing mood of triumphalism in cosmology is premature.
An Introduction to General Relativity and Cosmology
NASA Astrophysics Data System (ADS)
Plebanski, Jerzy; Krasinski, Andrzej
2006-08-01
1. How the theory of relativity came into being (a brief historical sketch); Part I. Elements of Differential Geometry: 2. A short sketch of two-dimensional differential geometries; 3. Tensors, tensor densities; 4. Covariant derivatives; 5. Parallel transport and geodesic lines; 6. Curvature of a manifold: flat manifolds; 7. Riemannian geometry; 8. Symmetries of Rieman spaces, invariance of tensors; 9. Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs; 10. The spatially homogeneous Bianchi-type spacetimes; 11. The Petrov classification by the spinor method; Part II. The Gravitation Theory: 12. The Einstein equations and the sources of a gravitational field; 13. The Maxwell and Einstein-Maxwell equations and the Kaluza-Klein theory; 14. Spherically symmetric gravitational field of isolated objects; 15. Relativistic hydrodynamics and thermodynamics; 16. Relativistic cosmology I: general geometry; 17. Relativistic cosmology II: the Robertson-Walker geometry; 18. Relativistic cosmology III: the Lemaître-Tolman geometry; 19. Relativistic cosmology IV: generalisations of L-T and related geometries; 20. The Kerr solution; 21. Subjects omitted in this book; References.
An Introduction to General Relativity and Cosmology
NASA Astrophysics Data System (ADS)
Plebanski, Jerzy; Krasinski, Andrzej
2012-09-01
1. How the theory of relativity came into being (a brief historical sketch); Part I. Elements of Differential Geometry: 2. A short sketch of two-dimensional differential geometries; 3. Tensors, tensor densities; 4. Covariant derivatives; 5. Parallel transport and geodesic lines; 6. Curvature of a manifold: flat manifolds; 7. Riemannian geometry; 8. Symmetries of Rieman spaces, invariance of tensors; 9. Methods to calculate the curvature quickly - Cartan forms and algebraic computer programs; 10. The spatially homogeneous Bianchi-type spacetimes; 11. The Petrov classification by the spinor method; Part II. The Gravitation Theory: 12. The Einstein equations and the sources of a gravitational field; 13. The Maxwell and Einstein-Maxwell equations and the Kaluza-Klein theory; 14. Spherically symmetric gravitational field of isolated objects; 15. Relativistic hydrodynamics and thermodynamics; 16. Relativistic cosmology I: general geometry; 17. Relativistic cosmology II: the Robertson-Walker geometry; 18. Relativistic cosmology III: the Lemaître-Tolman geometry; 19. Relativistic cosmology IV: generalisations of L-T and related geometries; 20. The Kerr solution; 21. Subjects omitted in this book; References.
Triangulation, Respondent Validation, and Democratic Participation in Mixed Methods Research
ERIC Educational Resources Information Center
Torrance, Harry
2012-01-01
Over the past 10 years or so the "Field" of "Mixed Methods Research" (MMR) has increasingly been exerting itself as something separate, novel, and significant, with some advocates claiming paradigmatic status. Triangulation is an important component of mixed methods designs. Triangulation has its origins in attempts to validate research findings…
Buie, W D; Thurston, O G; vanAerde, J E; Aherne, F X; Thomson, A B; Fedorak, R N
1993-01-01
This study compared the efficacy of a Bianchi bowel-lengthening procedure performed in residual ileum and jejunum of a 75% short bowel model. Eighteen female piglets underwent a 75% mid small bowel resection. After a 6-week period, animal weights were similar and pigs were randomly assigned to one of three treatment groups: (1) a control group receiving no further therapy; (2) a group receiving a Bianchi procedure in the residual jejunal segment; and (3) a group receiving a Bianchi procedure in the residual ileal segment. All were followed for a further 12 weeks. Jejunal Bianchi-treated short bowel animals demonstrated a greater final weight gain (78.8 +/- 4.9 kg) compared with nontreated short bowel (63.0 +/- 6.6 kg) and ileal Bianchi-treated short bowel groups (69.3 +/- 6.9 kg) in addition to a larger jejunal diameter. The increased weight gain in the jejunal Bianchi-treated group was not a consequence of initial bowel length, food intake, changes in bowel length, digestibility of nitrogen or fat, or nutritional status. Furthermore, kinetic constants for D-glucose absorption following 18 weeks of short-bowel syndrome demonstrated a lowered glucose maximal transport rate (Vmax) in animals with nontreated short bowel compared with sham-operated controls. Additionally, jejunal and ileal glucose Vmax was further lowered in the presence of a Bianchi procedure. We conclude that: (1) during short-bowel syndrome, body weight gain was significantly higher in animals when the Bianchi procedure was performed in jejunum; (2) the short-bowel syndrome decreased intestinal glucose absorption; and (3) the Bianchi procedure itself further impaired glucose transport. PMID:8429461
Finding a covering triangulation whose maximum angle is provably small
Mitchell, S.A.; Park, J.K.
1993-03-03
Given a planar straight-line graph, we find a covering triangulation whose maximum angle is as small as possible. A covering triangulation is a triangulation whose vertex set contains the input vertex set and whose edge set contains the input edge set. Such a triangulation differs from the usual Steiner triangulation in that we may not add a Steiner vertex on any input edge. Covering triangulations provide a convenient method for triangulating multiple regions sharing a common boundary, as each region can be triangulated independently. As it is possible that no finite covering triangulation is optimal in terms of its maximum angle, we propose an approximation algorithm. Our algorithm produces a covering triangulation whose maximum angle [gamma] is probably close to [gamma][sub opt], a lower bound on the maximum angle in any covering triangulation of the input graph. Note that we must have [gamma] [le] 3[gamma][sub opt], since we always have [gamma][sub opt] [ge] [pi]/3 and no triangulation can contain an angle of size greater than [pi]. We prove something significantly stronger. We show that [pi] [minus] [gamma] [ge] ([pi] [minus] [gamma][sub opt])/6, i.e., our [gamma] is not much closer to [pi] than is [gamma][sub opt]. This result represents the first nontrivial bound on a covering triangulation's maximum angle. We require a subroutine for the following problem: Given a polygon with holes, find a Steiner triangulation whose maximum angle is bounded away from [pi]. No angle larger than 8[pi]/9 is sufficient for the bound on [gamma] claimed above. The number of Steiner vertices added by our algorithm and its running time are highly dependent on the corresponding bounds for the subroutine. Given an n-vertex planar straight-line graph, we require O(n + S(n)) Steiner vertices and O(n log n + T(n)) time, where S(n) is the number of Steiner vertices added by the subroutine and T(n) is its running time for an O(n)-vertex polygon with holes.
Anisotropic cosmological models in f(G) gravity
NASA Astrophysics Data System (ADS)
Farasat Shamir, M.
2016-04-01
The main objective of this manuscript is to study the anisotropic universe in f(G) Gravity. For this purpose, locally rotationally symmetric Bianchi type I spacetime is considered. A viable f(G) model is used to explore the exact solutions of modified field equations. In particular, two families involving power law and exponential type solutions have been discussed. Some important cosmological parameters are calculated for the obtained solutions. Moreover, energy density and pressure of the universe is analyzed for the model under consideration.
NASA Astrophysics Data System (ADS)
Bae, Joseph H.
2015-04-01
A modified semi-classical method is used to construct both ground and excited state solutions to the canonically quantized vacuum Bianchi IX (Mixmaster) cosmological models. Employing a modified form of the semi-classical Ansatz we solve the relevant Wheeler-DeWitt equation asymptotically by integrating a set of linear transport equations along the flow of a suitably chosen solution to the corresponding Euclidean-signature Hamilton-Jacobi equation. For the Moncrief-Ryan (or ‘wormhole’) Hamilton-Jacobi solution, we compute the ground state quantum correction term associated with operator ordering ambiguities and show how higher order correction terms can be computed. We also determine the explicit, leading order forms of a family of excited states and show how to compute their quantum corrections as smooth, globally defined functions on the Bianchi IX minisuperspace. These excited state solutions are peaked away from the minisuperspace origin and are labeled by a pair of positive integers that can be plausibly interpreted as graviton excitation numbers for the two independent anisotropy degrees of freedom. The Euclidean-signature semi-classical method used here is applicable to more general models, representing a significant progress in the Wheeler-DeWitt approach to quantum gravity.
A global conformal extension theorem for perfect fluid Bianchi space-times
Luebbe, Christian Tod, Paul
2008-12-15
A global extension theorem is established for isotropic singularities in polytropic perfect fluid Bianchi space-times. When an extension is possible, the limiting behaviour of the physical space-time near the singularity is analysed.
On the asserted clash between the Freud and the Bianchi identities
NASA Astrophysics Data System (ADS)
Antoci, S.
1995-09-01
Through a constructive method it is shown that the claim advanced in recent times about a clash that should occur between the Freud and the Bianchi identities in Einstein's general theory of relativity is based on a faulty argument.
Bianchi-Baecklund transformations, conservation laws, and linearization of various field theories
Chau Wang, L L
1980-01-01
The discussion includes: the Sine-Gordon equation, parametric Bianchi-Baecklund transformations and the derivation of local conservation laws; chiral fields, parametric Bianchi-Baecklund transformations, local and non-local conservation laws, and linearization; super chiral fields, a parallel development similar to the chiral field; and self-dual Yang-Mills fields in 4-dimensional Euclidean space; loop-cpace chiral equations, parallel development but with subtlety. (GHT)
Cosmological solutions of f (T ) gravity
NASA Astrophysics Data System (ADS)
Paliathanasis, Andronikos; Barrow, John D.; Leach, P. G. L.
2016-07-01
In the cosmological scenario in f (T ) gravity, we find analytical solutions for an isotropic and homogeneous universe containing a dust fluid and radiation and for an empty anisotropic Bianchi I universe. The method that we apply is that of movable singularities of differential equations. For the isotropic universe, the solutions are expressed in terms of a Laurent expansion, while for the anisotropic universe we find a family of exact Kasner-like solutions in vacuum. Finally, we discuss when a nonlinear f (T ) -gravity theory provides solutions for the teleparallel equivalence of general relativity and derive conditions for exact solutions of general relativity to solve the field equations of an f (T ) theory.
Incremental triangulation by way of edge swapping and local optimization
NASA Technical Reports Server (NTRS)
Wiltberger, N. Lyn
1994-01-01
This document is intended to serve as an installation, usage, and basic theory guide for the two dimensional triangulation software 'HARLEY' written for the Silicon Graphics IRIS workstation. This code consists of an incremental triangulation algorithm based on point insertion and local edge swapping. Using this basic strategy, several types of triangulations can be produced depending on user selected options. For example, local edge swapping criteria can be chosen which minimizes the maximum interior angle (a MinMax triangulation) or which maximizes the minimum interior angle (a MaxMin or Delaunay triangulation). It should be noted that the MinMax triangulation is generally only locally optical (not globally optimal) in this measure. The MaxMin triangulation, however, is both locally and globally optical. In addition, Steiner triangulations can be constructed by inserting new sites at triangle circumcenters followed by edge swapping based on the MaxMin criteria. Incremental insertion of sites also provides flexibility in choosing cell refinement criteria. A dynamic heap structure has been implemented in the code so that once a refinement measure is specified (i.e., maximum aspect ratio or some measure of a solution gradient for the solution adaptive grid generation) the cell with the largest value of this measure is continually removed from the top of the heap and refined. The heap refinement strategy allows the user to specify either the number of cells desired or refine the mesh until all cell refinement measures satisfy a user specified tolerance level. Since the dynamic heap structure is constantly updated, the algorithm always refines the particular cell in the mesh with the largest refinement criteria value. The code allows the user to: triangulate a cloud of prespecified points (sites), triangulate a set of prespecified interior points constrained by prespecified boundary curve(s), Steiner triangulate the interior/exterior of prespecified boundary curve
Onomatopoeia characters extraction from comic images using constrained Delaunay triangulation
NASA Astrophysics Data System (ADS)
Liu, Xiangping; Shoji, Kenji; Mori, Hiroshi; Toyama, Fubito
2014-02-01
A method for extracting onomatopoeia characters from comic images was developed based on stroke width feature of characters, since they nearly have a constant stroke width in a number of cases. An image was segmented with a constrained Delaunay triangulation. Connected component grouping was performed based on the triangles generated by the constrained Delaunay triangulation. Stroke width calculation of the connected components was conducted based on the altitude of the triangles generated with the constrained Delaunay triangulation. The experimental results proved the effectiveness of the proposed method.
Nonlinear spinor fields in Bianchi type-VI0 spacetime
NASA Astrophysics Data System (ADS)
Saha, Bijan
2015-10-01
Within the scope of Bianchi type- V I 0 spacetime we study the role of spinor field on the evolution of the Universe. It is found that the presence of the non-trivial non-diagonal components of the energy-momentum tensor of the spinor field plays a vital role on the evolution of the Universe. As a result of their mutual influence, there occur two different scenarios. In one case the invariants constructed from the bilinear forms of the spinor field become trivial, thus giving rise to a massless and linear spinor field Lagrangian. According to the second scenario massive and nonlinear terms do not vanish and depending on the sign of the coupling constants we have either an expanding mode of expansion or the one that, after obtaining some maximum value, contracts and ends in a big crunch generating spacetime singularity. This result shows that the spinor field is highly sensitive to the gravitational one.
Numerical Bianchi type I solutions in semiclassical gravitation
Vitenti, Sandro D. P.; Mueller, Daniel
2006-09-15
It is believed that soon after the Planck era, spacetime should have a semiclassical nature. In this context we consider quantum fields propagating in a classical gravitational field and study the backreaction of these fields, using the expected value of the energy-momentum tensor as source of the gravitational field. According to this theory, the escape from general relativity theory is unavoidable. Two geometric counter-term are needed to regularize the divergences which come from the expected value. There is a parameter associated to each counter-term and in this work we found numerical solutions of this theory to particular initial conditions, for general Bianchi Type I spaces. We show that even though there are spurious solutions some of them can be considered physical. These physical solutions include de Sitter and Minkowski that are obtained asymptotically.
NASA Astrophysics Data System (ADS)
Krauss, L. M.
1999-01-01
The long-derided cosmological constant - a contrivance of Albert Einstein's that represents a bizarre form of energy inherent in space itself - is one of two contenders for explaining changes in the expansion rate of the Universe.
NASA Astrophysics Data System (ADS)
Banks, T.
This talk is a summary of work done in collaboration with Micha Berkooz, Greg Moore, Steve Shenker and Paul Steinhardt on a cosmology whose early history is described in terms of the moduli fields of string theory.
Surface Triangulation for CSG in Mercury
Engel, Daniel; O'Brien, Matthew J.
2015-08-26
Visualization routines for rendering complicated geometries are very useful for engineers and scientists who are trying to build 3D prototypes of their designs. A common way to rapidly add interesting features to a 3D model is through the use of a concept called Constructive Solid Geometry. CSG uses compositions of the boolean set operations to manipulate basic geometric primitives to form more complicated objects. The most common boolean operations employed are union, intersection, and subtraction. Most computer-aided design software packages contain some sort of ability visualize CSG. The typical workflow for the user is as follows: The user specifies the individual primitive components, the user arbitrarily combines each of these primitives with boolean operations, the software generates a CSG tree structure which normally stores these solids implicitly with their defining equation, the tree is traversed and a general algorithm is applied to render the appropriate geometry onto the screen. Algorithms for visualizing CSG have been extensively developed for over a decade. Points sampled from the implicit solids are typically used as input by variations of algorithms like marching cubes and point-cloud surface reconstruction. Here, we explain a surface triangulation method from the graphics community that is being used for surface visualization in the framework of a Monte-Carlo neutron transport code called Mercury.
Container integrity verification using laser triangulation
NASA Astrophysics Data System (ADS)
Busboom, Axel; Sequeira, Vítor
2007-04-01
We present a system for verifying the integrity of storage containers using a laser triangulation scanner, with applications in nuclear security. Any intrusion into the container shell and subsequent reconstruction of the surface inevitably leaves slight changes to the three-dimensional surface structure which the proposed system can detect. The setup consists of a laser line scanner, mounted on a rotation stage. We propose an auto-calibration procedure for this system which - from several scans of a planar calibration target acquired from different viewpoints - automatically determines the position and orientation of the rotation axis with respect to the scanner coordinate frame. We further present an algorithm for the automatic registration of two 3D scans of a cylindrical surface, not requiring any user interaction such as the identification of corresponding point pairs. We show that the algorithm accurately aligns two scans of the same object, acquired from different viewpoints. The accuracy of the overall system is dominated by the measurement uncertainty of the 3D scanner; residual errors resulting from the calibration and registration are subordinate. The system can reliably detect changes in the surface shape resulting from tampering.
DIVE in the cosmic web: voids with Delaunay triangulation from discrete matter tracer distributions
NASA Astrophysics Data System (ADS)
Zhao, Cheng; Tao, Charling; Liang, Yu; Kitaura, Francisco-Shu; Chuang, Chia-Hsun
2016-07-01
We present a novel parameter-free cosmological void finder (DIVE, Delaunay TrIangulation Void findEr) based on Delaunay Triangulation (DT), which efficiently computes the empty spheres constrained by a discrete set of tracers. We define the spheres as DT voids, and describe their properties, including a universal density profile together with an intrinsic scatter. We apply this technique on 100 halo catalogues with volumes of 2.5 h-1Gpc side each, with a bias and number density similar to the Baryon Oscillation Spectroscopic Survey CMASS luminous red galaxies, performed with the PATCHY code. Our results show that there are two main species of DT voids, which can be characterized by the radius: they have different responses to halo redshift space distortions, to number density of tracers, and reside in different dark matter environments. Based on dynamical arguments using the tidal field tensor, we demonstrate that large DT voids are hosted in expanding regions, whereas the haloes used to construct them reside in collapsing ones. Our approach is therefore able to efficiently determine the troughs of the density field from galaxy surveys, and can be used to study their clustering. We further study the power spectra of DT voids, and find that the bias of the two populations are different, demonstrating that the small DT voids are essentially tracers of groups of haloes.
NASA Astrophysics Data System (ADS)
Lesgourges, J.
2013-08-01
We present a self-contained summary of the theory of linear cosmological perturbations. We emphasize the effect of the six parameters of the minimal cosmological model, first, on the spectrum of Cosmic Microwave Background temperature anisotropies, and second, on the linear matter power spectrum. We briefly review at the end the possible impact of a few non-minimal dark matter and dark energy models.
Cardinality bounds for triangulations with bounded minimum angle
Mitchell, S.A.
1994-05-01
We consider bounding the cardinality of an arbitrary triangulation with smallest angle {alpha}. We show that if the local feature size (i.e. distance between disjoint vertices or edges) of the triangulation is within a constant factor of the local feature size of the input, then N < O(1/{alpha})M, where N is the cardinality of the triangulation and M is the cardinality of any other triangulation with smallest angle at least {alpha}. Previous results had an O(1/{alpha}{sup 1/{alpha}}) dependence. Our O(1/{alpha}) dependence is tight for input with a large length to height ratio, in which triangles may be oriented along the long dimension.
On triangulations of the plane by pencils of conics. II
Lazareva, V B; Shelekhov, A M
2013-06-30
The present work continues our previous paper in which all possible triangulations of the plane using three pencils of circles were listed. In the present article we find all projectively distinct triangulations of the plane by pencils of conics that are obtained by projecting regular three-webs, cut out on a nondegenerate cubic surface by three pencils of planes, whose axes lie on this surface. Bibliography: 6 titles.
Algebraic Error Based Triangulation and Metric of Lines
Wu, Fuchao; Zhang, Ming; Wang, Guanghui; Hu, Zhanyi
2015-01-01
Line triangulation, a classical geometric problem in computer vision, is to determine the 3D coordinates of a line based on its 2D image projections from more than two views of cameras with known projection matrices. Compared to point features, line segments are more robust to matching errors, occlusions, and image uncertainties. In addition to line triangulation, a better metric is needed to evaluate 3D errors of line triangulation. In this paper, the line triangulation problem is investigated by using the Lagrange multipliers theory. The main contributions include: (i) Based on the Lagrange multipliers theory, a formula to compute the Plücker correction is provided, and from the formula, a new linear algorithm, LINa, is proposed for line triangulation; (ii) two optimal algorithms, OPTa-I and OPTa-II, are proposed by minimizing the algebraic error; and (iii) two metrics on 3D line space, the orthogonal metric and the quasi-Riemannian metric, are introduced for the evaluation of line triangulations. Extensive experiments on synthetic data and real images are carried out to validate and demonstrate the effectiveness of the proposed algorithms. PMID:26218615
Triangulation of the Interstellar Magnetic Field
NASA Astrophysics Data System (ADS)
Schwadron, N. A.; Richardson, J. D.; Burlaga, L. F.; McComas, D. J.; Moebius, E.
2015-11-01
Determining the direction of the local interstellar magnetic field (LISMF) is important for understanding the heliosphere’s global structure, the properties of the interstellar medium, and the propagation of cosmic rays in the local galactic medium. Measurements of interstellar neutral atoms by Ulysses for He and by SOHO/SWAN for H provided some of the first observational insights into the LISMF direction. Because secondary neutral H is partially deflected by the interstellar flow in the outer heliosheath and this deflection is influenced by the LISMF, the relative deflection of H versus He provides a plane—the so-called B-V plane in which the LISMF direction should lie. Interstellar Boundary Explorer (IBEX) subsequently discovered a ribbon, the center of which is conjectured to be the LISMF direction. The most recent He velocity measurements from IBEX and those from Ulysses yield a B-V plane with uncertainty limits that contain the centers of the IBEX ribbon at 0.7-2.7 keV. The possibility that Voyager 1 has moved into the outer heliosheath now suggests that Voyager 1's direct observations provide another independent determination of the LISMF. We show that LISMF direction measured by Voyager 1 is >40° off from the IBEX ribbon center and the B-V plane. Taking into account the temporal gradient of the field direction measured by Voyager 1, we extrapolate to a field direction that passes directly through the IBEX ribbon center (0.7-2.7 keV) and the B-V plane, allowing us to triangulate the LISMF direction and estimate the gradient scale size of the magnetic field.
Triangulation of the Interstellar Magnetic Field
NASA Astrophysics Data System (ADS)
Schwadron, N. A.; Richardson, J. D.; Burlaga, L. F.; McComas, D. J.; Moebius, E.
2015-11-01
Determining the direction of the local interstellar magnetic field (LISMF) is important for understanding the heliosphere’s global structure, the properties of the interstellar medium, and the propagation of cosmic rays in the local galactic medium. Measurements of interstellar neutral atoms by Ulysses for He and by SOHO/SWAN for H provided some of the first observational insights into the LISMF direction. Because secondary neutral H is partially deflected by the interstellar flow in the outer heliosheath and this deflection is influenced by the LISMF, the relative deflection of H versus He provides a plane—the so-called B–V plane in which the LISMF direction should lie. Interstellar Boundary Explorer (IBEX) subsequently discovered a ribbon, the center of which is conjectured to be the LISMF direction. The most recent He velocity measurements from IBEX and those from Ulysses yield a B–V plane with uncertainty limits that contain the centers of the IBEX ribbon at 0.7–2.7 keV. The possibility that Voyager 1 has moved into the outer heliosheath now suggests that Voyager 1's direct observations provide another independent determination of the LISMF. We show that LISMF direction measured by Voyager 1 is >40° off from the IBEX ribbon center and the B–V plane. Taking into account the temporal gradient of the field direction measured by Voyager 1, we extrapolate to a field direction that passes directly through the IBEX ribbon center (0.7–2.7 keV) and the B–V plane, allowing us to triangulate the LISMF direction and estimate the gradient scale size of the magnetic field.
Quantum supersymmetric cosmology and its hidden Kac-Moody structure
NASA Astrophysics Data System (ADS)
Damour, Thibault; Spindel, Philippe
2013-08-01
We study the quantum dynamics of a supersymmetric squashed three-sphere by dimensionally reducing (to one timelike dimension) the action of D = 4 simple supergravity for an SO(3)-homogeneous (Bianchi IX) cosmological model. The quantization of the homogeneous gravitino field leads to a 64-dimensional fermionic Hilbert space. The algebra of the supersymmetry constraints and of the Hamiltonian one is found to close. One finds that the quantum Hamiltonian is built from operators that generate a 64-dimensional representation of the (infinite-dimensional) maximally compact sub-algebra of the rank-3 hyperbolic Kac-Moody algebra AE3. Some exponentials of these operators generate a spinorial extension of the Weyl group of AE3 which describe (in the small wavelength limit) the chaotic quantum evolution of the universe near the cosmological singularity.
Nonlinear stability of cosmological solutions in massive gravity
Felice, Antonio De; Gümrükçüoğlu, A. Emir; Lin, Chunshan; Mukohyama, Shinji E-mail: emir.gumrukcuoglu@ipmu.jp E-mail: shinji.mukohyama@ipmu.jp
2013-05-01
We investigate nonlinear stability of two classes of cosmological solutions in massive gravity: isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) solutions and anisotropic FLRW solutions. For this purpose we construct the linear cosmological perturbation theory around axisymmetric Bianchi type-I backgrounds. We then expand the background around the two classes of solutions, which are fixed points of the background evolution equation, and analyze linear perturbations on top of it. This provides a consistent truncation of nonlinear perturbations around these fixed point solutions and allows us to analyze nonlinear stability in a simple way. In particular, it is shown that isotropic FLRW solutions exhibit nonlinear ghost instability. On the other hand, anisotropic FLRW solutions are shown to be ghost-free for a range of parameters and initial conditions.
Observations on interfacing loop quantum gravity with cosmology
NASA Astrophysics Data System (ADS)
Pawłowski, Tomasz
2015-12-01
A simple idea of relating the loop quantum gravity (LQG) and loop quantum cosmology (LQC) degrees of freedom is introduced and used to define a relatively robust interface between these theories in context of toroidal Bianchi I model. The idea is an expansion of the construction originally introduced by Ashtekar and Wilson-Ewing and relies on explicit averaging of a certain subclass of spin networks over the subgroup of the diffeomorphisms remaining after the gauge fixing used in homogeneous LQC. It is based on the set of clearly defined principles and thus is a convenient tool to control the emergence and behavior of the cosmological degrees of freedom in studies of dynamics in canonical LQG. The constructed interface is further adapted to isotropic spacetimes. Relating the proposed LQG-LQC interface with some results on black hole entropy suggests a modification to the area gap value currently used in LQC.
NASA Astrophysics Data System (ADS)
Kraniotis, G. V.
In this work, we review recent work on string cosmology. The need for an inflationary era is well known. Problems of Standard Cosmology such as horizon, flatness, monopole and entropy find an elegant solution in the inflationary scenario. On the other hand no adequate inflationary model has been constructed so far. In this review we discuss the attempts that have been made in the field of string theory for obtaining an adequate Cosmological Inflationary Epoch. In particular, orbifold compactifications of string theory which are constrained by target-space duality symmetry offer as natural candidates for the role of inflatons the orbifold moduli. Orbifold moduli dynamics is very constrained by duality symmetry and offers a concrete framework for discussing Cosmological Inflation. We discuss the resulting cosmology assuming that nonperturbative dynamics generates a moduli potential which respects target-space modular invariance. Various modular forms for the nonperturbative superpotential and Kähler potential which include the absolute modular invariant j(T) besides the Dedekind eta function η(T) are discussed. We also review scale-factor duality and pre-Big-Bang scenarios in which inflation is driven by the kinetic terms of the dilaton modulus. In this context we discuss the problem of graceful exit and review recent attempts for solving the problem of exiting from inflation. The possibility of obtaining inflation through the D-terms in string models with anomalous UA(1) and other Abelian factors is reviewed. In this context we discuss how the slow-roll problem in supergravity models with F-term inflation can be solved by D-term inflation. We also briefly review the consequences of duality for a generalized Heisenberg uncertainty principle and the structure of space-time at short scales. The problem of the Cosmological Constant is also briefly discussed.
NASA Astrophysics Data System (ADS)
Narimani, Ali; Moss, Adam; Scott, Douglas
2012-10-01
Although it is well known that any consideration of the variations of fundamental constants should be restricted to their dimensionless combinations, the literature on variations of the gravitational constant G is entirely dimensionfull. To illustrate applications of this to cosmology, we explicitly give a dimensionless version of the parameters of the standard cosmological model, and describe the physics of both Big Bang Nucleosynthesis and recombination in a dimensionless manner. Rigorously determining how to talk about the model in a way which avoids physical dimensions is a requirement for proceeding with a calculation to constrain time-varying fundamental constants. The issue that appears to have been missed in many studies is that in cosmology the strength of gravity is bound up in the cosmological equations, and the epoch at which we live is a crucial part of the model. We argue that it is useful to consider the hypothetical situation of communicating with another civilization (with entirely different units), comparing only dimensionless constants, in order to decide if we live in a Universe governed by precisely the same physical laws. In this thought experiment, we would also have to compare epochs, which can be defined by giving the value of any one of the evolving cosmological parameters. By setting things up carefully in this way one can avoid inconsistent results when considering variable constants, caused by effectively fixing more than one parameter today. We show examples of this effect by considering microwave background anisotropies, being careful to maintain dimensionlessness throughout. We present Fisher matrix calculations to estimate how well the fine structure constants for electromagnetism and gravity can be determined with future microwave background experiments. We highlight how one can be misled by simply adding G to the usual cosmological parameter set.
Simulations of four-dimensional simplicial quantum gravity as dynamical triangulation
Agishtein, M.E.; Migdal, A.A. )
1992-04-20
In this paper, Four-Dimensional Simplicial Quantum Gravity is simulated using the dynamical triangulation approach. The authors studied simplicial manifolds of spherical topology and found the critical line for the cosmological constant as a function of the gravitational one, separating the phases of opened and closed Universe. When the bare cosmological constant approaches this line from above, the four-volume grows: the authors reached about 5 {times} 10{sup 4} simplexes, which proved to be sufficient for the statistical limit of infinite volume. However, for the genuine continuum theory of gravity, the parameters of the lattice model should be further adjusted to reach the second order phase transition point, where the correlation length grows to infinity. The authors varied the gravitational constant, and they found the first order phase transition, similar to the one found in three-dimensional model, except in 4D the fluctuations are rather large at the transition point, so that this is close to the second order phase transition. The average curvature in cutoff units is large and positive in one phase (gravity), and small negative in another (antigravity). The authors studied the fractal geometry of both phases, using the heavy particle propagator to define the geodesic map, as well as with the old approach using the shortest lattice paths.
NASA Astrophysics Data System (ADS)
Wong, Wan Yan
2008-11-01
In this thesis we focus on studying the physics of cosmological recombination and how the details of recombination affect the Cosmic Microwave Background (CMB) anisotropies. We present a detailed calculation of the spectral line distortions on the CMB spectrum arising from the Lyman-alpha and the lowest two-photon transitions in the recombination of hydrogen (H), and the corresponding lines from helium (He). The peak of these distortions mainly comes from the Lyman-alpha transition and occurs at about 170 microns, which is the Wien part of the CMB. The major theoretical limitation for extracting cosmological parameters from the CMB sky lies in the precision with which we can calculate the cosmological recombination process. With this motivation, we perform a multi-level calculation of the recombination of H and He with the addition of the spin-forbidden transition for neutral helium (He I), plus the higher order two-photon transitions for H and among singlet states of He I. We find that the inclusion of the spin-forbidden transition results in more than a percent change in the ionization fraction, while the other transitions give much smaller effects. Last we modify RECFAST by introducing one more parameter to reproduce recent numerical results for the speed-up of helium recombination. Together with the existing hydrogen `fudge factor', we vary these two parameters to account for the remaining dominant uncertainties in cosmological recombination. By using a Markov Chain Monte Carlo method with Planck forecast data, we find that we need to determine the parameters to better than 10% for He I and 1% for H, in order to obtain negligible effects on the cosmological parameters.
NASA Astrophysics Data System (ADS)
Bothun, Greg
2011-10-01
Ever since Aristotle placed us, with certainty, in the Center of the Cosmos, Cosmological models have more or less operated from a position of known truths for some time. As early as 1963, for instance, it was ``known'' that the Universe had to be 15-17 billion years old due to the suspected ages of globular clusters. For many years, attempts to determine the expansion age of the Universe (the inverse of the Hubble constant) were done against this preconceived and biased notion. Not surprisingly when more precise observations indicated a Hubble expansion age of 11-13 billion years, stellar models suddenly changed to produce a new age for globular cluster stars, consistent with 11-13 billion years. Then in 1980, to solve a variety of standard big bang problems, inflation was introduced in a fairly ad hoc manner. Inflation makes the simple prediction that the net curvature of spacetime is zero (i.e. spacetime is flat). The consequence of introducing inflation is now the necessary existence of a dark matter dominated Universe since the known baryonic material could comprise no more than 1% of the necessary energy density to make spacetime flat. As a result of this new cosmological ``truth'' a significant world wide effort was launched to detect the dark matter (which obviously also has particle physics implications). To date, no such cosmological component has been detected. Moreover, all available dynamical inferences of the mass density of the Universe showed in to be about 20% of that required for closure. This again was inconsistent with the truth that the real density of the Universe was the closure density (e.g. Omega = 1), that the observations were biased, and that 99% of the mass density had to be in the form of dark matter. That is, we know the universe is two component -- baryons and dark matter. Another prevailing cosmological truth during this time was that all the baryonic matter was known to be in galaxies that populated our galaxy catalogs. Subsequent
NASA Astrophysics Data System (ADS)
Marsh, David J. E.
2016-07-01
Axions comprise a broad class of particles that can play a major role in explaining the unknown aspects of cosmology. They are also well-motivated within high energy physics, appearing in theories related to CP-violation in the standard model, supersymmetric theories, and theories with extra-dimensions, including string theory, and so axion cosmology offers us a unique view onto these theories. I review the motivation and models for axions in particle physics and string theory. I then present a comprehensive and pedagogical view on the cosmology and astrophysics of axion-like particles, starting from inflation and progressing via BBN, the CMB, reionization and structure formation, up to the present-day Universe. Topics covered include: axion dark matter (DM); direct and indirect detection of axions, reviewing existing and future experiments; axions as dark radiation; axions and the cosmological constant problem; decays of heavy axions; axions and stellar astrophysics; black hole superradiance; axions and astrophysical magnetic fields; axion inflation, and axion DM as an indirect probe of inflation. A major focus is on the population of ultralight axions created via vacuum realignment, and its role as a DM candidate with distinctive phenomenology. Cosmological observations place robust constraints on the axion mass and relic density in this scenario, and I review where such constraints come from. I next cover aspects of galaxy formation with axion DM, and ways this can be used to further search for evidence of axions. An absolute lower bound on DM particle mass is established. It is ma > 10-24eV from linear observables, extending to ma ≳ 10-22eV from non-linear observables, and has the potential to reach ma ≳ 10-18eV in the future. These bounds are weaker if the axion is not all of the DM, giving rise to limits on the relic density at low mass. This leads to the exciting possibility that the effects of axion DM on structure formation could one day be detected
A mesh generator for tetrahedral elements using Delaunay triangulation
Yuan, J.S.; Fitzsimons, C.J. )
1993-03-01
A tetrahedral mesh generator has been developed. The generator is based on the Delaunay triangulation which is implemented by employing the insertion polyhedron algorithm. In this paper some new methods to deal with the problems associated with the three-dimensional Delaunay triangulation and the insertion polyhedron algorithm are presented: degeneracy, the crossing situation, identification of the internal elements and internal point generation. The generator works both for convex and non-convex domains, including those with high aspect-ratio subdomains. Some examples are given in this paper to illustrate the capability of the generator.
Research on pavement roughness based on the laser triangulation
NASA Astrophysics Data System (ADS)
Chen, Wenxue; Ni, Zhibin; Hu, Xinhan; Lu, Xiaofeng
2016-06-01
Pavement roughness is one of the most important factors for appraising highway construction. In this paper, we choose the laser triangulation to measure pavement roughness. The principle and configuration of laser triangulation are introduced. Based on this technology, the pavement roughness of a road surface is measured. The measurement results are given in this paper. The measurement range of this system is 50 μm. The measurement error of this technology is analyzed. This technology has an important significance to appraise the quality of highway after completion of the workload.
Digital aerial-triangulation system on personal computers
NASA Astrophysics Data System (ADS)
Tseng, Yi-Hsing; Chang, Shau-Yen
1994-08-01
This paper demonstrates a prototype of a PC-based digital aerial-triangulation system (PC- DATS). The system takes all of the procedures of aerial triangulation and is constructed by five working modules: preparation, interior orientation, tie point measurement, target point measurement, and bundle adjustment. All of the modules are integrated on the platform Microsoft-Windows. A test block containing 15 photos was processed by using the system. The operation was quite smooth, and the adjustment result shows an accuracy of about 0.3 pixel in average. The success of this proto-DATS was quite encouraging.
NASA Astrophysics Data System (ADS)
Kirillov, A. A.; Savelova, E. P.
2016-05-01
We describe in details the procedure how the Lobachevsky space can be factorized to a space of the constant negative curvature filled with a gas of wormholes. We show that such wormholes have throat sections in the form of tori and are traversable and stable in the cosmological context. The relation of such wormholes to the dark matter phenomenon is briefly described. We also discuss the possibility of the existence of analogous factorizations for all types of homogeneous spaces.
NASA Astrophysics Data System (ADS)
Grant, E.; Murdin, P.
2000-11-01
During the early Middle Ages (ca 500 to ca 1130) scholars with an interest in cosmology had little useful and dependable literature. They relied heavily on a partial Latin translation of PLATO's Timaeus by Chalcidius (4th century AD), and on a series of encyclopedic treatises associated with the names of Pliny the Elder (ca AD 23-79), Seneca (4 BC-AD 65), Macrobius (fl 5th century AD), Martianus ...
Homogeneous noncommutative quantum cosmology
Maceda, Marco; Macias, Alfredo; Pimentel, Luis O.
2008-09-15
Using the Groenewold-Moyal product, the noncommutative Bianchi IX model is constructed by imposing commutation relations on the minisuperspace variables ({omega},{beta}{sub +},{beta}{sub -}). A noncommutative 'wormhole' solution to the corresponding Wheeler-DeWitt equation is constructed and its behavior at fixed {omega} is analyzed.
Anisotropic, nonsingular early universe model leading to a realistic cosmology
Dechant, Pierre-Philippe; Lasenby, Anthony N.; Hobson, Michael P.
2009-02-15
We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a nonsingular 'pancaking' solution: the hypersurface volume goes to zero instantaneously at the 'big bang', but all physical quantities, such as curvature invariants and the matter energy density remain finite, and continue smoothly through the big bang. We demonstrate that there exist geodesics extending through the big bang, but that there are also incomplete geodesics that spiral infinitely around a topologically closed spatial dimension at the big bang, rendering it, at worst, a quasiregular singularity. The model is thus reminiscent of the Taub-NUT vacuum solution in that it has biaxial Bianchi IX geometry and its evolution exhibits a dimensionality reduction at a quasiregular singularity; the two models are, however, rather different, as we will show in a future work. Here we concentrate on the cosmological implications of our model and show how the scalar field drives both isotropization and inflation, thus raising the question of whether structure on the largest scales was laid down at a time when the universe was still oblate (as also suggested by [T. S. Pereira, C. Pitrou, and J.-P. Uzan, J. Cosmol. Astropart. Phys. 9 (2007) 6.][C. Pitrou, T. S. Pereira, and J.-P. Uzan, J. Cosmol. Astropart. Phys. 4 (2008) 4.][A. Guemruekcueoglu, C. Contaldi, and M. Peloso, J. Cosmol. Astropart. Phys. 11 (2007) 005.]). We also discuss the stability of our model to small perturbations around biaxiality and draw an analogy with cosmological perturbations. We conclude by presenting a separate, bouncing solution, which generalizes the known bouncing solution in closed FRW universes.
Anisotropic, nonsingular early universe model leading to a realistic cosmology
NASA Astrophysics Data System (ADS)
Dechant, Pierre-Philippe; Lasenby, Anthony N.; Hobson, Michael P.
2009-02-01
We present a novel cosmological model in which scalar field matter in a biaxial Bianchi IX geometry leads to a nonsingular “pancaking” solution: the hypersurface volume goes to zero instantaneously at the “big bang”, but all physical quantities, such as curvature invariants and the matter energy density remain finite, and continue smoothly through the big bang. We demonstrate that there exist geodesics extending through the big bang, but that there are also incomplete geodesics that spiral infinitely around a topologically closed spatial dimension at the big bang, rendering it, at worst, a quasiregular singularity. The model is thus reminiscent of the Taub-NUT vacuum solution in that it has biaxial Bianchi IX geometry and its evolution exhibits a dimensionality reduction at a quasiregular singularity; the two models are, however, rather different, as we will show in a future work. Here we concentrate on the cosmological implications of our model and show how the scalar field drives both isotropization and inflation, thus raising the question of whether structure on the largest scales was laid down at a time when the universe was still oblate (as also suggested by [T. S. Pereira, C. Pitrou, and J.-P. Uzan, J. Cosmol. Astropart. Phys.1475-7516 9 (2007) 6.10.1088/1475-7516/2007/09/006][C. Pitrou, T. S. Pereira, and J.-P. Uzan, J. Cosmol. Astropart. Phys.1475-7516 4 (2008) 4.10.1088/1475-7516/2008/04/004][A. Gümrükçüoǧlu, C. Contaldi, and M. Peloso, J. Cosmol. Astropart. Phys.1475-7516 11 (2007) 005.10.1088/1475-7516/2007/11/005]). We also discuss the stability of our model to small perturbations around biaxiality and draw an analogy with cosmological perturbations. We conclude by presenting a separate, bouncing solution, which generalizes the known bouncing solution in closed FRW universes.
Merging of intersecting triangulations for finite element modeling.
Cebral, J R; Löhner, R; Choyke, P L; Yim, P J
2001-06-01
Surface mesh generation over intersecting triangulations is a problem common to many branches of biomechanics. A new strategy for merging intersecting triangulations is described. The basis of the method is that object surfaces are represented as the zero-level iso-surface of the distance-to-surface function defined on a background grid. Thus, the triangulation of intersecting objects reduces to the extraction of an iso-surface from an unstructured grid. In a first step, a regular background mesh is constructed. For each point of the background grid, the closest distance to the surface of each object is computed. Background points are then classified as external or internal by checking the direction of the surface normal at the closest location and assigned a positive or negative distance, respectively. Finally, the zero-level iso-surface is constructed. This is the final triangulation of the intersecting objects. The overall accuracy is enhanced by adaptive refinement of the background grid elements. The resulting surface models are used as support surfaces to generate three-dimensional grids for finite element analysis. The algorithms are demonstrated by merging arterial branches independently reconstructed from contrast-enhanced magnetic resonance images and by adding extra features such as vascular stents. Although the methodology is presented in the context of finite element analysis of blood flow, the algorithms are general and can be applied in other areas as well. PMID:11470121
Multi-Sensor Triangulation of Multi-Source Spatial Data
NASA Technical Reports Server (NTRS)
Habib, Ayman; Kim, Chang-Jae; Bang, Ki-In
2007-01-01
The introduced methodologies are successful in: a) Ising LIDAR features for photogrammetric geo-refererncing; b) Delivering a geo-referenced imagery of the same quality as point-based geo-referencing procedures; c) Taking advantage of the synergistic characteristics of spatial data acquisition systems. The triangulation output can be used for the generation of 3-D perspective views.
The Use of Triangulation Methods in Qualitative Educational Research
ERIC Educational Resources Information Center
Oliver-Hoyo, Maria; Allen, DeeDee
2006-01-01
Triangulation involves the careful reviewing of data collected through different methods in order to achieve a more accurate and valid estimate of qualitative results for a particular construct. This paper describes how we used three qualitative methods of data collection to study attitudes of students toward graphing, hands-on activities, and…
A Simple Quality Triangulation Algorithm for Complex Geometries
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper presents a new and simple algorithm for quality triangulation in complex geometries. The proposed algorithm is based on an initial equilateral triangle mesh covering the whole domain. The mesh nodes close to the boundary edges satisfy the so-called non-encroaching criterion: the distance ...
Einstein-Weyl field equations in a Bianchi type-IX space-time
Kolassis, C.A.; Le Denmat, G.
1984-07-15
It is proved that there exists no solution of the combined gravitational-neutrino field equations in general relativity if the space-time metric admits a group of isometries of Bianchi type IX and the neutrino field has geodesic and shearfree rays.
Imparting small vorticity to a Bianchi type-VIh empty spacetime
NASA Astrophysics Data System (ADS)
Batakis, Nikos A.
1981-04-01
We present and briefly discuss a Bianchi type-VIh empty spacetime. The field equations have been solved after being linearized with respect to a parameter which imparts vorticity to the model. The limit of zero vorticity is an already known solution.
Inhomogeneous generalizations of Bianchi Type VIh universes with stiff perfect fluid and radiation
NASA Astrophysics Data System (ADS)
Roy, S. R.; Prasad, A.
1995-03-01
Families of inhomogeneous models filled with a stiff perfect fluid and radiation have been derived in which there is no flow of total momentum. The models are generalizations of those of Bianchi Type VIh and are discussed for some particular forms of the arbitrary functions appearing in them.
Bardeen, J.M.
1986-01-01
The last several years have seen a tremendous ferment of activity in astrophysical cosmology. Much of the theoretical impetus has come from particle physics theories of the early universe and candidates for dark matter, but what promise to be even more significant are improved direct observations of high z galaxies and intergalactic matter, deeper and more comprehensive redshift surveys, and the increasing power of computer simulations of the dynamical evolution of large scale structure. Upper limits on the anisotropy of the microwave background radiation are gradually getting tighter and constraining more severely theoretical scenarios for the evolution of the universe. 47 refs.
NASA Astrophysics Data System (ADS)
Wickramasinghe, N. C.; Hoyle, Fred
1998-07-01
The central regions of galaxies could provide the most promising venues for the large-scale synthesis of prebiotic molecules by Miller-Urey type processes.Exploding supermassive stars would produce the basic chemical elements necessary to form molecules in high-density mass flows under near-thermodynamic conditions. Such molecules are then acted upon by X-rays in a manner that simulates the conditions required for Miller-Urey type processing. The Miller-Urey molecular products could initially lead to the origination and dispersal of microbial life on a cosmological scale. Thereafter the continuing production of such molecules would serve as the feedstock of life.
ERIC Educational Resources Information Center
Fosco, Gregory M.; Grych, John H.
2010-01-01
Although triangulation into parental conflict is a risk factor for child and adolescent maladjustment, little is known about how triangulation affects adolescents' functioning or the factors that lead children to be drawn into parental disagreements. This prospective study examined the relations between triangulation, appraisals of conflict, and…
The Cosmological Constant in Quantum Cosmology
Wu Zhongchao
2008-10-10
Hawking proposed that the cosmological constant is probably zero in quantum cosmology in 1984. By using the right configuration for the wave function of the universe, a complete proof is found very recently.
On a renormalization group scheme for causal dynamical triangulations
NASA Astrophysics Data System (ADS)
Cooperman, Joshua H.
2016-03-01
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme—in concert with finite size scaling analysis—is essential to this aim. Formulating and implementing such a scheme in the present context raises novel and notable conceptual and technical problems. I explored these problems, and, building on standard techniques, suggested potential solutions in a previous paper (Cooperman, arXiv:gr-qc/1410.0026). As an application of these solutions, I now propose a renormalization group scheme for causal dynamical triangulations. This scheme differs significantly from that studied recently by Ambjørn, Görlich, Jurkiewicz, Kreienbuehl, and Loll.
Numerical conformal mapping using cross-ratios and Delaunay triangulation
Driscoll, T.A.; Vavasis, S.A.
1998-11-01
The authors propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the Schwarz-Christoffel transformation. The new algorithm, CRDT (for cross-ratios of the Delaunay triangulation), based on cross-ratios of the prevertices, and also on cross-ratios of quadrilaterals in a Delaunay triangulation of the polygon. The CRDT algorithm produces an accurate representation of the Riemann mapping even in the presence of arbitrary long, thin regions in the polygon, unlike any previous conformal mapping algorithm. They believe that CRDT solves all difficulties with crowding and global convergence, although these facts depend on conjectures that they have so far not been able to prove. They demonstrate convergence with computational experiments. The Riemann mapping has applications in two-dimensional potential theory and mesh generation. They demonstrate CRDT on problems in long, thin regions in which no other known algorithm can perform comparably.
Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation.
Gao, Zhanheng; Yu, Zeyun; Holst, Michael
2012-12-01
Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing "bad" triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method. PMID:23144522
Personal authentication using hand vein triangulation and knuckle shape.
Kumar, Ajay; Prathyusha, K Venkata
2009-09-01
This paper presents a new approach to authenticate individuals using triangulation of hand vein images and simultaneous extraction of knuckle shape information. The proposed method is fully automated and employs palm dorsal hand vein images acquired from the low-cost, near infrared, contactless imaging. The knuckle tips are used as key points for the image normalization and extraction of region of interest. The matching scores are generated in two parallel stages: (i) hierarchical matching score from the four topologies of triangulation in the binarized vein structures and (ii) from the geometrical features consisting of knuckle point perimeter distances in the acquired images. The weighted score level combination from these two matching scores are used to authenticate the individuals. The achieved experimental results from the proposed system using contactless palm dorsal-hand vein images are promising (equal error rate of 1.14%) and suggest more user friendly alternative for user identification. PMID:19447728
Type III radio source located by Ulysses/Wind triangulation
NASA Astrophysics Data System (ADS)
Reiner, M. J.; Fainberg, J.; Kaiser, M. L.; Stone, R. G.
1998-02-01
Radio triangulation from the widely separated Ulysses and Wind spacecraft is used to reconstruct the trajectory of a type III radio burst in the 3D heliosphere. The derived radio trajectory follows a (Parker) spiral path corresponding to a solar wind speed of about 200 km/s and progresses to the south of the ecliptic plane. These remote radio observations also measure the interplanetary plasma density along the path of the radio source. The derived average density-distance scale is very similar to the previously derived RAE density scale, which was determined in a different way. The results of the radio triangulation, combined with a drift rate analysis, give an average electron exciter speed of about 0.3 c. The radio source size and the brightness temperature as viewed from Ulysses and Wind are determined and compared as a function of observing frequency.
Discovery and problem solving: Triangulation as a weak heuristic
NASA Technical Reports Server (NTRS)
Rochowiak, Daniel
1987-01-01
Recently the artificial intelligence community has turned its attention to the process of discovery and found that the history of science is a fertile source for what Darden has called compiled hindsight. Such hindsight generates weak heuristics for discovery that do not guarantee that discoveries will be made but do have proven worth in leading to discoveries. Triangulation is one such heuristic that is grounded in historical hindsight. This heuristic is explored within the general framework of the BACON, GLAUBER, STAHL, DALTON, and SUTTON programs. In triangulation different bases of information are compared in an effort to identify gaps between the bases. Thus, assuming that the bases of information are relevantly related, the gaps that are identified should be good locations for discovery and robust analysis.
Evaluating habitat selection with radio-telemetry triangulation error
Samuel, M.D.; Kenow, K.P.
1992-01-01
Radio-telemetry triangulation errors result in the mislocation of animals and misclassification of habitat use. We present analytical methods that provide improved estimates of habitat use when misclassification probabilities can be determined. When misclassification probabilities cannot be determined, we use random subsamples from the error distribution of an estimated animal location to improve habitat use estimates. We conducted Monte Carlo simulations to evaluate the effects of this subsampling method, triangulation error, number of animal locations, habitat availability, and habitat complexity on bias and variation in habitat use estimates. Results for the subsampling method are illustrated using habitat selection by redhead ducks (Aythya americana ). We recommend the subsampling method with a minimum of 50 random points to reduce problems associated with habitat misclassification.
Evaluating habitat selection with radio-telemetry triangulation error
Samuel, M.D.; Kenow, K.P.
1992-01-01
Radio-telemetry triangulation errors result in the mislocation of animals and misclassification of habitat use. We present analytical methods that provide improved estimates of habitat use when misclassification probabilities can be determined. When misclassification probabilities cannot be determined, we use random subsamples from the error distribution of an estimated animal location to improve habitat use estimates. We conducted Monte Carlo simulations to evaluate the effects of this subsampling method, triangulation error, number of animal locations, habitat availability, and habitat complexity on bias and variation in habitat use estimates. Results for the subsampling method are illustrated using habitat selection by redhead ducks (Aythya americana). We recommend the subsampling method with a minimum of 50 random points to reduce problems associated with habitat misclassification.
Detectability of active triangulation range finder: a solar irradiance approach.
Liu, Huizhe; Gao, Jason; Bui, Viet Phuong; Liu, Zhengtong; Lee, Kenneth Eng Kian; Peh, Li-Shiuan; Png, Ching Eng
2016-06-27
Active triangulation range finders are widely used in a variety of applications such as robotics and assistive technologies. The power of the laser source should be carefully selected in order to satisfy detectability and still remain eye-safe. In this paper, we present a systematic approach to assess the detectability of an active triangulation range finder in an outdoor environment. For the first time, we accurately quantify the background noise of a laser system due to solar irradiance by coupling the Perez all-weather sky model and ray tracing techniques. The model is validated with measurements with a modeling error of less than 14.0%. Being highly generic and sufficiently flexible, the proposed model serves as a guide to define a laser system for any geographical location and microclimate. PMID:27410637
Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation
Gao, Zhanheng; Yu, Zeyun; Holst, Michael
2012-01-01
Despite its great success in improving the quality of a tetrahedral mesh, the original optimal Delaunay triangulation (ODT) is designed to move only inner vertices and thus cannot handle input meshes containing “bad” triangles on boundaries. In the current work, we present an integrated approach called boundary-optimized Delaunay triangulation (B-ODT) to smooth (improve) a tetrahedral mesh. In our method, both inner and boundary vertices are repositioned by analytically minimizing the error between a paraboloid function and its piecewise linear interpolation over the neighborhood of each vertex. In addition to the guaranteed volume-preserving property, the proposed algorithm can be readily adapted to preserve sharp features in the original mesh. A number of experiments are included to demonstrate the performance of our method. PMID:23144522
Experiences with systematic triangulation at the Global Environment Facility.
Carugi, Carlo
2016-04-01
Systematic triangulation may address common challenges in evaluation, such as the scarcity or unreliability of data, or the complexities of comparing and cross-checking evidence from diverse disciplines. Used to identify key evaluation findings, its application has proven to be effective in addressing the limitations encountered in country-level evaluation analysis conducted by the Independent Evaluation Office of the Global Environment Facility (GEF). These include the scarcity or unreliability of national statistics on environmental indicators and data series, especially in Least Developed Countries; challenges in evaluating the impacts of GEF projects; and inherent difficulties in defining the GEF portfolio of projects prior to the undertaking of the evaluation. In addition to responding to the need for further developing triangulation protocols, procedures and/or methodologies advocated by some authors, the approach offers a contribution to evaluation practice. This applies particularly to those evaluation units tasked with country-level evaluations in international organizations, facing similar constraints. PMID:26724715
Krioukov, Dmitri; Kitsak, Maksim; Sinkovits, Robert S.; Rideout, David; Meyer, David; Boguñá, Marián
2012-01-01
Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the large-scale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology. PMID:23162688
Earth parameters from global satellite triangulation and trilateration
NASA Technical Reports Server (NTRS)
Mueller, I. I.
1974-01-01
Results obtained from 159-station global satellite triangulation and trilateration (including Baker-Nunn, BC-4, PC-1000 camera observations, SECOR, C-Band radar and EDM distance measurements) indicate differences in the semidiameter and orientation of the earth compared to results obtained from dynamic satellite solutions. Geoidal undulations obtained can be made consistent with dynamically determined ones at the expense of slight changes in the currently accepted parameters defining the gravity field of the level ellipsoid.
Adaptive mesh generation for viscous flows using Delaunay triangulation
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1988-01-01
A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.
Fast triangulated vortex methods for the 2D Euler equations
Russo, G. ); Strain, J.A. )
1994-04-01
Vortex methods for inviscid incompressible two-dimensional fluid flow are usually based on blob approximations. This paper presents a vortex method in which the vorticity is approximated by a piecewise polynomial interpolant on a Delaunay triangulation of the vortices. An efficient reconstruction of the Delaunay triangulation at each step makes the method accurate for long times. The vertices of the triangulation move with the fluid velocity, which is reconstructed from the vorticity via a simplified fast multipole method for the Biot-Savart law with a continuous source distribution. The initial distribution of vortices is constructed from the initial vorticity field by an adaptive approximation method which produces good accuracy even for discontinuous initial data. Numerical results show that the method is highly accurate over long time intervals. Experiments with single and multiple circular and elliptical rotating patches of both piecewise constant and smooth vorticity indicate that the method produces much smaller errors than blob methods with the same number of degrees of freedom, at little additional cost. Generalizations to domains with boundaries, viscous flow, and three space dimensions are discussed. 52 refs., 28 figs., 2 tabs.
Optical Triangulation-Based Microtopographic Inspection of Surfaces
Costa, Manuel F. M.
2012-01-01
The non-invasive inspection of surfaces is a major issue in a wide variety of industries and research laboratories. The vast and increasing range of surface types, tolerance requirements and measurement constraints demanded during the last decades represents a major research effort in the development of new methods, systems and metrological strategies. The discreet dimensional evaluation the rugometric characterization and the profilometric inspection seem to be insufficient in many instances. The full microtopographic inspection has became a common requirement. Among the different systems developed, optical methods have the most important role and among those triangulation-based ones have gained a major status thanks to their flexibility, reliability and robustness. In this communication we will provide a brief historical review on the development of optical triangulation application to the dimensional inspection of objects and surfaces and on the work done at the Microtopography Laboratory of the Physics Department of the University of Minho, Portugal, in the development of methods and systems of optical triangulation-based microtopographic inspection of surfaces. PMID:22666036
Fast triangulated vortex methods for the 2D Eulen equations
NASA Astrophysics Data System (ADS)
Russo, Giovanni; Strain, John A.
1994-04-01
Vortex methods for inviscid incompressible two-dimensional fluid flow are usually based on blob approximations. This paper presents a vortex method in which the vorticity is approximated by a piecewise polynomial interpolant on a Delaunay triangulation of the vortices. An efficient reconstruction of the Delaunay triangulation at each step makes the method accurate for long times. The vertices of the triangulation move with the fluid velocity, which is reconstructed from the vorticity via a simplified fast multipole method for the Biot-Savart law with a continuous source distribution. The initial distribution of vortices is constructed from the initial vorticity field by an adaptive approximation method which produces good accuracy even for discontinuous initial data. Numerical results show that the method is highly accurate over long time intervals. Experiments with single and multiple circular and elliptical rotating patches of both piecewise constant and smooth vorticity indicate that the method produces much smaller errors than blob methods with the same number of degrees of freedom, at little additional cost. Generalizations to domains with boundaries, viscous flow, and three space dimensions are discussed.
An exotic k-essence interpretation of interactive cosmological models
NASA Astrophysics Data System (ADS)
Forte, Mónica
2016-01-01
We define a generalization of scalar fields with non-canonical kinetic term which we call exotic k-essence or, briefly, exotik. These fields are generated by the global description of cosmological models with two interactive fluids in the dark sector and under certain conditions they correspond to usual k-essences. The formalism is applied to the cases of constant potential and of inverse square potential and also we develop the purely exotik version for the modified holographic Ricci type (MHR) of dark energy, where the equations of state are not constant. With the kinetic function F=1+mx and the inverse square potential we recover, through the interaction term, the identification between k-essences and quintessences of an exponential potential, already known for Friedmann-Robertson-Walker and Bianchi type I geometries. Worked examples are shown that include the self-interacting MHR and also models with crossing of the phantom divide line (PDL).
Isotropic and anisotropic bouncing cosmologies in Palatini gravity
Barragan, Carlos; Olmo, Gonzalo J.
2010-10-15
We study isotropic and anisotropic (Bianchi I) cosmologies in Palatini f(R) and f(R,R{sub {mu}{nu}R}{sup {mu}{nu}}) theories of gravity with a perfect fluid and consider the existence of nonsingular bouncing solutions in the early universe. We find that all f(R) models with isotropic bouncing solutions develop shear singularities in the anisotropic case. On the contrary, the simple quadratic model R+aR{sup 2}/R{sub P}+R{sub {mu}{nu}R}{sup {mu}{nu}/}R{sub P} exhibits regular bouncing solutions in both isotropic and anisotropic cases for a wide range of equations of state, including dust (for a<0) and radiation (for arbitrary a). It thus represents a purely gravitational solution to the big bang singularity and anisotropy problems of general relativity without the need for exotic (w>1) sources of matter/energy or extra degrees of freedom.
Effect of bulk Lorentz violation on anisotropic brane cosmologies
Heydari-Fard, Malihe
2012-04-01
The effect of Lorentz invariance violation in cosmology has attracted a considerable amount of attention. By using a dynamical vector field assumed to point in the bulk direction, with Lorentz invariance holding on the brane, we extend the notation of Lorentz violation in four dimensions Jacobson to a five-dimensional brane-world. We obtain the general solution of the field equations in an exact parametric form for Bianchi type I space-time, with perfect fluid as a matter source. We show that the brane universe evolves from an isotropic/anisotropic state to an isotropic de Sitter inflationary phase at late time. The early time behavior of anisotropic brane universe is largely dependent on the Lorentz violating parameters β{sub i},i = 1,2,3 and the equation of state of the matter, while its late time behavior is independent of these parameters.
Refining a triangulation of a planar straight-line graph to eliminate large angles
Mitchell, S.A.
1993-05-13
Triangulations without large angles have a number of applications in numerical analysis and computer graphics. In particular, the convergence of a finite element calculation depends on the largest angle of the triangulation. Also, the running time of a finite element calculation is dependent on the triangulation size, so having a triangulation with few Steiner points is also important. Bern, Dobkin and Eppstein pose as an open problem the existence of an algorithm to triangulate a planar straight-line graph (PSLG) without large angles using a polynomial number of Steiner points. We solve this problem by showing that any PSLG with {upsilon} vertices can be triangulated with no angle larger than 7{pi}/8 by adding O({upsilon}{sup 2}log {upsilon}) Steiner points in O({upsilon}{sup 2} log{sup 2} {upsilon}) time. We first triangulate the PSLG with an arbitrary constrained triangulation and then refine that triangulation by adding additional vertices and edges. Some PSLGs require {Omega}({upsilon}{sup 2}) Steiner points in any triangulation achieving any largest angle bound less than {pi}. Hence the number of Steiner points added by our algorithm is within a log {upsilon} factor of worst case optimal. We note that our refinement algorithm works on arbitrary triangulations: Given any triangulation, we show how to refine it so that no angle is larger than 7{pi}/8. Our construction adds O(nm+nplog m) vertices and runs in time O(nm+nplog m) log(m+ p)), where n is the number of edges, m is one plus the number of obtuse angles, and p is one plus the number of holes and interior vertices in the original triangulation. A previously considered problem is refining a constrained triangulation of a simple polygon, where p = 1. For this problem we add O({upsilon}{sup 2}) Steiner points, which is within a constant factor of worst case optimal.
NASA Technical Reports Server (NTRS)
Bradas, James C.; Fennelly, Alphonsus J.; Smalley, Larry L.
1987-01-01
It is shown that a generalized (or 'power law') inflationary phase arises naturally and inevitably in a simple (Bianchi type-I) anisotropic cosmological model in the self-consistent Einstein-Cartan gravitation theory with the improved stress-energy-momentum tensor with the spin density of Ray and Smalley (1982, 1983). This is made explicit by an analytical solution of the field equations of motion of the fluid variables. The inflation is caused by the angular kinetic energy density due to spin. The model further elucidates the relationship between fluid vorticity, the angular velocity of the inertially dragged tetrads, and the precession of the principal axes of the shear ellipsoid. Shear is not effective in damping the inflation.
NASA Astrophysics Data System (ADS)
Bradas, James C.; Fennelly, Alphonsus J.; Smalley, Larry L.
1987-04-01
It is shown that a generalized (or 'power law') inflationary phase arises naturally and inevitably in a simple (Bianchi type-I) anisotropic cosmological model in the self-consistent Einstein-Cartan gravitation theory with the improved stress-energy-momentum tensor with the spin density of Ray and Smalley (1982, 1983). This is made explicit by an analytical solution of the field equations of motion of the fluid variables. The inflation is caused by the angular kinetic energy density due to spin. The model further elucidates the relationship between fluid vorticity, the angular velocity of the inertially dragged tetrads, and the precession of the principal axes of the shear ellipsoid. Shear is not effective in damping the inflation.
How universe evolves with cosmological and gravitational constants
NASA Astrophysics Data System (ADS)
Xue, She-Sheng
2015-08-01
With a basic varying space-time cutoff ℓ ˜, we study a regularized and quantized Einstein-Cartan gravitational field theory and its domains of ultraviolet-unstable fixed point gir ≳ 0 and ultraviolet-stable fixed point guv ≈ 4 / 3 of the gravitational gauge coupling g = (4 / 3) G /GNewton. Because the fundamental operators of quantum gravitational field theory are dimension-2 area operators, the cosmological constant is inversely proportional to the squared correlation length Λ ∝ξ-2. The correlation length ξ characterizes an infrared size of a causally correlate patch of the universe. The cosmological constant Λ and the gravitational constant G are related by a generalized Bianchi identity. As the basic space-time cutoff ℓ ˜ decreases and approaches to the Planck length ℓpl, the universe undergoes inflation in the domain of the ultraviolet-unstable fixed point gir, then evolves to the low-redshift universe in the domain of ultraviolet-stable fixed point guv. We give the quantitative description of the low-redshift universe in the scaling-invariant domain of the ultraviolet-stable fixed point guv, and its deviation from the ΛCDM can be examined by low-redshift (z ≲ 1) cosmological observations, such as supernova Type Ia.
A note on tilted Bianchi type VIh models: the type III bifurcation
NASA Astrophysics Data System (ADS)
Coley, A. A.; Hervik, S.
2008-10-01
In this note we complete the analysis of Hervik, van den Hoogen, Lim and Coley (2007 Class. Quantum Grav. 24 3859) of the late-time behaviour of tilted perfect fluid Bianchi type III models. We consider models with dust, and perfect fluids stiffer than dust, and eludicate the late-time behaviour by studying the centre manifold which dominates the behaviour of the model at late times. In the dust case, this centre manifold is three-dimensional and can be considered a double bifurcation as the two parameters (h and γ) of the type VIh model are varied. We therefore complete the analysis of the late-time behaviour of tilted ever-expanding Bianchi models of types I VIII.
Degravitation, inflation and the cosmological constant as an afterglow
NASA Astrophysics Data System (ADS)
Patil, Subodh P.
2009-01-01
In this report, we adopt the phenomenological approach of taking the degravitation paradigm seriously as a consistent modification of gravity in the IR, and investigate its consequences for various cosmological situations. We motivate degravitation — where Netwon's constant is promoted to a scale dependent filter function — as arising from either a small (resonant) mass for the graviton, or as an effect in semi-classical gravity. After addressing how the Bianchi identities are to be satisfied in such a set up, we turn our attention towards the cosmological consequences of degravitation. By considering the example filter function corresponding to a resonantly massive graviton (with a filter scale larger than the present horizon scale), we show that slow roll inflation, hybrid inflation and old inflation remain quantitatively unchanged. We also find that the degravitation mechanism inherits a memory of past energy densities in the present epoch in such a way that is likely significant for present cosmological evolution. For example, if the universe underwent inflation in the past due to it having tunneled out of some false vacuum, we find that degravitation implies a remnant `afterglow' cosmological constant, whose scale immediately afterwards is parametrically suppressed by the filter scale (L) in Planck units Λ ~ l2pl/L2. We discuss circumstances through which this scenario reasonably yields the presently observed value for Λ ~ O(10-120). We also find that in a universe still currently trapped in some false vacuum state, resonance graviton models of degravitation only degravitate initially Planck or GUT scale energy densities down to the presently observed value over timescales comparable to the filter scale. We argue that different functional forms for the filter function will yield similar conclusions. In this way, we argue that although the degravitation models we study have the potential to explain why the cosmological constant is not large in addition to
NASA Astrophysics Data System (ADS)
Harling, B. v.
2010-02-01
In this thesis, we study throats in the early, hot universe. Throats are a common feature of the landscape of type IIB string theory. If a throat is heated during cosmological evolution, energy is subsequently transferred to other throats and to the standard model. We calculate the heat transfer rate and the decay rate of throat-localized Kaluza-Klein states in a ten-dimensional model. For the calculation, we employ the dual description of the throats in terms of gauge theories. We discuss modifications of the decay rate which arise in flux compactifications and for Klebanov-Strassler throats and emphasize the role of tachyonic scalars in such throats in mediating decays of Kaluza-Klein modes. Our results are also applicable to the energy transfer from the heated standard model to throats. We determine the resulting energy density in throats at our epoch in dependence of their infrared scales and of the reheating temperature. The Kaluza-Klein modes in the throats decay to other sectors with a highly suppressed rate. If their lifetime is longer than the age of the universe, they are an interesting dark matter candidate. We show that, if the reheating temperature was 10^10 - 10^11 GeV, throats with infrared scales in the range of 10^5 GeV to 10^10 GeV can account for the observed dark matter. We identify several scenarios where this type of dark matter is sufficiently stable but where decays to the standard model can be discovered via gamma-ray observations.
(An)Isotropic models in scalar and scalar-tensor cosmologies
NASA Astrophysics Data System (ADS)
Belinchón, José Antonio
2012-04-01
We study how the constants G and Λ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models ("quintessence") with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi V, VII0 and IX, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we arrive at the conclusion that the solutions are isotropic and noninflationary while the cosmological constant behaves as a positive decreasing time function (in agreement with the current observations) and the gravitational constant behaves as a growing time function.
On the viability of the truncated Israel-Stewart theory in cosmology
NASA Astrophysics Data System (ADS)
Shogin, Dmitry; Amund Amundsen, Per; Hervik, Sigbjørn
2015-10-01
We apply the causal Israel-Stewart theory of irreversible thermodynamics to model the matter content of the Universe as a dissipative fluid with bulk and shear viscosity. Along with the full transport equations we consider their widely used truncated version. By implementing a dynamical systems approach to Bianchi type IV and V cosmological models with and without cosmological constant, we determine the future asymptotic states of such Universes and show that the truncated Israel-Stewart theory leads to solutions essentially different from the full theory. The solutions of the truncated theory may also manifest unphysical properties. Finally, we find that in the full theory shear viscosity can give a substantial rise to dissipative fluxes, driving the fluid extremely far from equilibrium, where the linear Israel-Stewart theory ceases to be valid.
Hex-dominant mesh generation using 3D constrained triangulation
OWEN,STEVEN J.
2000-05-30
A method for decomposing a volume with a prescribed quadrilateral surface mesh, into a hexahedral-dominated mesh is proposed. With this method, known as Hex-Morphing (H-Morph), an initial tetrahedral mesh is provided. Tetrahedral are transformed and combined starting from the boundary and working towards the interior of the volume. The quadrilateral faces of the hexahedra are treated as internal surfaces, which can be recovered using constrained triangulation techniques. Implementation details of the edge and face recovery process are included. Examples and performance of the H-Morph algorithm are also presented.
A hand-held triangulation sensor for small features measurement
NASA Astrophysics Data System (ADS)
Abramovich, Gil; Harding, Kevin
2010-11-01
This paper describes progressive generations of hand held triangulation sensors for measuring small features, from edge breaks to corrosion pits. We describe the design considerations, ergonomics, packaging and interface between the device and part, such as the sensor tip and optional fixtures. We then present a customized design to address different types of surface features and defects. Next, we present the calibration concept, and its execution. The paper closes by summarizing system performance evaluation experiments and their results. It was shown that the system is capable of measuring edges down to a radius of 250 microns at a repeatability of 50 microns.
Foliations and 2+1 causal dynamical triangulation models
Konopka, Tomasz
2006-01-15
The original models of causal dynamical triangulations construct space-time by arranging a set of simplices in layers separated by a fixed timelike distance. The importance of the foliation structure in the 2+1 dimensional model is studied by considering variations in which this property is relaxed. It turns out that the fixed-lapse condition can be equivalently replaced by a set of global constraints that have geometrical interpretation. On the other hand, the introduction of new types of simplices that puncture the foliating sheets in general leads to different low-energy behavior compared to the original model.
NASA Astrophysics Data System (ADS)
Ellis, George F. R.
2014-12-01
This is the text of part of the Cosmology course at the Special Courses at the National Observatory of Rio de Janeiro - CCE. The first part summarises cosmology today, including issues where significant questions reman, and the second part is dedicated to the 1+3 covariant formalism for cosmology.
Computing 2D constrained delaunay triangulation using the GPU.
Qi, Meng; Cao, Thanh-Tung; Tan, Tiow-Seng
2013-05-01
We propose the first graphics processing unit (GPU) solution to compute the 2D constrained Delaunay triangulation (CDT) of a planar straight line graph (PSLG) consisting of points and edges. There are many existing CPU algorithms to solve the CDT problem in computational geometry, yet there has been no prior approach to solve this problem efficiently using the parallel computing power of the GPU. For the special case of the CDT problem where the PSLG consists of just points, which is simply the normal Delaunay triangulation (DT) problem, a hybrid approach using the GPU together with the CPU to partially speed up the computation has already been presented in the literature. Our work, on the other hand, accelerates the entire computation on the GPU. Our implementation using the CUDA programming model on NVIDIA GPUs is numerically robust, and runs up to an order of magnitude faster than the best sequential implementations on the CPU. This result is reflected in our experiment with both randomly generated PSLGs and real-world GIS data having millions of points and edges. PMID:23492377
a Modified Method for Image Triangulation Using Inclined Angles
NASA Astrophysics Data System (ADS)
Alsadik, Bashar
2016-06-01
The ongoing technical improvements in photogrammetry, Geomatics, computer vision (CV), and robotics offer new possibilities for many applications requiring efficient acquisition of three-dimensional data. Image orientation is one of these important techniques in many applications like mapping, precise measurements, 3D modeling and navigation. Image orientation comprises three main techniques of resection, intersection (triangulation) and relative orientation, which are conventionally solved by collinearity equations or by using projection and fundamental matrices. However, different problems still exist in the state - of -the -art of image orientation because of the nonlinearity and the sensitivity to proper initialization and spatial distribution of the points. In this research, a modified method is presented to solve the triangulation problem using inclined angles derived from the measured image coordinates and based on spherical trigonometry rules and vector geometry. The developed procedure shows promising results compared to collinearity approach and to converge to the global minimum even when starting from far approximations. This is based on the strong geometric constraint offered by the inclined angles that are enclosed between the object points and the camera stations. Numerical evaluations with perspective and panoramic images are presented and compared with the conventional solution of collinearity equations. The results show the efficiency of the developed model and the convergence of the solution to global minimum even with improper starting values.
Automated Photogrammetric Image Matching with Sift Algorithm and Delaunay Triangulation
NASA Astrophysics Data System (ADS)
Karagiannis, Georgios; Antón Castro, Francesc; Mioc, Darka
2016-06-01
An algorithm for image matching of multi-sensor and multi-temporal satellite images is developed. The method is based on the SIFT feature detector proposed by Lowe in (Lowe, 1999). First, SIFT feature points are detected independently in two images (reference and sensed image). The features detected are invariant to image rotations, translations, scaling and also to changes in illumination, brightness and 3-dimensional viewpoint. Afterwards, each feature of the reference image is matched with one in the sensed image if, and only if, the distance between them multiplied by a threshold is shorter than the distances between the point and all the other points in the sensed image. Then, the matched features are used to compute the parameters of the homography that transforms the coordinate system of the sensed image to the coordinate system of the reference image. The Delaunay triangulations of each feature set for each image are computed. The isomorphism of the Delaunay triangulations is determined to guarantee the quality of the image matching. The algorithm is implemented in Matlab and tested on World-View 2, SPOT6 and TerraSAR-X image patches.
Dynamic ray tracing and its application in triangulated media
Rueger, A.
1993-07-01
Hale and Cohen (1991) developed software to generate two-dimensional computer models of complex geology. Their method uses a triangulation technique designed to support efficient and accurate computation of seismic wavefields for models of the earth`s interior. Subsequently, Hale (1991) used this triangulation approach to perform dynamic ray tracing and create synthetic seismograms based on the method of Gaussian beams. Here, I extend this methodology to allow an increased variety of ray-theoretical experiments. Specifically, the developed program GBmod (Gaussian Beam MODeling) can produce arbitrary multiple sequences and incorporate attenuation and density variations. In addition, I have added an option to perform Fresnel-volume ray tracing (Cerveny and Soares, 1992). Corrections for reflection and transmission losses at interfaces, and for two-and-one-half-dimensional (2.5-D) spreading are included. However, despite these enhancements, difficulties remain in attempts to compute accurate synthetic seismograms if strong lateral velocity inhomogeneities are present. Here, these problems are discussed and, to a certain extent, reduced. I provide example computations of high-frequency seismograms based on the method of Gaussian beams to exhibit the advantages and disadvantages of the proposed modeling method and illustrate new features for both surface and vertical seismic profiling (VSP) acquisition geometries.
4-D XRD for strain in many grains using triangulation
Bale, Hrishikesh A.; Hanan, Jay C.; Tamura, Nobumichi
2006-12-31
Determination of the strains in a polycrystalline materialusing 4-D XRD reveals sub-grain and grain-to-grain behavior as a functionof stress. Here 4-D XRD involves an experimental procedure usingpolychromatic micro-beam X-radiation (micro-Laue) to characterizepolycrystalline materials in spatial location as well as with increasingstress. The in-situ tensile loading experiment measured strain in a modelaluminum-sapphire metal matrix composite using the Advanced Light Source,Beam-line 7.3.3. Micro-Laue resolves individual grains in thepolycrystalline matrix. Results obtained from a list of grains sorted bycrystallographic orientation depict the strain states within and amongindividual grains. Locating the grain positions in the planeperpendicular to the incident beam is trivial. However, determining theexact location of grains within a 3-D space is challenging. Determiningthe depth of the grains within the matrix (along the beam direction)involved a triangulation method tracing individual rays that producespots on the CCD back to the point of origin. Triangulation wasexperimentally implemented by simulating a 3-D detector capturingmultiple diffraction images while increasing the camera to sampledistance. Hence by observing the intersection of rays from multiple spotsbelonging to the corresponding grain, depth is calculated. Depthresolution is a function of the number of images collected, grain to beamsize ratio, and the pixel resolution of the CCD. The 4DXRD methodprovides grain morphologies, strain behavior of each grain, andinteractions of the matrix grains with each other and the centrallylocated single crystal fiber.
Generating Triangulated Macromolecular Surfaces by Euclidean Distance Transform
Xu, Dong; Zhang, Yang
2009-01-01
Macromolecular surfaces are fundamental representations of their three-dimensional geometric shape. Accurate calculation of protein surfaces is of critical importance in the protein structural and functional studies including ligand-protein docking and virtual screening. In contrast to analytical or parametric representation of macromolecular surfaces, triangulated mesh surfaces have been proved to be easy to describe, visualize and manipulate by computer programs. Here, we develop a new algorithm of EDTSurf for generating three major macromolecular surfaces of van der Waals surface, solvent-accessible surface and molecular surface, using the technique of fast Euclidean Distance Transform (EDT). The triangulated surfaces are constructed directly from volumetric solids by a Vertex-Connected Marching Cube algorithm that forms triangles from grid points. Compared to the analytical result, the relative error of the surface calculations by EDTSurf is <2–4% depending on the grid resolution, which is 1.5–4 times lower than the methods in the literature; and yet, the algorithm is faster and costs less computer memory than the comparative methods. The improvements in both accuracy and speed of the macromolecular surface determination should make EDTSurf a useful tool for the detailed study of protein docking and structure predictions. Both source code and the executable program of EDTSurf are freely available at http://zhang.bioinformatics.ku.edu/EDTSurf. PMID:19956577
The finite body triangulation: algorithms, subgraphs, homogeneity estimation and application.
Carson, Cantwell G; Levine, Jonathan S
2016-09-01
The concept of a finite body Dirichlet tessellation has been extended to that of a finite body Delaunay 'triangulation' to provide a more meaningful description of the spatial distribution of nonspherical secondary phase bodies in 2- and 3-dimensional images. A finite body triangulation (FBT) consists of a network of minimum edge-to-edge distances between adjacent objects in a microstructure. From this is also obtained the characteristic object chords formed by the intersection of the object boundary with the finite body tessellation. These two sets of distances form the basis of a parsimonious homogeneity estimation. The characteristics of the spatial distribution are then evaluated with respect to the distances between objects and the distances within them. Quantitative analysis shows that more physically representative distributions can be obtained by selecting subgraphs, such as the relative neighbourhood graph and the minimum spanning tree, from the finite body tessellation. To demonstrate their potential, we apply these methods to 3-dimensional X-ray computed tomographic images of foamed cement and their 2-dimensional cross sections. The Python computer code used to estimate the FBT is made available. Other applications for the algorithm - such as porous media transport and crack-tip propagation - are also discussed. PMID:26917441
Analytic self-gravitating Skyrmions, cosmological bounces and AdS wormholes
NASA Astrophysics Data System (ADS)
Ayón-Beato, Eloy; Canfora, Fabrizio; Zanelli, Jorge
2016-01-01
We present a self-gravitating, analytic and globally regular Skyrmion solution of the Einstein-Skyrme system with winding number w = ± 1, in presence of a cosmological constant. The static spacetime metric is the direct product R ×S3 and the Skyrmion is the self-gravitating generalization of the static hedgehog solution of Manton and Ruback with unit topological charge. This solution can be promoted to a dynamical one in which the spacetime is a cosmology of the Bianchi type-IX with time-dependent scale and squashing coefficients. Remarkably, the Skyrme equations are still identically satisfied for all values of these parameters. Thus, the complete set of field equations for the Einstein-Skyrme-Λ system in the topological sector reduces to a pair of coupled, autonomous, nonlinear differential equations for the scale factor and a squashing coefficient. These equations admit analytic bouncing cosmological solutions in which the universe contracts to a minimum non-vanishing size, and then expands. A non-trivial byproduct of this solution is that a minor modification of the construction gives rise to a family of stationary, regular configurations in General Relativity with negative cosmological constant supported by an SU (2) nonlinear sigma model. These solutions represent traversable AdS wormholes with NUT parameter in which the only "exotic matter" required for their construction is a negative cosmological constant.
Philosophical Roots of Cosmology
NASA Astrophysics Data System (ADS)
Ivanovic, M.
2008-10-01
We shall consider the philosophical roots of cosmology in the earlier Greek philosophy. Our goal is to answer the question: Are earlier Greek theories of pure philosophical-mythological character, as often philosophers cited it, or they have scientific character. On the bases of methodological criteria, we shall contend that the latter is the case. In order to answer the question about contemporary situation of the relation philosophy-cosmology, we shall consider the next question: Is contemporary cosmology completely independent of philosophical conjectures? The answer demands consideration of methodological character about scientific status of contemporary cosmology. We also consider some aspects of the relation contemporary philosophy-cosmology.
NASA Astrophysics Data System (ADS)
Tipler, Frank J.
1996-10-01
It is generally believed that it is not possible to rigorously analyze a homogeneous and isotropic cosmological model in Newtonian mechanics. I show on the contrary that if Newtonian gravity theory is rewritten in geometrical language in the manner outlined in 1923-1924 by Élie Cartan [Ann. Ecole Norm. Sup. 40, 325-412 (1923); 41, 1-25 (1924)], then Newtonian cosmology is as rigorous as Friedmann cosmology. In particular, I show that the equation of geodesic deviation in Newtonian cosmology is exactly the same as equation of geodesic deviation in the Friedmann universe, and that this equation can be integrated to yield a constraint equation formally identical to the Friedmann equation. However, Newtonian cosmology is more general than Friedmann cosmology: Ever-expanding and recollapsing universes are allowed in any noncompact homogeneous and isotropic spatial topology. I shall give a brief history of attempts to do cosmology in the framework of Newtonian mechanics.
A comprehensive study on GPS-assisted aerial triangulation
NASA Astrophysics Data System (ADS)
Ebadi, Hamid
Aerial Triangulation (AT) has been used for mapping purposes for a long time to provide 3D coordinates of object points on the ground. This technique uses series of overlapping photographs, and some control points, in order to establish the relationship between the image coordinate system and object coordinate system. In the process of bundle block adjustment, image coordinate observations and coordinates of the ground control points are simultaneously adjusted and the exterior orientation parameters, as well as the ground coordinates of all tie and pass points, are estimated. One of the biggest challenges in AT is to reduce the number of control points. One effective way is to directly measure the exterior orientation parameters of the camera at the time of exposure. Airborne kinematic GPS (Global Positioning System) provides a means of determining the position of the aerial camera at each instant of exposure. The combined GPS-photogrammetric block adjustment takes advantage of weighted GPS observations, which significantly reduces the number of ground control points needed in a conventional block adjustment. A comprehensive software package, GAP (General Adjustment Program), was developed in this research to effectively integrate and adjust GPS, geodetic, and photogrammetric observations. Optimization of the GPS-photogrammetric bundle block adjustments for both simulated large scale mapping and real medium scale mapping was carried out. Aspects of reliability, and precision, as well as practical considerations, for an airborne GPS-photogrammetry system were also investigated. GPS coordinates of the camera exposure stations do not permit recovery of the roll angle of the aircraft in a GPS single strip triangulation. Therefore, ground control points are still required in addition to the GPS coordinates of exposure stations to overcome this problem, and to eliminate singularity of the normal matrix in the least squares adjustment. A new technique for GPS single
A Working Model of Pedagogical Triangulation: A Holistic Approach to Peer-Revision Workshops.
ERIC Educational Resources Information Center
Eades, Carol
2002-01-01
Describes the specific elements of "pedagogical triangulation" along with the results of applying this approach in a first-semester college English class. Considers how pedagogical triangulation enhances student confidence, capacity, capability, and collaboration, all vital elements for worthwhile peer-revision workshops. (SG)
A near-optimal heuristic for minimum weight triangulation of convex polygons
Levcopoulos, C.; Krznaric, D.
1997-06-01
A linear-time heuristic for minimum weight triangulation of convex polygons is presented. This heuristic produces a triangulation of length within a factor 1 + {epsilon} from the optimum, where {epsilon} is an arbitrarily small positive constant. This is the first sub-cubic algorithm which guarantees such an approximation factor, and it has interesting applications.
The Differential Impact of Parental Warmth on Externalizing Problems among Triangulated Adolescents
Etkin, R. G.; Koss, K. J.; Cummings, E. M.; Davies, P. T.
2013-01-01
Triangulation is a family-wide process in which children are inappropriately involved in interparental conflict, placing them at heightened risk for adjustment problems. A common form of triangulation occurs by parents pressuring their children to take sides, which may result in feelings of being “torn” between parents. Externalizing behaviors in particular may develop as adolescents feel caught in the middle of conflict and forced to choose a side. However, the nature of the triadic process of triangulation may be impacted by dyadic-level relationships within the family. The present study thus explores how positive parenting processes may alter the relations between triangulation and adolescent externalizing problems. Mothers, fathers, and adolescents (n = 301 families) provided assessments of adolescent externalizing problems, triangulation, and maternal and paternal warmth. Analyses revealed a three-way interaction between triangulation and maternal and paternal warmth predicting adolescent externalizing problems; child gender also moderated these relations. Among highly triangulated youth, boys displayed increased externalizing problems when both parents exhibited low or high warmth whereas girls showed increased behavior problems in the context of low maternal but high paternal warmth. These findings indicate the importance of examining the broader family context and gender when considering the impact of triangulation during adolescence. PMID:24796159
Skin lesion image segmentation using Delaunay Triangulation for melanoma detection.
Pennisi, Andrea; Bloisi, Domenico D; Nardi, Daniele; Giampetruzzi, Anna Rita; Mondino, Chiara; Facchiano, Antonio
2016-09-01
Developing automatic diagnostic tools for the early detection of skin cancer lesions in dermoscopic images can help to reduce melanoma-induced mortality. Image segmentation is a key step in the automated skin lesion diagnosis pipeline. In this paper, a fast and fully-automatic algorithm for skin lesion segmentation in dermoscopic images is presented. Delaunay Triangulation is used to extract a binary mask of the lesion region, without the need of any training stage. A quantitative experimental evaluation has been conducted on a publicly available database, by taking into account six well-known state-of-the-art segmentation methods for comparison. The results of the experimental analysis demonstrate that the proposed approach is highly accurate when dealing with benign lesions, while the segmentation accuracy significantly decreases when melanoma images are processed. This behavior led us to consider geometrical and color features extracted from the binary masks generated by our algorithm for classification, achieving promising results for melanoma detection. PMID:27215953
Experimental study on subaperture testing with iterative triangulation algorithm.
Yan, Lisong; Wang, Xiaokun; Zheng, Ligong; Zeng, Xuefeng; Hu, Haixiang; Zhang, Xuejun
2013-09-23
Applying the iterative triangulation stitching algorithm, we provide an experimental demonstration by testing a Φ120 mm flat mirror, a Φ1450 mm off-axis parabolic mirror and a convex hyperboloid mirror. By comparing the stitching results with the self-examine subaperture, it shows that the reconstruction results are in consistent with that of the subaperture testing. As all the experiments are conducted with a 5-dof adjustment platform with big adjustment errors, it proves that using the above mentioned algorithm, the subaperture stitching can be easily performed without a precise positioning system. In addition, with the algorithm, we accomplish the coordinate unification between the testing and processing that makes it possible to guide the processing by the stitching result. PMID:24104151
Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulation.
Gao, Zhanheng; Yu, Zeyun; Holst, Michael
2013-01-01
A method of triangular surface mesh smoothing is presented to improve angle quality by extending the original optimal Delaunay triangulation (ODT) to surface meshes. The mesh quality is improved by solving a quadratic optimization problem that minimizes the approximated interpolation error between a parabolic function and its piecewise linear interpolation defined on the mesh. A suboptimal problem is derived to guarantee a unique, analytic solution that is significantly faster with little loss in accuracy as compared to the optimal one. In addition to the quality-improving capability, the proposed method has been adapted to remove noise while faithfully preserving sharp features such as edges and corners of a mesh. Numerous experiments are included to demonstrate the performance of the method. PMID:23580890
Triangulation-Based Camera Calibration For Machine Vision Systems
NASA Astrophysics Data System (ADS)
Bachnak, Rafic A.; Celenk, Mehmet
1990-04-01
This paper describes a camera calibration procedure for stereo-based machine vision systems. The method is based on geometric triangulation using only a single image of three distinctive points. Both the intrinsic and extrinsic parameters of the system are determined. The procedure is performed only once at the initial set-up using a simple camera model. The effective focal length is extended in such a way that a linear transformation exists between the camera image plane and the output digital image. Only three world points are needed to find the extended focal length and the transformation matrix elements that relates the camera position and orientation to a real world coordinate system. The parameters of the system are computed by solving a set of linear equations. Experimental results show that the method, when used in a stereo system developed in this research, produces reasonably accurate 3-D measurements.
NASA Technical Reports Server (NTRS)
Saxena, N. K.
1972-01-01
Whether any significant increment to accuracy could be transferred from a super-control continental net (continental satellite net or super-transcontinental traverse) to the fundamental geodetic net (first-order triangulation) is discussed. This objective was accomplished by evaluating the positional accuracy improvement for a triangulation station, which is near the middle of the investigated geodetic triangulation net, by using various station constraints over its geodetic position. This investigation on a 1858 kilometer long triangulation chain shows that the super-control net can provide a useful constraint to the investigated geodetic triangulation net, and thus can improve it only when the accuracy of super-control net is at least 1 part in 500,000.
NASA Astrophysics Data System (ADS)
Bojowald, Martin
The universe, ultimately, is to be described by quantum theory. Quantum aspects of all there is, including space and time, may not be significant for many purposes, but are crucial for some. And so a quantum description of cosmology is required for a complete and consistent worldview. At any rate, even if we were not directly interested in regimes where quantum cosmology plays a role, a complete physical description could not stop at a stage before the whole universe is reached. Quantum theory is essential in the microphysics of particles, atoms, molecules, solids, white dwarfs and neutron stars. Why should one expect this ladder of scales to end at a certain size? If regimes are sufficiently violent and energetic, quantum effects are non-negligible even on scales of the whole cosmos; this is realized at least once in the history of the universe: at the big bang where the classical theory of general relativity would make energy densities diverge.
Structure formation in the Dvali Gabadadze Porrati cosmological model
NASA Astrophysics Data System (ADS)
Koyama, Kazuya; Maartens, Roy
2006-01-01
The DGP brane-world model provides an alternative to the standard LCDM cosmology, in which the late universe accelerates due to a modification of gravity rather than vacuum energy. The cosmological constant Λ in LCDM is replaced by a single parameter, the crossover scale rc, in DGP. The supernova redshift observations can be fitted by both models, with Λ ~ H02 and rc ~ H0-1. This degeneracy is broken by structure formation, which is suppressed in different ways in the two models. There is some confusion in the literature about how the standard linear growth factor is modified in the DGP model. While the luminosity distance can be computed purely from the modified four-dimensional Friedman equation, the evolution of density perturbations requires an analysis of the five-dimensional gravitational field. We show that if the five-dimensional effects are inappropriately neglected, then the four-dimensional Bianchi identities are violated and the computed growth factor is incorrect. By using the five-dimensional equations, we derive the correct growth factor.
NASA Astrophysics Data System (ADS)
Ghiti, M. F.; Mebarki, N.; Aissaoui, H.
2015-08-01
The noncommutative Bianchi I curved space-time vierbeins and spin connections are derived. Moreover, the corresponding noncommutative Dirac equation as well as its solutions are presented. As an application within the quantum field theory approach using Bogoliubov transformations, the von Neumann fermion-antifermion pair creation quantum entanglement entropy is studied. It is shown that its behavior is strongly dependent on the value of the noncommutativity θ parameter, k⊥-modes frequencies and the structure of the curved space-time. Various discussions of the obtained features are presented.
The Momentum 4-Vector Imparted by Gravitational Waves in Bianchi-Type Metrics
NASA Astrophysics Data System (ADS)
Havare, Ali; Korunur, Murat; Salti, Mustafa
2006-01-01
Considering the Møller, Weinberg and Qadir-Sharif's definitions in general relativity, we find the momentum 4-vector of the closed universe based on the Bianchi-type metrics. The momentum 4-vector (due to matter plus fields) is found to be zero. This result supports the viewpoints of Albrow and Tryon and extends the previous works by Cooperstock Israelit, Rosen, Johri et al., Banerjee Sen and Vargas who investigated the problem of the energy in Friedmann Robertson Walker universe and Saltı-Havare who studied the problem of the energy-momentum of the viscous Kasner-type space-times.
Dark Energy Models and Laws of Thermodynamics in Bianchi i Model
NASA Astrophysics Data System (ADS)
Sharif, M.; Saleem, Rabia
2012-10-01
This paper is devoted to check validity of the laws of thermodynamics for locally rotationally symmetric (LRS) Bianchi type I (BI) universe model which is filled with combination of dark matter and dark energy (DE). We take two types of DE models, i.e. generalized holographic DE (HDE) and generalized Ricci DE (RDE). It is proved that the first and generalized second law of thermodynamics (GSLT) are valid on the apparent horizon for both the models. Further, we take fixed radius L of the apparent horizon with original holographic or RDE. We conclude that the first and GSLT do not hold on the horizon of fixed radius L for both the models.
Rotating and expanding Bianchi type-IX model in f(R,T) theory of gravity
NASA Astrophysics Data System (ADS)
Sofuoğlu, Değer
2016-01-01
The spatially homogeneous shear-free, rotating and expanding Bianchi type-IX universe has been considered in the presence of perfect fluid in f(R,T) theory of gravity. The exact solution of the field equations has been obtained and the functional form of f(R,T)=R+2f(T) gravity has been reconstructed. The existence of such a solution suggests that the general relativistic shear-free perfect fluid conjecture which claims that a shear-free perfect fluid cannot rotate and expand at the same time, is not valid in this modified theory.
Cosmological anisotropy from non-comoving dark matter and dark energy
Harko, Tiberiu; Lobo, Francisco S. N. E-mail: flobo@cii.fc.ul.pt
2013-07-01
We consider a cosmological model in which the two major fluid components of the Universe, dark energy and dark matter, flow with distinct four-velocities. This cosmological configuration is equivalent to a single anisotropic fluid, expanding with a four-velocity that is an appropriate combination of the two fluid four-velocities. The energy density of the single cosmological fluid is larger than the sum of the energy densities of the two perfect fluids, i.e., dark energy and dark matter, respectively, and contains a correction term due to the anisotropy generated by the differences in the four-velocities. Furthermore, the gravitational field equations of the two-fluid anisotropic cosmological model are obtained for a Bianchi type I geometry. By assuming that the non-comoving motion of the dark energy and dark matter induces small perturbations in the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker type cosmological background, and that the anisotropy parameter is small, the equations of the cosmological perturbations due to the non-comoving nature of the two major components are obtained. The time evolution of the metric perturbations is explicitly obtained for the cases of the exponential and power law background cosmological expansion. The imprints of a non-comoving dark energy - dark matter on the Cosmic Microwave Background and on the luminosity distance are briefly discussed, and the temperature anisotropies and the quadrupole are explicitly obtained in terms of the metric perturbations of the flat background metric. Therefore, if there is a slight difference between the four-velocities of the dark energy and dark matter, the Universe would acquire some anisotropic characteristics, and its geometry will deviate from the standard FLRW one. In fact, the recent Planck results show that the presence of an intrinsic large scale anisotropy in the Universe cannot be excluded a priori, so that the model presented in this work can be considered as a
Wong, Yvonne Y. Y.
2008-01-24
I give an overview of the effects of neutrinos on cosmology, focussing in particular on the role played by neutrinos in the evolution of cosmological perturbations. I discuss how recent observations of the cosmic microwave background and the large-scale structure of galaxies can probe neutrino masses with greater precision than current laboratory experiments. I describe several new techniques that will be used to probe cosmology in the future.
Hamiltonian cosmology of bigravity
NASA Astrophysics Data System (ADS)
Soloviev, V. O.
The purpose of this talk is to give an introduction both to the Hamiltonian formalism and to the cosmological equations of bigravity. In the Hamiltonian language we provide a study of flat-space cosmology in bigravity and massive gravity constructed mostly with de Rham, Gabadadze, Tolley (dRGT) potential. It is demonstrated that the Hamiltonian methods are powerful not only in proving the absence of the Boulware-Deser ghost, but also in addressing cosmological problems.
NASA Astrophysics Data System (ADS)
López-Corredoira, M.
2009-08-01
Certain results of observational cosmology cast critical doubt on the foundations of standard cosmology but leave most cosmologists untroubled. Alternative cosmological models that differ from the Big Bang have been published and defended by heterodox scientists; however, most cosmologists do not heed these. This may be because standard theory is correct and all other ideas and criticisms are incorrect, but it is also to a great extent due to sociological phenomena such as the ``snowball effect'' or ``groupthink''. We might wonder whether cosmology, the study of the Universe as a whole, is a science like other branches of physics or just a dominant ideology.
NASA Astrophysics Data System (ADS)
Li, En-Kun; Zhang, Yu; Geng, Jin-Ling; Duan, Peng-Fei
2015-11-01
Generalized second law of thermodynamics in the Bianchi Type I universe with the generalized holographic Ricci dark energy model is studied in this paper. The behavior of dark energy's equation of state parameter indicates that it is matter-like in the early time of the universe but phantom-like in the future. By analysing the evolution of the deviations of state parameter and the total pressure of the universe, we find that for an anisotropic Bianchi Type I universe, it transits from a high anisotropy stage to a more homogeneous stage in the near past. Using the normal entropy given by Gibbs' law of thermodynamics, it is proved that the generalized second law of thermodynamics does not always satisfied throughout the history of the universe when we assume the universe is enclosed by the generalized Ricci scalar radius R_{gr}. It becomes invalid in the near past to the future, and the formation of the galaxies will be helpful in explaining such phenomenon, for that the galaxies's formation is an entropy increase process. The negative change rate of the horizon entropy and internal entropy occur in different period indicates that the influences of galaxies formation is wiped from internal to the universe's horizon.
Genus dependence of the number of (non-)orientable surface triangulations
NASA Astrophysics Data System (ADS)
Krüger, Benedikt; Mecke, Klaus
2016-04-01
Topological triangulations of orientable and nonorientable surfaces with arbitrary genus have important applications in quantum geometry, graph theory and statistical physics. However, until now, only the asymptotics for 2-spheres have been known analytically, and exact counts of triangulations are only available for both small genera and triangulations. We apply the Wang-Landau algorithm to calculate the number N (m ,h ) of triangulations for several orders of magnitude in system size m and type h (equals genus in orientable triangulations). We verify that the limit of the entropy density of triangulations is independent of genus and orientability and are able to determine the next-to-leading-order and the next-to-next-to-leading-order terms. We conjecture for the number of surface triangulations the asymptotic behavior
Cosmologies with quasiregular singularities. II. Stability considerations
Konkowski, D.A.; Helliwell, T.M.
1985-03-15
The stability properties of a class of spacetimes with quasiregular singularities is discussed. Quasiregular singularities are the end points of incomplete, inextendible geodesics at which the Riemann tensor and its derivatives remain at least bounded in all parallel-propagated orthonormal (PPON) frames; observers approaching such a singularity would find that their world lines come to an end in a finite proper time. The Taub-NUT (Newman-Unti-Tamburino)-type cosmologies investigated are R/sup 1/ x T/sup 3/ and R/sup 3/ x S/sup 1/ flat Kasner spacetimes, the two-parameter family of spatially homogeneous but anisotropic Bianchi type-IX Taub-NUT spacetimes, and an infinite-dimensional family of Einstein-Rosen-Gowdy spacetimes studied by Moncrief. The behavior of matter near the quasiregular singularity in each of these spacetimes is explored through an examination of the behavior of the stress-energy tensors and scalars for conformally coupled and minimally coupled, massive and massless scalar waves as observed in both coordinate and PPON frames. A conjecture is postulated concerning the stability of the nature of the singularity in these spacetimes. The conjecture for a Taub-NUT-type background spacetime is that if a test-field stress-energy tensor evaluated in a PPON frame mimics the behavior of the Riemann tensor components which indicate a particular type of singularity (quasiregular, nonscalar curvature, or scalar curvature), then a complete nonlinear backreaction calculation, in which the fields are allowed to influence the geometry, would show that this type of singularity actually occurs. Evidence supporting the conjecture is presented for spacetimes whose symmetries are unchanged when fields with the same symmetries are added.
Muecke, E.P.; Saias, I.; Zhu, B.
1996-05-01
This paper studies the point location problem in Delaunay triangulations without preprocessing and additional storage. The proposed procedure finds the query point simply by walking through the triangulation, after selecting a good starting point by random sampling. The analysis generalizes and extends a recent result of d = 2 dimensions by proving this procedure to take expected time close to O(n{sup 1/(d+1)}) for point location in Delaunay triangulations of n random points in d = 3 dimensions. Empirical results in both two and three dimensions show that this procedure is efficient in practice.
NASA Astrophysics Data System (ADS)
Damour, T.
2003-10-01
We briefly review two aspects of string cosmology: 1) the presence of chaos in the generic cosmological solutions of the tree-level low-energy effective actions coming out of string theory, and 2) the remarkable link between the latter chaos and the Weyl groups of some hyperbolic Kac-Moody algebras.
NASA Astrophysics Data System (ADS)
Damour, Thibault
We briefly review two aspects of string cosmology: (1) the presence of chaos in the generic cosmological solutions of the tree-level low-energy effective actions coming out of string theory, and (2) the remarkable link between the latter chaos and the Weyl groups of some hyperbolic Kac-Moody algebras.
Klebanov, I.; Susskind, L.
1988-10-01
We review Coleman's wormhole mechanism for the vanishing of the cosmological constant. We find a discouraging result that wormholes much bigger than the Planck size are generated. We also consider the implications of the wormhole theory for cosmology. 7 refs., 2 figs.
NASA Astrophysics Data System (ADS)
Hawking, S. W.
2001-09-01
The large N approximation should hold in cosmology even at the origin of the universe. I use ADS-CFT to calculate the effective action and obtain a cosmological model in which inflation is driven by the trace anomaly. Despite having ghosts, this model can agree with observations.
McAllister, Liam P.; Silverstein, Eva
2007-10-22
We give an overview of the status of string cosmology. We explain the motivation for the subject, outline the main problems, and assess some of the proposed solutions. Our focus is on those aspects of cosmology that benefit from the structure of an ultraviolet-complete theory.
Exploring bouncing cosmologies with cosmological surveys
NASA Astrophysics Data System (ADS)
Cai, Yi-Fu
2014-08-01
From recent observational data two significant directions have been made in the field of theoretical cosmology recently. First, we are now able to make use of present observations, such as the Planck and BICEP2 data, to examine theoretical predictions from the standard inflationary ΛCDM which were made decades of years ago. Second, we can search for new cosmological signatures as a way to explore physics beyond the standard cosmic paradigm. In particular, a subset of early universe models admit a nonsingular bouncing solution that attempts to address the issue of the big bang singularity. These models have achieved a series of considerable developments in recent years, in particular in their perturbative frameworks, which made brand-new predictions of cosmological signatures that could be visible in current and forthcoming observations. Herein we present two representative paradigms of early universe physics. The first is the reputed new matter (or matter-ekpyrotic) bounce scenario in which the universe starts with a matter-dominated contraction phase and transitions into an ekpyrotic phase. In the setting of this paradigm, we have proposed some possible mechanisms of generating a red tilt for primordial curvature perturbations and confront the general predictions with recent cosmological observations. The second is the matter-bounce inflation scenario which can be viewed as an extension of inflationary cosmology with a matter contraction before inflation. We present a class of possible model constructions and review the implications on the current CMB experiments. Lastly a review of significant achievements of these paradigms beyond the inflationary ΛCDM model is made, which is expected to shed new light on the future direction of observational cosmology.
A triangulation-based approach to automatically repair GIS polygons
NASA Astrophysics Data System (ADS)
Ledoux, Hugo; Arroyo Ohori, Ken; Meijers, Martijn
2014-05-01
Although the validation of a single GIS polygon can be considered as a solved issue, the repair of an invalid polygon has not received much attention and is still in practice a semi-manual and time-consuming task. We investigate in this paper algorithms to automatically repair a single polygon. Automated repair algorithms can be considered as interpreting ambiguous or ill-defined polygons and returning a coherent and clearly defined output (the definition of the international standards in our case). We present a novel approach, based on the use of a constrained triangulation, to automatically repair invalid polygons. Our approach is conceptually simple and easy to implement as it is mostly based on labelling triangles. It is also flexible: it permits us to implement different repair paradigms (we describe two in the paper). We have implemented our algorithms, and we report on experiments made with large real-world polygons that are often used by practitioners in different disciplines. We show that our approach is faster and more scalable than alternative tools.