WorldWideScience

Sample records for network gravity equations

  1. Exact RG flow equations and quantum gravity

    de Alwis, S. P.

    2018-03-01

    We discuss the different forms of the functional RG equation and their relation to each other. In particular we suggest a generalized background field version that is close in spirit to the Polchinski equation as an alternative to the Wetterich equation to study Weinberg's asymptotic safety program for defining quantum gravity, and argue that the former is better suited for this purpose. Using the heat kernel expansion and proper time regularization we find evidence in support of this program in agreement with previous work.

  2. On the Langevin equation for stochastic quantization of gravity

    Nakazawa, Naohito.

    1989-10-01

    We study the Langevin equation for stochastic quantization of gravity. By introducing two independent variables with a second-class constraint for the gravitational field, we formulate a pair of the Langevin equations for gravity which couples with white noises. After eliminating the multiplier field for the second-class constraint, we show that the equations leads to stochastic quantization of gravity including an unique superspace metric. (author)

  3. Equations of motion in linearised gravity

    Hogan, P.A.; Imaeda, M.

    1979-01-01

    A straightforward approach to studying the motion of the sources of some Robinson-Trautman gravitational fields in linearised gravity is described. It involves expanding the Robinson-Trautman line-element about Minkowskian space-time in powers of a small parameter (the 'mass' of the source). The linearised field equations are solved in vacuo by first specifying the source world-line in the background Minkowskian space-time. Functions of integration are determined by the requirement that terms be excluded from the field (Riemann tensor) of the particle which are singular along null-rays emanating into the future from events on the source world-line in the background space-time. As an example the world-line is taken to be the history of a uniformly accelerated particle. It is shown that the present solution agrees with the exact solution of Levi-Civta to this problem, in the linear approximation. (author)

  4. A class of solutions for the strong gravity equations

    Salam, A.; Strathdee, J.

    1976-12-01

    We solve the Einstein equation for strong gravity in the limit that weak gravity is neglected. The class of solutions we find reduces to the Schwarzschild solution (with the weak gravity Newtonian constant replaced by a strong coupling parameter) in the limit M 2 →0 where M is the mass of the strong gravity spin-2 meson. These solutions may be of relevance for the problem of defining temperature in hadronic physics

  5. Equations of motion in relativistic gravity

    Lämmerzahl, Claus; Schutz, Bernard

    2015-01-01

     The present volume aims to be a comprehensive survey on the derivation of the equations of motion, both in General Relativity as well as in alternative gravity theories. The topics covered range from the description of test bodies, to self-gravitating (heavy) bodies, to current and future observations. Emphasis is put on the coverage of various approximation methods (e.g., multipolar, post-Newtonian, self-force methods) which are extensively used in the context of the relativistic problem of motion. Applications discussed in this volume range from the motion of binary systems -- and the gravitational waves emitted by such systems -- to observations of the galactic center. In particular the impact of choices at a fundamental theoretical level on the interpretation of experiments is highlighted. This book provides a broad and up-do-date status report, which will not only be of value for the experts working in this field, but also may serve as a guideline for students with background in General Relativity who ...

  6. Topspin networks in loop quantum gravity

    Duston, Christopher L

    2012-01-01

    We discuss the extension of loop quantum gravity to topspin networks, a proposal which allows topological information to be encoded in spin networks. We will show that this requires minimal changes to the phase space, C*-algebra and Hilbert space of cylindrical functions. We will also discuss the area and Hamiltonian operators, and show how they depend on the topology. This extends the idea of ‘background independence’ in loop quantum gravity to include topology as well as geometry. It is hoped this work will confirm the usefulness of the topspin network formalism and open up several new avenues for research into quantum gravity. (paper)

  7. Field equations for gravity quadratic in the curvature

    Rose, B.

    1992-01-01

    Vacuum field equations for gravity are studied having their origin in a Lagrangian quadratic in the curvature. The motivation for this choice of the Lagrangian-namely the treating of gravity in a strict analogy to gauge theories of Yang-Mills type-is criticized, especially the implied view of connections as gauge potentials with no dynamical relation to the metric. The correct field equations with respect to variation of the connections and the metric independently are given. We deduce field equations which differs from previous ones by variation of the metric, the torsion, and the nonmetricity from which the connections are built. 6 refs

  8. Field Equations for Lovelock Gravity: An Alternative Route

    Sumanta Chakraborty

    2018-01-01

    Full Text Available We present an alternative derivation of the gravitational field equations for Lovelock gravity starting from Newton’s law, which is closer in spirit to the thermodynamic description of gravity. As a warm up exercise, we have explicitly demonstrated that, projecting the Riemann curvature tensor appropriately and taking a cue from Poisson’s equation, Einstein’s equations immediately follow. The above derivation naturally generalizes to Lovelock gravity theories where an appropriate curvature tensor satisfying the symmetries as well as the Bianchi derivative properties of the Riemann tensor has to be used. Interestingly, in the above derivation, the thermodynamic route to gravitational field equations, suited for null hypersurfaces, emerges quiet naturally.

  9. An Einstein equation for discrete quantum gravity

    Gudder, Stan

    2012-01-01

    The basic framework for this article is the causal set approach to discrete quantum gravity (DQG). Let $Q_n$ be the collection of causal sets with cardinality not greater than $n$ and let $K_n$ be the standard Hilbert space of complex-valued functions on $Q_n$. The formalism of DQG presents us with a decoherence matrix $D_n(x,y)$, $x,y\\in Q_n$. There is a growth order in $Q_n$ and a path in $Q_n$ is a maximal chain relative to this order. We denote the set of paths in $Q_n$ by $\\Omega_n$. For...

  10. Minimal Liouville gravity correlation numbers from Douglas string equation

    Belavin, Alexander; Dubrovin, Boris; Mukhametzhanov, Baur

    2014-01-01

    We continue the study of (q,p) Minimal Liouville Gravity with the help of Douglas string equation. We generalize the results of http://dx.doi.org/10.1016/0550-3213(91)90548-Chttp://dx.doi.org/10.1088/1751-8113/42/30/304004, where Lee-Yang series (2,2s+1) was studied, to (3,3s+p 0 ) Minimal Liouville Gravity, where p 0 =1,2. We demonstrate that there exist such coordinates τ m,n on the space of the perturbed Minimal Liouville Gravity theories, in which the partition function of the theory is determined by the Douglas string equation. The coordinates τ m,n are related in a non-linear fashion to the natural coupling constants λ m,n of the perturbations of Minimal Lioville Gravity by the physical operators O m,n . We find this relation from the requirement that the correlation numbers in Minimal Liouville Gravity must satisfy the conformal and fusion selection rules. After fixing this relation we compute three- and four-point correlation numbers when they are not zero. The results are in agreement with the direct calculations in Minimal Liouville Gravity available in the literature http://dx.doi.org/10.1103/PhysRevLett.66.2051http://dx.doi.org/10.1007/s11232-005-0003-3http://dx.doi.org/10.1007/s11232-006-0075-8

  11. Equation of state in the presence of gravity

    Kim, Hyeong-Chan; Kang, Gungwon

    2016-11-01

    We investigate how an equation of state for matter is affected when a gravity is present. For this purpose, we consider a box of ideal gas in the presence of Newtonian gravity. In addition to the ordinary thermodynamic quantities, a characteristic variable that represents a weight per unit area relative to the average pressure is required in order to describe a macroscopic state of the gas. Although the density and the pressure are not uniform due to the presence of gravity, the ideal gas law itself is satisfied for the thermodynamic quantities when averaged over the system. Assuming that the system follows an adiabatic process further, we obtain a new relation between the averaged pressure and density, which differs from the conventional equation of state for the ideal gas in the absence of gravity. Applying our results to a small volume in a Newtonian star, however, we find that the conventional one is reliable for most astrophysical situations when the characteristic scale is small. On the other hand, gravity effects become significant near the surface of a Newtonian star.

  12. General heavenly equation governs anti-self-dual gravity

    Malykh, A A [Department of Numerical Modelling, Russian State Hydrometeorlogical University, Malookhtinsky pr 98, 195196 St Petersburg (Russian Federation); Sheftel, M B, E-mail: andrei-malykh@mail.ru, E-mail: mikhail.sheftel@boun.edu.tr [Department of Physics, Bogazici University, 34342 Bebek, Istanbul (Turkey)

    2011-04-15

    We show that the general heavenly equation, suggested recently by Doubrov and Ferapontov (2010 arXiv:0910.3407v2 [math.DG]), governs anti-self-dual (ASD) gravity. We derive ASD Ricci-flat vacuum metric governed by the general heavenly equation, null tetrad and basis of 1-forms for this metric. We present algebraic exact solutions of the general heavenly equation as a set of zeros of homogeneous polynomials in independent and dependent variables. A real solution is obtained for the case of a neutral signature.

  13. The electrical network of maize root apex is gravity dependent.

    Masi, Elisa; Ciszak, Marzena; Comparini, Diego; Monetti, Emanuela; Pandolfi, Camilla; Azzarello, Elisa; Mugnai, Sergio; Baluška, Frantisek; Mancuso, Stefano

    2015-01-15

    Investigations carried out on maize roots under microgravity and hypergravity revealed that gravity conditions have strong effects on the network of plant electrical activity. Both the duration of action potentials (APs) and their propagation velocities were significantly affected by gravity. Similarly to what was reported for animals, increased gravity forces speed-up APs and enhance synchronized electrical events also in plants. The root apex transition zone emerges as the most active, as well as the most sensitive, root region in this respect.

  14. Gravity Effects on Information Filtering and Network Evolving

    Liu, Jin-Hu; Zhang, Zi-Ke; Chen, Lingjiao; Liu, Chuang; Yang, Chengcheng; Wang, Xueqi

    2014-01-01

    In this paper, based on the gravity principle of classical physics, we propose a tunable gravity-based model, which considers tag usage pattern to weigh both the mass and distance of network nodes. We then apply this model in solving the problems of information filtering and network evolving. Experimental results on two real-world data sets, Del.icio.us and MovieLens, show that it can not only enhance the algorithmic performance, but can also better characterize the properties of real networks. This work may shed some light on the in-depth understanding of the effect of gravity model. PMID:24622162

  15. NGS Gravity Network Data for the U.S.

    National Oceanic and Atmospheric Administration, Department of Commerce — The gravity network data (7,298 records) were gathered by various governmental organizations (and academia) using a variety of methods.

  16. A Note on Unsteady Temperature Equation For Gravity Flow of A ...

    We present an analytical study of unsteady temperature energy equation for gravity of a fluid with non – Newtonian behaviour through a porous medium. For the case of radial axisymmetric flow, the governing partial differential equation is transformed into an ordinary differential equation through similarity variables.

  17. Constraint propagation equations of the 3+1 decomposition of f(R) gravity

    Paschalidis, Vasileios; Shapiro, Stuart L; Halataei, Seyyed M H; Sawicki, Ignacy

    2011-01-01

    Theories of gravity other than general relativity (GR) can explain the observed cosmic acceleration without a cosmological constant. One such class of theories of gravity is f(R). Metric f(R) theories have been proven to be equivalent to Brans-Dicke (BD) scalar-tensor gravity without a kinetic term (ω = 0). Using this equivalence and a 3+1 decomposition of the theory, it has been shown that metric f(R) gravity admits a well-posed initial value problem. However, it has not been proven that the 3+1 evolution equations of metric f(R) gravity preserve the (Hamiltonian and momentum) constraints. In this paper, we show that this is indeed the case. In addition, we show that the mathematical form of the constraint propagation equations in BD-equilavent f(R) gravity and in f(R) gravity in both the Jordan and Einstein frames is exactly the same as in the standard ADM 3+1 decomposition of GR. Finally, we point out that current numerical relativity codes can incorporate the 3+1 evolution equations of metric f(R) gravity by modifying the stress-energy tensor and adding an additional scalar field evolution equation. We hope that this work will serve as a starting point for relativists to develop fully dynamical codes for valid f(R) models.

  18. Semigroup methods for evolution equations on networks

    Mugnolo, Delio

    2014-01-01

    This concise text is based on a series of lectures held only a few years ago and originally intended as an introduction to known results on linear hyperbolic and parabolic equations.  Yet the topic of differential equations on graphs, ramified spaces, and more general network-like objects has recently gained significant momentum and, well beyond the confines of mathematics, there is a lively interdisciplinary discourse on all aspects of so-called complex networks. Such network-like structures can be found in virtually all branches of science, engineering and the humanities, and future research thus calls for solid theoretical foundations.      This book is specifically devoted to the study of evolution equations – i.e., of time-dependent differential equations such as the heat equation, the wave equation, or the Schrödinger equation (quantum graphs) – bearing in mind that the majority of the literature in the last ten years on the subject of differential equations of graphs has been devoted to ellip...

  19. On the equivalence of vacuum equations of gauge quadratic theory of gravity and general relativity theory

    Zhitnikov, V.V.; Ponomarev, V.N.

    1986-01-01

    An attempt is made to compare the solution of field equations, corresponding to quadratic equations for the fields (g μν , Γ μν α ) in gauge gravitation theory (GGT) with general relativity theory solutions. Without restrictions for a concrete type of metrics only solutions of equations, for which torsion turns to zero, are considered. Equivalence of vacuum equations of gauge quadratic theory of gravity and general relativity theory is proved using the Newman-Penrose formalism

  20. Equivalent equations of motion for gravity and entropy

    Czech, Bartłomiej; Lamprou, Lampros; McCandlish, Samuel; Mosk, Benjamin; Sully, James

    2017-01-01

    We demonstrate an equivalence between the wave equation obeyed by the entanglement entropy of CFT subregions and the linearized bulk Einstein equation in Anti-de Sitter space. In doing so, we make use of the formalism of kinematic space https://www.doi.org/10.1007/JHEP10(2015)175 and fields on this space, introduced in https://www.doi.org/10.1007/JHEP07(2016)129. We show that the gravitational dynamics are equivalent to a gauge invariant wave-equation on kinematic space and that this equation arises in natural correspondence to the conformal Casimir equation in the CFT.

  1. Equations of motion for a rotor blade, including gravity, pitch action and rotor speed variations

    Kallesøe, Bjarne Skovmose

    2007-01-01

    This paper extends Hodges-Dowell's partial differential equations of blade motion, by including the effects from gravity, pitch action and varying rotor speed. New equations describing the pitch action and rotor speeds are also derived. The physical interpretation of the individual terms...... in the equations is discussed. The partial differential equations of motion are approximated by ordinary differential equations of motion using an assumed mode method. The ordinary differential equations are used to simulate a sudden pitch change of a rotating blade. This work is a part of a project on pitch blade...

  2. Capillary-gravity waves and the Navier-Stokes equation

    Behroozi, F.; Podolefsky, N.

    2001-01-01

    Water waves are a source of great fascination for undergraduates and thus provide an excellent context for introducing some important topics in fluid dynamics. In this paper we introduce the potential theory for incompressible and inviscid flow and derive the differential equation that governs the behaviour of the velocity potential. Next we obtain the harmonic solutions of the velocity potential by a very general argument. These solutions in turn yield the equations for the velocity and displacement of a water element under the action of a harmonic wave. Finally we obtain the dispersion relation for surface waves by requiring that the harmonic solutions satisfy the Navier-Stokes equation. (author)

  3. Averaging problem in general relativity, macroscopic gravity and using Einstein's equations in cosmology.

    Zalaletdinov, R. M.

    1998-04-01

    The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the geometry of macroscopic space-time, which follows from averaging Cartan's structure equations, is described and the correlation tensors present in the theory are discussed. The macroscopic field equations (averaged Einstein's equations) derived in the framework of the approach are presented and their structure is analysed. The correspondence principle for macroscopic gravity is formulated and a definition of the stress-energy tensor for the macroscopic gravitational field is proposed. It is shown that the physical meaning of using Einstein's equations with a hydrodynamic stress-energy tensor in looking for cosmological models means neglecting all gravitational field correlations. The system of macroscopic gravity equations to be solved when the correlations are taken into consideration is given and described.

  4. Data reduction and tying in regional gravity surveys—results from a new gravity base station network and the Bouguer gravity anomaly map for northeastern Mexico

    Hurtado-Cardador, Manuel; Urrutia-Fucugauchi, Jaime

    2006-12-01

    Since 1947 Petroleos Mexicanos (Pemex) has conducted oil exploration projects using potential field methods. Geophysical exploration companies under contracts with Pemex carried out gravity anomaly surveys that were referred to different floating data. Each survey comprises observations of gravity stations along highways, roads and trails at intervals of about 500 m. At present, 265 separate gravimeter surveys that cover 60% of the Mexican territory (mainly in the oil producing regions of Mexico) are available. This gravity database represents the largest, highest spatial resolution information, and consequently has been used in the geophysical data compilations for the Mexico and North America gravity anomaly maps. Regional integration of gravimeter surveys generates gradients and spurious anomalies in the Bouguer anomaly maps at the boundaries of the connected surveys due to the different gravity base stations utilized. The main objective of this study is to refer all gravimeter surveys from Pemex to a single new first-order gravity base station network, in order to eliminate problems of gradients and spurious anomalies. A second objective is to establish a network of permanent gravity base stations (BGP), referred to a single base from the World Gravity System. Four regional loops of BGP covering eight States of Mexico were established to support the tie of local gravity base stations from each of the gravimeter surveys located in the vicinity of these loops. The third objective is to add the gravity constants, measured and calculated, for each of the 265 gravimeter surveys to their corresponding files in the Pemex and Instituto Mexicano del Petroleo database. The gravity base used as the common datum is the station SILAG 9135-49 (Latin American System of Gravity) located in the National Observatory of Tacubaya in Mexico City. We present the results of the installation of a new gravity base network in northeastern Mexico, reference of the 43 gravimeter surveys

  5. Epidemics in networks: a master equation approach

    Cotacallapa, M; Hase, M O

    2016-01-01

    A problem closely related to epidemiology, where a subgraph of ‘infected’ links is defined inside a larger network, is investigated. This subgraph is generated from the underlying network by a random variable, which decides whether a link is able to propagate a disease/information. The relaxation timescale of this random variable is examined in both annealed and quenched limits, and the effectiveness of propagation of disease/information is analyzed. The dynamics of the model is governed by a master equation and two types of underlying network are considered: one is scale-free and the other has exponential degree distribution. We have shown that the relaxation timescale of the contagion variable has a major influence on the topology of the subgraph of infected links, which determines the efficiency of spreading of disease/information over the network. (paper)

  6. Epidemics in networks: a master equation approach

    Cotacallapa, M.; Hase, M. O.

    2016-02-01

    A problem closely related to epidemiology, where a subgraph of ‘infected’ links is defined inside a larger network, is investigated. This subgraph is generated from the underlying network by a random variable, which decides whether a link is able to propagate a disease/information. The relaxation timescale of this random variable is examined in both annealed and quenched limits, and the effectiveness of propagation of disease/information is analyzed. The dynamics of the model is governed by a master equation and two types of underlying network are considered: one is scale-free and the other has exponential degree distribution. We have shown that the relaxation timescale of the contagion variable has a major influence on the topology of the subgraph of infected links, which determines the efficiency of spreading of disease/information over the network.

  7. A dynamic ventilation model for gravity sewer networks.

    Wang, Y C; Nobi, N; Nguyen, T; Vorreiter, L

    2012-01-01

    To implement any effective odour and corrosion control technology in the sewer network, it is imperative that the airflow through gravity sewer airspaces be quantified. This paper presents a full dynamic airflow model for gravity sewer systems. The model, which is developed using the finite element method, is a compressible air transport model. The model has been applied to the North Head Sewerage Ocean Outfall System (NSOOS) and calibrated using the air pressure and airflow data collected during October 2008. Although the calibration is focused on forced ventilation, the model can be applied to natural ventilation as well.

  8. Parallel Vector Fields and Einstein Equations of Gravity | Mahara ...

    In this paper, we prove that no nontrivial timelike or spacelike parallel vector field exists in a region where the gravitational field created by macroscopic bodies and governed by Einstein's equations does not vanish. In other words, we prove that the existence of such vector fields in a region implies the vanishing of the ...

  9. FLRW Cosmology with Horava-Lifshitz Gravity: Impacts of Equations of State

    Tawfik, A.; Abou El Dahab, E.

    2017-07-01

    Inspired by Lifshitz theory for quantum critical phenomena in condensed matter, Horava proposed a theory for quantum gravity with an anisotropic scaling in ultraviolet. In Horava-Lifshitz gravity (HLG), we have studied the impacts of six types of equations of state on the evolution of various cosmological parameters such as Hubble parameters and scale factor. From the comparison of the general relativity gravity with the HLG with detailed and without with non-detailed balance conditions, remarkable differences are found. Also, a noticeable dependence of singular and non-singular Big Bang on the equations of state is observed. We conclude that HLG explains various epochs in the early universe and might be able to reproduce the entire cosmic history with and without singular Big Bang.

  10. The incompressible non-relativistic Navier-Stokes equation from gravity

    Bhattacharyya, Sayantani; Minwalla, Shiraz; Wadia, Spenta R.

    2009-01-01

    We note that the equations of relativistic hydrodynamics reduce to the incompressible Navier-Stokes equations in a particular scaling limit. In this limit boundary metric fluctuations of the underlying relativistic system turn into a forcing function identical to the action of a background electromagnetic field on the effectively charged fluid. We demonstrate that special conformal symmetries of the parent relativistic theory descend to 'accelerated boost' symmetries of the Navier-Stokes equations, uncovering a conformal symmetry structure of these equations. Applying our scaling limit to holographically induced fluid dynamics, we find gravity dual descriptions of an arbitrary solution of the forced non-relativistic incompressible Navier-Stokes equations. In the holographic context we also find a simple forced steady state shear solution to the Navier-Stokes equations, and demonstrate that this solution turns unstable at high enough Reynolds numbers, indicating a possible eventual transition to turbulence.

  11. The Gravity of Photons and the Necessary Rectification of Einstein Equation

    Lo C. Y.

    2006-01-01

    Full Text Available It is pointed out that Special Relativity together with the principle of causality implies that the gravity of an electromagnetic wave is an accompanying gravitational wave propagating with the same speed. Since a gravitational wave carries energy-momentum, this accompanying wave would make the energy-stress tensor of the light to be different from the electromagnetic energy-stress tensor, and thus can produce a geodesic equation for the photons. Moreover, it is found that the appropriate Einstein equation must additionally have the photonic energy-stress tensor with the antigravity coupling in the source term. This would correct that, in disagreement with the calculations for the bending of light, existing solutions of gravity for an electromagnetic wave, is unbounded. This rectification is confirmed by calculating the gravity of electromagnetic plane-waves. The gravity of an electromagnetic wave is indeed an accompanying gravitational wave. Moreover, these calculations show the first time that Special Relativity and General Relativity are compatible because the physical meaning of coordinates has been clarified. The success of this rectification makes General Relativity standing out further among theories of gravity.

  12. Quantum-Wave Equation and Heisenberg Inequalities of Covariant Quantum Gravity

    Claudio Cremaschini

    2017-07-01

    Full Text Available Key aspects of the manifestly-covariant theory of quantum gravity (Cremaschini and Tessarotto 2015–2017 are investigated. These refer, first, to the establishment of the four-scalar, manifestly-covariant evolution quantum wave equation, denoted as covariant quantum gravity (CQG wave equation, which advances the quantum state ψ associated with a prescribed background space-time. In this paper, the CQG-wave equation is proved to follow at once by means of a Hamilton–Jacobi quantization of the classical variational tensor field g ≡ g μ ν and its conjugate momentum, referred to as (canonical g-quantization. The same equation is also shown to be variational and to follow from a synchronous variational principle identified here with the quantum Hamilton variational principle. The corresponding quantum hydrodynamic equations are then obtained upon introducing the Madelung representation for ψ , which provides an equivalent statistical interpretation of the CQG-wave equation. Finally, the quantum state ψ is proven to fulfill generalized Heisenberg inequalities, relating the statistical measurement errors of quantum observables. These are shown to be represented in terms of the standard deviations of the metric tensor g ≡ g μ ν and its quantum conjugate momentum operator.

  13. Horizon thermodynamics and gravitational field equations in Horava-Lifshitz gravity

    Cai Ronggen; Ohta, Nobuyoshi

    2010-01-01

    We explore the relationship between the first law of thermodynamics and gravitational field equation at a static, spherically symmetric black hole horizon in Horava-Lifshitz theory with/without detailed balance. It turns out that as in the cases of Einstein gravity and Lovelock gravity, the gravitational field equation can be cast to a form of the first law of thermodynamics at the black hole horizon. This way we obtain the expressions for entropy and mass in terms of black hole horizon, consistent with those from other approaches. We also define a generalized Misner-Sharp energy for static, spherically symmetric spacetimes in Horava-Lifshitz theory. The generalized Misner-Sharp energy is conserved in the case without matter field, and its variation gives the first law of black hole thermodynamics at the black hole horizon.

  14. Monthly gravity field recovery from GRACE orbits and K-band measurements using variational equations approach

    Changqing Wang

    2015-07-01

    Full Text Available The Gravity Recovery and Climate Experiment (GRACE mission can significantly improve our knowledge of the temporal variability of the Earth's gravity field. We obtained monthly gravity field solutions based on variational equations approach from GPS-derived positions of GRACE satellites and K-band range-rate measurements. The impact of different fixed data weighting ratios in temporal gravity field recovery while combining the two types of data was investigated for the purpose of deriving the best combined solution. The monthly gravity field solution obtained through above procedures was named as the Institute of Geodesy and Geophysics (IGG temporal gravity field models. IGG temporal gravity field models were compared with GRACE Release05 (RL05 products in following aspects: (i the trend of the mass anomaly in China and its nearby regions within 2005–2010; (ii the root mean squares of the global mass anomaly during 2005–2010; (iii time-series changes in the mean water storage in the region of the Amazon Basin and the Sahara Desert between 2005 and 2010. The results showed that IGG solutions were almost consistent with GRACE RL05 products in above aspects (i–(iii. Changes in the annual amplitude of mean water storage in the Amazon Basin were 14.7 ± 1.2 cm for IGG, 17.1 ± 1.3 cm for the Centre for Space Research (CSR, 16.4 ± 0.9 cm for the GeoForschungsZentrum (GFZ and 16.9 ± 1.2 cm for the Jet Propulsion Laboratory (JPL in terms of equivalent water height (EWH, respectively. The root mean squares of the mean mass anomaly in Sahara were 1.2 cm, 0.9 cm, 0.9 cm and 1.2 cm for temporal gravity field models of IGG, CSR, GFZ and JPL, respectively. Comparison suggested that IGG temporal gravity field solutions were at the same accuracy level with the latest temporal gravity field solutions published by CSR, GFZ and JPL.

  15. Minimal Liouville gravity on the torus via the Douglas string equation

    Spodyneiko, Lev

    2015-01-01

    In this paper we assume that the partition function in minimal Liouville gravity (MLG) obeys the Douglas string equation. This conjecture makes it possible to compute the torus correlation numbers in (3,p) MLG. We perform this calculation using also the resonance relations between the coupling constants in the KdV frame and in the Liouville frame. We obtain explicit expressions for the torus partition function and for the one- and two-point correlation numbers. (paper)

  16. Equations of motion for massive spin 2 field coupled to gravity

    Buchbinder, I.L.; Gitman, D.M.; Krykhtin, V.A.; Pershin, V.D.

    2000-01-01

    We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in α' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory

  17. Structural equation models from paths to networks

    Westland, J Christopher

    2015-01-01

    This compact reference surveys the full range of available structural equation modeling (SEM) methodologies.  It reviews applications in a broad range of disciplines, particularly in the social sciences where many key concepts are not directly observable.  This is the first book to present SEM’s development in its proper historical context–essential to understanding the application, strengths and weaknesses of each particular method.  This book also surveys the emerging path and network approaches that complement and enhance SEM, and that will grow in importance in the near future.  SEM’s ability to accommodate unobservable theory constructs through latent variables is of significant importance to social scientists.  Latent variable theory and application are comprehensively explained, and methods are presented for extending their power, including guidelines for data preparation, sample size calculation, and the special treatment of Likert scale data.  Tables of software, methodologies and fit st...

  18. On the propagation of Einstein's equations with quasi-Maxwellian equations of gravity

    Novello, M.; Salim, J.M.

    1985-01-01

    It is proved that an affirmation proposed in a recent paper of Lesche and Som in which they argue about the non equivalence in the use of Weyl conformal tensor instead of the fuel curvature tensor in Bianchi identities regarded as the equation of evolution is wrong. (L.C.) [pt

  19. Reconstruction from scalar-tensor theory and the inhomogeneous equation of state in f(T) gravity

    Said, Jackson Levi [University of Malta, Institute of Space Sciences and Astronomy, Msida (Malta); University of Malta, Department of Physics, Msida (Malta)

    2017-12-15

    General relativity (GR) characterizes gravity as a geometric properly exhibited as curvature on spacetime. Teleparallelism describes gravity through torsional properties, and can reproduce GR at the level of equations. Similar to f(R) gravity, on taking a generalization, f(T) gravity can produce various modifications its gravitational mechanism. The resulting field equations are inherently distinct to f(R) gravity in that they are second order. In the present work, f(T) gravity is examined in the cosmological context with a number of solutions reconstructed by means of an auxiliary scalar field. To do this, various forms of the Hubble parameter are considered with an f(T) Lagrangian emerging for each instance. In addition, the inhomogeneous equation of state (EoS) is investigated with a particular Hubble parameter model used to show how this can be used to reconstruct the f(T) Lagrangian. Observationally, the auxiliary scalar field and the exotic terms in the FRW field equations give the same results, meaning that the variation in the Hubble parameter may be interpreted as the need to reformulate gravity in some way, as in f(T) gravity. (orig.)

  20. Reconstruction from scalar-tensor theory and the inhomogeneous equation of state in f(T) gravity

    Said, Jackson Levi

    2017-01-01

    General relativity (GR) characterizes gravity as a geometric properly exhibited as curvature on spacetime. Teleparallelism describes gravity through torsional properties, and can reproduce GR at the level of equations. Similar to f(R) gravity, on taking a generalization, f(T) gravity can produce various modifications its gravitational mechanism. The resulting field equations are inherently distinct to f(R) gravity in that they are second order. In the present work, f(T) gravity is examined in the cosmological context with a number of solutions reconstructed by means of an auxiliary scalar field. To do this, various forms of the Hubble parameter are considered with an f(T) Lagrangian emerging for each instance. In addition, the inhomogeneous equation of state (EoS) is investigated with a particular Hubble parameter model used to show how this can be used to reconstruct the f(T) Lagrangian. Observationally, the auxiliary scalar field and the exotic terms in the FRW field equations give the same results, meaning that the variation in the Hubble parameter may be interpreted as the need to reformulate gravity in some way, as in f(T) gravity. (orig.)

  1. Equation of state and viscosities from a gravity dual of the gluon plasma

    R. Yaresko

    2015-07-01

    Full Text Available Employing new precision data of the equation of state of the SU(3 Yang–Mills theory (gluon plasma the dilaton potential of a gravity-dual model is adjusted in the temperature range (1–10Tc within a bottom-up approach. The ratio of bulk viscosity to shear viscosity follows then as ζ/η≈πΔvs2 for Δvs2<0.2 and achieves a maximum value of 0.94 at Δvs2≈0.3, where Δvs2≡1/3−vs2 is the non-conformality measure and vs2 is the velocity of sound squared, while the ratio of shear viscosity to entropy density is known as (4π−1 for the considered set-up with Hilbert action on the gravity side.

  2. Trade-FDI Linkages in a System of Gravity Equations for German Regional Data

    Mitze, Timo; Alecke, Björn; Untiedt, Gerhard

    We analyse the nature of German trade-FDI linkages within the EU27 based on a simultaneous equation gravity approach for imports, exports, in- and outward FDI stocks.We adopt both a Hausman-Taylor (1981) IV approach (3SLS-GMM) and rival non-IV estimation (the system extension to the Fixed Effects...... substitutive links between trade flows and outward FDI in line with earlier empirical evidence for Germany. Building upon German state level data we are also able to analyse the sensitivity of the results for regional sub-samples. The latter disaggregation hints at structural differences among the trade...

  3. An introduction to neural network methods for differential equations

    Yadav, Neha; Kumar, Manoj

    2015-01-01

    This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks, and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed...

  4. Critical behavior in two-dimensional quantum gravity and equations of motion of the string

    Das, S.R.; Dhar, A.; Wadia, S.R.

    1990-01-01

    The authors show how consistent quantization determines the renormalization of couplings in a quantum field theory coupled to gravity in two dimensions. The special status of couplings corresponding to conformally invariant matter is discussed. In string theory, where the dynamical degree of freedom of the two-dimensional metric plays the role of time in target space, these renormalization group equations are themselves the classical equations of motion. Time independent solutions, like classical vacuua, correspond to the situation in which matter is conformally invariant. Time dependent solutions, like tunnelling configurations between vacuua, correspond to special trajectories in theory space. The authors discuss an example of such a trajectory in the space containing the c ≤ 1 minimal models. The authors also discuss the connection between this work and the recent attempts to construct non-pertubative string theories based on matrix models

  5. Killing vector fields in three dimensions: a method to solve massive gravity field equations

    Guerses, Metin, E-mail: gurses@fen.bilkent.edu.t [Department of Mathematics, Faculty of Sciences, Bilkent University, 06800 Ankara (Turkey)

    2010-10-21

    Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.

  6. Algorithms for optimization of branching gravity-driven water networks

    Dardani, Ian; Jones, Gerard F.

    2018-05-01

    The design of a water network involves the selection of pipe diameters that satisfy pressure and flow requirements while considering cost. A variety of design approaches can be used to optimize for hydraulic performance or reduce costs. To help designers select an appropriate approach in the context of gravity-driven water networks (GDWNs), this work assesses three cost-minimization algorithms on six moderate-scale GDWN test cases. Two algorithms, a backtracking algorithm and a genetic algorithm, use a set of discrete pipe diameters, while a new calculus-based algorithm produces a continuous-diameter solution which is mapped onto a discrete-diameter set. The backtracking algorithm finds the global optimum for all but the largest of cases tested, for which its long runtime makes it an infeasible option. The calculus-based algorithm's discrete-diameter solution produced slightly higher-cost results but was more scalable to larger network cases. Furthermore, the new calculus-based algorithm's continuous-diameter and mapped solutions provided lower and upper bounds, respectively, on the discrete-diameter global optimum cost, where the mapped solutions were typically within one diameter size of the global optimum. The genetic algorithm produced solutions even closer to the global optimum with consistently short run times, although slightly higher solution costs were seen for the larger network cases tested. The results of this study highlight the advantages and weaknesses of each GDWN design method including closeness to the global optimum, the ability to prune the solution space of infeasible and suboptimal candidates without missing the global optimum, and algorithm run time. We also extend an existing closed-form model of Jones (2011) to include minor losses and a more comprehensive two-part cost model, which realistically applies to pipe sizes that span a broad range typical of GDWNs of interest in this work, and for smooth and commercial steel roughness values.

  7. Algorithms for optimization of branching gravity-driven water networks

    I. Dardani

    2018-05-01

    Full Text Available The design of a water network involves the selection of pipe diameters that satisfy pressure and flow requirements while considering cost. A variety of design approaches can be used to optimize for hydraulic performance or reduce costs. To help designers select an appropriate approach in the context of gravity-driven water networks (GDWNs, this work assesses three cost-minimization algorithms on six moderate-scale GDWN test cases. Two algorithms, a backtracking algorithm and a genetic algorithm, use a set of discrete pipe diameters, while a new calculus-based algorithm produces a continuous-diameter solution which is mapped onto a discrete-diameter set. The backtracking algorithm finds the global optimum for all but the largest of cases tested, for which its long runtime makes it an infeasible option. The calculus-based algorithm's discrete-diameter solution produced slightly higher-cost results but was more scalable to larger network cases. Furthermore, the new calculus-based algorithm's continuous-diameter and mapped solutions provided lower and upper bounds, respectively, on the discrete-diameter global optimum cost, where the mapped solutions were typically within one diameter size of the global optimum. The genetic algorithm produced solutions even closer to the global optimum with consistently short run times, although slightly higher solution costs were seen for the larger network cases tested. The results of this study highlight the advantages and weaknesses of each GDWN design method including closeness to the global optimum, the ability to prune the solution space of infeasible and suboptimal candidates without missing the global optimum, and algorithm run time. We also extend an existing closed-form model of Jones (2011 to include minor losses and a more comprehensive two-part cost model, which realistically applies to pipe sizes that span a broad range typical of GDWNs of interest in this work, and for smooth and commercial steel

  8. Gravity

    Gamow, George

    2003-01-01

    A distinguished physicist and teacher, George Gamow also possessed a special gift for making the intricacies of science accessible to a wide audience. In Gravity, he takes an enlightening look at three of the towering figures of science who unlocked many of the mysteries behind the laws of physics: Galileo, the first to take a close look at the process of free and restricted fall; Newton, originator of the concept of gravity as a universal force; and Einstein, who proposed that gravity is no more than the curvature of the four-dimensional space-time continuum.Graced with the author's own draw

  9. Stochastic analysis of complex reaction networks using binomial moment equations.

    Barzel, Baruch; Biham, Ofer

    2012-09-01

    The stochastic analysis of complex reaction networks is a difficult problem because the number of microscopic states in such systems increases exponentially with the number of reactive species. Direct integration of the master equation is thus infeasible and is most often replaced by Monte Carlo simulations. While Monte Carlo simulations are a highly effective tool, equation-based formulations are more amenable to analytical treatment and may provide deeper insight into the dynamics of the network. Here, we present a highly efficient equation-based method for the analysis of stochastic reaction networks. The method is based on the recently introduced binomial moment equations [Barzel and Biham, Phys. Rev. Lett. 106, 150602 (2011)]. The binomial moments are linear combinations of the ordinary moments of the probability distribution function of the population sizes of the interacting species. They capture the essential combinatorics of the reaction processes reflecting their stoichiometric structure. This leads to a simple and transparent form of the equations, and allows a highly efficient and surprisingly simple truncation scheme. Unlike ordinary moment equations, in which the inclusion of high order moments is prohibitively complicated, the binomial moment equations can be easily constructed up to any desired order. The result is a set of equations that enables the stochastic analysis of complex reaction networks under a broad range of conditions. The number of equations is dramatically reduced from the exponential proliferation of the master equation to a polynomial (and often quadratic) dependence on the number of reactive species in the binomial moment equations. The aim of this paper is twofold: to present a complete derivation of the binomial moment equations; to demonstrate the applicability of the moment equations for a representative set of example networks, in which stochastic effects play an important role.

  10. Equations of motion for massive spin 2 field coupled to gravity

    Buchbinder, I.L. E-mail: ilb@mail.tomsknet.ru; Gitman, D.M. E-mail: gitman@fma.if.usp.br; Krykhtin, V.A. E-mail: krykhtin@phys.dfe.tpu.edu.ru; Pershin, V.D. E-mail: pershin@ic.tsu.ru

    2000-09-18

    We investigate the problems of consistency and causality for the equations of motion describing massive spin two field in external gravitational and massless scalar dilaton fields in arbitrary spacetime dimension. From the field theoretical point of view we consider a general classical action with non-minimal couplings and find gravitational and dilaton background on which this action describes a theory consistent with the flat space limit. In the case of pure gravitational background all field components propagate causally. We show also that the massive spin two field can be consistently described in arbitrary background by means of the lagrangian representing an infinite series in the inverse mass. Within string theory we obtain equations of motion for the massive spin two field coupled to gravity from the requirement of quantum Weyl invariance of the corresponding two-dimensional sigma-model. In the lowest order in {alpha}' we demonstrate that these effective equations of motion coincide with consistent equations derived in field theory.

  11. Conformal gravity, the Einstein equations and spaces of complex null geodesics

    Baston, R.J.; Mason, L.J.

    1987-07-01

    The aim of the paper is to give a twistorial characterisation of the field equations of conformal gravity and of Einstein spacetimes. Strong evidence is provided for a particularly concise characterisation of these equations in terms of 'formal neighbourhoods'of the space of complex null geodesics. Second-order perturbations of the metric of complexified Minkowski space are considered. These correspond to certain infinitesimal deformations of its space of complex null geodesics, PN. PN has a natural codimension one embedding into a larger space. It is shown that deformations extend automatically to the fourth-order embedding (that is, the fourth formal neighbourhood). They extend to the fifth formal neighbourhood if and only if the corresponding perturbation in the metric has vanishing Bach tensor. Finally, deformations which extend to the sixth formal neighbourhood correspond to perturbations in the metric that are conformally related to ones satisfying the Einstein equations. The authors present arguments which suggest that the results will also hold when spacetime is fully curved.

  12. Conformal gravity, the Einstein equations and spaces of complex null geodesics

    Baston, R.J.; Mason, L.J.

    1987-01-01

    The aim of the paper is to give a twistorial characterisation of the field equations of conformal gravity and of Einstein spacetimes. Strong evidence is provided for a particularly concise characterisation of these equations in terms of 'formal neighbourhoods'of the space of complex null geodesics. Second-order perturbations of the metric of complexified Minkowski space are considered. These correspond to certain infinitesimal deformations of its space of complex null geodesics, PN. PN has a natural codimension one embedding into a larger space. It is shown that deformations extend automatically to the fourth-order embedding (that is, the fourth formal neighbourhood). They extend to the fifth formal neighbourhood if and only if the corresponding perturbation in the metric has vanishing Bach tensor. Finally, deformations which extend to the sixth formal neighbourhood correspond to perturbations in the metric that are conformally related to ones satisfying the Einstein equations. The authors present arguments which suggest that the results will also hold when spacetime is fully curved. (author)

  13. Bulk entanglement gravity without a boundary: Towards finding Einstein's equation in Hilbert space

    Cao, ChunJun; Carroll, Sean M.

    2018-04-01

    We consider the emergence from quantum entanglement of spacetime geometry in a bulk region. For certain classes of quantum states in an appropriately factorized Hilbert space, a spatial geometry can be defined by associating areas along codimension-one surfaces with the entanglement entropy between either side. We show how radon transforms can be used to convert these data into a spatial metric. Under a particular set of assumptions, the time evolution of such a state traces out a four-dimensional spacetime geometry, and we argue using a modified version of Jacobson's "entanglement equilibrium" that the geometry should obey Einstein's equation in the weak-field limit. We also discuss how entanglement equilibrium is related to a generalization of the Ryu-Takayanagi formula in more general settings, and how quantum error correction can help specify the emergence map between the full quantum-gravity Hilbert space and the semiclassical limit of quantum fields propagating on a classical spacetime.

  14. Field lines of gravity, their curvature and torsion, the Lagrange and the Hamilton equations of the plumbline

    E. W. Grafarend

    1997-06-01

    Full Text Available The length of the gravitational field lines/of the orthogonal trajectories of a family of gravity equipotential surfaces/of the plumbline between a terrestrial topographic point and a point on a reference equipotential surface like the geoid í also known as the orthometric height í plays a central role in Satellite Geodesy as well as in Physical Geodesy. As soon as we determine the geometry of the Earth pointwise by means of a satellite GPS (Global Positioning System: «global problem solver» we are left with the problem of converting ellipsoidal heights (geometric heights into orthometric heights (physical heights. For the computation of the plumbline we derive its three differential equations of first order as well as the three geodesic equations of second order. The three differential equations of second order take the form of a Newton differential equation when we introduce the parameter time via the Marussi gauge on a conformally flat three-dimensional Riemann manifold and the generalized force field, the gradient of the superpotential, namely the modulus of gravity squared and taken half. In particular, we compute curvature and torsion of the plumbline and prove their functional relationship to the second and third derivatives of the gravity potential. For a spherically symmetric gravity field, curvature and torsion of the plumbline are zero, the plumbline is straight. Finally we derive the three Lagrangean as well as the six Hamiltonian differential equations of the plumbline, in particular in their star form with respect to Marussi gauge.

  15. gravity

    We study the cosmological dynamics for R p exp( λ R ) gravity theory in the metric formalism, using dynamical systems approach. Considering higher-dimensional FRW geometries in case of an imperfect fluid which has two different scale factors in the normal and extra dimensions, we find the exact solutions, and study its ...

  16. Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

    Wu Ning; Zhang Dahua

    2007-01-01

    A systematic method is developed to study the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton's second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.

  17. Three-Dimensional Coupled NLS Equations for Envelope Gravity Solitary Waves in Baroclinic Atmosphere and Modulational Instability

    Baojun Zhao

    2018-01-01

    Full Text Available Envelope gravity solitary waves are an important research hot spot in the field of solitary wave. And the weakly nonlinear model equations system is a part of the research of envelope gravity solitary waves. Because of the lack of technology and theory, previous studies tried hard to reduce the variable numbers and constructed the two-dimensional model in barotropic atmosphere and could only describe the propagation feature in a direction. But for the propagation of envelope gravity solitary waves in real ocean ridges and atmospheric mountains, the three-dimensional model is more appropriate. Meanwhile, the baroclinic problem of atmosphere is also an inevitable topic. In the paper, the three-dimensional coupled nonlinear Schrödinger (CNLS equations are presented to describe the evolution of envelope gravity solitary waves in baroclinic atmosphere, which are derived from the basic dynamic equations by employing perturbation and multiscale methods. The model overcomes two disadvantages: (1 baroclinic problem and (2 propagation path problem. Then, based on trial function method, we deduce the solution of the CNLS equations. Finally, modulational instability of wave trains is also discussed.

  18. Flow equation of quantum Einstein gravity in a higher-derivative truncation

    Lauscher, O.; Reuter, M.

    2002-01-01

    Motivated by recent evidence indicating that quantum Einstein gravity (QEG) might be nonperturbatively renormalizable, the exact renormalization group equation of QEG is evaluated in a truncation of theory space which generalizes the Einstein-Hilbert truncation by the inclusion of a higher-derivative term (R 2 ). The beta functions describing the renormalization group flow of the cosmological constant, Newton's constant, and the R 2 coupling are computed explicitly. The fixed point properties of the 3-dimensional flow are investigated, and they are confronted with those of the 2-dimensional Einstein-Hilbert flow. The non-Gaussian fixed point predicted by the latter is found to generalize to a fixed point on the enlarged theory space. In order to test the reliability of the R 2 truncation near this fixed point we analyze the residual scheme dependence of various universal quantities; it turns out to be very weak. The two truncations are compared in detail, and their numerical predictions are found to agree with a surprisingly high precision. Because of the consistency of the results it appears increasingly unlikely that the non-Gaussian fixed point is an artifact of the truncation. If it is present in the exact theory QEG is probably nonperturbatively renormalizable and ''asymptotically safe.'' We discuss how the conformal factor problem of Euclidean gravity manifests itself in the exact renormalization group approach and show that, in the R 2 truncation, the investigation of the fixed point is not afflicted with this problem. Also the Gaussian fixed point of the Einstein-Hilbert truncation is analyzed; it turns out that it does not generalize to a corresponding fixed point on the enlarged theory space

  19. Neural network error correction for solving coupled ordinary differential equations

    Shelton, R. O.; Darsey, J. A.; Sumpter, B. G.; Noid, D. W.

    1992-01-01

    A neural network is presented to learn errors generated by a numerical algorithm for solving coupled nonlinear differential equations. The method is based on using a neural network to correctly learn the error generated by, for example, Runge-Kutta on a model molecular dynamics (MD) problem. The neural network programs used in this study were developed by NASA. Comparisons are made for training the neural network using backpropagation and a new method which was found to converge with fewer iterations. The neural net programs, the MD model and the calculations are discussed.

  20. A solution of nonlinear equation for the gravity wave spectra from Adomian decomposition method: a first approach

    Antonio Gledson Goulart

    2013-12-01

    Full Text Available In this paper, the equation for the gravity wave spectra in mean atmosphere is analytically solved without linearization by the Adomian decomposition method. As a consequence, the nonlinear nature of problem is preserved and the errors found in the results are only due to the parameterization. The results, with the parameterization applied in the simulations, indicate that the linear solution of the equation is a good approximation only for heights shorter than ten kilometers, because the linearization the equation leads to a solution that does not correctly describe the kinetic energy spectra.

  1. Field Equations for Abelian Vector Fields in the Bianchi Type I Metric in the Framework of Teleparallel Gravity

    Triyanta; Zen, F. P.; Supardi; Wardaya, A. Y.

    2010-01-01

    Gauge theory, under the framework of quantum field theory, has successfully described three fundamental interactions: electromagnetic, weak, and strong interactions. Problems of describing the gravitational interaction in a similar manner has not been satisfied yet until now. Teleparallel gravity (TG) is one proposal describing gravitational field as a gauge field. This theory is quite new and it is equivalent to Einstein's general relativity. But as gravitational field in TG is expressed by torsion, rather than curvature, it gives an alternative framework for solving problems on gravity. This paper will present solution of the dynamical equation of abelian vector fields under the framework of TG in the Bianchi type I spacetime.

  2. Generalized master equations for non-Poisson dynamics on networks.

    Hoffmann, Till; Porter, Mason A; Lambiotte, Renaud

    2012-10-01

    The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Accordingly, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that this equation reduces to the standard rate equations when the underlying process is Poissonian and that its stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We conduct numerical simulations and also derive analytical results for the stationary solution under the assumption that all edges have the same waiting-time distribution. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.

  3. Constructing general partial differential equations using polynomial and neural networks.

    Zjavka, Ladislav; Pedrycz, Witold

    2016-01-01

    Sum fraction terms can approximate multi-variable functions on the basis of discrete observations, replacing a partial differential equation definition with polynomial elementary data relation descriptions. Artificial neural networks commonly transform the weighted sum of inputs to describe overall similarity relationships of trained and new testing input patterns. Differential polynomial neural networks form a new class of neural networks, which construct and solve an unknown general partial differential equation of a function of interest with selected substitution relative terms using non-linear multi-variable composite polynomials. The layers of the network generate simple and composite relative substitution terms whose convergent series combinations can describe partial dependent derivative changes of the input variables. This regression is based on trained generalized partial derivative data relations, decomposed into a multi-layer polynomial network structure. The sigmoidal function, commonly used as a nonlinear activation of artificial neurons, may transform some polynomial items together with the parameters with the aim to improve the polynomial derivative term series ability to approximate complicated periodic functions, as simple low order polynomials are not able to fully make up for the complete cycles. The similarity analysis facilitates substitutions for differential equations or can form dimensional units from data samples to describe real-world problems. Copyright © 2015 Elsevier Ltd. All rights reserved.

  4. Recent findings on sinks for sulfide in gravity sewer networks

    Nielsen, Asbjørn Haaning; Hvitved-Jacobsen, Thorkild; Vollertsen, Jes

    2006-01-01

    summarizes this newly obtained knowledge and emphasizes important implications of the findings. Model simulations of the in-sewer processes important for the sulfur cycle showed that sulfide oxidation in the wetted biofilm is typically the most important sink for dissolved sulfide in gravity sewers. However...

  5. Image recovery using diffusion equation embedded neural network

    Torkamani-Azar, F.

    2001-01-01

    Artificial neural networks with their inherent parallelism have been shown to perform well in many processing applications. In this paper, a new self-organizing approach for the recovery of gray level images degraded by additive noise based on embedding the diffusion equation in a neural network (without using a priori knowledge about the image point spread function, noise or original image) is described which enhances and restores gray levels of degraded images and is for application in low-level processing. Two learning features have been proposed which would be effective in the practical implementation of such a network. The recovery procedure needs some parameter estimation such as different error goals. While the required computation is not excessive, the procedure dose not require too many iterations and convergence is very fast. In addition, through the simulation the new network showed that it has superior ability to give a better quality result with a minimum of the sum of the squared error

  6. Accounting for time- and space-varying changes in the gravity field to improve the network adjustment of relative-gravity data

    Kennedy, Jeffrey R.; Ferre, Ty P.A.

    2015-01-01

    The relative gravimeter is the primary terrestrial instrument for measuring spatially and temporally varying gravitational fields. The background noise of the instrument—that is, non-linear drift and random tares—typically requires some form of least-squares network adjustment to integrate data collected during a campaign that may take several days to weeks. Here, we present an approach to remove the change in the observed relative-gravity differences caused by hydrologic or other transient processes during a single campaign, so that the adjusted gravity values can be referenced to a single epoch. The conceptual approach is an example of coupled hydrogeophysical inversion, by which a hydrologic model is used to inform and constrain the geophysical forward model. The hydrologic model simulates the spatial variation of the rate of change of gravity as either a linear function of distance from an infiltration source, or using a 3-D numerical groundwater model. The linear function can be included in and solved for as part of the network adjustment. Alternatively, the groundwater model is used to predict the change of gravity at each station through time, from which the accumulated gravity change is calculated and removed from the data prior to the network adjustment. Data from a field experiment conducted at an artificial-recharge facility are used to verify our approach. Maximum gravity change due to hydrology (observed using a superconducting gravimeter) during the relative-gravity field campaigns was up to 2.6 μGal d−1, each campaign was between 4 and 6 d and one month elapsed between campaigns. The maximum absolute difference in the estimated gravity change between two campaigns, two months apart, using the standard network adjustment method and the new approach, was 5.5 μGal. The maximum gravity change between the same two campaigns was 148 μGal, and spatial variation in gravity change revealed zones of preferential infiltration and areas of relatively

  7. Network Reconstruction From High-Dimensional Ordinary Differential Equations.

    Chen, Shizhe; Shojaie, Ali; Witten, Daniela M

    2017-01-01

    We consider the task of learning a dynamical system from high-dimensional time-course data. For instance, we might wish to estimate a gene regulatory network from gene expression data measured at discrete time points. We model the dynamical system nonparametrically as a system of additive ordinary differential equations. Most existing methods for parameter estimation in ordinary differential equations estimate the derivatives from noisy observations. This is known to be challenging and inefficient. We propose a novel approach that does not involve derivative estimation. We show that the proposed method can consistently recover the true network structure even in high dimensions, and we demonstrate empirical improvement over competing approaches. Supplementary materials for this article are available online.

  8. Analysis of datum-instability effect on calculated results of data from Longmen Mountain regional gravity network

    Sun Shaoan

    2011-11-01

    Full Text Available A statistical correlation method is used to study the effect of instability of the calculation datum (used in traditional method of indirect adjustment on calculated gravity results, using data recorded by Long-men Mountain regional gravity network during 1996 – 2007. The result shows that when this effect is corrected, anomalous gravity changes before the 2008 Wenchuan Ms8.0 earthquake become obvious and characteristically distinctive. Thus the datum-stability problem must be considered when processing and analyzing data recorded by a regional gravity network.

  9. Innovation diffusion equations on correlated scale-free networks

    Bertotti, M.L., E-mail: marialetizia.bertotti@unibz.it [Free University of Bozen–Bolzano, Faculty of Science and Technology, Bolzano (Italy); Brunner, J., E-mail: johannes.brunner@tis.bz.it [TIS Innovation Park, Bolzano (Italy); Modanese, G., E-mail: giovanni.modanese@unibz.it [Free University of Bozen–Bolzano, Faculty of Science and Technology, Bolzano (Italy)

    2016-07-29

    Highlights: • The Bass diffusion model can be formulated on scale-free networks. • In the trickle-down version, the hubs adopt earlier and act as monitors. • We improve the equations in order to describe trickle-up diffusion. • Innovation is generated at the network periphery, and hubs can act as stiflers. • We compare diffusion times, in dependence on the scale-free exponent. - Abstract: We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to geographic and logistic influences (like for instance Alpine regions). We consider both the diffusion peak times of the total population and of the link classes. In the familiar trickle-down processes the adoption curve of the hubs is found to anticipate the total adoption in a predictable way. In a major departure from the standard model, we model a trickle-up process by introducing heterogeneous publicity coefficients (which can also be negative for the hubs, thus turning them into stiflers) and a stochastic term which represents the erratic generation of innovation at the periphery of the network. The results confirm the robustness of the Bass model and expand considerably its range of applicability.

  10. Innovation diffusion equations on correlated scale-free networks

    Bertotti, M.L.; Brunner, J.; Modanese, G.

    2016-01-01

    Highlights: • The Bass diffusion model can be formulated on scale-free networks. • In the trickle-down version, the hubs adopt earlier and act as monitors. • We improve the equations in order to describe trickle-up diffusion. • Innovation is generated at the network periphery, and hubs can act as stiflers. • We compare diffusion times, in dependence on the scale-free exponent. - Abstract: We introduce a heterogeneous network structure into the Bass diffusion model, in order to study the diffusion times of innovation or information in networks with a scale-free structure, typical of regions where diffusion is sensitive to geographic and logistic influences (like for instance Alpine regions). We consider both the diffusion peak times of the total population and of the link classes. In the familiar trickle-down processes the adoption curve of the hubs is found to anticipate the total adoption in a predictable way. In a major departure from the standard model, we model a trickle-up process by introducing heterogeneous publicity coefficients (which can also be negative for the hubs, thus turning them into stiflers) and a stochastic term which represents the erratic generation of innovation at the periphery of the network. The results confirm the robustness of the Bass model and expand considerably its range of applicability.

  11. Quantum gravity vacuum and invariants of embedded spin networks

    Mikovic, A

    2003-01-01

    We show that the path integral for the three-dimensional SU(2) BF theory with a Wilson loop or a spin network function inserted can be understood as the Rovelli-Smolin loop transform of a wavefunction in the Ashtekar connection representation, where the wavefunction satisfies the constraints of quantum general relativity with zero cosmological constant. This wavefunction is given as a product of the delta functions of the SU(2) field strength and therefore it can be naturally associated with a flat connection spacetime. The loop transform can be defined rigorously via the quantum SU(2) group, as a spin foam state sum model, so that one obtains invariants of spin networks embedded in a three-manifold. These invariants define a flat connection vacuum state in the q-deformed spin network basis. We then propose a modification of this construction in order to obtain a vacuum state corresponding to the flat metric spacetime

  12. New solutions of the Einstein equations for the Mixmaster and Taub Universe models and the anti gravity phenomena

    Melendez L, L.

    2004-01-01

    In the first part of this work, starting from Einstein's equations of the Classical General Relativity, a new kind of solutions for the Mixmaster model are explored. By dispensing with the extension to the complex variable field, which is usual in problems such as the Laplace equation or the harmonic oscillator, in a similar manner to that of Quantum Mechanics, the equations appear to have solutions that belong to the complex General Relativity. A first integral is performed by establishing a separation of the first derivatives. Then a second integral is obtained once the respective equations with separate variables are found and whose integrals provide a family of complex solutions. However, reality conditions do not seem to be easily imposed at this stage. Above all, it is significant that the classical Einstein's equations for the debatably integrable Mixmaster model present complex solutions. In the second part of this work, following a specific strategy in which the cosmological time variables are operated upon, a new family of solutions to the empty Taub universe is found. Among the characteristics of such a family, it stands the positive acceleration provided by the tri-curvature property of this universe to two of the three scale factors of the Taub model. This effect of the tri-curvature results not in a restoring force such as normal gravity but in the conversion of the Taub cosmology into an accelerating universe. (Author)

  13. Population equations for degree-heterogenous neural networks

    Kähne, M.; Sokolov, I. M.; Rüdiger, S.

    2017-11-01

    We develop a statistical framework for studying recurrent networks with broad distributions of the number of synaptic links per neuron. We treat each group of neurons with equal input degree as one population and derive a system of equations determining the population-averaged firing rates. The derivation rests on an assumption of a large number of neurons and, additionally, an assumption of a large number of synapses per neuron. For the case of binary neurons, analytical solutions can be constructed, which correspond to steps in the activity versus degree space. We apply this theory to networks with degree-correlated topology and show that complex, multi-stable regimes can result for increasing correlations. Our work is motivated by the recent finding of subnetworks of highly active neurons and the fact that these neurons tend to be connected to each other with higher probability.

  14. Stochastic solution of population balance equations for reactor networks

    Menz, William J.; Akroyd, Jethro; Kraft, Markus

    2014-01-01

    This work presents a sequential modular approach to solve a generic network of reactors with a population balance model using a stochastic numerical method. Full-coupling to the gas-phase is achieved through operator-splitting. The convergence of the stochastic particle algorithm in test networks is evaluated as a function of network size, recycle fraction and numerical parameters. These test cases are used to identify methods through which systematic and statistical error may be reduced, including by use of stochastic weighted algorithms. The optimal algorithm was subsequently used to solve a one-dimensional example of silicon nanoparticle synthesis using a multivariate particle model. This example demonstrated the power of stochastic methods in resolving particle structure by investigating the transient and spatial evolution of primary polydispersity, degree of sintering and TEM-style images. Highlights: •An algorithm is presented to solve reactor networks with a population balance model. •A stochastic method is used to solve the population balance equations. •The convergence and efficiency of the reported algorithms are evaluated. •The algorithm is applied to simulate silicon nanoparticle synthesis in a 1D reactor. •Particle structure is reported as a function of reactor length and time

  15. Atmospheric gravity waves observed by an international network of micro-barographs

    Marty, Julien

    2010-01-01

    The Comprehensive Nuclear-Test-Ban Treaty Organization (CTBTO) manages an international network of forty-two operational infra-sound stations recording the pressure fluctuations produced at the ground surface by infrasonic waves. This thesis demonstrates that most of these stations also accurately detect the pressure fluctuations in the entire gravity wave band. This work includes carrying out and analyzing several metrological laboratory experiments and a field campaign (M2008) in Mongolia in 2008. The layout of the experiments as well as the interpretation of their results gave rise to the development of a new linear spectral numerical model able to simulate the generation and propagation of gravity waves. This model was used to quantify the gravity waves produced by the atmospheric cooling that occurs during solar eclipses. The pressure fluctuations expected at ground level were estimated and compared to the data recorded during the 1 August 2008 solar eclipse by the CTBTO and M2008 stations. A detailed data analysis reveals two waves with similar time-frequency characteristics to those simulated for a stratospheric and tropospheric cooling. This constitutes, to our knowledge, a unique result. The validation of worldwide and pluri-annual pressure measurements in the entire gravity wave band allowed the statistical study of gravity wave spectra and atmospheric tides. The work presented throughout this thesis has led to the publication of two articles. A third one is in the drafting process. (author)

  16. Gravity and the Spin-2 Planar Schrödinger Equation

    Bergshoeff, Eric A.; Rosseel, Jan; Townsend, Paul K.

    2018-04-01

    A Schrödinger equation proposed for the Girvin-MacDonald-Platzman gapped spin-2 mode of fractional quantum Hall states is found from a novel nonrelativistic limit, applicable only in 2 +1 dimensions, of the massive spin-2 Fierz-Pauli field equations. It is also found from a novel null reduction of the linearized Einstein field equations in 3 +1 dimensions, and in this context a uniform distribution of spin-2 particles implies, via a Brinkmann-wave solution of the nonlinear Einstein equations, a confining harmonic oscillator potential for the individual particles.

  17. Using structural equation modeling for network meta-analysis.

    Tu, Yu-Kang; Wu, Yun-Chun

    2017-07-14

    Network meta-analysis overcomes the limitations of traditional pair-wise meta-analysis by incorporating all available evidence into a general statistical framework for simultaneous comparisons of several treatments. Currently, network meta-analyses are undertaken either within the Bayesian hierarchical linear models or frequentist generalized linear mixed models. Structural equation modeling (SEM) is a statistical method originally developed for modeling causal relations among observed and latent variables. As random effect is explicitly modeled as a latent variable in SEM, it is very flexible for analysts to specify complex random effect structure and to make linear and nonlinear constraints on parameters. The aim of this article is to show how to undertake a network meta-analysis within the statistical framework of SEM. We used an example dataset to demonstrate the standard fixed and random effect network meta-analysis models can be easily implemented in SEM. It contains results of 26 studies that directly compared three treatment groups A, B and C for prevention of first bleeding in patients with liver cirrhosis. We also showed that a new approach to network meta-analysis based on the technique of unrestricted weighted least squares (UWLS) method can also be undertaken using SEM. For both the fixed and random effect network meta-analysis, SEM yielded similar coefficients and confidence intervals to those reported in the previous literature. The point estimates of two UWLS models were identical to those in the fixed effect model but the confidence intervals were greater. This is consistent with results from the traditional pairwise meta-analyses. Comparing to UWLS model with common variance adjusted factor, UWLS model with unique variance adjusted factor has greater confidence intervals when the heterogeneity was larger in the pairwise comparison. The UWLS model with unique variance adjusted factor reflects the difference in heterogeneity within each comparison

  18. Detection of large-scale concentric gravity waves from a Chinese airglow imager network

    Lai, Chang; Yue, Jia; Xu, Jiyao; Yuan, Wei; Li, Qinzeng; Liu, Xiao

    2018-06-01

    Concentric gravity waves (CGWs) contain a broad spectrum of horizontal wavelengths and periods due to their instantaneous localized sources (e.g., deep convection, volcanic eruptions, or earthquake, etc.). However, it is difficult to observe large-scale gravity waves of >100 km wavelength from the ground for the limited field of view of a single camera and local bad weather. Previously, complete large-scale CGW imagery could only be captured by satellite observations. In the present study, we developed a novel method that uses assembling separate images and applying low-pass filtering to obtain temporal and spatial information about complete large-scale CGWs from a network of all-sky airglow imagers. Coordinated observations from five all-sky airglow imagers in Northern China were assembled and processed to study large-scale CGWs over a wide area (1800 km × 1 400 km), focusing on the same two CGW events as Xu et al. (2015). Our algorithms yielded images of large-scale CGWs by filtering out the small-scale CGWs. The wavelengths, wave speeds, and periods of CGWs were measured from a sequence of consecutive assembled images. Overall, the assembling and low-pass filtering algorithms can expand the airglow imager network to its full capacity regarding the detection of large-scale gravity waves.

  19. Modeling gravity-dependent plasticity of the angular vestibuloocular reflex with a physiologically based neural network.

    Xiang, Yongqing; Yakushin, Sergei B; Cohen, Bernard; Raphan, Theodore

    2006-12-01

    A neural network model was developed to explain the gravity-dependent properties of gain adaptation of the angular vestibuloocular reflex (aVOR). Gain changes are maximal at the head orientation where the gain is adapted and decrease as the head is tilted away from that position and can be described by the sum of gravity-independent and gravity-dependent components. The adaptation process was modeled by modifying the weights and bias values of a three-dimensional physiologically based neural network of canal-otolith-convergent neurons that drive the aVOR. Model parameters were trained using experimental vertical aVOR gain values. The learning rule aimed to reduce the error between eye velocities obtained from experimental gain values and model output in the position of adaptation. Although the model was trained only at specific head positions, the model predicted the experimental data at all head positions in three dimensions. Altering the relative learning rates of the weights and bias improved the model-data fits. Model predictions in three dimensions compared favorably with those of a double-sinusoid function, which is a fit that minimized the mean square error at every head position and served as the standard by which we compared the model predictions. The model supports the hypothesis that gravity-dependent adaptation of the aVOR is realized in three dimensions by a direct otolith input to canal-otolith neurons, whose canal sensitivities are adapted by the visual-vestibular mismatch. The adaptation is tuned by how the weights from otolith input to the canal-otolith-convergent neurons are adapted for a given head orientation.

  20. Optimization of a Time-Lapse Gravity Network for Carbon Sequestration

    Appriou, D.; Strickland, C. E.; Ruprecht Yonkofski, C. M.

    2017-12-01

    The objective of this study is to evaluate what could be a comprehensive and optimal state of the art gravity monitoring network that would meet the UIC class VI regulation and insure that 90% of the CO2 injected remain underground. Time-lapse gravity surveys have a long history of effective applications of monitoring temporal density changes in the subsurface. For decades, gravity measurements have been used for a wide range of applications. The interest of time-lapse gravity surveys for monitoring carbon sequestration sites started recently. The success of their deployment in such sites depends upon a combination of favorable conditions, such as the reservoir geometry, depth, thickness, density change over time induced by the CO2 injection and the location of the instrument. In most cases, the density changes induced by the CO2 plume in the subsurface are not detectable from the surface but the use of borehole gravimeters can provide excellent results. In the framework of the National Assessment and Risk Partnership (NRAP) funded by the Department of Energy, the evaluation of the effectiveness of the gravity monitoring of a CO2 storage site has been assessed using multiple synthetic scenarios implemented on a community model developed for the Kimberlina site (e.g., fault leakage scenarios, borehole leakage). The Kimberlina carbon sequestration project was a pilot project located in southern San Joaquin Valley, California, aimed to safely inject 250,000 t CO2/yr for four years. Although the project was cancelled in 2012, the site characterization efforts resulted in the development of a geologic model. In this study, we present the results of the time-lapse gravity monitoring applied on different multiphase flow and reactive transport models developed by Lawrence Berkeley National Laboratory (i.e., no leakage, permeable fault zone, wellbore leakage). Our monitoring approach considers an ideal network, consisting of multiple vertical and horizontal instrumented

  1. Neutrino emission, equation of state and the role of strong gravity

    Caballero, O. L., E-mail: ocaballe@uoguelph.ca [Department of Physics, University of Guelph, Guelph, Ontario N1G 2W1 (Canada)

    2016-07-07

    Neutron-star mergers are interesting for several reasons: they are proposed as the progenitors of short gamma-ray bursts, they have been speculated to be a site for the synthesis of heavy elements, and they emit gravitational waves possibly detectable at terrestrial facilities. The understanding of the merger process, from the pre-merger stage to the final compact object-accreting system involves detailed knowledge of numerical relativity and nuclear physics. In particular, key ingredients for the evolution of the merger are neutrino physics and the matter equation of state. We present some aspects of neutrino emission from binary neutron star mergers showing the impact that the equation of state has on neutrinos and discuss some spectral quantities relevant to their detection such as energies and luminosities far from the source.

  2. Renormalization group equation and scaling solutions for f(R) gravity in exponential parametrization

    Ohta, Nobuyoshi; Percacci, Roberto; Vacca, Gian Paolo

    2016-01-01

    We employ the exponential parametrization of the metric and a ''physical'' gauge fixing procedure to write a functional flow equation for the gravitational effective average action in an f(R) truncation. The background metric is a four-sphere and the coarse-graining procedure contains three free parameters. We look for scaling solutions, i.e. non-Gaussian fixed points for the function f. For a discrete set of values of the parameters, we find simple global solutions of quadratic polynomial form. For other values, global solutions can be found numerically. Such solutions can be extended in certain regions of parameter space and have two relevant directions. We discuss the merits and the shortcomings of this procedure. (orig.)

  3. New numerical approximation for solving fractional delay differential equations of variable order using artificial neural networks

    Zúñiga-Aguilar, C. J.; Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Alvarado-Martínez, V. M.; Romero-Ugalde, H. M.

    2018-02-01

    In this paper, we approximate the solution of fractional differential equations with delay using a new approach based on artificial neural networks. We consider fractional differential equations of variable order with the Mittag-Leffler kernel in the Liouville-Caputo sense. With this new neural network approach, an approximate solution of the fractional delay differential equation is obtained. Synaptic weights are optimized using the Levenberg-Marquardt algorithm. The neural network effectiveness and applicability were validated by solving different types of fractional delay differential equations, linear systems with delay, nonlinear systems with delay and a system of differential equations, for instance, the Newton-Leipnik oscillator. The solution of the neural network was compared with the analytical solutions and the numerical simulations obtained through the Adams-Bashforth-Moulton method. To show the effectiveness of the proposed neural network, different performance indices were calculated.

  4. Modeling the future evolution of the virtual water trade network: A combination of network and gravity models

    Sartori, Martina; Schiavo, Stefano; Fracasso, Andrea; Riccaboni, Massimo

    2017-12-01

    The paper investigates how the topological features of the virtual water (VW) network and the size of the associated VW flows are likely to change over time, under different socio-economic and climate scenarios. We combine two alternative models of network formation -a stochastic and a fitness model, used to describe the structure of VW flows- with a gravity model of trade to predict the intensity of each bilateral flow. This combined approach is superior to existing methodologies in its ability to replicate the observed features of VW trade. The insights from the models are used to forecast future VW flows in 2020 and 2050, under different climatic scenarios, and compare them with future water availability. Results suggest that the current trend of VW exports is not sustainable for all countries. Moreover, our approach highlights that some VW importers might be exposed to "imported water stress" as they rely heavily on imports from countries whose water use is unsustainable.

  5. Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity

    Aquilanti, Vincenzo; Bitencourt, Ana Carla P.; Ferreira, Cristiane da S.; Marzuoli, Annalisa; Ragni, Mirco

    2008-11-01

    The mathematical apparatus of quantum-mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the underlying combinatorial aspects. SU(2) recoupling theory, involving Wigner's 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, nowadays plays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory—and of its extension to other Lie and quantum groups—by using the collective term of 'spin networks'. Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper, we list and discuss some aspects of these developments—such as for instance the hyperquantization algorithm—as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.

  6. Massive gravity from bimetric gravity

    Baccetti, Valentina; Martín-Moruno, Prado; Visser, Matt

    2013-01-01

    We discuss the subtle relationship between massive gravity and bimetric gravity, focusing particularly on the manner in which massive gravity may be viewed as a suitable limit of bimetric gravity. The limiting procedure is more delicate than currently appreciated. Specifically, this limiting procedure should not unnecessarily constrain the background metric, which must be externally specified by the theory of massive gravity itself. The fact that in bimetric theories one always has two sets of metric equations of motion continues to have an effect even in the massive gravity limit, leading to additional constraints besides the one set of equations of motion naively expected. Thus, since solutions of bimetric gravity in the limit of vanishing kinetic term are also solutions of massive gravity, but the contrary statement is not necessarily true, there is no complete continuity in the parameter space of the theory. In particular, we study the massive cosmological solutions which are continuous in the parameter space, showing that many interesting cosmologies belong to this class. (paper)

  7. Structural Observability and Sensor Node Selection for Complex Networks Governed by Nonlinear Balance Equations

    Kawano, Yu; Cao, Ming

    2017-01-01

    We define and then study the structural observability for a class of complex networks whose dynamics are governed by the nonlinear balance equations. Although related notions of observability of such complex networks have been studied before and in particular, necessary conditions have been reported

  8. Development of Sediment Deposition Height Capacity Equation in Sewer Networks

    Song, Yangho; Jo, Deokjun; Lee, Jungho

    2017-04-01

    Sediment characteristics and transport processes in sewers are markedly different from river. There is a wide range of particle densities and smaller particle size variation in sewers. Sediment supply and the available erodible material are more limited in sewers, and the diverse hydraulic characteristics in sewer systems are more unsteady. Prevention of sewer sediment accumulation, which can cause major sewer operational problems, is imperative and has been an immense concern for engineers. The effects of sediment formation in sewer systems, an appropriate sediment transport modelling with the ability to determine the location and depth of sediment deposit is needed. It is necessary to design efficiently considering the transfer and settling phenomena of the sediment coming into the sewer systems. During transport in the sewer, the minimum shear flow velocity and possible shear stress at which the sediment is transported smoothly. However, the interaction of sediment and fluid within the sewer systems has been very complex and the rigorous theoretical handling of this problem has not been developed. It is derived from the empirical values obtained from the river bed. The basic theory that particles float is based on the balance between sedimentation of particles by gravity and turbulent diffusion of fluids. There are many variables related. Representative parameters include complex phenomena due to collisions between particles, particles and fluids, and interactions between particles and tube walls. In general, the main parameters that form the boundary between the main transport and sediment are particle size, density, volume fraction, pipe diameter and gravity. As the particle size and volume concentration increase, the minimum feed rate increases and the same tendency is observed for the change of the capillary diameter. Based on this tendency, this study has developed a sediment deposition height capacity formula to take into consideration the sewer discharge

  9. Nonlinearly Activated Neural Network for Solving Time-Varying Complex Sylvester Equation.

    Li, Shuai; Li, Yangming

    2013-10-28

    The Sylvester equation is often encountered in mathematics and control theory. For the general time-invariant Sylvester equation problem, which is defined in the domain of complex numbers, the Bartels-Stewart algorithm and its extensions are effective and widely used with an O(n³) time complexity. When applied to solving the time-varying Sylvester equation, the computation burden increases intensively with the decrease of sampling period and cannot satisfy continuous realtime calculation requirements. For the special case of the general Sylvester equation problem defined in the domain of real numbers, gradient-based recurrent neural networks are able to solve the time-varying Sylvester equation in real time, but there always exists an estimation error while a recently proposed recurrent neural network by Zhang et al [this type of neural network is called Zhang neural network (ZNN)] converges to the solution ideally. The advancements in complex-valued neural networks cast light to extend the existing real-valued ZNN for solving the time-varying real-valued Sylvester equation to its counterpart in the domain of complex numbers. In this paper, a complex-valued ZNN for solving the complex-valued Sylvester equation problem is investigated and the global convergence of the neural network is proven with the proposed nonlinear complex-valued activation functions. Moreover, a special type of activation function with a core function, called sign-bi-power function, is proven to enable the ZNN to converge in finite time, which further enhances its advantage in online processing. In this case, the upper bound of the convergence time is also derived analytically. Simulations are performed to evaluate and compare the performance of the neural network with different parameters and activation functions. Both theoretical analysis and numerical simulations validate the effectiveness of the proposed method.

  10. Generalized activity equations for spiking neural network dynamics

    Michael A Buice

    2013-11-01

    Full Text Available Much progress has been made in uncovering the computational capabilities of spiking neural networks. However, spiking neurons will always be more expensive to simulate compared to rate neurons because of the inherent disparity in time scales - the spike duration time is much shorter than the inter-spike time, which is much shorter than any learning time scale. In numerical analysis, this is a classic stiff problem. Spiking neurons are also much more difficult to study analytically. One possible approach to making spiking networks more tractable is to augment mean field activity models with some information about spiking correlations. For example, such a generalized activity model could carry information about spiking rates and correlations between spikes self-consistently. Here, we will show how this can be accomplished by constructing a complete formal probabilistic description of the network and then expanding around a small parameter such as the inverse of the number of neurons in the network. The mean field theory of the system gives a rate-like description. The first order terms in the perturbation expansion keep track of covariances.

  11. Causal structure of oscillations in gene regulatory networks: Boolean analysis of ordinary differential equation attractors.

    Sun, Mengyang; Cheng, Xianrui; Socolar, Joshua E S

    2013-06-01

    A common approach to the modeling of gene regulatory networks is to represent activating or repressing interactions using ordinary differential equations for target gene concentrations that include Hill function dependences on regulator gene concentrations. An alternative formulation represents the same interactions using Boolean logic with time delays associated with each network link. We consider the attractors that emerge from the two types of models in the case of a simple but nontrivial network: a figure-8 network with one positive and one negative feedback loop. We show that the different modeling approaches give rise to the same qualitative set of attractors with the exception of a possible fixed point in the ordinary differential equation model in which concentrations sit at intermediate values. The properties of the attractors are most easily understood from the Boolean perspective, suggesting that time-delay Boolean modeling is a useful tool for understanding the logic of regulatory networks.

  12. Solving differential equations with unknown constitutive relations as recurrent neural networks

    Hagge, Tobias J.; Stinis, Panagiotis; Yeung, Enoch H.; Tartakovsky, Alexandre M.

    2017-12-08

    We solve a system of ordinary differential equations with an unknown functional form of a sink (reaction rate) term. We assume that the measurements (time series) of state variables are partially available, and use a recurrent neural network to “learn” the reaction rate from this data. This is achieved by including discretized ordinary differential equations as part of a recurrent neural network training problem. We extend TensorFlow’s recurrent neural network architecture to create a simple but scalable and effective solver for the unknown functions, and apply it to a fedbatch bioreactor simulation problem. Use of techniques from recent deep learning literature enables training of functions with behavior manifesting over thousands of time steps. Our networks are structurally similar to recurrent neural networks, but differ in purpose, and require modified training strategies.

  13. Using the Multiplicative Schwarz Alternating Algorithm (MSAA) for Solving the Large Linear System of Equations Related to Global Gravity Field Recovery up to Degree and Order 120

    Safari, A.; Sharifi, M. A.; Amjadiparvar, B.

    2010-05-01

    The GRACE mission has substantiated the low-low satellite-to-satellite tracking (LL-SST) concept. The LL-SST configuration can be combined with the previously realized high-low SST concept in the CHAMP mission to provide a much higher accuracy. The line of sight (LOS) acceleration difference between the GRACE satellite pair is the mostly used observable for mapping the global gravity field of the Earth in terms of spherical harmonic coefficients. In this paper, mathematical formulae for LOS acceleration difference observations have been derived and the corresponding linear system of equations has been set up for spherical harmonic up to degree and order 120. The total number of unknowns is 14641. Such a linear equation system can be solved with iterative solvers or direct solvers. However, the runtime of direct methods or that of iterative solvers without a suitable preconditioner increases tremendously. This is the reason why we need a more sophisticated method to solve the linear system of problems with a large number of unknowns. Multiplicative variant of the Schwarz alternating algorithm is a domain decomposition method, which allows it to split the normal matrix of the system into several smaller overlaped submatrices. In each iteration step the multiplicative variant of the Schwarz alternating algorithm solves linear systems with the matrices obtained from the splitting successively. It reduces both runtime and memory requirements drastically. In this paper we propose the Multiplicative Schwarz Alternating Algorithm (MSAA) for solving the large linear system of gravity field recovery. The proposed algorithm has been tested on the International Association of Geodesy (IAG)-simulated data of the GRACE mission. The achieved results indicate the validity and efficiency of the proposed algorithm in solving the linear system of equations from accuracy and runtime points of view. Keywords: Gravity field recovery, Multiplicative Schwarz Alternating Algorithm, Low

  14. Numerical Solution of Fuzzy Differential Equations with Z-numbers Using Bernstein Neural Networks

    Raheleh Jafari

    2017-01-01

    Full Text Available The uncertain nonlinear systems can be modeled with fuzzy equations or fuzzy differential equations (FDEs by incorporating the fuzzy set theory. The solutions of them are applied to analyze many engineering problems. However, it is very difficult to obtain solutions of FDEs. In this paper, the solutions of FDEs are approximated by two types of Bernstein neural networks. Here, the uncertainties are in the sense of Z-numbers. Initially the FDE is transformed into four ordinary differential equations (ODEs with Hukuhara differentiability. Then neural models are constructed with the structure of ODEs. With modified back propagation method for Z- number variables, the neural networks are trained. The theory analysis and simulation results show that these new models, Bernstein neural networks, are effective to estimate the solutions of FDEs based on Z-numbers.

  15. Stochastic differential equations for quantum dynamics of spin-boson networks

    Mandt, Stephan; Sadri, Darius; Houck, Andrew A; Türeci, Hakan E

    2015-01-01

    A popular approach in quantum optics is to map a master equation to a stochastic differential equation, where quantum effects manifest themselves through noise terms. We generalize this approach based on the positive-P representation to systems involving spin, in particular networks or lattices of interacting spins and bosons. We test our approach on a driven dimer of spins and photons, compare it to the master equation, and predict a novel dynamic phase transition in this system. Our numerical approach has scaling advantages over existing methods, but typically requires regularization in terms of drive and dissipation. (paper)

  16. On the solution of a rational matrix equation arising in G-networks

    B. Meini (Beatrice); T. Nesti (Tommaso)

    2017-01-01

    textabstractWe consider the problem of solving a rational matrix equation arising in the solution of G-networks. We propose and analyze two numerical methods: a fixed point iteration and the Newton–Raphson method. The fixed point iteration is shown to be globally convergent with linear convergence

  17. Hermite Functional Link Neural Network for Solving the Van der Pol-Duffing Oscillator Equation.

    Mall, Susmita; Chakraverty, S

    2016-08-01

    Hermite polynomial-based functional link artificial neural network (FLANN) is proposed here to solve the Van der Pol-Duffing oscillator equation. A single-layer hermite neural network (HeNN) model is used, where a hidden layer is replaced by expansion block of input pattern using Hermite orthogonal polynomials. A feedforward neural network model with the unsupervised error backpropagation principle is used for modifying the network parameters and minimizing the computed error function. The Van der Pol-Duffing and Duffing oscillator equations may not be solved exactly. Here, approximate solutions of these types of equations have been obtained by applying the HeNN model for the first time. Three mathematical example problems and two real-life application problems of Van der Pol-Duffing oscillator equation, extracting the features of early mechanical failure signal and weak signal detection problems, are solved using the proposed HeNN method. HeNN approximate solutions have been compared with results obtained by the well known Runge-Kutta method. Computed results are depicted in term of graphs. After training the HeNN model, we may use it as a black box to get numerical results at any arbitrary point in the domain. Thus, the proposed HeNN method is efficient. The results reveal that this method is reliable and can be applied to other nonlinear problems too.

  18. Unified Framework for Deriving Simultaneous Equation Algorithms for Water Distribution Networks

    The known formulations for steady state hydraulics within looped water distribution networks are re-derived in terms of linear and non-linear transformations of the original set of partly linear and partly non-linear equations that express conservation of mass and energy. All of ...

  19. Networked traffic state estimation involving mixed fixed-mobile sensor data using Hamilton-Jacobi equations

    Canepa, Edward S.; Claudel, Christian G.

    2017-01-01

    Nowadays, traffic management has become a challenge for urban areas, which are covering larger geographic spaces and facing the generation of different kinds of traffic data. This article presents a robust traffic estimation framework for highways modeled by a system of Lighthill Whitham Richards equations that is able to assimilate different sensor data available. We first present an equivalent formulation of the problem using a Hamilton–Jacobi equation. Then, using a semi-analytic formula, we show that the model constraints resulting from the Hamilton–Jacobi equation are linear ones. We then pose the problem of estimating the traffic density given incomplete and inaccurate traffic data as a Mixed Integer Program. We then extend the density estimation framework to highway networks with any available data constraint and modeling junctions. Finally, we present a travel estimation application for a small network using real traffic measurements obtained obtained during Mobile Century traffic experiment, and comparing the results with ground truth data.

  20. Networked traffic state estimation involving mixed fixed-mobile sensor data using Hamilton-Jacobi equations

    Canepa, Edward S.

    2017-06-19

    Nowadays, traffic management has become a challenge for urban areas, which are covering larger geographic spaces and facing the generation of different kinds of traffic data. This article presents a robust traffic estimation framework for highways modeled by a system of Lighthill Whitham Richards equations that is able to assimilate different sensor data available. We first present an equivalent formulation of the problem using a Hamilton–Jacobi equation. Then, using a semi-analytic formula, we show that the model constraints resulting from the Hamilton–Jacobi equation are linear ones. We then pose the problem of estimating the traffic density given incomplete and inaccurate traffic data as a Mixed Integer Program. We then extend the density estimation framework to highway networks with any available data constraint and modeling junctions. Finally, we present a travel estimation application for a small network using real traffic measurements obtained obtained during Mobile Century traffic experiment, and comparing the results with ground truth data.

  1. Application of cellular neural network (CNN) method to the nuclear reactor dynamics equations

    Hadad, K.; Piroozmand, A.

    2007-01-01

    This paper describes the application of a multilayer cellular neural network (CNN) to model and solve the nuclear reactor dynamic equations. An equivalent electrical circuit is analyzed and the governing equations of a bare, homogeneous reactor core are modeled via CNN. The validity of the CNN result is compared with numerical solution of the system of nonlinear governing partial differential equations (PDE) using MATLAB. Steady state as well as transient simulations, show very good comparison between the two methods. We used our CNN model to simulate space-time response of different reactivity excursions in a typical nuclear reactor. On line solution of reactor dynamic equations is used as an aid to reactor operation decision making. The complete algorithm could also be implemented using very large scale integrated circuit (VLSI) circuitry. The efficiency of the calculation method makes it useful for small size nuclear reactors such as the ones used in space missions

  2. A rapid numerical method for solving Serre-Green-Naghdi equations describing long free surface gravity waves

    Favrie, N.; Gavrilyuk, S.

    2017-07-01

    A new numerical method for solving the Serre-Green-Naghdi (SGN) equations describing dispersive waves on shallow water is proposed. From the mathematical point of view, the SGN equations are the Euler-Lagrange equations for a ‘master’ lagrangian submitted to a differential constraint which is the mass conservation law. One major numerical challenge in solving the SGN equations is the resolution of an elliptic problem at each time instant. This is the most time-consuming part of the numerical method. The idea is to replace the ‘master’ lagrangian by a one-parameter family of ‘augmented’ lagrangians, depending on a greater number of variables, for which the corresponding Euler-Lagrange equations are hyperbolic. In such an approach, the ‘master’ lagrangian is recovered by the augmented lagrangian in some limit (for example, when the corresponding parameter is large). The choice of such a family of augmented lagrangians is proposed and discussed. The corresponding hyperbolic system is numerically solved by a Godunov type method. Numerical solutions are compared with exact solutions to the SGN equations. It appears that the computational time in solving the hyperbolic system is much lower than in the case where the elliptic operator is inverted. The new method is applied, in particular, to the study of ‘Favre waves’ representing non-stationary undular bores produced after reflection of the fluid flow with a free surface at an immobile wall.

  3. Re-evaluation of the AASHTO-flexible pavement design equation with neural network modeling.

    Tiğdemir, Mesut

    2014-01-01

    Here we establish that equivalent single-axle loads values can be estimated using artificial neural networks without the complex design equality of American Association of State Highway and Transportation Officials (AASHTO). More importantly, we find that the neural network model gives the coefficients to be able to obtain the actual load values using the AASHTO design values. Thus, those design traffic values that might result in deterioration can be better calculated using the neural networks model than with the AASHTO design equation. The artificial neural network method is used for this purpose. The existing AASHTO flexible pavement design equation does not currently predict the pavement performance of the strategic highway research program (Long Term Pavement Performance studies) test sections very accurately, and typically over-estimates the number of equivalent single axle loads needed to cause a measured loss of the present serviceability index. Here we aimed to demonstrate that the proposed neural network model can more accurately represent the loads values data, compared against the performance of the AASHTO formula. It is concluded that the neural network may be an appropriate tool for the development of databased-nonparametric models of pavement performance.

  4. Simulation electromagnetic scattering on bodies through integral equation and neural networks methods

    Lvovich, I. Ya; Preobrazhenskiy, A. P.; Choporov, O. N.

    2018-05-01

    The paper deals with the issue of electromagnetic scattering on a perfectly conducting diffractive body of a complex shape. Performance calculation of the body scattering is carried out through the integral equation method. Fredholm equation of the second time was used for calculating electric current density. While solving the integral equation through the moments method, the authors have properly described the core singularity. The authors determined piecewise constant functions as basic functions. The chosen equation was solved through the moments method. Within the Kirchhoff integral approach it is possible to define the scattered electromagnetic field, in some way related to obtained electrical currents. The observation angles sector belongs to the area of the front hemisphere of the diffractive body. To improve characteristics of the diffractive body, the authors used a neural network. All the neurons contained a logsigmoid activation function and weighted sums as discriminant functions. The paper presents the matrix of weighting factors of the connectionist model, as well as the results of the optimized dimensions of the diffractive body. The paper also presents some basic steps in calculation technique of the diffractive bodies, based on the combination of integral equation and neural networks methods.

  5. Comparison of Control Approaches in Genetic Regulatory Networks by Using Stochastic Master Equation Models, Probabilistic Boolean Network Models and Differential Equation Models and Estimated Error Analyzes

    Caglar, Mehmet Umut; Pal, Ranadip

    2011-03-01

    Central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid''. However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of cell level data and probabilistic - nonlinear nature of interactions. Several models widely used to analyze and simulate these types of nonlinear interactions. Stochastic Master Equation (SME) models give probabilistic nature of the interactions in a detailed manner, with a high calculation cost. On the other hand Probabilistic Boolean Network (PBN) models give a coarse scale picture of the stochastic processes, with a less calculation cost. Differential Equation (DE) models give the time evolution of mean values of processes in a highly cost effective way. The understanding of the relations between the predictions of these models is important to understand the reliability of the simulations of genetic regulatory networks. In this work the success of the mapping between SME, PBN and DE models is analyzed and the accuracy and affectivity of the control policies generated by using PBN and DE models is compared.

  6. An Improved Recurrent Neural Network for Complex-Valued Systems of Linear Equation and Its Application to Robotic Motion Tracking.

    Ding, Lei; Xiao, Lin; Liao, Bolin; Lu, Rongbo; Peng, Hua

    2017-01-01

    To obtain the online solution of complex-valued systems of linear equation in complex domain with higher precision and higher convergence rate, a new neural network based on Zhang neural network (ZNN) is investigated in this paper. First, this new neural network for complex-valued systems of linear equation in complex domain is proposed and theoretically proved to be convergent within finite time. Then, the illustrative results show that the new neural network model has the higher precision and the higher convergence rate, as compared with the gradient neural network (GNN) model and the ZNN model. Finally, the application for controlling the robot using the proposed method for the complex-valued systems of linear equation is realized, and the simulation results verify the effectiveness and superiorness of the new neural network for the complex-valued systems of linear equation.

  7. Combining region- and network-level brain-behavior relationships in a structural equation model.

    Bolt, Taylor; Prince, Emily B; Nomi, Jason S; Messinger, Daniel; Llabre, Maria M; Uddin, Lucina Q

    2018-01-15

    Brain-behavior associations in fMRI studies are typically restricted to a single level of analysis: either a circumscribed brain region-of-interest (ROI) or a larger network of brain regions. However, this common practice may not always account for the interdependencies among ROIs of the same network or potentially unique information at the ROI-level, respectively. To account for both sources of information, we combined measurement and structural components of structural equation modeling (SEM) approaches to empirically derive networks from ROI activity, and to assess the association of both individual ROIs and their respective whole-brain activation networks with task performance using three large task-fMRI datasets and two separate brain parcellation schemes. The results for working memory and relational tasks revealed that well-known ROI-performance associations are either non-significant or reversed when accounting for the ROI's common association with its corresponding network, and that the network as a whole is instead robustly associated with task performance. The results for the arithmetic task revealed that in certain cases, an ROI can be robustly associated with task performance, even when accounting for its associated network. The SEM framework described in this study provides researchers additional flexibility in testing brain-behavior relationships, as well as a principled way to combine ROI- and network-levels of analysis. Copyright © 2017 Elsevier Inc. All rights reserved.

  8. influence of gravity

    Animesh Mukherjee

    1991-01-01

    Full Text Available Based upon Biot's [1965] theory of initial stresses of hydrostatic nature produced by the effect of gravity, a study is made of surface waves in higher order visco-elastic media under the influence of gravity. The equation for the wave velocity of Stonely waves in the presence of viscous and gravitational effects is obtained. This is followed by particular cases of surface waves including Rayleigh waves and Love waves in the presence of viscous and gravity effects. In all cases the wave-velocity equations are found to be in perfect agreement with the corresponding classical results when the effects of gravity and viscosity are neglected.

  9. Ordinary differential equations and Boolean networks in application to modelling of 6-mercaptopurine metabolism.

    Lavrova, Anastasia I; Postnikov, Eugene B; Zyubin, Andrey Yu; Babak, Svetlana V

    2017-04-01

    We consider two approaches to modelling the cell metabolism of 6-mercaptopurine, one of the important chemotherapy drugs used for treating acute lymphocytic leukaemia: kinetic ordinary differential equations, and Boolean networks supplied with one controlling node, which takes continual values. We analyse their interplay with respect to taking into account ATP concentration as a key parameter of switching between different pathways. It is shown that the Boolean networks, which allow avoiding the complexity of general kinetic modelling, preserve the possibility of reproducing the principal switching mechanism.

  10. Chiral gravity, log gravity, and extremal CFT

    Maloney, Alexander; Song Wei; Strominger, Andrew

    2010-01-01

    We show that the linearization of all exact solutions of classical chiral gravity around the AdS 3 vacuum have positive energy. Nonchiral and negative-energy solutions of the linearized equations are infrared divergent at second order, and so are removed from the spectrum. In other words, chirality is confined and the equations of motion have linearization instabilities. We prove that the only stationary, axially symmetric solutions of chiral gravity are BTZ black holes, which have positive energy. It is further shown that classical log gravity--the theory with logarithmically relaxed boundary conditions--has finite asymptotic symmetry generators but is not chiral and hence may be dual at the quantum level to a logarithmic conformal field theories (CFT). Moreover we show that log gravity contains chiral gravity within it as a decoupled charge superselection sector. We formally evaluate the Euclidean sum over geometries of chiral gravity and show that it gives precisely the holomorphic extremal CFT partition function. The modular invariance and integrality of the expansion coefficients of this partition function are consistent with the existence of an exact quantum theory of chiral gravity. We argue that the problem of quantizing chiral gravity is the holographic dual of the problem of constructing an extremal CFT, while quantizing log gravity is dual to the problem of constructing a logarithmic extremal CFT.

  11. Quantum Gravity

    Giribet, G E

    2005-01-01

    Claus Kiefer presents his book, Quantum Gravity, with his hope that '[the] book will convince readers of [the] outstanding problem [of unification and quantum gravity] and encourage them to work on its solution'. With this aim, the author presents a clear exposition of the fundamental concepts of gravity and the steps towards the understanding of its quantum aspects. The main part of the text is dedicated to the analysis of standard topics in the formulation of general relativity. An analysis of the Hamiltonian formulation of general relativity and the canonical quantization of gravity is performed in detail. Chapters four, five and eight provide a pedagogical introduction to the basic concepts of gravitational physics. In particular, aspects such as the quantization of constrained systems, the role played by the quadratic constraint, the ADM decomposition, the Wheeler-de Witt equation and the problem of time are treated in an expert and concise way. Moreover, other specific topics, such as the minisuperspace approach and the feasibility of defining extrinsic times for certain models, are discussed as well. The ninth chapter of the book is dedicated to the quantum gravitational aspects of string theory. Here, a minimalistic but clear introduction to string theory is presented, and this is actually done with emphasis on gravity. It is worth mentioning that no hard (nor explicit) computations are presented, even though the exposition covers the main features of the topic. For instance, black hole statistical physics (within the framework of string theory) is developed in a pedagogical and concise way by means of heuristical arguments. As the author asserts in the epilogue, the hope of the book is to give 'some impressions from progress' made in the study of quantum gravity since its beginning, i.e., since the end of 1920s. In my opinion, Kiefer's book does actually achieve this goal and gives an extensive review of the subject. (book review)

  12. A universal concept based on cellular neural networks for ultrafast and flexible solving of differential equations.

    Chedjou, Jean Chamberlain; Kyamakya, Kyandoghere

    2015-04-01

    This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering approach, especially while considering the various scientific and engineering applications of this ultrafast, energy-and-memory-efficient, and high-precise NDE solver concept. For illustration purposes, three NDE models are demonstratively solved, and related CNN templates are derived and used: the periodically excited Duffing equation, the Mathieu equation, and the transport equation.

  13. Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity

    Gaburro, Elena; Castro, Manuel J.; Dumbser, Michael

    2018-06-01

    In this work, we present a novel second-order accurate well-balanced arbitrary Lagrangian-Eulerian (ALE) finite volume scheme on moving nonconforming meshes for the Euler equations of compressible gas dynamics with gravity in cylindrical coordinates. The main feature of the proposed algorithm is the capability of preserving many of the physical properties of the system exactly also on the discrete level: besides being conservative for mass, momentum and total energy, also any known steady equilibrium between pressure gradient, centrifugal force, and gravity force can be exactly maintained up to machine precision. Perturbations around such equilibrium solutions are resolved with high accuracy and with minimal dissipation on moving contact discontinuities even for very long computational times. This is achieved by the novel combination of well-balanced path-conservative finite volume schemes, which are expressly designed to deal with source terms written via non-conservative products, with ALE schemes on moving grids, which exhibit only very little numerical dissipation on moving contact waves. In particular, we have formulated a new HLL-type and a novel Osher-type flux that are both able to guarantee the well balancing in a gas cloud rotating around a central object. Moreover, to maintain a high level of quality of the moving mesh, we have adopted a nonconforming treatment of the sliding interfaces that appear due to the differential rotation. A large set of numerical tests has been carried out in order to check the accuracy of the method close and far away from the equilibrium, both, in one- and two-space dimensions.

  14. Using Equation-Free Computation to Accelerate Network-Free Stochastic Simulation of Chemical Kinetics.

    Lin, Yen Ting; Chylek, Lily A; Lemons, Nathan W; Hlavacek, William S

    2018-06-21

    The chemical kinetics of many complex systems can be concisely represented by reaction rules, which can be used to generate reaction events via a kinetic Monte Carlo method that has been termed network-free simulation. Here, we demonstrate accelerated network-free simulation through a novel approach to equation-free computation. In this process, variables are introduced that approximately capture system state. Derivatives of these variables are estimated using short bursts of exact stochastic simulation and finite differencing. The variables are then projected forward in time via a numerical integration scheme, after which a new exact stochastic simulation is initialized and the whole process repeats. The projection step increases efficiency by bypassing the firing of numerous individual reaction events. As we show, the projected variables may be defined as populations of building blocks of chemical species. The maximal number of connected molecules included in these building blocks determines the degree of approximation. Equation-free acceleration of network-free simulation is found to be both accurate and efficient.

  15. Modeling delay in genetic networks: from delay birth-death processes to delay stochastic differential equations.

    Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Bennett, Matthew R; Josić, Krešimir; Ott, William

    2014-05-28

    Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.

  16. Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

    Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William [Department of Mathematics, University of Houston, Houston, Texas 77004 (United States); Bennett, Matthew R. [Department of Biochemistry and Cell Biology, Rice University, Houston, Texas 77204, USA and Institute of Biosciences and Bioengineering, Rice University, Houston, Texas 77005 (United States); Josić, Krešimir [Department of Mathematics, University of Houston, Houston, Texas 77004 (United States); Department of Biology and Biochemistry, University of Houston, Houston, Texas 77204 (United States)

    2014-05-28

    Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay.

  17. Modeling delay in genetic networks: From delay birth-death processes to delay stochastic differential equations

    Gupta, Chinmaya; López, José Manuel; Azencott, Robert; Ott, William; Bennett, Matthew R.; Josić, Krešimir

    2014-01-01

    Delay is an important and ubiquitous aspect of many biochemical processes. For example, delay plays a central role in the dynamics of genetic regulatory networks as it stems from the sequential assembly of first mRNA and then protein. Genetic regulatory networks are therefore frequently modeled as stochastic birth-death processes with delay. Here, we examine the relationship between delay birth-death processes and their appropriate approximating delay chemical Langevin equations. We prove a quantitative bound on the error between the pathwise realizations of these two processes. Our results hold for both fixed delay and distributed delay. Simulations demonstrate that the delay chemical Langevin approximation is accurate even at moderate system sizes. It captures dynamical features such as the oscillatory behavior in negative feedback circuits, cross-correlations between nodes in a network, and spatial and temporal information in two commonly studied motifs of metastability in biochemical systems. Overall, these results provide a foundation for using delay stochastic differential equations to approximate the dynamics of birth-death processes with delay

  18. Spatial Treatment of the Slab-geometry Discrete Ordinates Equations Using Artificial Neural Networks

    Brantley, P S

    2001-01-01

    An artificial neural network (ANN) method is developed for treating the spatial variable of the one-group slab-geometry discrete ordinates (S N ) equations in a homogeneous medium with linearly anisotropic scattering. This ANN method takes advantage of the function approximation capability of multilayer ANNs. The discrete ordinates angular flux is approximated by a multilayer ANN with a single input representing the spatial variable x and N outputs representing the angular flux in each of the discrete ordinates angular directions. A global objective function is formulated which measures how accurately the output of the ANN approximates the solution of the discrete ordinates equations and boundary conditions at specified spatial points. Minimization of this objective function determines the appropriate values for the parameters of the ANN. Numerical results are presented demonstrating the accuracy of the method for both fixed source and incident angular flux problems

  19. The earth's shape and gravity

    Garland, G D; Wilson, J T

    2013-01-01

    The Earth's Shape and Gravity focuses on the progress of the use of geophysical methods in investigating the interior of the earth and its shape. The publication first offers information on gravity, geophysics, geodesy, and geology and gravity measurements. Discussions focus on gravity measurements and reductions, potential and equipotential surfaces, absolute and relative measurements, and gravity networks. The text then elaborates on the shape of the sea-level surface and reduction of gravity observations. The text takes a look at gravity anomalies and structures in the earth's crust; interp

  20. Inference of gene regulatory networks with sparse structural equation models exploiting genetic perturbations.

    Xiaodong Cai

    Full Text Available Integrating genetic perturbations with gene expression data not only improves accuracy of regulatory network topology inference, but also enables learning of causal regulatory relations between genes. Although a number of methods have been developed to integrate both types of data, the desiderata of efficient and powerful algorithms still remains. In this paper, sparse structural equation models (SEMs are employed to integrate both gene expression data and cis-expression quantitative trait loci (cis-eQTL, for modeling gene regulatory networks in accordance with biological evidence about genes regulating or being regulated by a small number of genes. A systematic inference method named sparsity-aware maximum likelihood (SML is developed for SEM estimation. Using simulated directed acyclic or cyclic networks, the SML performance is compared with that of two state-of-the-art algorithms: the adaptive Lasso (AL based scheme, and the QTL-directed dependency graph (QDG method. Computer simulations demonstrate that the novel SML algorithm offers significantly better performance than the AL-based and QDG algorithms across all sample sizes from 100 to 1,000, in terms of detection power and false discovery rate, in all the cases tested that include acyclic or cyclic networks of 10, 30 and 300 genes. The SML method is further applied to infer a network of 39 human genes that are related to the immune function and are chosen to have a reliable eQTL per gene. The resulting network consists of 9 genes and 13 edges. Most of the edges represent interactions reasonably expected from experimental evidence, while the remaining may just indicate the emergence of new interactions. The sparse SEM and efficient SML algorithm provide an effective means of exploiting both gene expression and perturbation data to infer gene regulatory networks. An open-source computer program implementing the SML algorithm is freely available upon request.

  1. The Thouless-Anderson-Palmer equation for an analogue neural network with temporally fluctuating white synaptic noise

    Ichiki, Akihisa; Shiino, Masatoshi

    2007-01-01

    Effects of synaptic noise on the retrieval process of associative memory neural networks are studied from the viewpoint of neurobiological and biophysical understanding of information processing in the brain. We investigate the statistical mechanical properties of stochastic analogue neural networks with temporally fluctuating synaptic noise, which is assumed to be white noise. Such networks, in general, defy the use of the replica method, since they have no energy concept. The self-consistent signal-to-noise analysis (SCSNA), which is an alternative to the replica method for deriving a set of order parameter equations, requires no energy concept and thus becomes available in studying networks without energy functions. Applying the SCSNA to stochastic networks requires the knowledge of the Thouless-Anderson-Palmer (TAP) equation which defines the deterministic networks equivalent to the original stochastic ones. The study of the TAP equation which is of particular interest for the case without energy concept is very less, while it is closely related to the SCSNA in the case with energy concept. This paper aims to derive the TAP equation for networks with synaptic noise together with a set of order parameter equations by a hybrid use of the cavity method and the SCSNA

  2. Group field theory and tensor networks: towards a Ryu–Takayanagi formula in full quantum gravity

    Chirco, Goffredo; Oriti, Daniele; Zhang, Mingyi

    2018-06-01

    We establish a dictionary between group field theory (thus, spin networks and random tensors) states and generalized random tensor networks. Then, we use this dictionary to compute the Rényi entropy of such states and recover the Ryu–Takayanagi formula, in two different cases corresponding to two different truncations/approximations, suggested by the established correspondence.

  3. Consistent initial conditions for the Saint-Venant equations in river network modeling

    C.-W. Yu

    2017-09-01

    Full Text Available Initial conditions for flows and depths (cross-sectional areas throughout a river network are required for any time-marching (unsteady solution of the one-dimensional (1-D hydrodynamic Saint-Venant equations. For a river network modeled with several Strahler orders of tributaries, comprehensive and consistent synoptic data are typically lacking and synthetic starting conditions are needed. Because of underlying nonlinearity, poorly defined or inconsistent initial conditions can lead to convergence problems and long spin-up times in an unsteady solver. Two new approaches are defined and demonstrated herein for computing flows and cross-sectional areas (or depths. These methods can produce an initial condition data set that is consistent with modeled landscape runoff and river geometry boundary conditions at the initial time. These new methods are (1 the pseudo time-marching method (PTM that iterates toward a steady-state initial condition using an unsteady Saint-Venant solver and (2 the steady-solution method (SSM that makes use of graph theory for initial flow rates and solution of a steady-state 1-D momentum equation for the channel cross-sectional areas. The PTM is shown to be adequate for short river reaches but is significantly slower and has occasional non-convergent behavior for large river networks. The SSM approach is shown to provide a rapid solution of consistent initial conditions for both small and large networks, albeit with the requirement that additional code must be written rather than applying an existing unsteady Saint-Venant solver.

  4. Terrestrial gravity data analysis for interim gravity model improvement

    1987-01-01

    This is the first status report for the Interim Gravity Model research effort that was started on June 30, 1986. The basic theme of this study is to develop appropriate models and adjustment procedures for estimating potential coefficients from terrestrial gravity data. The plan is to use the latest gravity data sets to produce coefficient estimates as well as to provide normal equations to NASA for use in the TOPEX/POSEIDON gravity field modeling program.

  5. A parallel algorithm for solving linear equations arising from one-dimensional network problems

    Mesina, G.L.

    1991-01-01

    One-dimensional (1-D) network problems, such as those arising from 1- D fluid simulations and electrical circuitry, produce systems of sparse linear equations which are nearly tridiagonal and contain a few non-zero entries outside the tridiagonal. Most direct solution techniques for such problems either do not take advantage of the special structure of the matrix or do not fully utilize parallel computer architectures. We describe a new parallel direct linear equation solution algorithm, called TRBR, which is especially designed to take advantage of this structure on MIMD shared memory machines. The new method belongs to a family of methods which split the coefficient matrix into the sum of a tridiagonal matrix T and a matrix comprised of the remaining coefficients R. Efficient tridiagonal methods are used to algebraically simplify the linear system. A smaller auxiliary subsystem is created and solved and its solution is used to calculate the solution of the original system. The newly devised BR method solves the subsystem. The serial and parallel operation counts are given for the new method and related earlier methods. TRBR is shown to have the smallest operation count in this class of direct methods. Numerical results are given. Although the algorithm is designed for one-dimensional networks, it has been applied successfully to three-dimensional problems as well. 20 refs., 2 figs., 4 tabs

  6. Gravity interpretation via EULDPH

    Ebrahimzadeh Ardestani, V.

    2003-01-01

    Euler's homogeneity equation for determining the coordinates of the source body especially to estimate the depth (EULDPH) is discussed at this paper. This method is applied to synthetic and high-resolution real data such as gradiometric or microgravity data. Low-quality gravity data especially in the areas with a complex geology structure has rarely been used. The Bouguer gravity anomalies are computed from absolute gravity data after the required corrections. Bouguer anomaly is transferred to residual gravity anomaly. The gravity gradients are estimated from residual anomaly values. Bouguer anomaly is the gravity gradients, using EULDPH. The coordinates of the perturbing body will be determined. Two field examples one in the east of Tehran (Mard Abad) where we would like to determine the location of the anomaly (hydrocarbon) and another in the south-east of Iran close to the border with Afghanistan (Nosrat Abad) where we are exploring chromite are presented

  7. Reconstructing Genetic Regulatory Networks Using Two-Step Algorithms with the Differential Equation Models of Neural Networks.

    Chen, Chi-Kan

    2017-07-26

    The identification of genetic regulatory networks (GRNs) provides insights into complex cellular processes. A class of recurrent neural networks (RNNs) captures the dynamics of GRN. Algorithms combining the RNN and machine learning schemes were proposed to reconstruct small-scale GRNs using gene expression time series. We present new GRN reconstruction methods with neural networks. The RNN is extended to a class of recurrent multilayer perceptrons (RMLPs) with latent nodes. Our methods contain two steps: the edge rank assignment step and the network construction step. The former assigns ranks to all possible edges by a recursive procedure based on the estimated weights of wires of RNN/RMLP (RE RNN /RE RMLP ), and the latter constructs a network consisting of top-ranked edges under which the optimized RNN simulates the gene expression time series. The particle swarm optimization (PSO) is applied to optimize the parameters of RNNs and RMLPs in a two-step algorithm. The proposed RE RNN -RNN and RE RMLP -RNN algorithms are tested on synthetic and experimental gene expression time series of small GRNs of about 10 genes. The experimental time series are from the studies of yeast cell cycle regulated genes and E. coli DNA repair genes. The unstable estimation of RNN using experimental time series having limited data points can lead to fairly arbitrary predicted GRNs. Our methods incorporate RNN and RMLP into a two-step structure learning procedure. Results show that the RE RMLP using the RMLP with a suitable number of latent nodes to reduce the parameter dimension often result in more accurate edge ranks than the RE RNN using the regularized RNN on short simulated time series. Combining by a weighted majority voting rule the networks derived by the RE RMLP -RNN using different numbers of latent nodes in step one to infer the GRN, the method performs consistently and outperforms published algorithms for GRN reconstruction on most benchmark time series. The framework of two

  8. Design of Gravity Survey Network using Fractal Theory to Delineate Hydrocarbon bearing Jabera Structure, Vindhyan Basin, Central India

    Dimri, V. P.; Srivastava, R. P.; Vedanti, N.

    2006-12-01

    A gravity survey network was designed using fractal dimension analysis to delineate a domal structure (Jabera dome) reported in southeastern part of the Vindhyan basin, Central India. This area is also regarded as a `high risk-high reward' frontier area for hydrocarbon exploration in previous studies, hence our aim was to delineate shape and lateral extent of the reported domal structure. Based on the synthetic grid, designed using the concept of fractal dimension, gravity data is collected in Jabera-Damoh area of Vindhyan basin. The collected data is random, but the data density is significant, hence the data points are sorted in a way so that they are close to the synthetic grid points of given grid interval. After sorting the data, again the fractal dimension analysis using box counting method has been carried out to avoid the aliasing in the data due to interpolation and also to know the optimum number of data points sufficient for desired quality of Bouguer anomaly maps. Optimization of number of stations takes care of time and cost involved in the survey and the detectibility limit ensures that the data collected is good enough to resolve the target body under study. The fractal dimension analysis gives clue to select these parameters. It showed that it is always preferable to have well distributed station locations instead of clustering the observation points at some geologically known feature because clustering of data points below required station spacing is not going to add much information where as equally distributed observation points add the information. The study area lies in a difficult terrain of Vindhayn basin, hence according to the accessibility, fractal dimension analysis of the real data sorted approximately at regular grid intervals on 2,3, and 4 km has been done and using the concept of optimum gridding interval Bouguer anomaly maps of the region are prepared. The preliminary depth values of the major interfaces in the area were obtained

  9. Gravity waves, Tides and Planetary wave characteristics revealed by network of MLT radars over Indian region

    Venkat Ratnam, Madineni; Karanam, Kishore Kumar; Sunkara, Eswaraiah; Vijaya Bhaskara Rao, S.; Subrahmanyam, K. V.; Ramanjaneyulu, L.

    2016-07-01

    Mesosphere and Lower Thermosphere (MLT) mean winds, gravity waves, tidal and planetary wave characteristics are investigated using two years (2013-2015) of advanced meteor radar installed at Tirupathi (13.63oN, 79.4oE), India. The observations reveal the presence of high frequency gravity waves (30-120 minutes), atmospheric tides (diurnal, semi-diurnal and terr-diurnal) along with long period oscillations in both zonal and meridional winds. Background mean zonal winds show clear semi-annual oscillation in the mesosphere, whereas meridional winds are characterized by annual oscillation as expected. Diurnal tide amplitudes are significantly larger (60-80 m/s) than semi-diurnal (10-20 m/s) and terr-diurnal (5-8 m/s) tides and larger in meridional than zonal winds. The measured meridional components are in good agreement with Global Scale Wave Model (GSWM-09) predictions than zonal up to ~90 km in all the seasons, except fall equinox. Diurnal tidal phase matches well than the amplitudes between observations and model predictions. However, no similarity is being found in the semi-diurnal tides between observations and model. The measurements are further compared with nearby Thumba meteor radar (8.5oN, 77oE) observations. Some differences do exist between the measurements from Tirupati and Thumba meteor radar and model outputs at greater heights and the possible reasons are discussed. SVU meteor radar observations clearly showed the dominance of well-known ultra-fast kelvin waves (3.5 days), 5-8 day, 16 day, 27 day, and 30-40 day oscillations. Due to higher meteor count extending up to 110 km, we could investigate the variability of these PWs and oscillations covering wider range (70-110 km) for the first time. Significant change above 100 km is noticed in all the above mentioned PW activity and oscillations. We also used ERA-Interim reanalysis data sets available at 0.125x0.125 degree grids for investigating the characteristics of these PW right from surface to 1 h

  10. Solitons in Newtonian gravity

    Goetz, G.

    1988-01-01

    It is shown that the plane-wave solutions for the equations governing the motion of a self-gravitating isothermal fluid in Newtonian hydrodynamics are generated by a sine-Gordon equation which is solvable by an 'inverse scattering' transformation. A transformation procedure is outlined by means of which one can construct solutions of the gravity system out of a pair of solutions of the sine-Gordon equation, which are interrelated via an auto-Baecklund transformation. In general the solutions to the gravity system are obtained in a parametric representation in terms of characteristic coordinates. All solutions of the gravity system generated by the one-and two-soliton solutions of the sine-Gordon equation can be constructed explicitly. These might provide models for the evolution of flat structures as they are predicted to arise in the process of galaxy formation. (author)

  11. QML-AiNet: An immune network approach to learning qualitative differential equation models.

    Pang, Wei; Coghill, George M

    2015-02-01

    In this paper, we explore the application of Opt-AiNet, an immune network approach for search and optimisation problems, to learning qualitative models in the form of qualitative differential equations. The Opt-AiNet algorithm is adapted to qualitative model learning problems, resulting in the proposed system QML-AiNet. The potential of QML-AiNet to address the scalability and multimodal search space issues of qualitative model learning has been investigated. More importantly, to further improve the efficiency of QML-AiNet, we also modify the mutation operator according to the features of discrete qualitative model space. Experimental results show that the performance of QML-AiNet is comparable to QML-CLONALG, a QML system using the clonal selection algorithm (CLONALG). More importantly, QML-AiNet with the modified mutation operator can significantly improve the scalability of QML and is much more efficient than QML-CLONALG.

  12. Sparse Additive Ordinary Differential Equations for Dynamic Gene Regulatory Network Modeling.

    Wu, Hulin; Lu, Tao; Xue, Hongqi; Liang, Hua

    2014-04-02

    The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. High-dimensional linear ODE models have been proposed to identify GRNs, but with a limitation of the linear regulation effect assumption. In this article, we propose a sparse additive ODE (SA-ODE) model, coupled with ODE estimation methods and adaptive group LASSO techniques, to model dynamic GRNs that could flexibly deal with nonlinear regulation effects. The asymptotic properties of the proposed method are established and simulation studies are performed to validate the proposed approach. An application example for identifying the nonlinear dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.

  13. Iterative Systems Biology for Medicine – time for advancing from network signature to mechanistic equations

    Gomez-Cabrero, David

    2017-05-09

    The rise and growth of Systems Biology following the sequencing of the human genome has been astounding. Early on, an iterative wet-dry methodology was formulated which turned out as a successful approach in deciphering biological complexity. Such type of analysis effectively identified and associated molecular network signatures operative in biological processes across different systems. Yet, it has proven difficult to distinguish between causes and consequences, thus making it challenging to attack medical questions where we require precise causative drug targets and disease mechanisms beyond a web of associated markers. Here we review principal advances with regard to identification of structure, dynamics, control, and design of biological systems, following the structure in the visionary review from 2002 by Dr. Kitano. Yet, here we find that the underlying challenge of finding the governing mechanistic system equations enabling precision medicine remains open thus rendering clinical translation of systems biology arduous. However, stunning advances in raw computational power, generation of high-precision multi-faceted biological data, combined with powerful algorithms hold promise to set the stage for data-driven identification of equations implicating a fundamental understanding of living systems during health and disease.

  14. Classical Weyl transverse gravity

    Oda, Ichiro [University of the Ryukyus, Department of Physics, Faculty of Science, Nishihara, Okinawa (Japan)

    2017-05-15

    We study various classical aspects of the Weyl transverse (WTDiff) gravity in a general space-time dimension. First of all, we clarify a classical equivalence among three kinds of gravitational theories, those are, the conformally invariant scalar tensor gravity, Einstein's general relativity and the WTDiff gravity via the gauge-fixing procedure. Secondly, we show that in the WTDiff gravity the cosmological constant is a mere integration constant as in unimodular gravity, but it does not receive any radiative corrections unlike the unimodular gravity. A key point in this proof is to construct a covariantly conserved energy-momentum tensor, which is achieved on the basis of this equivalence relation. Thirdly, we demonstrate that the Noether current for the Weyl transformation is identically vanishing, thereby implying that the Weyl symmetry existing in both the conformally invariant scalar tensor gravity and the WTDiff gravity is a ''fake'' symmetry. We find it possible to extend this proof to all matter fields, i.e. the Weyl-invariant scalar, vector and spinor fields. Fourthly, it is explicitly shown that in the WTDiff gravity the Schwarzschild black hole metric and a charged black hole one are classical solutions to the equations of motion only when they are expressed in the Cartesian coordinate system. Finally, we consider the Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmology and provide some exact solutions. (orig.)

  15. Hybrid dynamic modeling of Escherichia coli central metabolic network combining Michaelis–Menten and approximate kinetic equations

    Costa, Rafael S.; Machado, Daniel; Rocha, Isabel

    2010-01-01

    , represent nowadays the limiting factor in the construction of such models. In this study, we compare four alternative modeling approaches based on Michaelis–Menten kinetics for the bi-molecular reactions and different types of simplified rate equations for the remaining reactions (generalized mass action......The construction of dynamic metabolic models at reaction network level requires the use of mechanistic enzymatic rate equations that comprise a large number of parameters. The lack of knowledge on these equations and the difficulty in the experimental identification of their associated parameters...

  16. Stoichiometric network analysis and associated dimensionless kinetic equations. Application to a model of the Bray-Liebhafsky reaction.

    Schmitz, Guy; Kolar-Anić, Ljiljana Z; Anić, Slobodan R; Cupić, Zeljko D

    2008-12-25

    The stoichiometric network analysis (SNA) introduced by B. L. Clarke is applied to a simplified model of the complex oscillating Bray-Liebhafsky reaction under batch conditions, which was not examined by this method earlier. This powerful method for the analysis of steady-states stability is also used to transform the classical differential equations into dimensionless equations. This transformation is easy and leads to a form of the equations combining the advantages of classical dimensionless equations with the advantages of the SNA. The used dimensionless parameters have orders of magnitude given by the experimental information about concentrations and currents. This simplifies greatly the study of the slow manifold and shows which parameters are essential for controlling its shape and consequently have an important influence on the trajectories. The effectiveness of these equations is illustrated on two examples: the study of the bifurcations points and a simple sensitivity analysis, different from the classical one, more based on the chemistry of the studied system.

  17. Carroll versus Galilei gravity

    Bergshoeff, Eric [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Gomis, Joaquim [Departament de Física Cuàntica i Astrofísica and Institut de Ciències del Cosmos,Universitat de Barcelona,Martí i Franquès 1, E-08028 Barcelona (Spain); Rollier, Blaise [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Rosseel, Jan [Faculty of Physics, University of Vienna,Boltzmanngasse 5, A-1090 Vienna (Austria); Veldhuis, Tonnis ter [Centre for Theoretical Physics, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands)

    2017-03-30

    We consider two distinct limits of General Relativity that in contrast to the standard non-relativistic limit can be taken at the level of the Einstein-Hilbert action instead of the equations of motion. One is a non-relativistic limit and leads to a so-called Galilei gravity theory, the other is an ultra-relativistic limit yielding a so-called Carroll gravity theory. We present both gravity theories in a first-order formalism and show that in both cases the equations of motion (i) lead to constraints on the geometry and (ii) are not sufficient to solve for all of the components of the connection fields in terms of the other fields. Using a second-order formalism we show that these independent components serve as Lagrange multipliers for the geometric constraints we found earlier. We point out a few noteworthy differences between Carroll and Galilei gravity and give some examples of matter couplings.

  18. A Combined Gravity Compensation Method for INS Using the Simplified Gravity Model and Gravity Database.

    Zhou, Xiao; Yang, Gongliu; Wang, Jing; Wen, Zeyang

    2018-05-14

    In recent decades, gravity compensation has become an important way to reduce the position error of an inertial navigation system (INS), especially for a high-precision INS, because of the extensive application of high precision inertial sensors (accelerometers and gyros). This paper first deducts the INS's solution error considering gravity disturbance and simulates the results. Meanwhile, this paper proposes a combined gravity compensation method using a simplified gravity model and gravity database. This new combined method consists of two steps all together. Step 1 subtracts the normal gravity using a simplified gravity model. Step 2 first obtains the gravity disturbance on the trajectory of the carrier with the help of ELM training based on the measured gravity data (provided by Institute of Geodesy and Geophysics; Chinese Academy of sciences), and then compensates it into the error equations of the INS, considering the gravity disturbance, to further improve the navigation accuracy. The effectiveness and feasibility of this new gravity compensation method for the INS are verified through vehicle tests in two different regions; one is in flat terrain with mild gravity variation and the other is in complex terrain with fierce gravity variation. During 2 h vehicle tests, the positioning accuracy of two tests can improve by 20% and 38% respectively, after the gravity is compensated by the proposed method.

  19. On higher derivative gravity

    Accioly, A.J.

    1987-01-01

    A possible classical route conducting towards a general relativity theory with higher-derivatives starting, in a sense, from first principles, is analysed. A completely causal vacuum solution with the symmetries of the Goedel universe is obtained in the framework of this higher-derivative gravity. This very peculiar and rare result is the first known vcuum solution of the fourth-order gravity theory that is not a solution of the corresponding Einstein's equations.(Author) [pt

  20. Singularity: Raychaudhuri equation once again

    Cosmology; Raychaudhuri equation; Universe; quantum gravity; loop quan- tum gravity ... than the observation verifying the prediction of theory. This gave .... which was now expanding, would have had a singular beginning in a hot Big Bang.

  1. Neural network versus activity-specific prediction equations for energy expenditure estimation in children.

    Ruch, Nicole; Joss, Franziska; Jimmy, Gerda; Melzer, Katarina; Hänggi, Johanna; Mäder, Urs

    2013-11-01

    The aim of this study was to compare the energy expenditure (EE) estimations of activity-specific prediction equations (ASPE) and of an artificial neural network (ANNEE) based on accelerometry with measured EE. Forty-three children (age: 9.8 ± 2.4 yr) performed eight different activities. They were equipped with one tri-axial accelerometer that collected data in 1-s epochs and a portable gas analyzer. The ASPE and the ANNEE were trained to estimate the EE by including accelerometry, age, gender, and weight of the participants. To provide the activity-specific information, a decision tree was trained to recognize the type of activity through accelerometer data. The ASPE were applied to the activity-type-specific data recognized by the tree (Tree-ASPE). The Tree-ASPE precisely estimated the EE of all activities except cycling [bias: -1.13 ± 1.33 metabolic equivalent (MET)] and walking (bias: 0.29 ± 0.64 MET; P MET) and walking (bias: 0.61 ± 0.72 MET) and underestimated the EE of cycling (bias: -0.90 ± 1.18 MET; P MET, Tree-ASPE: 0.08 ± 0.21 MET) and walking (ANNEE 0.61 ± 0.72 MET, Tree-ASPE: 0.29 ± 0.64 MET) were significantly smaller in the Tree-ASPE than in the ANNEE (P < 0.05). The Tree-ASPE was more precise in estimating the EE than the ANNEE. The use of activity-type-specific information for subsequent EE prediction equations might be a promising approach for future studies.

  2. Neural Network Training by Integration of Adjoint Systems of Equations Forward in Time

    Toomarian, Nikzad (Inventor); Barhen, Jacob (Inventor)

    1999-01-01

    A method and apparatus for supervised neural learning of time dependent trajectories exploits the concepts of adjoint operators to enable computation of the gradient of an objective functional with respect to the various parameters of the network architecture in a highly efficient manner. Specifically. it combines the advantage of dramatic reductions in computational complexity inherent in adjoint methods with the ability to solve two adjoint systems of equations together forward in time. Not only is a large amount of computation and storage saved. but the handling of real-time applications becomes also possible. The invention has been applied it to two examples of representative complexity which have recently been analyzed in the open literature and demonstrated that a circular trajectory can be learned in approximately 200 iterations compared to the 12000 reported in the literature. A figure eight trajectory was achieved in under 500 iterations compared to 20000 previously required. Tbc trajectories computed using our new method are much closer to the target trajectories than was reported in previous studies.

  3. Cellular neural networks, the Navier-Stokes equation, and microarray image reconstruction.

    Zineddin, Bachar; Wang, Zidong; Liu, Xiaohui

    2011-11-01

    Although the last decade has witnessed a great deal of improvements achieved for the microarray technology, many major developments in all the main stages of this technology, including image processing, are still needed. Some hardware implementations of microarray image processing have been proposed in the literature and proved to be promising alternatives to the currently available software systems. However, the main drawback of those proposed approaches is the unsuitable addressing of the quantification of the gene spot in a realistic way without any assumption about the image surface. Our aim in this paper is to present a new image-reconstruction algorithm using the cellular neural network that solves the Navier-Stokes equation. This algorithm offers a robust method for estimating the background signal within the gene-spot region. The MATCNN toolbox for Matlab is used to test the proposed method. Quantitative comparisons are carried out, i.e., in terms of objective criteria, between our approach and some other available methods. It is shown that the proposed algorithm gives highly accurate and realistic measurements in a fully automated manner within a remarkably efficient time.

  4. Alternative Hamiltonian representation for gravity

    Rosas-RodrIguez, R [Instituto de Fisica, Universidad Autonoma de Puebla, Apdo. Postal J-48, 72570, Puebla, Pue. (Mexico)

    2007-11-15

    By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity.

  5. Alternative Hamiltonian representation for gravity

    Rosas-RodrIguez, R

    2007-01-01

    By using a Hamiltonian formalism for fields wider than the canonical one, we write the Einstein vacuum field equations in terms of alternative variables. This variables emerge from the Ashtekar's formalism for gravity

  6. New solutions of the Einstein equations for the Mixmaster and Taub Universe models and the anti gravity phenomena; Nuevas soluciones de las ecuaciones de Einstein para los modelos de Universo Mixmaster y Taub y el fenomeno de la antigravedad

    Melendez L, L

    2004-07-01

    In the first part of this work, starting from Einstein's equations of the Classical General Relativity, a new kind of solutions for the Mixmaster model are explored. By dispensing with the extension to the complex variable field, which is usual in problems such as the Laplace equation or the harmonic oscillator, in a similar manner to that of Quantum Mechanics, the equations appear to have solutions that belong to the complex General Relativity. A first integral is performed by establishing a separation of the first derivatives. Then a second integral is obtained once the respective equations with separate variables are found and whose integrals provide a family of complex solutions. However, reality conditions do not seem to be easily imposed at this stage. Above all, it is significant that the classical Einstein's equations for the debatably integrable Mixmaster model present complex solutions. In the second part of this work, following a specific strategy in which the cosmological time variables are operated upon, a new family of solutions to the empty Taub universe is found. Among the characteristics of such a family, it stands the positive acceleration provided by the tri-curvature property of this universe to two of the three scale factors of the Taub model. This effect of the tri-curvature results not in a restoring force such as normal gravity but in the conversion of the Taub cosmology into an accelerating universe. (Author)

  7. The quantization of gravity

    Gerhardt, Claus

    2018-01-01

    A unified quantum theory incorporating the four fundamental forces of nature is one of the major open problems in physics. The Standard Model combines electro-magnetism, the strong force and the weak force, but ignores gravity. The quantization of gravity is therefore a necessary first step to achieve a unified quantum theory. In this monograph a canonical quantization of gravity has been achieved by quantizing a geometric evolution equation resulting in a gravitational wave equation in a globally hyperbolic spacetime. Applying the technique of separation of variables we obtain eigenvalue problems for temporal and spatial self-adjoint operators where the temporal operator has a pure point spectrum with eigenvalues $\\lambda_i$ and related eigenfunctions, while, for the spatial operator, it is possible to find corresponding eigendistributions for each of the eigenvalues $\\lambda_i$, if the Cauchy hypersurface is asymptotically Euclidean or if the quantized spacetime is a black hole with a negative cosmological ...

  8. Massive Gravity

    de Rham, Claudia

    2014-01-01

    We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali–Gabadadze–Porrati model (DGP), cascading gravity, and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware–Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally, we present alt...

  9. Nonlinear recurrent neural networks for finite-time solution of general time-varying linear matrix equations.

    Xiao, Lin; Liao, Bolin; Li, Shuai; Chen, Ke

    2018-02-01

    In order to solve general time-varying linear matrix equations (LMEs) more efficiently, this paper proposes two nonlinear recurrent neural networks based on two nonlinear activation functions. According to Lyapunov theory, such two nonlinear recurrent neural networks are proved to be convergent within finite-time. Besides, by solving differential equation, the upper bounds of the finite convergence time are determined analytically. Compared with existing recurrent neural networks, the proposed two nonlinear recurrent neural networks have a better convergence property (i.e., the upper bound is lower), and thus the accurate solutions of general time-varying LMEs can be obtained with less time. At last, various different situations have been considered by setting different coefficient matrices of general time-varying LMEs and a great variety of computer simulations (including the application to robot manipulators) have been conducted to validate the better finite-time convergence of the proposed two nonlinear recurrent neural networks. Copyright © 2017 Elsevier Ltd. All rights reserved.

  10. Massive Conformal Gravity

    Faria, F. F.

    2014-01-01

    We construct a massive theory of gravity that is invariant under conformal transformations. The massive action of the theory depends on the metric tensor and a scalar field, which are considered the only field variables. We find the vacuum field equations of the theory and analyze its weak-field approximation and Newtonian limit.

  11. A Trick of Gravity

    Newburgh, Ronald

    2010-01-01

    It's both surprising and rewarding when an old, standard problem reveals a subtlety that expands its pedagogic value. I realized recently that the role of gravity in the range equation for a projectile is not so simple as first appears. This realization may be completely obvious to others but was quite new to me.

  12. Transparent and accurate reporting increases reliability, utility, and impact of your research: reporting guidelines and the EQUATOR Network

    Schulz Kenneth F

    2010-04-01

    Full Text Available Abstract Although current electronic methods of scientific publishing offer increased opportunities for publishing all research studies and describing them in sufficient detail, health research literature still suffers from many shortcomings. These shortcomings seriously undermine the value and utility of the literature and waste scarce resources invested in the research. In recent years there have been several positive steps aimed at improving this situation, such as a strengthening of journals' policies on research publication and the wide requirement to register clinical trials. The EQUATOR (Enhancing the QUAlity and Transparency Of health Research Network is an international initiative set up to advance high quality reporting of health research studies; it promotes good reporting practices including the wider implementation of reporting guidelines. EQUATOR provides free online resources http://www.equator-network.org supported by education and training activities and assists in the development of robust reporting guidelines. This paper outlines EQUATOR's goals and activities and offers suggestions for organizations and individuals involved in health research on how to strengthen research reporting.

  13. Cellular neural network to the spherical harmonics approximation of neutron transport equation in x–y geometry

    Pirouzmand, Ahmad; Hadad, Kamal

    2012-01-01

    Highlights: ► This paper describes the solution of time-dependent neutron transport equation. ► We use a novel method based on cellular neural networks (CNNs) coupled with the spherical harmonics method. ► We apply the CNN model to simulate step and ramp perturbation transients in a core. ► The accuracy and capabilities of the CNN model are examined for x–y geometry. - Abstract: In an earlier paper we utilized a novel method using cellular neural networks (CNNs) coupled with spherical harmonics method to solve the steady state neutron transport equation in x–y geometry. Here, the previous work is extended to the study of time-dependent neutron transport equation. To achieve this goal, an equivalent electrical circuit based on a second-order form of time-dependent neutron transport equation and one equivalent group of neutron precursor density is obtained by the CNN method. The CNN model is used to simulate step and ramp perturbation transients in a typical 2D core.

  14. Hybrid modeling of the crosstalk between signaling and transcriptional networks using ordinary differential equations and multi-valued logic.

    Khan, Faiz M; Schmitz, Ulf; Nikolov, Svetoslav; Engelmann, David; Pützer, Brigitte M; Wolkenhauer, Olaf; Vera, Julio

    2014-01-01

    A decade of successful results indicates that systems biology is the appropriate approach to investigate the regulation of complex biochemical networks involving transcriptional and post-transcriptional regulations. It becomes mandatory when dealing with highly interconnected biochemical networks, composed of hundreds of compounds, or when networks are enriched in non-linear motifs like feedback and feedforward loops. An emerging dilemma is to conciliate models of massive networks and the adequate description of non-linear dynamics in a suitable modeling framework. Boolean networks are an ideal representation of massive networks that are humble in terms of computational complexity and data demand. However, they are inappropriate when dealing with nested feedback/feedforward loops, structural motifs common in biochemical networks. On the other hand, models of ordinary differential equations (ODEs) cope well with these loops, but they require enormous amounts of quantitative data for a full characterization of the model. Here we propose hybrid models, composed of ODE and logical sub-modules, as a strategy to handle large scale, non-linear biochemical networks that include transcriptional and post-transcriptional regulations. We illustrate the construction of this kind of models using as example a regulatory network centered on E2F1, a transcription factor involved in cancer. The hybrid modeling approach proposed is a good compromise between quantitative/qualitative accuracy and scalability when considering large biochemical networks with a small highly interconnected core, and module of transcriptionally regulated genes that are not part of critical regulatory loops. This article is part of a Special Issue entitled: Computational Proteomics, Systems Biology & Clinical Implications. Guest Editor: Yudong Cai. Copyright © 2013 Elsevier B.V. All rights reserved.

  15. Euler-Lagrange Equations of Networks with Higher-Order Elements

    Z. Biolek

    2017-06-01

    Full Text Available The paper suggests a generalization of the classic Euler-Lagrange equation for circuits compounded of arbitrary elements from Chua’s periodic table. Newly defined potential functions for general (α, β elements are used for the construction of generalized Lagrangians and generalized dissipative functions. Also procedures of drawing the Euler-Lagrange equations are demonstrated.

  16. An improved gravity compensation method for high-precision free-INS based on MEC–BP–AdaBoost

    Zhou, Xiao; Yang, Gongliu; Wang, Jing; Li, Jing

    2016-01-01

    In recent years, with the rapid improvement of inertial sensors (accelerometers and gyroscopes), gravity compensation has become more important for improving navigation accuracy in inertial navigation systems (INS), especially for high-precision INS. This paper proposes a mind evolutionary computation (MEC) back propagation (BP) AdaBoost algorithm neural-network-based gravity compensation method that estimates the gravity disturbance on the track based on measured gravity data. A MEC–BP–AdaBoost network-based gravity compensation algorithm used in the training process to establish the prediction model takes the carrier position (longitude and latitude) provided by INS as the input data and the gravity disturbance as the output data, and then compensates the obtained gravity disturbance into the INS’s error equations to restrain the position error propagation. The MEC–BP–AdaBoost algorithm can not only effectively avoid BP neural networks being trapped in local extrema, but also perfectly solve the nonlinearity between the input and output data that cannot be solved by traditional interpolation methods, such as least-square collocation (LSC) interpolation. The accuracy and feasibility of the proposed interpolation method are verified through numerical tests. A comparison of several other compensation methods applied in field experiments, including LSC interpolation and traditional BP interpolation, highlights the superior performance of the proposed method. The field experiment results show that the maximum value of the position error can reduce by 28% with the proposed gravity compensation method. (paper)

  17. Error estimation in the neural network solution of ordinary differential equations.

    Filici, Cristian

    2010-06-01

    In this article a method of error estimation for the neural approximation of the solution of an Ordinary Differential Equation is presented. Some examples of the application of the method support the theory presented. Copyright 2010. Published by Elsevier Ltd.

  18. Surfing surface gravity waves

    Pizzo, Nick

    2017-11-01

    A simple criterion for water particles to surf an underlying surface gravity wave is presented. It is found that particles travelling near the phase speed of the wave, in a geometrically confined region on the forward face of the crest, increase in speed. The criterion is derived using the equation of John (Commun. Pure Appl. Maths, vol. 6, 1953, pp. 497-503) for the motion of a zero-stress free surface under the action of gravity. As an example, a breaking water wave is theoretically and numerically examined. Implications for upper-ocean processes, for both shallow- and deep-water waves, are discussed.

  19. Structural equation modelling of determinants of customer satisfaction of mobile network providers: Case of Kolkata, India

    Shibashish Chakraborty

    2014-12-01

    Full Text Available The Indian market of mobile network providers is growing rapidly. India is the second largest market of mobile network providers in the world and there is intense competition among existing players. In such a competitive market, customer satisfaction becomes a key issue. The objective of this paper is to develop a customer satisfaction model of mobile network providers in Kolkata. The results indicate that generic requirements (an aggregation of output quality and perceived value, flexibility, and price are the determinants of customer satisfaction. This study offers insights for mobile network providers to understand the determinants of customer satisfaction.

  20. Control of Stochastic Master Equation Models of Genetic Regulatory Networks by Approximating Their Average Behavior

    Umut Caglar, Mehmet; Pal, Ranadip

    2010-10-01

    The central dogma of molecular biology states that ``information cannot be transferred back from protein to either protein or nucleic acid.'' However, this assumption is not exactly correct in most of the cases. There are a lot of feedback loops and interactions between different levels of systems. These types of interactions are hard to analyze due to the lack of data in the cellular level and probabilistic nature of interactions. Probabilistic models like Stochastic Master Equation (SME) or deterministic models like differential equations (DE) can be used to analyze these types of interactions. SME models based on chemical master equation (CME) can provide detailed representation of genetic regulatory system, but their use is restricted by the large data requirements and computational costs of calculations. The differential equations models on the other hand, have low calculation costs and much more adequate to generate control procedures on the system; but they are not adequate to investigate the probabilistic nature of interactions. In this work the success of the mapping between SME and DE is analyzed, and the success of a control policy generated by DE model with respect to SME model is examined. Index Terms--- Stochastic Master Equation models, Differential Equation Models, Control Policy Design, Systems biology

  1. An intrinsically irreversible, neural-network-like approach to the Schrödinger equation and some results of application to drive nuclear synthesis research work

    Abundo, Ugo [Neural Calculus Lab, J. Von Neumann Foundation, v.Clelia 15, 00181 Rome, Italy Opensharelab, Open Power Association, v.Genzano 95, 00179 Rome (Italy)

    2015-03-10

    An analogy is drawn among the irreversible evolution of a neural-network-based A.I., an information field associated to spacetime configurations and the behaviour of entities described by the Schrödinger equation.

  2. Why Do You Adopt Social Networking Sites? Investigating the Driving Factors through Structural Equation Modelling

    Jan, Muhammad Tahir

    2017-01-01

    Purpose: The purpose of this paper is to investigate those factors that are associated with the adoption of social networking sites from the perspective of Muslim users residing in Malaysia. Design/methodology/approach: A complete self-administered questionnaire was collected from 223 Muslim users of social networking sites in Malaysia. Both…

  3. Cellular neural networks (CNN) simulation for the TN approximation of the time dependent neutron transport equation in slab geometry

    Hadad, Kamal; Pirouzmand, Ahmad; Ayoobian, Navid

    2008-01-01

    This paper describes the application of a multilayer cellular neural network (CNN) to model and solve the time dependent one-speed neutron transport equation in slab geometry. We use a neutron angular flux in terms of the Chebyshev polynomials (T N ) of the first kind and then we attempt to implement the equations in an equivalent electrical circuit. We apply this equivalent circuit to analyze the T N moments equation in a uniform finite slab using Marshak type vacuum boundary condition. The validity of the CNN results is evaluated with numerical solution of the steady state T N moments equations by MATLAB. Steady state, as well as transient simulations, shows a very good comparison between the two methods. We used our CNN model to simulate space-time response of total flux and its moments for various c (where c is the mean number of secondary neutrons per collision). The complete algorithm could be implemented using very large-scale integrated circuit (VLSI) circuitry. The efficiency of the calculation method makes it useful for neutron transport calculations

  4. Quantum Gravity Experiments

    Cahill R. T.

    2015-10-01

    Full Text Available A new quantum gravity experiment is reported with the data confirming the generali- sation of the Schrödinger equation to include the interaction of the wave function with dynamical space. Dynamical space turbulence, via this interaction process, raises and lowers the energy of the electron wave function, which is detected by observing conse- quent variations in the electron quantum barrier tunnelling rate in reverse-biased Zener diodes. This process has previously been reported and enabled the measurement of the speed of the dynamical space flow, which is consistent with numerous other detection experiments. The interaction process is dependent on the angle between the dynamical space flow velocity and the direction of the electron flow in the diode, and this depen- dence is experimentally demonstrated. This interaction process explains gravity as an emergent quantum process, so unifying quantum phenomena and gravity. Gravitational waves are easily detected.

  5. Horizon thermodynamics in fourth-order gravity

    Meng-Sen Ma

    2017-03-01

    Full Text Available In the framework of horizon thermodynamics, the field equations of Einstein gravity and some other second-order gravities can be rewritten as the thermodynamic identity: dE=TdS−PdV. However, in order to construct the horizon thermodynamics in higher-order gravity, we have to simplify the field equations firstly. In this paper, we study the fourth-order gravity and convert it to second-order gravity via a so-called “Legendre transformation” at the cost of introducing two other fields besides the metric field. With this simplified theory, we implement the conventional procedure in the construction of the horizon thermodynamics in 3 and 4 dimensional spacetime. We find that the field equations in the fourth-order gravity can also be written as the thermodynamic identity. Moreover, we can use this approach to derive the same black hole mass as that by other methods.

  6. A fixed point approach towards stability of delay differential equations with applications to neural networks

    Chen, Guiling

    2013-01-01

    This thesis studies asymptotic behavior and stability of determinsitic and stochastic delay differential equations. The approach used in this thesis is based on fixed point theory, which does not resort to any Liapunov function or Liapunov functional. The main contribution of this thesis is to study

  7. Nonlocal gravity

    Mashhoon, Bahram

    2017-01-01

    Relativity theory is based on a postulate of locality, which means that the past history of the observer is not directly taken into account. This book argues that the past history should be taken into account. In this way, nonlocality---in the sense of history dependence---is introduced into relativity theory. The deep connection between inertia and gravitation suggests that gravity could be nonlocal, and in nonlocal gravity the fading gravitational memory of past events must then be taken into account. Along this line of thought, a classical nonlocal generalization of Einstein's theory of gravitation has recently been developed. A significant consequence of this theory is that the nonlocal aspect of gravity appears to simulate dark matter. According to nonlocal gravity theory, what astronomers attribute to dark matter should instead be due to the nonlocality of gravitation. Nonlocality dominates on the scale of galaxies and beyond. Memory fades with time; therefore, the nonlocal aspect of gravity becomes wea...

  8. Contravariant gravity on Poisson manifolds and Einstein gravity

    Kaneko, Yukio; Watamura, Satoshi; Muraki, Hisayoshi

    2017-01-01

    A relation between gravity on Poisson manifolds proposed in Asakawa et al (2015 Fortschr. Phys . 63 683–704) and Einstein gravity is investigated. The compatibility of the Poisson and Riemann structures defines a unique connection, the contravariant Levi-Civita connection, and leads to the idea of the contravariant gravity. The Einstein–Hilbert-type action yields an equation of motion which is written in terms of the analog of the Einstein tensor, and it includes couplings between the metric and the Poisson tensor. The study of the Weyl transformation reveals properties of those interactions. It is argued that this theory can have an equivalent description as a system of Einstein gravity coupled to matter. As an example, it is shown that the contravariant gravity on a two-dimensional Poisson manifold can be described by a real scalar field coupled to the metric in a specific manner. (paper)

  9. Neural networks dynamic hysteresis model for piezoceramic actuator based on hysteresis operator of first-order differential equation

    Dang Xuanju; Tan Yonghong

    2005-01-01

    A new neural networks dynamic hysteresis model for piezoceramic actuator is proposed by combining the Preisach model with diagonal recurrent neural networks. The Preisach model is based on elementary rate-independent operators and is not suitable for modeling piezoceramic actuator across a wide frequency band because of the rate-dependent hysteresis characteristic of the piezoceramic actuator. The structure of the developed model is based on the structure of the Preisach model, in which the rate-independent relay hysteresis operators (cells) are replaced by the rate-dependent hysteresis operators of first-order differential equation. The diagonal recurrent neural networks being modified by an adjustable factor can be used to model the hysteresis behavior of the pizeoceramic actuator because its structure is similar to the structure of the modified Preisach model. Therefore, the proposed model not only possesses that of the Preisach model, but also can be used for describing its dynamic hysteresis behavior. Through the experimental results of both the approximation and the prediction, the effectiveness of the neural networks dynamic hysteresis model for the piezoceramic actuator is demonstrated

  10. Tensor Galileons and gravity

    Chatzistavrakidis, Athanasios [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Khoo, Fech Scen [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Schupp, Peter [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany)

    2017-03-13

    The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

  11. Instantons and gravity

    Konopleva, N.P.

    1996-01-01

    The problems of application of nonperturbative quantization methods in the theories of the gauge fields and gravity are discussed. Unification of interactions is considered in the framework of the geometrical gauge fields theory. Vacuum conception in the unified theory of interactions and instantons role in the vacuum structure are analyzed. The role of vacuum solutions of Einstein equations in definition of the gauge field vacuum is demonstrated

  12. Modeling Fluid’s Dynamics with Master Equations in Ultrametric Spaces Representing the Treelike Structure of Capillary Networks

    Andrei Khrennikov

    2016-07-01

    Full Text Available We present a new conceptual approach for modeling of fluid flows in random porous media based on explicit exploration of the treelike geometry of complex capillary networks. Such patterns can be represented mathematically as ultrametric spaces and the dynamics of fluids by ultrametric diffusion. The images of p-adic fields, extracted from the real multiscale rock samples and from some reference images, are depicted. In this model the porous background is treated as the environment contributing to the coefficients of evolutionary equations. For the simplest trees, these equations are essentially less complicated than those with fractional differential operators which are commonly applied in geological studies looking for some fractional analogs to conventional Euclidean space but with anomalous scaling and diffusion properties. It is possible to solve the former equation analytically and, in particular, to find stationary solutions. The main aim of this paper is to attract the attention of researchers working on modeling of geological processes to the novel utrametric approach and to show some examples from the petroleum reservoir static and dynamic characterization, able to integrate the p-adic approach with multifractals, thermodynamics and scaling. We also present a non-mathematician friendly review of trees and ultrametric spaces and pseudo-differential operators on such spaces.

  13. Evolution of a Network of Vortex Loops in He-II: Exact Solution of the Rate Equation

    Nemirovskii, Sergey K.

    2006-01-01

    The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the ''rate equation'' for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact powerlike solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l)∝l -5/2 obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection

  14. Evolution of a network of vortex loops in He-II: exact solution of the rate equation.

    Nemirovskii, Sergey K

    2006-01-13

    The evolution of a network of vortex loops in He-II due to the fusion and breakdown of vortex loops is studied. We perform investigation on the base of the "rate equation" for the distribution function n(l) of number of loops of length l. By use of the special ansatz we have found the exact power-like solution of the rate equation in a stationary case. That solution is the famous equilibrium distribution n(l) proportional l(-5/2) obtained earlier from thermodynamic arguments. Our result, however, is not equilibrium; it describes the state with two mutual fluxes of the length (or energy) in l space. Analyzing this solution we drew several results on the structure and dynamics of the vortex tangle in the superfluid turbulent helium. In particular, we obtained that the mean radius of the curvature is of the order of interline space and that the decay of the vortex tangle obeys the Vinen equation. We also evaluated the full rate of reconnection.

  15. Neural network based online simultaneous policy update algorithm for solving the HJI equation in nonlinear H∞ control.

    Wu, Huai-Ning; Luo, Biao

    2012-12-01

    It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

  16. Stochastic Gravity: Theory and Applications

    Hu Bei Lok

    2008-05-01

    Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein–Langevin equation, which has, in addition, sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bitensor, which describes the fluctuations of quantum-matter fields in curved spacetimes. A new improved criterion for the validity of semiclassical gravity may also be formulated from the viewpoint of this theory. In the first part of this review we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to the correlation functions. The functional approach uses the Feynman–Vernon influence functional and the Schwinger–Keldysh closed-time-path effective action methods. In the second part, we describe three applications of stochastic gravity. First, we consider metric perturbations in a Minkowski spacetime, compute the two-point correlation functions of these perturbations and prove that Minkowski spacetime is a stable solution of semiclassical gravity. Second, we discuss structure formation from the stochastic-gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, using the Einstein–Langevin equation, we discuss the backreaction of Hawking radiation and the behavior of metric fluctuations for both the quasi-equilibrium condition of a black-hole in a box and the fully nonequilibrium condition of an evaporating black hole spacetime. Finally, we briefly discuss the theoretical structure of stochastic gravity in relation to quantum gravity and point out

  17. Gravity as Quantum Entanglement Force

    Lee, Jae-Weon; Kim, Hyeong-Chan; Lee, Jungjai

    2010-01-01

    We conjecture that the total quantum entanglement of matter and vacuum in the universe tends to increase with time, like entropy, and that an effective force is associated with this tendency. We also suggest that gravity and dark energy are types of quantum entanglement forces, similar to Verlinde's entropic force, and give holographic dark energy with an equation of state comparable to current observational data. This connection between quantum entanglement and gravity could give some new in...

  18. Gravity with Intermediate Goods Trade

    Sujin Jang

    2017-12-01

    Full Text Available This paper derives the gravity equation with intermediate goods trade. We extend a standard monopolistic competition model to incorporate intermediate goods trade, and show that the gravity equation with intermediates trade is identical to the one without it except in that gross output should be used as the output measure instead of value added. We also show that the output elasticity of trade is significantly underestimated when value added is used as the output measure. This implies that with the conventional gravity equation, the contribution of output growth can be substantially underestimated and the role of trade costs reduction can be exaggerated in explaining trade expansion, as we demonstrate for the case of Korea's trade growth between 1995 and 2007.

  19. Gravity brake

    Lujan, Richard E.

    2001-01-01

    A mechanical gravity brake that prevents hoisted loads within a shaft from free-falling when a loss of hoisting force occurs. A loss of hoist lifting force may occur in a number of situations, for example if a hoist cable were to break, the brakes were to fail on a winch, or the hoist mechanism itself were to fail. Under normal hoisting conditions, the gravity brake of the invention is subject to an upward lifting force from the hoist and a downward pulling force from a suspended load. If the lifting force should suddenly cease, the loss of differential forces on the gravity brake in free-fall is translated to extend a set of brakes against the walls of the shaft to stop the free fall descent of the gravity brake and attached load.

  20. Analogue Gravity

    Barceló Carlos

    2005-12-01

    Full Text Available Analogue models of (and for gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity.

  1. Quantum Gravity

    Alvarez, Enrique

    2004-01-01

    Gravitons should have momentum just as photons do; and since graviton momentum would cause compression rather than elongation of spacetime outside of matter; it does not appear that gravitons are compatible with Swartzchild's spacetime curvature. Also, since energy is proportional to mass, and mass is proportional to gravity; the energy of matter is proportional to gravity. The energy of matter could thus contract space within matter; and because of the inter-connectedness of space, cause the...

  2. Statistical estimation of absolute gravity values | Aku | Science World ...

    Gravity measurements at stations in northwestern Nigeria were assumed to be random variables. Gravity data collected was used to illustrate the gravity network adjustment theories. Residuals of the network were inspected to detect gross errors by standardizing the residuals. Computed standard deviation for unit weight ...

  3. Robust variable selection method for nonparametric differential equation models with application to nonlinear dynamic gene regulatory network analysis.

    Lu, Tao

    2016-01-01

    The gene regulation network (GRN) evaluates the interactions between genes and look for models to describe the gene expression behavior. These models have many applications; for instance, by characterizing the gene expression mechanisms that cause certain disorders, it would be possible to target those genes to block the progress of the disease. Many biological processes are driven by nonlinear dynamic GRN. In this article, we propose a nonparametric differential equation (ODE) to model the nonlinear dynamic GRN. Specially, we address following questions simultaneously: (i) extract information from noisy time course gene expression data; (ii) model the nonlinear ODE through a nonparametric smoothing function; (iii) identify the important regulatory gene(s) through a group smoothly clipped absolute deviation (SCAD) approach; (iv) test the robustness of the model against possible shortening of experimental duration. We illustrate the usefulness of the model and associated statistical methods through a simulation and a real application examples.

  4. Statistical mechanics of stochastic neural networks: Relationship between the self-consistent signal-to-noise analysis, Thouless-Anderson-Palmer equation, and replica symmetric calculation approaches

    Shiino, Masatoshi; Yamana, Michiko

    2004-01-01

    We study the statistical mechanical aspects of stochastic analog neural network models for associative memory with correlation type learning. We take three approaches to derive the set of the order parameter equations for investigating statistical properties of retrieval states: the self-consistent signal-to-noise analysis (SCSNA), the Thouless-Anderson-Palmer (TAP) equation, and the replica symmetric calculation. On the basis of the cavity method the SCSNA can be generalized to deal with stochastic networks. We establish the close connection between the TAP equation and the SCSNA to elucidate the relationship between the Onsager reaction term of the TAP equation and the output proportional term of the SCSNA that appear in the expressions for the local fields

  5. Shear strength estimation of the concrete beams reinforced with FRP; comparison of artificial neural network and equations of regulations

    Mahmood Akbari

    2017-12-01

    Full Text Available In recent years, numerous experimental tests were done on the concrete beams reinforced with the fiber-reinforced polymer (FRP. In this way, some equations were proposed to estimate the shear strength of the beams reinforced with FRP. The aim of this study is to explore the feasibility of using a feed-forward artificial neural network (ANN model to predict the ultimate shear strength of the beams strengthened with FRP composites. For this purpose, a database consists of 304 reinforced FRP concrete beams have been collected from the available articles on the analysis of shear behavior of these beams. The inputs to the ANN model consists of the 11 variables including the geometric dimensions of the section, steel reinforcement amount, FRP amount and the properties of the concrete, steel reinforcement and FRP materials while the output variable is the shear strength of the FRP beam. To assess the performance of the ANN model for estimating the shear strength of the reinforced beams, the outputs of the ANN are compared to those of equations of the Iranian code (Publication No. 345 and the American code (ACI 440. The comparisons between the outputs of Iran and American regulations with those of the proposed model indicates that the predictive power of this model is much better than the experimental codes. Specifically, for under study data, mean absolute relative error (MARE criteria is 13%, 34% and 39% for the ANN model, the American and the Iranian codes, respectively.

  6. Analogue Gravity

    Carlos Barceló

    2011-05-01

    Full Text Available Analogue gravity is a research programme which investigates analogues of general relativistic gravitational fields within other physical systems, typically but not exclusively condensed matter systems, with the aim of gaining new insights into their corresponding problems. Analogue models of (and for gravity have a long and distinguished history dating back to the earliest years of general relativity. In this review article we will discuss the history, aims, results, and future prospects for the various analogue models. We start the discussion by presenting a particularly simple example of an analogue model, before exploring the rich history and complex tapestry of models discussed in the literature. The last decade in particular has seen a remarkable and sustained development of analogue gravity ideas, leading to some hundreds of published articles, a workshop, two books, and this review article. Future prospects for the analogue gravity programme also look promising, both on the experimental front (where technology is rapidly advancing and on the theoretical front (where variants of analogue models can be used as a springboard for radical attacks on the problem of quantum gravity.

  7. Black holes in pure Lovelock gravities

    Cai Ronggen; Ohta, Nobuyoshi

    2006-01-01

    Lovelock gravity is a fascinating extension of general relativity, whose action consists of dimensionally extended Euler densities. Compared to other higher order derivative gravity theories, Lovelock gravity is attractive since it has a lot of remarkable features such as the fact that there are no more than second order derivatives with respect to the metric in its equations of motion, and that the theory is free of ghosts. Recently, in the study of black strings and black branes in Lovelock gravity, a special class of Lovelock gravity is considered, which is named pure Lovelock gravity, where only one Euler density term exists. In this paper we study black hole solutions in the special class of Lovelock gravity and associated thermodynamic properties. Some interesting features are found, which are quite different from the corresponding ones in general relativity

  8. Application of median-equation approach for outlier detection in geodetic networks

    Serif Hekimoglu

    Full Text Available In geodetic measurements some outliers may occur sometimes in data sets, depending on different reasons. There are two main approaches to detect outliers as Tests for outliers (Baarda's and Pope's Tests and robust methods (Danish method, Huber method etc.. These methods use the Least Squares Estimation (LSE. The outliers affect the LSE results, especially it smears the effects of the outliers on the good observations and sometimes wrong results may be obtained. To avoid these effects, a method that does not use LSE should be preferred. The median is a high breakdown point estimator and if it is applied for the outlier detection, reliable results can be obtained. In this study, a robust method which uses median with or as a treshould value on median residuals that are obtained from median equations is proposed. If the a priori variance of the observations is known, the reliability of the new approch is greater than the one in the case where the a priori variance is unknown.

  9. Superconducting gravity gradiometer for sensitive gravity measurements. I. Theory

    Chan, H.A.; Paik, H.J.

    1987-01-01

    Because of the equivalence principle, a global measurement is necessary to distinguish gravity from acceleration of the reference frame. A gravity gradiometer is therefore an essential instrument needed for precision tests of gravity laws and for applications in gravity survey and inertial navigation. Superconductivity and SQUID (superconducting quantum interference device) technology can be used to obtain a gravity gradiometer with very high sensitivity and stability. A superconducting gravity gradiometer has been developed for a null test of the gravitational inverse-square law and space-borne geodesy. Here we present a complete theoretical model of this instrument. Starting from dynamical equations for the device, we derive transfer functions, a common mode rejection characteristic, and an error model of the superconducting instrument. Since a gradiometer must detect a very weak differential gravity signal in the midst of large platform accelerations and other environmental disturbances, the scale factor and common mode rejection stability of the instrument are extremely important in addition to its immunity to temperature and electromagnetic fluctuations. We show how flux quantization, the Meissner effect, and properties of liquid helium can be utilized to meet these challenges

  10. On 3D Minimal Massive Gravity

    Alishahiha, Mohsen; Naseh, Ali; Shirzad, Ahmad

    2014-12-03

    We study linearized equations of motion of the newly proposed three dimensional gravity, known as minimal massive gravity, using its metric formulation. We observe that the resultant linearized equations are exactly the same as that of TMG by making use of a redefinition of the parameters of the model. In particular the model admits logarithmic modes at the critical points. We also study several vacuum solutions of the model, specially at a certain limit where the contribution of Chern-Simons term vanishes.

  11. Radion and holographic brane gravity

    Kanno, Sugumi; Soda, Jiro

    2002-01-01

    The low energy effective theory for the Randall-Sundrum two-brane system is investigated with an emphasis on the role of the nonlinear radion in the brane world. The equations of motion in the bulk are solved using a low energy expansion method. This allows us, through the junction conditions, to deduce the effective equations of motion for gravity on the brane. It is shown that the gravity on the brane world is described by a quasi-scalar-tensor theory with a specific coupling function ω(Ψ)=3Ψ/2(1-Ψ) on the positive tension brane and ω(Φ)=-3Φ/2(1+Φ) on the negative tension brane, where Ψ and Φ are nonlinear realizations of the radion on the positive and negative tension branes, respectively. In contrast with the usual scalar-tensor gravity, the quasi-scalar-tensor gravity couples with two kinds of matter; namely, the matter on both positive and negative tension branes, with different effective gravitational coupling constants. In particular, the radion disguised as the scalar fields Ψ and Φ couples with the sum of the traces of the energy-momentum tensor on both branes. In the course of the derivation, it is revealed that the radion plays an essential role in converting the nonlocal Einstein gravity with generalized dark radiation to local quasi-scalar-tensor gravity. For completeness, we also derive the effective action for our theory by substituting the bulk solution into the original action. It is also shown that quasi-scalar-tensor gravity works as a hologram at low energy in the sense that the bulk geometry can be reconstructed from the solution of quasi-scalar-tensor gravity

  12. Simulating Gravity

    Pipinos, Savas

    2010-01-01

    This article describes one classroom activity in which the author simulates the Newtonian gravity, and employs the Euclidean Geometry with the use of new technologies (NT). The prerequisites for this activity were some knowledge of the formulae for a particle free fall in Physics and most certainly, a good understanding of the notion of similarity…

  13. Cellular gravity

    F.C. Gruau; J.T. Tromp (John)

    1999-01-01

    textabstractWe consider the problem of establishing gravity in cellular automata. In particular, when cellular automata states can be partitioned into empty, particle, and wall types, with the latter enclosing rectangular areas, we desire rules that will make the particles fall down and pile up on

  14. Gravity across Space and Time

    Klasing, Mariko; Milionis, Petros; Zymek, Robert

    2016-01-01

    How well can the standard gravity equation account for the evolution of global trade flows over the long run? This paper provides the first systematic attempt to answer this question using a newly-assembled data set of bilateral trade flows, income levels and trade frictions that spans the years

  15. Generalized Vaidya spacetime for cubic gravity

    Ruan, Shan-Ming

    2016-03-01

    We present a kind of generalized Vaidya solution of a new cubic gravity in five dimensions whose field equations in spherically symmetric spacetime are always second order like the Lovelock gravity. We also study the thermodynamics of its spherically symmetric apparent horizon and get its entropy expression and generalized Misner-Sharp energy. Finally, we present the first law and second law hold in this gravity. Although all the results are analogous to those in Lovelock gravity, we in fact introduce the contribution of a new cubic term in five dimensions where the cubic Lovelock term is just zero.

  16. Quantum gravity

    Isham, C.

    1989-01-01

    Gravitational effects are seen as arising from a curvature in spacetime. This must be reconciled with gravity's apparently passive role in quantum theory to achieve a satisfactory quantum theory of gravity. The development of grand unified theories has spurred the search, with forces being of equal strength at a unification energy of 10 15 - 10 18 GeV, with the ''Plank length'', Lp ≅ 10 -35 m. Fundamental principles of general relativity and quantum mechanics are outlined. Gravitons are shown to have spin-0, as mediators of gravitation force in the classical sense or spin-2 which are related to the quantisation of general relativity. Applying the ideas of supersymmetry to gravitation implies partners for the graviton, especially the massless spin 3/2 fermion called a gravitino. The concept of supersymmetric strings is introduced and discussed. (U.K.)

  17. Quantum gravity

    Markov, M.A.; West, P.C.

    1984-01-01

    This book discusses the state of the art of quantum gravity, quantum effects in cosmology, quantum black-hole physics, recent developments in supergravity, and quantum gauge theories. Topics considered include the problems of general relativity, pregeometry, complete cosmological theories, quantum fluctuations in cosmology and galaxy formation, a new inflationary universe scenario, grand unified phase transitions and the early Universe, the generalized second law of thermodynamics, vacuum polarization near black holes, the relativity of vacuum, black hole evaporations and their cosmological consequences, currents in supersymmetric theories, the Kaluza-Klein theories, gauge algebra and quantization, and twistor theory. This volume constitutes the proceedings of the Second Seminar on Quantum Gravity held in Moscow in 1981

  18. Measuring Gravity in International Trade Flows

    E. Young Song

    2004-12-01

    Full Text Available The purpose of this paper is two-fold. One is to clarify the concept of gravity in international trade flows. The other is to measure the strength of gravity in international trade flows in a way that is consistent with a well-defined concept of gravity. This paper shows that the widely accepted belief that specialization is the source of gravity is not well grounded on theory. We propose to define gravity in international trade as the force that makes the market shares of an exporting country constant in all importing countries, regardless of their sizes. In a stochastic context, we should interpret it as implying that the strength of gravity increases i as the correlation between market shares and market sizes gets weaker and ii as the variance of market shares gets smaller. We estimate an empirical gravity equation thoroughly based on this definition of gravity. We find that a strong degree of gravity exists in most bilateral trade, regardless of income levels of countries, and in trade of most manThe purpose of this paper is two-fold. One is to clarify the concept of gravity in international trade flows. The other is to measure the strength of gravity in international trade flows in a way that is consistent with a well-defined concept of gravity. This paper shows that the widely accepted belief that specialization is the source of gravity is not well grounded on theory. We propose to define gravity in international trade as the force that makes the market shares of an exporting country constant in all importing countries, regardless of their sizes. In a stochastic context, we should interpret it as implying that the strength of gravity increases i as the correlation between market shares and market sizes gets weaker and ii as the variance of market shares gets smaller. We estimate an empirical gravity equation thoroughly based on this definition of gravity. We find that a strong degree of gravity exists in most bilateral trade, regardless of

  19. What goes up... gravity and scientific method

    Kosso, Peter

    2017-01-01

    The concept of gravity provides a natural phenomenon that is simultaneously obvious and obscure; we all know what it is, but rarely question why it is. The simple observation that 'what goes up must come down' contrasts starkly with our current scientific explanation of gravity, which involves challenging and sometimes counterintuitive concepts. With such extremes between the plain and the perplexing, gravity forces a sharp focus on scientific method. Following the history of gravity from Aristotle to Einstein, this clear account highlights the logic of scientific method for non-specialists. Successive theories of gravity and the evidence for each are presented clearly and rationally, focusing on the fundamental ideas behind them. Using only high-school level algebra and geometry, the author emphasizes what the equations mean rather than how they are derived, making this accessible for all those curious about gravity and how science really works.

  20. Is nonrelativistic gravity possible?

    Kocharyan, A. A.

    2009-01-01

    We study nonrelativistic gravity using the Hamiltonian formalism. For the dynamics of general relativity (relativistic gravity) the formalism is well known and called the Arnowitt-Deser-Misner (ADM) formalism. We show that if the lapse function is constrained correctly, then nonrelativistic gravity is described by a consistent Hamiltonian system. Surprisingly, nonrelativistic gravity can have solutions identical to relativistic gravity ones. In particular, (anti-)de Sitter black holes of Einstein gravity and IR limit of Horava gravity are locally identical.

  1. Quintic quasi-topological gravity

    Cisterna, Adolfo [Vicerrectoría académica, Universidad Central de Chile,Toesca 1783 Santiago (Chile); Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile,Casilla 567, Valdivia (Chile); Guajardo, Luis; Hassaïne, Mokhtar [Instituto de Matemática y Física, Universidad de Talca,Casilla 747, Talca (Chile); Oliva, Julio [Departamento de Física, Universidad de Concepción,Casilla, 160-C, Concepción (Chile)

    2017-04-11

    We construct a quintic quasi-topological gravity in five dimensions, i.e. a theory with a Lagrangian containing R{sup 5} terms and whose field equations are of second order on spherically (hyperbolic or planar) symmetric spacetimes. These theories have recently received attention since when formulated on asymptotically AdS spacetimes might provide for gravity duals of a broad class of CFTs. For simplicity we focus on five dimensions. We show that this theory fulfils a Birkhoff’s Theorem as it is the case in Lovelock gravity and therefore, for generic values of the couplings, there is no s-wave propagating mode. We prove that the spherically symmetric solution is determined by a quintic algebraic polynomial equation which resembles Wheeler’s polynomial of Lovelock gravity. For the black hole solutions we compute the temperature, mass and entropy and show that the first law of black holes thermodynamics is fulfilled. Besides of being of fourth order in general, we show that the field equations, when linearized around AdS are of second order, and therefore the theory does not propagate ghosts around this background. Besides the class of theories originally introduced in https://arxiv.org/abs/1003.4773, the general geometric structure of these Lagrangians remains an open problem.

  2. Lovelock-Brans-Dicke gravity

    Wenjie Tian, David; Booth, Ivan

    2016-02-01

    According to Lovelock’s theorem, the Hilbert-Einstein and the Lovelock actions are indistinguishable from their field equations. However, they have different scalar-tensor counterparts, which correspond to the Brans-Dicke and the Lovelock-Brans-Dicke (LBD) gravities, respectively. In this paper the LBD model of alternative gravity with the Lagrangian density {{L}}{LBD}=\\frac{1}{16π }≤ft[φ ≤ft(R+\\frac{a}{\\sqrt{-g}}{}*{RR}+b{ G }\\right)-\\frac{{ω }{{L}}}{φ }{{{\

  3. Semiclassical unimodular gravity

    Fiol, Bartomeu; Garriga, Jaume

    2010-01-01

    Classically, unimodular gravity is known to be equivalent to General Relativity (GR), except for the fact that the effective cosmological constant Λ has the status of an integration constant. Here, we explore various formulations of unimodular gravity beyond the classical limit. We first consider the non-generally covariant action formulation in which the determinant of the metric is held fixed to unity. We argue that the corresponding quantum theory is also equivalent to General Relativity for localized perturbative processes which take place in generic backgrounds of infinite volume (such as asymptotically flat spacetimes). Next, using the same action, we calculate semiclassical non-perturbative quantities, which we expect will be dominated by Euclidean instanton solutions. We derive the entropy/area ratio for cosmological and black hole horizons, finding agreement with GR for solutions in backgrounds of infinite volume, but disagreement for backgrounds with finite volume. In deriving the above results, the path integral is taken over histories with fixed 4-volume. We point out that the results are different if we allow the 4-volume of the different histories to vary over a continuum range. In this ''generalized'' version of unimodular gravity, one recovers the full set of Einstein's equations in the classical limit, including the trace, so Λ is no longer an integration constant. Finally, we consider the generally covariant theory due to Henneaux and Teitelboim, which is classically equivalent to unimodular gravity. In this case, the standard semiclassical GR results are recovered provided that the boundary term in the Euclidean action is chosen appropriately

  4. Kampanje mjerenja apsolutnog i relativnog ubrzanja sile teže u „Osnovnoj gravimetrijskoj mreži Bosne i Hercegovine“ : Measurement campaign of absolute and relative gravity in "Basic gravimetric network of Bosnia and Herzegovina"

    Hasumana Abaza

    2014-12-01

    Full Text Available Mjerenje apsolutnog ubrzanja sile Zemljine teže u Bosni i Hercegovini izvršeno je na četiri stanice, a u okviru projekta “Izgradnja kapaciteta za unapređenje zemljišne administracije i procedura u Bosni i Hercegovini“. Mjerenje relativnog ubrzanja sile Zemljine teže također je završeno u Osnovnoj gravimetrijskoj mreži BiH na 60 tačaka, te je izvršeno povezivanje sa stanicama na kojim je mjereno apsolutno ubrzanje sile teže. Do sada urađen posao je odlična osnova za nastavak radova na regionalnom gravimetrijskom premjeru na putu ka konačnom cilju određivanja geoida za teritoriju BiH. : Absolute gravity measurements in Bosnia and Herzegovina were carried out at four stations within the project "Capacity building for improving land administration and procedures in Bosnia and Herzegovina“ - CILAP. Relative gravity measurements were also completed in the primary gravimetric network of Bosnia and Herzegovina at 60 points, followed by connecting points with absolute gravity data. So far, completed work is an excellent basis for continuing on regional gravity measurements and determining the geoid for the territory of Bosnia and Herzegovina.

  5. Miniaturised Gravity Sensors for Remote Gravity Surveys.

    Middlemiss, R. P.; Bramsiepe, S. G.; Hough, J.; Paul, D. J.; Rowan, S.; Samarelli, A.; Hammond, G.

    2016-12-01

    Gravimetry lets us see the world from a completely different perspective. The ability to measure tiny variations in gravitational acceleration (g), allows one to see not just the Earth's gravitational pull, but the influence of smaller objects. The more accurate the gravimeter, the smaller the objects one can see. Gravimetry has applications in many different fields: from tracking magma moving under volcanoes before eruptions; to locating hidden tunnels. The top commercial gravimeters weigh tens of kg and cost at least $100,000, limiting the situations in which they can be used. By contrast, smart phones use a MEMS (microelectromechanical system) accelerometer that can measure the orientation of the device. These are not nearly sensitive or stable enough to be used for the gravimetry but they are cheap, light-weight and mass-producible. At Glasgow University we have developed a MEMS device with both the stability and sensitivity for useful gravimetric measurements. This was demonstrated by a measurement of the Earth tides - the first time this has been achieved with a MEMS sensor. A gravimeter of this size opens up the possiblility for new gravity imaging modalities. Thousands of gravimeters could be networked over a survey site, storing data on an SD card or communicating wirelessly to a remote location. These devices could also be small enough to be carried by a UAVs: airborne gravity surveys could be carried out at low altitude by mulitple UAVs, or UAVs could be used to deliver ground based gravimeters to remote or inaccessible locations.

  6. A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems.

    Liu, Tao; Huang, Jie

    2017-04-17

    This paper presents a discrete-time recurrent neural network approach to solving systems of linear equations with two features. First, the system of linear equations may not have a unique solution. Second, the system matrix is not known precisely, but a sequence of matrices that converges to the unknown system matrix exponentially is known. The problem is motivated from solving the output regulation problem for linear systems. Thus, an application of our main result leads to an online solution to the output regulation problem for linear systems.

  7. Initial value formulation of higher derivative gravity

    Noakes, D.R.

    1983-01-01

    The initial value problem is considered for the conformally coupled scalar field and higher derivative gravity, by expressing the equations of each theory in harmonic coordinates. For each theory it is shown that the (vacuum) equations can take the form of a diagonal hyperbolic system with constraints on the initial data. Consequently these theories possess well-posed initial value formulations

  8. Antigravity: Spin-gravity coupling in action

    Plyatsko, Roman; Fenyk, Mykola

    2016-08-01

    The typical motions of a spinning test particle in Schwarzschild's background which show the strong repulsive action of the highly relativistic spin-gravity coupling are considered using the exact Mathisson-Papapetrou equations. An approximated approach to choice solutions of these equations which describe motions of the particle's proper center of mass is developed.

  9. Noncommutative gravity

    Schupp, P.

    2007-01-01

    Heuristic arguments suggest that the classical picture of smooth commutative spacetime should be replaced by some kind of quantum / noncommutative geometry at length scales and energies where quantum as well as gravitational effects are important. Motivated by this idea much research has been devoted to the study of quantum field theory on noncommutative spacetimes. More recently the focus has started to shift back to gravity in this context. We give an introductory overview to the formulation of general relativity in a noncommutative spacetime background and discuss the possibility of exact solutions. (author)

  10. Infinite degeneracy of states in quantum gravity

    Hackett, Jonathan; Wan Yidun

    2011-01-01

    The setting of Braided Ribbon Networks is used to present a general result in spin-networks embedded in manifolds: the existence of an infinite number of species of conserved quantities. Restricted to three-valent networks the number of such conserved quantities in a given network is shown to be determined by the number of nodes in the network. The implication of these conserved quantities is discussed in the context of Loop Quantum Gravity.

  11. A network thermodynamic method for numerical solution of the Nernst-Planck and Poisson equation system with application to ionic transport through membranes.

    Horno, J; González-Caballero, F; González-Fernández, C F

    1990-01-01

    Simple techniques of network thermodynamics are used to obtain the numerical solution of the Nernst-Planck and Poisson equation system. A network model for a particular physical situation, namely ionic transport through a thin membrane with simultaneous diffusion, convection and electric current, is proposed. Concentration and electric field profiles across the membrane, as well as diffusion potential, have been simulated using the electric circuit simulation program, SPICE. The method is quite general and extremely efficient, permitting treatments of multi-ion systems whatever the boundary and experimental conditions may be.

  12. Conformal Gravity

    Hooft, G.

    2012-01-01

    The dynamical degree of freedom for the gravitational force is the metric tensor, having 10 locally independent degrees of freedom (of which 4 can be used to fix the coordinate choice). In conformal gravity, we split this field into an overall scalar factor and a nine-component remainder. All unrenormalizable infinities are in this remainder, while the scalar component can be handled like any other scalar field such as the Higgs field. In this formalism, conformal symmetry is spontaneously broken. An imperative demand on any healthy quantum gravity theory is that black holes should be described as quantum systems with micro-states as dictated by the Hawking-Bekenstein theory. This requires conformal symmetry that may be broken spontaneously but not explicitly, and this means that all conformal anomalies must cancel out. Cancellation of conformal anomalies yields constraints on the matter sector as described by some universal field theory. Thus black hole physics may eventually be of help in the construction of unified field theories. (author)

  13. Loop Quantum Gravity.

    Rovelli, Carlo

    2008-01-01

    The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime , is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler's "spacetime foam" intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n -point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

  14. Loop Quantum Gravity

    Rovelli Carlo

    2008-07-01

    Full Text Available The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime, is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler’s “spacetime foam” intuition. (iii Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv A derivation of the Bekenstein–Hawking black-hole entropy. (v Low-energy calculations, yielding n-point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

  15. Limnimeter and rain gauge FDI in sewer networks using an interval parity equations based detection approach and an enhanced isolation scheme

    Puig Cayuela, Vicenç; Blesa Izquierdo, Joaquim

    2013-01-01

    In this paper, a methodology for limnimeter and rain-gauge fault detection and isolation (FDI) in sewer networks is presented. The proposed model based FDI approach uses interval parity equations for fault detection in order to enhance robustness against modelling errors and noise. They both are assumed unknown but bounded, following the so-called interval (or set-membership) approach. On the other hand, fault isolation relies on an algorithm that reasons using several fault signature matrice...

  16. Southern Africa Gravity Data

    National Oceanic and Atmospheric Administration, Department of Commerce — This data base (14,559 records) was received in January 1986. Principal gravity parameters include elevation and observed gravity. The observed gravity values are...

  17. NGS Absolute Gravity Data

    National Oceanic and Atmospheric Administration, Department of Commerce — The NGS Absolute Gravity data (78 stations) was received in July 1993. Principal gravity parameters include Gravity Value, Uncertainty, and Vertical Gradient. The...

  18. Topics in quantum gravity

    Lamon, Raphael

    2010-06-29

    Quantum gravity is an attempt to unify general relativity with quantum mechanics which are the two highly successful fundamental theories of theoretical physics. The main difficulty in this unification arises from the fact that, while general relativity describes gravity as a macroscopic geometrical theory, quantum mechanics explains microscopic phenomena. As a further complication, not only do both theories describe different scales but also their philosophical ramifications and the mathematics used to describe them differ in a dramatic way. Consequently, one possible starting point of an attempt at a unification is quantum mechanics, i.e. particle physics, and try to incorporate gravitation. This pathway has been chosen by particle physicists which led to string theory. On the other hand, loop quantum gravity (LQG) chooses the other possibility, i.e. it takes the geometrical aspects of gravity seriously and quantizes geometry. The first part of this thesis deals with a generalization of loop quantum cosmology (LQC) to toroidal topologies. LQC is a quantization of homogenous solutions of Einstein's field equations using tools from LQG. First the general concepts of closed topologies is introduced with special emphasis on Thurston's theorem and its consequences. It is shown that new degrees of freedom called Teichmueller parameters come into play and their dynamics can be described by a Hamiltonian. Several numerical solutions for a toroidal universe are presented and discussed. Following the guidelines of LQG this dynamics are rewritten using the Ashtekar variables and numerical solutions are shown. However, in order to find a suitable Hilbert space a canonical transformation must be performed. On the other hand this transformation makes the quantization of geometrical quantities less tractable such that two different ways are presented. It is shown that in both cases the spectrum of such geometrical operators depends on the initial value problem

  19. Topics in quantum gravity

    Lamon, Raphael

    2010-01-01

    Quantum gravity is an attempt to unify general relativity with quantum mechanics which are the two highly successful fundamental theories of theoretical physics. The main difficulty in this unification arises from the fact that, while general relativity describes gravity as a macroscopic geometrical theory, quantum mechanics explains microscopic phenomena. As a further complication, not only do both theories describe different scales but also their philosophical ramifications and the mathematics used to describe them differ in a dramatic way. Consequently, one possible starting point of an attempt at a unification is quantum mechanics, i.e. particle physics, and try to incorporate gravitation. This pathway has been chosen by particle physicists which led to string theory. On the other hand, loop quantum gravity (LQG) chooses the other possibility, i.e. it takes the geometrical aspects of gravity seriously and quantizes geometry. The first part of this thesis deals with a generalization of loop quantum cosmology (LQC) to toroidal topologies. LQC is a quantization of homogenous solutions of Einstein's field equations using tools from LQG. First the general concepts of closed topologies is introduced with special emphasis on Thurston's theorem and its consequences. It is shown that new degrees of freedom called Teichmueller parameters come into play and their dynamics can be described by a Hamiltonian. Several numerical solutions for a toroidal universe are presented and discussed. Following the guidelines of LQG this dynamics are rewritten using the Ashtekar variables and numerical solutions are shown. However, in order to find a suitable Hilbert space a canonical transformation must be performed. On the other hand this transformation makes the quantization of geometrical quantities less tractable such that two different ways are presented. It is shown that in both cases the spectrum of such geometrical operators depends on the initial value problem. Furthermore, we

  20. Minimal theory of massive gravity

    De Felice, Antonio; Mukohyama, Shinji

    2016-01-01

    We propose a new theory of massive gravity with only two propagating degrees of freedom. While the homogeneous and isotropic background cosmology and the tensor linear perturbations around it are described by exactly the same equations as those in the de Rham–Gabadadze–Tolley (dRGT) massive gravity, the scalar and vector gravitational degrees of freedom are absent in the new theory at the fully nonlinear level. Hence the new theory provides a stable nonlinear completion of the self-accelerating cosmological solution that was originally found in the dRGT theory. The cosmological solution in the other branch, often called the normal branch, is also rendered stable in the new theory and, for the first time, makes it possible to realize an effective equation-of-state parameter different from (either larger or smaller than) −1 without introducing any extra degrees of freedom.

  1. Minimal theory of massive gravity

    Antonio De Felice

    2016-01-01

    Full Text Available We propose a new theory of massive gravity with only two propagating degrees of freedom. While the homogeneous and isotropic background cosmology and the tensor linear perturbations around it are described by exactly the same equations as those in the de Rham–Gabadadze–Tolley (dRGT massive gravity, the scalar and vector gravitational degrees of freedom are absent in the new theory at the fully nonlinear level. Hence the new theory provides a stable nonlinear completion of the self-accelerating cosmological solution that was originally found in the dRGT theory. The cosmological solution in the other branch, often called the normal branch, is also rendered stable in the new theory and, for the first time, makes it possible to realize an effective equation-of-state parameter different from (either larger or smaller than −1 without introducing any extra degrees of freedom.

  2. Newtonian gravity in loop quantum gravity

    Smolin, Lee

    2010-01-01

    We apply a recent argument of Verlinde to loop quantum gravity, to conclude that Newton's law of gravity emerges in an appropriate limit and setting. This is possible because the relationship between area and entropy is realized in loop quantum gravity when boundaries are imposed on a quantum spacetime.

  3. Assessing Hypothetical Gravity Control Propulsion

    Millis, Marc G.

    2006-01-01

    Gauging the benefits of hypothetical gravity control propulsion is difficult, but addressable. The major challenge is that such breakthroughs are still only notional concepts rather than being specific methods from which performance can be rigorously quantified. A recent assessment by Tajmar and Bertolami used the rocket equation to correct naive misconceptions, but a more fundamental analysis requires the use of energy as the basis for comparison. The energy of a rocket is compared to an ide...

  4. MORE: mixed optimization for reverse engineering--an application to modeling biological networks response via sparse systems of nonlinear differential equations.

    Sambo, Francesco; de Oca, Marco A Montes; Di Camillo, Barbara; Toffolo, Gianna; Stützle, Thomas

    2012-01-01

    Reverse engineering is the problem of inferring the structure of a network of interactions between biological variables from a set of observations. In this paper, we propose an optimization algorithm, called MORE, for the reverse engineering of biological networks from time series data. The model inferred by MORE is a sparse system of nonlinear differential equations, complex enough to realistically describe the dynamics of a biological system. MORE tackles separately the discrete component of the problem, the determination of the biological network topology, and the continuous component of the problem, the strength of the interactions. This approach allows us both to enforce system sparsity, by globally constraining the number of edges, and to integrate a priori information about the structure of the underlying interaction network. Experimental results on simulated and real-world networks show that the mixed discrete/continuous optimization approach of MORE significantly outperforms standard continuous optimization and that MORE is competitive with the state of the art in terms of accuracy of the inferred networks.

  5. Gauge-invariant flow equation

    Wetterich, C.

    2018-06-01

    We propose a closed gauge-invariant functional flow equation for Yang-Mills theories and quantum gravity that only involves one macroscopic gauge field or metric. It is based on a projection on physical and gauge fluctuations. Deriving this equation from a functional integral we employ the freedom in the precise choice of the macroscopic field and the effective average action in order to realize a closed and simple form of the flow equation.

  6. Equivalence of two-dimensional gravities

    Mohammedi, N.

    1990-01-01

    The authors find the relationship between the Jackiw-Teitelboim model of two-dimensional gravity and the SL(2,R) induced gravity. These are shown to be related to a two-dimensional gauge theory obtained by dimensionally reducing the Chern-Simons action of the 2 + 1 dimensional gravity. The authors present an explicit solution to the equations of motion of the auxiliary field of the Jackiw-Teitelboim model in the light-cone gauge. A renormalization of the cosmological constant is also given

  7. Anomaly freedom in perturbative loop quantum gravity

    Bojowald, Martin; Hossain, Golam Mortuza; Kagan, Mikhail; Shankaranarayanan, S.

    2008-01-01

    A fully consistent linear perturbation theory for cosmology is derived in the presence of quantum corrections as they are suggested by properties of inverse volume operators in loop quantum gravity. The underlying constraints present a consistent deformation of the classical system, which shows that the discreteness in loop quantum gravity can be implemented in effective equations without spoiling space-time covariance. Nevertheless, nontrivial quantum corrections do arise in the constraint algebra. Since correction terms must appear in tightly controlled forms to avoid anomalies, detailed insights for the correct implementation of constraint operators can be gained. The procedures of this article thus provide a clear link between fundamental quantum gravity and phenomenology.

  8. 2D gravity and random matrices

    Zinn-Justin, J.

    1990-01-01

    Recent progress in 2D gravity coupled to d ≤ 1 matter, based on a representation of discrete gravity in terms of random matrices, is reported. The matrix problem can be solved in many cases by the introduction of suitable orthogonal polynomials. Alternatively in the continuum limit the orthogonal polynomial method can be shown to be equivalent to the construction of representation of the canonical commutation relations in terms of differential operators. In the case of pure gravity or discrete Ising-like matter the sum over topologies is reduced to the solution of non-linear differential equations. The d = 1 problem can be solved by semiclassical methods

  9. Lanczos–Lovelock models of gravity

    Padmanabhan, T.; Kothawala, D.

    2013-01-01

    Lanczos–Lovelock models of gravity represent a natural and elegant generalization of Einstein’s theory of gravity to higher dimensions. They are characterized by the fact that the field equations only contain up to second derivatives of the metric even though the action functional can be a quadratic or higher degree polynomial in the curvature tensor. Because these models share several key properties of Einstein’s theory they serve as a useful set of candidate models for testing the emergent paradigm for gravity. This review highlights several geometrical and thermodynamical aspects of Lanczos–Lovelock models which have attracted recent attention

  10. Aspects of Quadratic Gravity

    Alvarez-Gaume, Luis; Kounnas, Costas; Lust, Dieter; Riotto, Antonio

    2016-01-01

    We discuss quadratic gravity where terms quadratic in the curvature tensor are included in the action. After reviewing the corresponding field equations, we analyze in detail the physical propagating modes in some specific backgrounds. First we confirm that the pure $R^2$ theory is indeed ghost free. Then we point out that for flat backgrounds the pure $R^2$ theory propagates only a scalar massless mode and no spin-two tensor mode. However, the latter emerges either by expanding the theory around curved backgrounds like de Sitter or anti-de Sitter, or by changing the long-distance dynamics by introducing the standard Einstein term. In both cases, the theory is modified in the infrared and a propagating graviton is recovered. Hence we recognize a subtle interplay between the UV and IR properties of higher order gravity. We also calculate the corresponding Newton's law for general quadratic curvature theories. Finally, we discuss how quadratic actions may be obtained from a fundamental theory like string- or M-...

  11. Duality in linearized gravity

    Henneaux, Marc; Teitelboim, Claudio

    2005-01-01

    We show that duality transformations of linearized gravity in four dimensions, i.e., rotations of the linearized Riemann tensor and its dual into each other, can be extended to the dynamical fields of the theory so as to be symmetries of the action and not just symmetries of the equations of motion. Our approach relies on the introduction of two superpotentials, one for the spatial components of the spin-2 field and the other for their canonically conjugate momenta. These superpotentials are two-index, symmetric tensors. They can be taken to be the basic dynamical fields and appear locally in the action. They are simply rotated into each other under duality. In terms of the superpotentials, the canonical generator of duality rotations is found to have a Chern-Simons-like structure, as in the Maxwell case

  12. Gravity, a geometrical course

    Frè, Pietro Giuseppe

    2013-01-01

    Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications,  updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes.   Volume One is dedicated to the development of the theory and basic physical applications. It guides the reader from the foundation of special relativity to Einstein field equations, illustrating some basic applications in astrophysics. A detailed  account  of the historical and conceptual development of the theory is combined with the presentation of its mathematical foundations.  Differe...

  13. Quantum Gravity (Cambridge Monographs on Mathematical Physics)

    Kiefer, C

    2005-01-01

    mechanics, general relativity and other topics. According to the level of the reader, this part can be skipped or studied as interesting material on its own. The penetrating theme of the whole book (its leitmotiv) is background independence. In non-gravitational theories, dynamical fields are formulated on a fixed background spacetime that plays the role of an absolute structure in the theory. In general relativity, on the other hand, there is no background structure - all fields are dynamical. This was a confusing point already during the development of general relativity and led Albert Einstein in 1913 erroneously to give up general covariance before recognizing his error and presenting his final correct field equations that are of course covariant. This story is instructive, circling around the famous 'hole problem', and is told in detail in Rovelli's book. Its solution is that points on a bare manifold do not make sense in physics; everything, including the gravitational field, is dragged around by a diffeomorphism - there is just no background available, only the fields exist. In loop quantum gravity, physical space (called 'quantum geometry') itself is formed by loop-like quantum states: a suitable orthonormal basis is provided by spin-network states (a spin-network is a graph with edges and nodes, where spins are assigned to the edges), and the quantum geometry is a superposition of such states. Time and space in the usual sense have disappeared. In the second half of his book, Rovelli discusses at length the major successes of this approach. First of all, the formalism yields a unique kinematical Hilbert space for the quantum states obeying the Gauss and diffeomorphism constraints. Secondly, there exist two important operators that are connected, respectively, with area and volume in the classical limit. These operators have a discrete spectrum and thus provide elementary 'quanta' of area and volume. This gives a vague hint of a discrete structure at the Planck

  14. The Juno Gravity Science Instrument

    Asmar, Sami W.; Bolton, Scott J.; Buccino, Dustin R.; Cornish, Timothy P.; Folkner, William M.; Formaro, Roberto; Iess, Luciano; Jongeling, Andre P.; Lewis, Dorothy K.; Mittskus, Anthony P.; Mukai, Ryan; Simone, Lorenzo

    2017-11-01

    The Juno mission's primary science objectives include the investigation of Jupiter interior structure via the determination of its gravitational field. Juno will provide more accurate determination of Jupiter's gravity harmonics that will provide new constraints on interior structure models. Juno will also measure the gravitational response from tides raised on Jupiter by Galilean satellites. This is accomplished by utilizing Gravity Science instrumentation to support measurements of the Doppler shift of the Juno radio signal by NASA's Deep Space Network at two radio frequencies. The Doppler data measure the changes in the spacecraft velocity in the direction to Earth caused by the Jupiter gravity field. Doppler measurements at X-band (˜ 8 GHz) are supported by the spacecraft telecommunications subsystem for command and telemetry and are used for spacecraft navigation as well as Gravity Science. The spacecraft also includes a Ka-band (˜ 32 GHz) translator and amplifier specifically for the Gravity Science investigation contributed by the Italian Space Agency. The use of two radio frequencies allows for improved accuracy by removal of noise due to charged particles along the radio signal path.

  15. Cellular neural network to the spherical harmonics approximation of neutron transport equation in x-y geometry. Part I: Modeling and verification for time-independent solution

    Pirouzmand, Ahmad; Hadad, Kamal

    2011-01-01

    Highlights: → This paper describes the solution of time-independent neutron transport equation. → Using a novel method based on cellular neural networks (CNNs) coupled with P N method. → Utilize the CNN model to simulate spatial scalar flux distribution in steady state. → The accuracy, stability, and capabilities of CNN model are examined in x-y geometry. - Abstract: This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (P N ) to solve the time-independent neutron transport equation in x-y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.

  16. Solution of weakly compressible isothermal flow in landfill gas collection networks

    Nec, Y [Thompson Rivers University, Kamloops, British Columbia (Canada); Huculak, G, E-mail: cranberryana@gmail.com, E-mail: greg@gnhconsulting.ca [GNH Consulting, Delta, British Columbia (Canada)

    2017-12-15

    Pipe networks collecting gas in sanitary landfills operate under the regime of a weakly compressible isothermal flow of ideal gas. The effect of compressibility has been traditionally neglected in this application in favour of simplicity, thereby creating a conceptual incongruity between the flow equations and thermodynamic equation of state. Here the flow is solved by generalisation of the classic Darcy–Weisbach equation for an incompressible steady flow in a pipe to an ordinary differential equation, permitting continuous variation of density, viscosity and related fluid parameters, as well as head loss or gain due to gravity, in isothermal flow. The differential equation is solved analytically in the case of ideal gas for a single edge in the network. Thereafter the solution is used in an algorithm developed to construct the flow equations automatically for a network characterised by an incidence matrix, and determine pressure distribution, flow rates and all associated parameters therein. (paper)

  17. Solution of weakly compressible isothermal flow in landfill gas collection networks

    Nec, Y.; Huculak, G.

    2017-12-01

    Pipe networks collecting gas in sanitary landfills operate under the regime of a weakly compressible isothermal flow of ideal gas. The effect of compressibility has been traditionally neglected in this application in favour of simplicity, thereby creating a conceptual incongruity between the flow equations and thermodynamic equation of state. Here the flow is solved by generalisation of the classic Darcy-Weisbach equation for an incompressible steady flow in a pipe to an ordinary differential equation, permitting continuous variation of density, viscosity and related fluid parameters, as well as head loss or gain due to gravity, in isothermal flow. The differential equation is solved analytically in the case of ideal gas for a single edge in the network. Thereafter the solution is used in an algorithm developed to construct the flow equations automatically for a network characterised by an incidence matrix, and determine pressure distribution, flow rates and all associated parameters therein.

  18. Solution of weakly compressible isothermal flow in landfill gas collection networks

    Nec, Y; Huculak, G

    2017-01-01

    Pipe networks collecting gas in sanitary landfills operate under the regime of a weakly compressible isothermal flow of ideal gas. The effect of compressibility has been traditionally neglected in this application in favour of simplicity, thereby creating a conceptual incongruity between the flow equations and thermodynamic equation of state. Here the flow is solved by generalisation of the classic Darcy–Weisbach equation for an incompressible steady flow in a pipe to an ordinary differential equation, permitting continuous variation of density, viscosity and related fluid parameters, as well as head loss or gain due to gravity, in isothermal flow. The differential equation is solved analytically in the case of ideal gas for a single edge in the network. Thereafter the solution is used in an algorithm developed to construct the flow equations automatically for a network characterised by an incidence matrix, and determine pressure distribution, flow rates and all associated parameters therein. (paper)

  19. The Cause of Gravity

    Byrne, Michael

    1999-01-01

    Einstein said that gravity is an acceleration like any other acceleration. But gravity causes relativistic effects at non-relativistic speeds; so gravity could have relativistic origins. And since the strong force is thought to cause most of mass, and mass is proportional to gravity; the strong force is therefore also proportional to gravity. The strong force could thus cause relativistic increases of mass through the creation of virtual gluons; along with a comparable contraction of space ar...

  20. 2D higher spin gravity and the multimatrix models

    Awada, M.; Qiu Zongan

    1990-01-01

    We quantize W-gravity coupled to matter fields in the conformal gauge and obtain the critical exponents. We demonstrate explicitly how the generators of the W-algebra are described by an infinite set of conserved charges of the KdV hierarchy. We obtain the generalized hamiltonian equation of motion and show that it contains the class of universal differential equations of the matrix models. Thus we propose that these models describe pure W-gravity theories of the A-type. Consequently we give a new set of universal equations that correspond to other types of W-gravity theories. (orig.)

  1. Exact Solutions in 3D New Massive Gravity

    Ahmedov, Haji; Aliev, Alikram N.

    2011-01-01

    We show that the field equations of new massive gravity (NMG) consist of a massive (tensorial) Klein-Gordon-type equation with a curvature-squared source term and a constraint equation. We also show that, for algebraic type D and N spacetimes, the field equations of topologically massive gravity (TMG) can be thought of as the “square root” of the massive Klein-Gordon-type equation. Using this fact, we establish a simple framework for mapping all types D and N solutions of TMG into NMG. Finally, we present new examples of types D and N solutions to NMG.

  2. Allowance for influence of gravity field nonuniformity

    Tsysar, A. P.

    1987-03-01

    The constants of a quartz-metal pendulum used in higher-order gravimetric networks have been determined and a formula has been derived for the total correction for gravity field nonuniformity measurements made with the pendulum. Nomograms were constructed on the basis of these formulas and are used in introducing corrections into pendulum measurements. A table was prepared giving the components of the correction for some values of the derivatives of gravity potential from surrounding masses. Errors can be caused by building walls, the pedestal on which the instrument sits and other factors, and these must be taken into account since they increase the normal gravity gradient. After introducing these correction components for the nonuniform gravity field, the gravity field at the measurement point is related to the instrument point coinciding with the middle of the pendulum knife blade.

  3. Observational tests of modified gravity

    Jain, Bhuvnesh; Zhang Pengjie

    2008-01-01

    Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the Universe. Modified gravity theories have richer observational consequences for large-scale structures than conventional dark energy models, in that different observables are not described by a single growth factor even in the linear regime. We examine the relationships between perturbations in the metric potentials, density and velocity fields, and discuss strategies for measuring them using gravitational lensing, galaxy cluster abundances, galaxy clustering/dynamics, and the integrated Sachs-Wolfe effect. We show how a broad class of gravity theories can be tested by combining these probes. A robust way to interpret observations is by constraining two key functions: the ratio of the two metric potentials, and the ratio of the gravitational 'constant' in the Poisson equation to Newton's constant. We also discuss quasilinear effects that carry signatures of gravity, such as through induced three-point correlations. Clustering of dark energy can mimic features of modified gravity theories and thus confuse the search for distinct signatures of such theories. It can produce pressure perturbations and anisotropic stresses, which break the equality between the two metric potentials even in general relativity. With these two extra degrees of freedom, can a clustered dark energy model mimic modified gravity models in all observational tests? We show with specific examples that observational constraints on both the metric potentials and density perturbations can in principle distinguish modifications of gravity from dark energy models. We compare our result with other recent studies that have slightly different assumptions (and apparently contradictory conclusions).

  4. Loop equations in the theory of gravitation

    Makeenko, Yu.M.; Voronov, N.A.

    1981-01-01

    Loop-space variables (matrices of parallel transport) for the theory of gravitation are described. Loop equations, which are equivalent to the Einstein equations, are derived in the classical case. Loop equations are derived for gravity with cosmological constant as well. An analogy with the loop-space approach in Yang-Mills theory is discussed [ru

  5. Brane-Localized Gravity

    Gregory, Ruth

    2007-01-01

    The study of braneworlds has been an area of intense activity over the past decade, with thousands of papers being written, and many important technical advances being made. This book focuses on a particular aspect of braneworlds, namely perturbative gravity in one specific model: the Randall-Sundrum model. The book starts with an overview of the Randall-Sundrum model, discussing anti-de Sitter (AdS) space and the Israel equations in some detail. It then moves on to discuss cosmological branes, focusing on branes with constant curvature. The book then turns to brane gravity, i.e. what do we, as brane observers, perceive the gravitational interaction to be on the brane as derived from the actual five-dimensional gravitational physics? After a derivation of the general brane equations from the Israel equations, the remainder of the book deals with perturbative gravity. This part of the book is extremely detailed, with calculations given explicitly. Overall, the book is quite pedagogical in style, with the aim being to explain in detail the topics it chooses to cover. While it is not unusual to have books written on current and extremely popular research areas, it is unusual to have calculations written so explicitly. This is both a strength and a weakness of this book. It is a strength because the calculations are presented in a detail that students learning the topic will definitely appreciate; however, the narrow focus of the book also means that it lacks perspective and fails to present the broader context. In choosing to focus on one particular aspect of Randall-Sundrum branes, the book has not managed to communicate why a large number of theorists have worked so intensively on this model. In its early stages, the explicit detail of the Randall-Sundrum model would be extremely useful for a student starting out in this research area. In addition, the calculational detail later in the computation of the graviton propagator on the brane would also be welcome not

  6. Expectation values in quantum gravity

    Jordan, R.D.

    1986-01-01

    The purpose of this dissertation is to develop new methods for calculating expectation values of field operators, in situations where particle creation is important. The goal is to apply these techniques to quantum gravity, to see if the initial singularity in the universe might be avoided in the quantum theory. Standard effective action theory is modified to produce effective field equations satisfied by the expectation value of the field in an in state, as opposed to the usual in-out amplitude. Diagrammatic rules are found for calculation of the new field equations, and are used to show that the equations are real and causal up to two loop order. The theory also provides a simple check of unitarity, which is carried out, again up to two loops. Just as the standard effective field equations can be derived by analytic continuation from a theory defined in Euclidean space, so can the modified equations be obtained from a modified contour rotation of the Euclidean theory. This result is used to prove a recent conjecture which yields a simple rule for finding the real, causal equations. The new formalism is applied to two gravitational systems. First, the stability of flat space time is studied by finding the equation satisfied by small perturbations of Minkowski space

  7. Friendship networks and psychological well-being from late adolescence to young adulthood: a gender-specific structural equation modeling approach.

    Miething, Alexander; Almquist, Ylva B; Östberg, Viveca; Rostila, Mikael; Edling, Christofer; Rydgren, Jens

    2016-07-11

    The importance of supportive social relationships for psychological well-being has been previously recognized, but the direction of associations between both dimensions and how they evolve when adolescents enter adulthood have scarcely been addressed. The present study aims to examine the gender-specific associations between self-reported friendship network quality and psychological well-being of young people during the transition from late adolescence to young adulthood by taking into account the direction of association. A random sample of Swedes born in 1990 were surveyed at age 19 and again at age 23 regarding their own health and their relationships with a maximum of five self-nominated friends. The response rate was 55.3 % at baseline and 43.7 % at follow-up, resulting in 772 cases eligible for analysis. Gender-specific structural equation modeling was conducted to explore the associations between network quality and well-being. The measurement part included a latent measure of well-being, whereas the structural part accounted for autocorrelation for network quality and for well-being over time and further examined the cross-lagged associations. The results show that network quality increased while well-being decreased from age 19 to age 23. Females reported worse well-being at both time points, whereas no gender differences were found for network quality. Network quality at age 19 predicted network quality at age 23, and well-being at age 19 predicted well-being at age 23. The results further show positive correlations between network quality and well-being for males and females alike. The strength of the correlations diminished over time but remained significant at age 23. Simultaneously testing social causation and social selection in a series of competing models indicates that while there were no cross-lagged associations among males, there was a weak reverse association between well-being at age 19 and network quality at age 23 among females. The study

  8. Polytropic and Chaplygin f(T)-gravity models

    Karami, K; Abdolmaleki, A

    2012-01-01

    We reconstruct different f(T)-gravity models corresponding to a set of dark energy scenarios containing the polytropic, the standard Chaplygin and the generalized Chaplygin gas models. We also derive the equation of state parameter of the selected f(T)-gravity models and obtain the necessary conditions for crossing the phantom-divide line.

  9. Modeling genome-wide dynamic regulatory network in mouse lungs with influenza infection using high-dimensional ordinary differential equations.

    Wu, Shuang; Liu, Zhi-Ping; Qiu, Xing; Wu, Hulin

    2014-01-01

    The immune response to viral infection is regulated by an intricate network of many genes and their products. The reverse engineering of gene regulatory networks (GRNs) using mathematical models from time course gene expression data collected after influenza infection is key to our understanding of the mechanisms involved in controlling influenza infection within a host. A five-step pipeline: detection of temporally differentially expressed genes, clustering genes into co-expressed modules, identification of network structure, parameter estimate refinement, and functional enrichment analysis, is developed for reconstructing high-dimensional dynamic GRNs from genome-wide time course gene expression data. Applying the pipeline to the time course gene expression data from influenza-infected mouse lungs, we have identified 20 distinct temporal expression patterns in the differentially expressed genes and constructed a module-based dynamic network using a linear ODE model. Both intra-module and inter-module annotations and regulatory relationships of our inferred network show some interesting findings and are highly consistent with existing knowledge about the immune response in mice after influenza infection. The proposed method is a computationally efficient, data-driven pipeline bridging experimental data, mathematical modeling, and statistical analysis. The application to the influenza infection data elucidates the potentials of our pipeline in providing valuable insights into systematic modeling of complicated biological processes.

  10. BRS invariant stochastic quantization of Einstein gravity

    Nakazawa, Naohito.

    1989-11-01

    We study stochastic quantization of gravity in terms of a BRS invariant canonical operator formalism. By introducing artificially canonical momentum variables for the original field variables, a canonical formulation of stochastic quantization is proposed in the sense that the Fokker-Planck hamiltonian is the generator of the fictitious time translation. Then we show that there exists a nilpotent BRS symmetry in an enlarged phase space of the first-class constrained systems. The phase space is spanned by the dynamical variables, their canonical conjugate momentum variables, Faddeev-Popov ghost and anti-ghost. We apply the general BRS invariant formulation to stochastic quantization of gravity which is described as a second-class constrained system in terms of a pair of Langevin equations coupled with white noises. It is shown that the stochastic action of gravity includes explicitly the De Witt's type superspace metric which leads to a geometrical interpretation of quantum gravity analogous to nonlinear σ-models. (author)

  11. Born-Infeld gravity in Weitzenboeck spacetime

    Ferraro, Rafael; Fiorini, Franco

    2008-01-01

    Using the teleparallel equivalent of general relativity formulated in Weitzenboeck spacetime, we thoroughly explore a kind of Born-Infeld regular gravity leading to second order field equations for the vielbein components. We explicitly solve the equations of motion for two examples: the extended Banados-Teitelboim-Zanelli black hole, which exists even if the cosmological constant is positive, and a cosmological model with matter, where the scale factor is well behaved, thus giving a singularity-free solution.

  12. Instantons in quantum gravity

    Pope, C.N.

    1980-02-01

    The material contained in this thesis is concerned with the functional integral approach to the quantum theory of gravity. It seems to be necessary to work with metrics of positive definite signature (Euclidean metrics) and then analytically continue the result back to the Lorentzian regime. The dominant contributions to the functional integral come from metrics which are stationary points of the action, i.e. classical solutions of the Euclideanized Einstein equations. These are known as Gravitational Instantons. Boundary conditions have to be placed upon the metrics included in the functional integral, and these are determined by the physical problem being considered. Three types of boundary condition have arisen in this context, corresponding to (i) zero temperature physics, and the calculation of particle scattering amplitudes, (ii) finite temperature effects, such as black hole radiance, and (iii) the study of the structure of the gravitational vacuum on Planck length scales. Instantons in the first category are asymptotically flat in all four directions, those in the second are asymptotically flat in three directions and periodic in the fourth, and those which arise in studying the gravitational vacuum are compact without boundaries. Much of the thesis is concerned with considering these various kinds of instanton, and particularly with the effects of their non-trivial topology. One way in which this can be investigated is by means of the various topological index theorems, and these are applied to a variety of situations. Self-dual metrics seem to have particular significance in quantum gravity, and they are discussed in detail. Finally, some recent work on the calculation of the propagation of particles in the gravitational vacuum is described. (author)

  13. Quantum W3 gravity

    Schoutens, K.; van Nieuwenhuizen, P.; State Univ. of New York, Stony Brook, NY

    1991-11-01

    We briefly review some results in the theory of quantum W 3 gravity in the chiral gauge. We compare them with similar results in the analogous but simpler cases of d = 2 induced gauge theories and d = 2 induced gravity

  14. Urine specific gravity test

    ... medlineplus.gov/ency/article/003587.htm Urine specific gravity test To use the sharing features on this page, please enable JavaScript. Urine specific gravity is a laboratory test that shows the concentration ...

  15. Cadiz, California Gravity Data

    National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data (32 records) were gathered by Mr. Seth I. Gutman for AridTech Inc., Denver, Colorado using a Worden Prospector gravity meter. This data base...

  16. Andes 1997 Gravity Data

    National Oceanic and Atmospheric Administration, Department of Commerce — The Central Andes gravity data (6,151 records) were compiled by Professor Gotze and the MIGRA Group. This data base was received in April, 1997. Principal gravity...

  17. DNAG Gravity Data

    National Oceanic and Atmospheric Administration, Department of Commerce — The Decade of North American Geology (DNAG) gravity grid values, spaced at 6 km, were used to produce the Gravity Anomaly Map of North America (1987; scale...

  18. Gravity wave astronomy

    Pinheiro, R.

    1979-01-01

    The properties and production of gravitational radiation are described. The prospects for their detection are considered including the Weber apparatus and gravity-wave telescopes. Possibilities of gravity-wave astronomy are noted

  19. Northern Oklahoma Gravity Data

    National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data (710 records) were compiled by Professor Ahern. This data base was received in June 1992. Principal gravity parameters include latitude,...

  20. Idaho State Gravity Data

    National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data (24,284 records) were compiled by the U. S. Geological Survey. This data base was received on February 23, 1993. Principal gravity...

  1. Equation Chapter 1 Section 1Cross Layer Design for Localization in Large-Scale Underwater Sensor Networks

    Yuanfeng ZHANG

    2014-02-01

    Full Text Available There are many technical challenges for designing large-scale underwater sensor networks, especially the sensor node localization. Although many papers studied for large-scale sensor node localization, previous studies mainly study the location algorithm without the cross layer design for localization. In this paper, by utilizing the network hierarchical structure of underwater sensor networks, we propose a new large-scale underwater acoustic localization scheme based on cross layer design. In this scheme, localization is performed in a hierarchical way, and the whole localization process focused on the physical layer, data link layer and application layer. We increase the pipeline parameters which matched the acoustic channel, added in MAC protocol to increase the authenticity of the large-scale underwater sensor networks, and made analysis of different location algorithm. We conduct extensive simulations, and our results show that MAC layer protocol and the localization algorithm all would affect the result of localization which can balance the trade-off between localization accuracy, localization coverage, and communication cost.

  2. Strings and quantum gravity

    Vega, H.J. de

    1990-01-01

    One of the main challenges in theoretical physics today is the unification of all interactions including gravity. At present, string theories appear as the most promising candidates to achieve such a unification. However, gravity has not completely been incorporated in string theory, many technical and conceptual problems remain and a full quantum theory of gravity is still non-existent. Our aim is to properly understand strings in the context of quantum gravity. Attempts towards this are reviewed. (author)

  3. Acoustic-gravity modons in the atmosphere

    L. Stenflo

    Full Text Available It is shown that the equations governing low-frequency acoustic-gravity waves in a stable stratified atmosphere can have localized dipole-vortex solutions (modons. They propagate in the horizontal direction with a speed that is larger than that of all possible linear internal waves.

  4. Geometric Liouville gravity

    La, H.

    1992-01-01

    A new geometric formulation of Liouville gravity based on the area preserving diffeo-morphism is given and a possible alternative to reinterpret Liouville gravity is suggested, namely, a scalar field coupled to two-dimensional gravity with a curvature constraint

  5. Covariant w∞ gravity

    Bergshoeff, E.; Pope, C.N.; Stelle, K.S.

    1990-01-01

    We discuss the notion of higher-spin covariance in w∞ gravity. We show how a recently proposed covariant w∞ gravity action can be obtained from non-chiral w∞ gravity by making field redefinitions that introduce new gauge-field components with corresponding new gauge transformations.

  6. Induced quantum conformal gravity

    Novozhilov, Y.V.; Vassilevich, D.V.

    1988-11-01

    Quantum gravity is considered as induced by matter degrees of freedom and related to the symmetry breakdown in the low energy region of a non-Abelian gauge theory of fundamental fields. An effective action for quantum conformal gravity is derived where both the gravitational constant and conformal kinetic term are positive. Relation with induced classical gravity is established. (author). 15 refs

  7. Quantum Gravity Phenomenology

    Amelino-Camelia, Giovanni

    2003-01-01

    Comment: 9 pages, LaTex. These notes were prepared while working on an invited contribution to the November 2003 issue of Physics World, which focused on quantum gravity. They intend to give a non-technical introduction (accessible to readers from outside quantum gravity) to "Quantum Gravity Phenomenology"

  8. Gravity is Geometry.

    MacKeown, P. K.

    1984-01-01

    Clarifies two concepts of gravity--those of a fictitious force and those of how space and time may have geometry. Reviews the position of Newton's theory of gravity in the context of special relativity and considers why gravity (as distinct from electromagnetics) lends itself to Einstein's revolutionary interpretation. (JN)

  9. Stochastic Gravity: Theory and Applications

    Hu Bei Lok

    2004-01-01

    Full Text Available Whereas semiclassical gravity is based on the semiclassical Einstein equation with sources given by the expectation value of the stress-energy tensor of quantum fields, stochastic semiclassical gravity is based on the Einstein-Langevin equation, which has in addition sources due to the noise kernel. The noise kernel is the vacuum expectation value of the (operator-valued stress-energy bi-tensor which describes the fluctuations of quantum matter fields in curved spacetimes. In the first part, we describe the fundamentals of this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the stress-energy tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open systems concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise, and decoherence. We then focus on the properties of the stress-energy bi-tensor. We obtain a general expression for the noise kernel of a quantum field defined at two distinct points in an arbitrary curved spacetime as products of covariant derivatives of the quantum field's Green function. In the second part, we describe three applications of stochastic gravity theory. First, we consider metric perturbations in a Minkowski spacetime. We offer an analytical solution of the Einstein-Langevin equation and compute the two-point correlation functions for the linearized Einstein tensor and for the metric perturbations. Second, we discuss structure formation from the stochastic gravity viewpoint, which can go beyond the standard treatment by incorporating the full quantum effect of the inflaton fluctuations. Third, we discuss the backreaction

  10. Estimating Janka hardness from specific gravity for tropical and temperate species

    Michael C. Wiemann; David W. Green

    2007-01-01

    Using mean values for basic (green) specific gravity and Janka side hardness for individual species obtained from the world literature, regression equations were developed to predict side hardness from specific gravity. Statistical and graphical methods showed that the hardness–specific gravity relationship is the same for tropical and temperate hardwoods, but that the...

  11. A Immirzi-like parameter for 3D quantum gravity

    Bonzom, Valentin; Livine, Etera R

    2008-01-01

    We study an Immirzi-like ambiguity in three-dimensional quantum gravity. It shares some features with the Immirzi parameter of four-dimensional loop quantum gravity: it does not affect the equations of motion, but modifies the Poisson brackets and the constraint algebra at the canonical level. We focus on the length operator and show how to define it through non-commuting fluxes. We compute its spectrum and show the effect of this Immirzi-like ambiguity. Finally, we extend these considerations to 4D gravity and show how the different topological modifications of the action affect the canonical structure of loop quantum gravity

  12. Noether symmetry approach in f(G,T) gravity

    Shamir, M.F.; Ahmad, Mushtaq [National University of Computer and Emerging Sciences, Lahore Campus (Pakistan)

    2017-01-15

    We explore the recently introduced modified Gauss-Bonnet gravity (Sharif and Ikram in Eur Phys J C 76:640, 2016), f(G,T) pragmatic with G, the Gauss-Bonnet term, and T, the trace of the energy-momentum tensor. Noether symmetry approach has been used to develop some cosmologically viable f(G,T) gravity models. The Noether equations of modified gravity are reported for flat FRW universe. Two specific models have been studied to determine the conserved quantities and exact solutions. In particular, the well known deSitter solution is reconstructed for some specific choice of f(G,T) gravity model. (orig.)

  13. Exploring plane-symmetric solutions in f(R) gravity

    Shamir, M. F., E-mail: farasat.shamir@nu.edu.pk [National University of Computer and Emerging Sciences, Department of Sciences and Humanities (Pakistan)

    2016-02-15

    The modified theories of gravity, especially the f(R) gravity, have attracted much attention in the last decade. This paper is devoted to exploring plane-symmetric solutions in the context of metric f(R) gravity. We extend the work on static plane-symmetric vacuum solutions in f(R) gravity already available in the literature [1, 2]. The modified field equations are solved using the assumptions of both constant and nonconstant scalar curvature. Some well-known solutions are recovered with power-law and logarithmic forms of f(R) models.

  14. Classical geometrical interpretation of ghost fields and anomalies in Yang-Mills theory and quantum gravity

    Thierry-Mieg, J.

    1985-01-01

    This paper discusses the reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity

  15. Classical geometrical interpretation of ghost fields and anomalies in Yang-Mills theory and quantum gravity

    Thierry-Mieg, J.

    1985-01-01

    The reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity

  16. Constraints on modified gravity models from white dwarfs

    Banerjee, Srimanta; Singh, Tejinder P. [Department of Astronomy and Astrophysics, Tata Institute of Fundamental Research, Mumbai 400005, Maharashtra (India); Shankar, Swapnil, E-mail: srimanta.banerjee@tifr.res.in, E-mail: swapnil.shankar@cbs.ac.in, E-mail: tpsingh@tifr.res.in [Department of Physics, Centre for Excellence in Basic Sciences, Mumbai 400098, Maharashtra (India)

    2017-10-01

    Modified gravity theories can introduce modifications to the Poisson equation in the Newtonian limit. As a result, we expect to see interesting features of these modifications inside stellar objects. White dwarf stars are one of the most well studied stars in stellar astrophysics. We explore the effect of modified gravity theories inside white dwarfs. We derive the modified stellar structure equations and solve them to study the mass-radius relationships for various modified gravity theories. We also constrain the parameter space of these theories from observations.

  17. Variation of the gravity acceleration with the latitude and altitude

    Wilson Lopes

    2009-01-01

    Full Text Available The propose of this work is an equation for the module of the acceleration vector of the gravity, varying with the latitude and altitude. For this purpose, the following values of the gravity acceleration were used, at the sea level: in the equator, g0 = 9,7803 m/s2, and in the latitude of 450, gP = 9,8062 m/s2. The terrestrial profile were assumed as being a revolution ellipsoid, flattened in the poles, and the acceleration of the gravity varying with the altitude, at sea level, was considered dependent of the latitude too.

  18. Scales of gravity

    Dvali, Gia; Kolanovic, Marko; Nitti, Francesco; Gabadadze, Gregory

    2002-01-01

    We propose a framework in which the quantum gravity scale can be as low as 10 -3 eV. The key assumption is that the standard model ultraviolet cutoff is much higher than the quantum gravity scale. This ensures that we observe conventional weak gravity. We construct an explicit brane-world model in which the brane-localized standard model is coupled to strong 5D gravity of infinite-volume flat extra space. Because of the high ultraviolet scale, the standard model fields generate a large graviton kinetic term on the brane. This kinetic term 'shields' the standard model from the strong bulk gravity. As a result, an observer on the brane sees weak 4D gravity up to astronomically large distances beyond which gravity becomes five dimensional. Modeling quantum gravity above its scale by the closed string spectrum we show that the shielding phenomenon protects the standard model from an apparent phenomenological catastrophe due to the exponentially large number of light string states. The collider experiments, astrophysics, cosmology and gravity measurements independently point to the same lower bound on the quantum gravity scale, 10 -3 eV. For this value the model has experimental signatures both for colliders and for submillimeter gravity measurements. Black holes reveal certain interesting properties in this framework

  19. The role of satellite altimetry in gravity field modelling in coastal areas

    Andersen, Ole Baltazar; Knudsen, Per

    2000-01-01

    global uniform gravity information with very high resolution, and these global marine gravity fields are registered on a two by two minute grid corresponding to 4 by 4 kilometres at the equator. In this presentation several coastal complications in deriving the marine gravity field from satellite...... altimetry will be investigated using the KMS98 gravity field. Comparison with other sources of gravity field information like airborne and marine gravity observations will be carried out and two fundamentally different test areas (Azores and Skagerak) will be studied to investigated the different role...

  20. Emergent universe with wormholes in massive gravity

    Paul, B. C.; Majumdar, A. S.

    2018-03-01

    An emergent universe (EU) scenario is proposed to obtain a universe free from big-bang singularity. In this framework the present universe emerged from a static Einstein universe phase in the infinite past. A flat EU scenario is found to exist in Einstein’s gravity with a non-linear equation of state (EoS). It has been shown subsequently that a physically realistic EU model can be obtained considering cosmic fluid composed of interacting fluids with a non-linear equation of state. It results a viable cosmological model accommodating both early inflation and present accelerating phases. In the present paper, the origin of an initial static Einstein universe needed in the EU model is explored in a massive gravity theory which subsequently emerged to be a dynamically evolving universe. A new gravitational instanton solution in a flat universe is obtained in the massive gravity theory which is a dynamical wormhole that might play an important role in realizing the origin of the initial state of the emergent universe. The emergence of a Lorentzian universe from a Euclidean gravity is understood by a Wick rotation τ = i t . A universe with radiation at the beginning finally transits into the present observed universe with a non-linear EoS as the interactions among the fluids set in. Thus a viable flat EU scenario where the universe stretches back into time infinitely, with no big bang is permitted in a massive gravity.

  1. Nonperturbative quantum gravity

    Ambjørn, J.; Görlich, A.; Jurkiewicz, J.; Loll, R.

    2012-01-01

    Asymptotic safety describes a scenario in which general relativity can be quantized as a conventional field theory, despite being nonrenormalizable when expanding it around a fixed background geometry. It is formulated in the framework of the Wilsonian renormalization group and relies crucially on the existence of an ultraviolet fixed point, for which evidence has been found using renormalization group equations in the continuum. “Causal Dynamical Triangulations” (CDT) is a concrete research program to obtain a nonperturbative quantum field theory of gravity via a lattice regularization, and represented as a sum over spacetime histories. In the Wilsonian spirit one can use this formulation to try to locate fixed points of the lattice theory and thereby provide independent, nonperturbative evidence for the existence of a UV fixed point. We describe the formalism of CDT, its phase diagram, possible fixed points and the “quantum geometries” which emerge in the different phases. We also argue that the formalism may be able to describe a more general class of Hořava–Lifshitz gravitational models.

  2. Einstein gravity emerging from quantum weyl gravity

    Zee, A.

    1983-01-01

    We advocate a conformal invariant world described by the sum of the Weyl, Dirac, and Yang-Mills action. Quantum fluctuations bring back Einstein gravity so that the long-distance phenomenology is as observed. Formulas for the induced Newton's constant and Eddington's constant are derived in quantized Weyl gravity. We show that the analogue of the trace anomaly for the Weyl action is structurally similar to that for the Yang-Mills action

  3. A family of metric gravities

    Shuler, Robert

    2018-04-01

    The goal of this paper is to take a completely fresh approach to metric gravity, in which the metric principle is strictly adhered to but its properties in local space-time are derived from conservation principles, not inferred from a global field equation. The global field strength variation then gains some flexibility, but only in the regime of very strong fields (2nd-order terms) whose measurement is now being contemplated. So doing provides a family of similar gravities, differing only in strong fields, which could be developed into meaningful verification targets for strong fields after the manner in which far-field variations were used in the 20th century. General Relativity (GR) is shown to be a member of the family and this is demonstrated by deriving the Schwarzschild metric exactly from a suitable field strength assumption. The method of doing so is interesting in itself because it involves only one differential equation rather than the usual four. Exact static symmetric field solutions are also given for one pedagogical alternative based on potential, and one theoretical alternative based on inertia, and the prospects of experimentally differentiating these are analyzed. Whether the method overturns the conventional wisdom that GR is the only metric theory of gravity and that alternatives must introduce additional interactions and fields is somewhat semantical, depending on whether one views the field strength assumption as a field and whether the assumption that produces GR is considered unique in some way. It is of course possible to have other fields, and the local space-time principle can be applied to field gravities which usually are weak-field approximations having only time dilation, giving them the spatial factor and promoting them to full metric theories. Though usually pedagogical, some of them are interesting from a quantum gravity perspective. Cases are noted where mass measurement errors, or distributions of dark matter, can cause one

  4. The covariant formulation of f ( T ) gravity

    Krššák, Martin; Saridakis, Emmanuel N

    2016-01-01

    We show that the well-known problem of frame dependence and violation of local Lorentz invariance in the usual formulation of f ( T ) gravity is a consequence of neglecting the role of spin connection. We re-formulate f ( T ) gravity starting from, instead of the ‘pure tetrad’ teleparallel gravity, the covariant teleparallel gravity, using both the tetrad and the spin connection as dynamical variables, resulting in a fully covariant, consistent, and frame-independent version of f ( T ) gravity, which does not suffer from the notorious problems of the usual, pure tetrad, f ( T ) theory. We present the method to extract solutions for the most physically important cases, such as the Minkowski, the Friedmann–Robertson–Walker (FRW) and the spherically symmetric ones. We show that in covariant f ( T ) gravity we are allowed to use an arbitrary tetrad in an arbitrary coordinate system along with the corresponding spin connection, resulting always in the same physically relevant field equations. (paper)

  5. Focus on quantum Einstein gravity Focus on quantum Einstein gravity

    Ambjorn, Jan; Reuter, Martin; Saueressig, Frank

    2012-09-01

    The gravitational asymptotic safety program summarizes the attempts to construct a consistent and predictive quantum theory of gravity within Wilson's generalized framework of renormalization. Its key ingredient is a non-Gaussian fixed point of the renormalization group flow which controls the behavior of the theory at trans-Planckian energies and renders gravity safe from unphysical divergences. Provided that the fixed point comes with a finite number of ultraviolet-attractive (relevant) directions, this construction gives rise to a consistent quantum field theory which is as predictive as an ordinary, perturbatively renormalizable one. This opens up the exciting possibility of establishing quantum Einstein gravity as a fundamental theory of gravity, without introducing supersymmetry or extra dimensions, and solely based on quantization techniques that are known to work well for the other fundamental forces of nature. While the idea of gravity being asymptotically safe was proposed by Steven Weinberg more than 30 years ago [1], the technical tools for investigating this scenario only emerged during the last decade. Here a key role is played by the exact functional renormalization group equation for gravity, which allows the construction of non-perturbative approximate solutions for the RG-flow of the gravitational couplings. Most remarkably, all solutions constructed to date exhibit a suitable non-Gaussian fixed point, lending strong support to the asymptotic safety conjecture. Moreover, the functional renormalization group also provides indications that the central idea of a non-Gaussian fixed point providing a safe ultraviolet completion also carries over to more realistic scenarios where gravity is coupled to a suitable matter sector like the standard model. These theoretical successes also triggered a wealth of studies focusing on the consequences of asymptotic safety in a wide range of phenomenological applications covering the physics of black holes, early

  6. Hill functions for stochastic gene regulatory networks from master equations with split nodes and time-scale separation

    Lipan, Ovidiu; Ferwerda, Cameron

    2018-02-01

    The deterministic Hill function depends only on the average values of molecule numbers. To account for the fluctuations in the molecule numbers, the argument of the Hill function needs to contain the means, the standard deviations, and the correlations. Here we present a method that allows for stochastic Hill functions to be constructed from the dynamical evolution of stochastic biocircuits with specific topologies. These stochastic Hill functions are presented in a closed analytical form so that they can be easily incorporated in models for large genetic regulatory networks. Using a repressive biocircuit as an example, we show by Monte Carlo simulations that the traditional deterministic Hill function inaccurately predicts time of repression by an order of two magnitudes. However, the stochastic Hill function was able to capture the fluctuations and thus accurately predicted the time of repression.

  7. Eddington's theory of gravity and its progeny.

    Bañados, Máximo; Ferreira, Pedro G

    2010-07-02

    We resurrect Eddington's proposal for the gravitational action in the presence of a cosmological constant and extend it to include matter fields. We show that the Newton-Poisson equation is modified in the presence of sources and that charged black holes show great similarities with those arising in Born-Infeld electrodynamics coupled to gravity. When we consider homogeneous and isotropic space-times, we find that there is a minimum length (and maximum density) at early times, clearly pointing to an alternative theory of the big bang. We thus argue that the modern formulation of Eddington's theory, Born-Infeld gravity, presents us with a novel, nonsingular description of the Universe.

  8. Lower dimensional gravity

    Brown, J.D.

    1988-01-01

    This book addresses the subject of gravity theories in two and three spacetime dimensions. The prevailing philosophy is that lower dimensional models of gravity provide a useful arena for developing new ideas and insights, which are applicable to four dimensional gravity. The first chapter consists of a comprehensive introduction to both two and three dimensional gravity, including a discussion of their basic structures. In the second chapter, the asymptotic structure of three dimensional Einstein gravity with a negative cosmological constant is analyzed. The third chapter contains a treatment of the effects of matter sources in classical two dimensional gravity. The fourth chapter gives a complete analysis of particle pair creation by electric and gravitational fields in two dimensions, and the resulting effect on the cosmological constant

  9. Anomalies and gravity

    Mielke, Eckehard W.

    2006-01-01

    Anomalies in Yang-Mills type gauge theories of gravity are reviewed. Particular attention is paid to the relation between the Dirac spin, the axial current j5 and the non-covariant gauge spin C. Using diagrammatic techniques, we show that only generalizations of the U(1)- Pontrjagin four-form F and F = dC arise in the chiral anomaly, even when coupled to gravity. Implications for Ashtekar's canonical approach to quantum gravity are discussed

  10. Gravity inversion code

    Burkhard, N.R.

    1979-01-01

    The gravity inversion code applies stabilized linear inverse theory to determine the topography of a subsurface density anomaly from Bouguer gravity data. The gravity inversion program consists of four source codes: SEARCH, TREND, INVERT, and AVERAGE. TREND and INVERT are used iteratively to converge on a solution. SEARCH forms the input gravity data files for Nevada Test Site data. AVERAGE performs a covariance analysis on the solution. This document describes the necessary input files and the proper operation of the code. 2 figures, 2 tables

  11. Characteristics of gravity fields in the Jinggu M6.6 earthquake

    Sun Shaoan

    2014-11-01

    Full Text Available Based on the study of high-precision gravity data obtained from recent studies and the regional gravity network for Yunnan province, a variation in the regional gravity field was identified before the occurrence of the Yunnan Jinggu M6. 6 earthquake.

  12. New 'phase' of quantum gravity.

    Wang, Charles H-T

    2006-12-15

    The emergence of loop quantum gravity over the past two decades has stimulated a great resurgence of interest in unifying general relativity and quantum mechanics. Among a number of appealing features of this approach is the intuitive picture of quantum geometry using spin networks and powerful mathematical tools from gauge field theory. However, the present form of loop quantum gravity suffers from a quantum ambiguity, owing to the presence of a free (Barbero-Immirzi) parameter. Following the recent progress on conformal decomposition of gravitational fields, we present a new phase space for general relativity. In addition to spin-gauge symmetry, the new phase space also incorporates conformal symmetry making the description parameter free. The Barbero-Immirzi ambiguity is shown to occur only if the conformal symmetry is gauge fixed prior to quantization. By withholding its full symmetries, the new phase space offers a promising platform for the future development of loop quantum gravity. This paper aims to provide an exposition, at a reduced technical level, of the above theoretical advances and their background developments. Further details are referred to cited references.

  13. Entropy of Egypt's virtual water trade gravity field

    Karakatsanis, Georgios; Bierbach, Sandra

    2016-04-01

    The study investigates the entropy of Egypt's virtual water trade gravity distribution, in order to provide a chart of Egypt's embodied water balance in agricultural trade, in relation to distances with its major counterparties. Moreover, our calculations on the amount of the embodied water traded between Egypt and each of its partners take place according to a combination of available data on the blue, green and grey water footprints as well as the Food and Agriculture Organization (FAO) database of traded amounts per crop type. A study on the virtual water trade gravity, enables us to enrich former related studies (Fracasso 2014; Fracasso, Sartori and Schiavo 2014) via examining Egypt's water supply dependence on the Nile River and if comparative advantages -purely from the side of water quantities- can be identified via recognizing which water footprint categories are particularly high. Additionally, this methodology can comprise -from a fundamental level- a guide for revealing the importance of water footprint types for Egypt's agricultural sector; hence, Egypt's potential comparative advantages, as far as quantitative water endowments are exclusively concerned (without consideration of water or crop prices). Although it is pointed out very correctly by various authors (Antonelli and Sartori 2014) that the virtual water trade concept does not incorporate many important aspects of water supply -such as heavy water price subsidizing- to be used accurately for the identification of comparative advantages, we consider that the purely quantitative examination can provide strong fundamental indications -especially for green and grey water footprints, which are hypothesized to be less sensitive to subsidizing. In overall, this effect can very well provide a primary indication on the organization of the global alimentation trade network (Yang et al. 2006). The gravity equation used contains water footprint data for the 15 top traded crops and the distances for Egypt

  14. Modeling of gravity-imbibition and gravity-drainage processes: Analytic and numerical solutions

    Bech, N.; Jensen, O.K.; Nielsen, B.

    1991-01-01

    A matrix/fracture exchange model for a fractured reservoir simulator is described. Oil/water imbibition is obtained from a diffusion equation with water saturation as the dependent variable. Gas/oil gravity drainage and imbibition are calculated by taking into account the vertical saturation...... distribution in the matrix blocks....

  15. Covariant formulation of scalar-torsion gravity

    Hohmann, Manuel; Järv, Laur; Ualikhanova, Ulbossyn

    2018-05-01

    We consider a generalized teleparallel theory of gravitation, where the action contains an arbitrary function of the torsion scalar and a scalar field, f (T ,ϕ ) , thus encompassing the cases of f (T ) gravity and a nonminimally coupled scalar field as subclasses. The action is manifestly Lorentz invariant when besides the tetrad one allows for a flat but nontrivial spin connection. We derive the field equations and demonstrate how the antisymmetric part of the tetrad equations is automatically satisfied when the spin connection equation holds. The spin connection equation is a vital part of the covariant formulation, since it determines the spin connection associated with a given tetrad. We discuss how the spin connection equation can be solved in general and provide the cosmological and spherically symmetric examples. Finally, we generalize the theory to an arbitrary number of scalar fields.

  16. General relativity and gauge gravity theories of higher order

    Konopleva, N.P.

    1998-01-01

    It is a short review of today's gauge gravity theories and their relations with Einstein General Relativity. The conceptions of construction of the gauge gravity theories with higher derivatives are analyzed. GR is regarded as the gauge gravity theory corresponding to the choice of G ∞4 as the local gauge symmetry group and the symmetrical tensor of rank two g μν as the field variable. Using the mathematical technique, single for all fundamental interactions (namely variational formalism for infinite Lie groups), we can obtain Einstein's theory as the gauge theory without any changes. All other gauge approaches lead to non-Einstein theories of gravity. But above-mentioned mathematical technique permits us to construct the gauge gravity theory of higher order (for instance SO (3,1)-gravity) so that all vacuum solutions of Einstein equations are the solutions of the SO (3,1)-gravity theory. The structure of equations of SO(3,1)-gravity becomes analogous to Weeler-Misner geometrodynamics one

  17. SIMULTANEOUS DIFFERENTIAL EQUATION COMPUTER

    Collier, D.M.; Meeks, L.A.; Palmer, J.P.

    1960-05-10

    A description is given for an electronic simulator for a system of simultaneous differential equations, including nonlinear equations. As a specific example, a homogeneous nuclear reactor system including a reactor fluid, heat exchanger, and a steam boiler may be simulated, with the nonlinearity resulting from a consideration of temperature effects taken into account. The simulator includes three operational amplifiers, a multiplier, appropriate potential sources, and interconnecting R-C networks.

  18. Asymptomatic freedom in renormalisable gravity and supergravity

    Fradkin, E.S.; Tseytlin, A.A.

    1984-01-01

    This chapter demonstrates that renormalizable supergravity, which is a superextension of renormalizable quantum gravity, can be the basis for a natural ''induced supergravity'' theory. A perturbatively operational unified theory is needed for a description of the early stages of the Universe, and renormalizable quantum gravity is well suited for unification with the renormalizable Grand Unified Models of matter. Topics considered include one-loop counter-terms and renormalization group (RG) equations for pure renormalizable gravity; the consequences of asymptotic freedom; the inclusion of matter; conformal supergravities; and renormalizable supergravity models. It is concluded that the presented lagrangian, which contains a locally superconformal extension of the Yang-Mills and massless spinor lagrangians and the conformal supergravity term, shows that conformal supergravity may play an important role in a fundamental theory

  19. Newton-Cartan gravity and torsion

    Bergshoeff, Eric; Chatzistavrakidis, Athanasios; Romano, Luca; Rosseel, Jan

    2017-10-01

    We compare the gauging of the Bargmann algebra, for the case of arbitrary torsion, with the result that one obtains from a null-reduction of General Relativity. Whereas the two procedures lead to the same result for Newton-Cartan geometry with arbitrary torsion, the null-reduction of the Einstein equations necessarily leads to Newton-Cartan gravity with zero torsion. We show, for three space-time dimensions, how Newton-Cartan gravity with arbitrary torsion can be obtained by starting from a Schrödinger field theory with dynamical exponent z = 2 for a complex compensating scalar and next coupling this field theory to a z = 2 Schrödinger geometry with arbitrary torsion. The latter theory can be obtained from either a gauging of the Schrödinger algebra, for arbitrary torsion, or from a null-reduction of conformal gravity.

  20. Establishment of 2000 National Geodetic Control Network of China and It’s Technological Progress

    CHEN Junyong

    2007-02-01

    geocenter high precision geodesy control network in first time. 2. The function model of GPS network data processing is constructed, which is suitable for the characters of our country geodesy control network. The adjustment reference is united and some system errors are eliminated by using IGS stations as reference stations and rotation, scale parameters. 3. The contributions of each sub network are rational adjusted by using rational random model, variance component estimation in 2000 National GPS Geodetic Network adjustment. 4. The robust estimation, variance component estimation and function model including system error compensate parameters are adopted for GPS network data processing in the same time. The variance component estimation values of each sub network are avoided of the system error and gross error influence 5. The astronomical measurement control data of our country in the 20th century is unified reprocessing and the advanced astronomical measurement control data are obtained, which are corresponding to the international FK5 ephemeris. 6. The 50 thousands of three dimensional geo-center coordinate of our country geodetic stations are obtained by the combining processing the data of 2000 National GPS Geodetic Network and national astro-geodetic network. 7. The problem of quick calculating the huge normal equation in the personal computer is solved, where 200 thousands of unknown parameters are estimated using 500 thousands of observation data. 8. The observation weights of different kind of data are rationally determined by adopted the strict variance component estimation method in the huge network adjustment. 9. The national gravity fundamental network is extended to the South China Sea and Hong Kong area in the first time. And the gravity reference constructions of China west and northeast area are strengthen. A high precise, covering whole country and united reference gravity network is constructed. 10. The system error and reference error of relative

  1. Interior Alaska Bouguer Gravity Anomaly

    National Oceanic and Atmospheric Administration, Department of Commerce — A 1 kilometer Complete Bouguer Anomaly gravity grid of interior Alaska. Only those grid cells within 10 kilometers of a gravity data point have gravity values....

  2. Gravity measurements in southeastern Alaska reveal negative gravity rate of change caused by glacial isostatic adjustment

    Sun, W.; Miura, S.; Sato, T.; Sugano, T.; Freymueller, J.; Kaufman, M.; Larsen, C. F.; Cross, R.; Inazu, D.

    2010-12-01

    For the past 300 years, southeastern Alaska has undergone rapid ice-melting and land uplift attributable to global warming. Corresponding crustal deformation (3 cm/yr) caused by the Little Ice Age retreat is detectable with modern geodetic techniques such as GPS and tidal gauge measurements. Geodetic deformation provides useful information for assessing ice-melting rates, global warming effects, and subcrustal viscosity. Nevertheless, integrated geodetic observations, including gravity measurements, are important. To detect crustal deformation caused by glacial isostatic adjustment and to elucidate the viscosity structure in southeastern Alaska, Japanese and U.S. researchers began a joint 3-year project in 2006 using GPS, Earth tide, and absolute gravity measurements. A new absolute gravity network was established, comprising five sites around Glacier Bay, near Juneau, Alaska. This paper reports the network's gravity measurements during 2006-2008. The bad ocean model in this area hindered ocean loading correction: Large tidal residuals remain in the observations. Accurate tidal correction necessitated on-site tidal observation. Results show high observation precision for all five stations: day ice thickness changes. A gravity bias of about -13.2 ± 0.1 mGal exists between the Potsdam and current FG5 gravity data.

  3. Consistency of orthodox gravity

    Bellucci, S. [INFN, Frascati (Italy). Laboratori Nazionali di Frascati; Shiekh, A. [International Centre for Theoretical Physics, Trieste (Italy)

    1997-01-01

    A recent proposal for quantizing gravity is investigated for self consistency. The existence of a fixed-point all-order solution is found, corresponding to a consistent quantum gravity. A criterion to unify couplings is suggested, by invoking an application of their argument to more complex systems.

  4. Generalized pure Lovelock gravity

    Concha, Patrick; Rodríguez, Evelyn

    2017-11-01

    We present a generalization of the n-dimensional (pure) Lovelock Gravity theory based on an enlarged Lorentz symmetry. In particular, we propose an alternative way to introduce a cosmological term. Interestingly, we show that the usual pure Lovelock gravity is recovered in a matter-free configuration. The five and six-dimensional cases are explicitly studied.

  5. Generalized pure Lovelock gravity

    Patrick Concha

    2017-11-01

    Full Text Available We present a generalization of the n-dimensional (pure Lovelock Gravity theory based on an enlarged Lorentz symmetry. In particular, we propose an alternative way to introduce a cosmological term. Interestingly, we show that the usual pure Lovelock gravity is recovered in a matter-free configuration. The five and six-dimensional cases are explicitly studied.

  6. Circulation-based Modeling of Gravity Currents

    Meiburg, E. H.; Borden, Z.

    2013-05-01

    Atmospheric and oceanic flows driven by predominantly horizontal density differences, such as sea breezes, thunderstorm outflows, powder snow avalanches, and turbidity currents, are frequently modeled as gravity currents. Efforts to develop simplified models of such currents date back to von Karman (1940), who considered a two-dimensional gravity current in an inviscid, irrotational and infinitely deep ambient. Benjamin (1968) presented an alternative model, focusing on the inviscid, irrotational flow past a gravity current in a finite-depth channel. More recently, Shin et al. (2004) proposed a model for gravity currents generated by partial-depth lock releases, considering a control volume that encompasses both fronts. All of the above models, in addition to the conservation of mass and horizontal momentum, invoke Bernoulli's law along some specific streamline in the flow field, in order to obtain a closed system of equations that can be solved for the front velocity as function of the current height. More recent computational investigations based on the Navier-Stokes equations, on the other hand, reproduce the dynamics of gravity currents based on the conservation of mass and momentum alone. We propose that it should therefore be possible to formulate a fundamental gravity current model without invoking Bernoulli's law. The talk will show that the front velocity of gravity currents can indeed be predicted as a function of their height from mass and momentum considerations alone, by considering the evolution of interfacial vorticity. This approach does not require information on the pressure field and therefore avoids the need for an energy closure argument such as those invoked by the earlier models. Predictions by the new theory are shown to be in close agreement with direct numerical simulation results. References Von Karman, T. 1940 The engineer grapples with nonlinear problems, Bull. Am. Math Soc. 46, 615-683. Benjamin, T.B. 1968 Gravity currents and related

  7. Gravity Field Parameter Estimation Using QR Factorization

    Klokocnik, J.; Wagner, C. A.; McAdoo, D.; Kostelecky, J.; Bezdek, A.; Novak, P.; Gruber, C.; Marty, J.; Bruinsma, S. L.; Gratton, S.; Balmino, G.; Baboulin, M.

    2007-12-01

    This study compares the accuracy of the estimated geopotential coefficients when QR factorization is used instead of the classical method applied at our institute, namely the generation of normal equations that are solved by means of Cholesky decomposition. The objective is to evaluate the gain in numerical precision, which is obtained at considerable extra cost in terms of computer resources. Therefore, a significant increase in precision must be realized in order to justify the additional cost. Numerical simulations were done in order to examine the performance of both solution methods. Reference gravity gradients were simulated, using the EIGEN-GL04C gravity field model to degree and order 300, every 3 seconds along a near-circular, polar orbit at 250 km altitude. The simulation spanned a total of 60 days. A polar orbit was selected in this simulation in order to avoid the 'polar gap' problem, which causes inaccurate estimation of the low-order spherical harmonic coefficients. Regularization is required in that case (e.g., the GOCE mission), which is not the subject of the present study. The simulated gravity gradients, to which white noise was added, were then processed with the GINS software package, applying EIGEN-CG03 as the background gravity field model, followed either by the usual normal equation computation or using the QR approach for incremental linear least squares. The accuracy assessment of the gravity field recovery consists in computing the median error degree-variance spectra, accumulated geoid errors, geoid errors due to individual coefficients, and geoid errors calculated on a global grid. The performance, in terms of memory usage, required disk space, and CPU time, of the QR versus the normal equation approach is also evaluated.

  8. New Spin Foam Models of Quantum Gravity

    Miković, A.

    We give a brief and a critical review of the Barret-Crane spin foam models of quantum gravity. Then we describe two new spin foam models which are obtained by direct quantization of General Relativity and do not have some of the drawbacks of the Barret-Crane models. These are the model of spin foam invariants for the embedded spin networks in loop quantum gravity and the spin foam model based on the integration of the tetrads in the path integral for the Palatini action.

  9. f(Lovelock) theories of gravity

    Bueno, Pablo; Cano, Pablo A.; Óscar Lasso, A.; Ramírez, Pedro F.

    2016-04-01

    f(Lovelock) gravities are simple generalizations of the usual f( R) and Lovelock theories in which the gravitational action depends on some arbitrary function of the corresponding dimensionally-extended Euler densities. In this paper we study several aspects of these theories in general dimensions. We start by identifying the generalized boundary term which makes the gravitational variational problem well-posed. Then, we show that these theories are equivalent to certain scalar-tensor theories and how this relation is characterized by the Hessian of f. We also study the linearized equations of the theory on general maximally symmetric backgrounds. Remarkably, we find that these theories do not propagate the usual ghost-like massive gravitons characteristic of higher-derivative gravities on such backgrounds. In some non-trivial cases, the additional scalar associated to the trace of the metric perturbation is also absent, being the usual graviton the only dynamical field. In those cases, the linearized equations are exactly the same as in Einstein gravity up to an overall factor, making them appealing as holographic toy models. We also find constraints on the couplings of a broad family of five-dimensional f(Lovelock) theories using holographic entanglement entropy. Finally, we construct new analytic asymptotically flat and AdS/dS black hole solutions for some classes of f(Lovelock) gravities in various dimensions.

  10. f(Lovelock) theories of gravity

    Bueno, Pablo; Cano, Pablo A.; Óscar, Lasso A.; Ramírez, Pedro F.

    2016-01-01

    f(Lovelock) gravities are simple generalizations of the usual f(R) and Lovelock theories in which the gravitational action depends on some arbitrary function of the corresponding dimensionally-extended Euler densities. In this paper we study several aspects of these theories in general dimensions. We start by identifying the generalized boundary term which makes the gravitational variational problem well-posed. Then, we show that these theories are equivalent to certain scalar-tensor theories and how this relation is characterized by the Hessian of f. We also study the linearized equations of the theory on general maximally symmetric backgrounds. Remarkably, we find that these theories do not propagate the usual ghost-like massive gravitons characteristic of higher-derivative gravities on such backgrounds. In some non-trivial cases, the additional scalar associated to the trace of the metric perturbation is also absent, being the usual graviton the only dynamical field. In those cases, the linearized equations are exactly the same as in Einstein gravity up to an overall factor, making them appealing as holographic toy models. We also find constraints on the couplings of a broad family of five-dimensional f(Lovelock) theories using holographic entanglement entropy. Finally, we construct new analytic asymptotically flat and AdS/dS black hole solutions for some classes of f(Lovelock) gravities in various dimensions.

  11. Newtonian hydrodynamic equations with relativistic pressure and velocity

    Hwang, Jai-chan [Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 702-701 (Korea, Republic of); Noh, Hyerim [Korea Astronomy and Space Science Institute, Daejeon 305-348 (Korea, Republic of); Fabris, Júlio; Piattella, Oliver F.; Zimdahl, Winfried, E-mail: jchan@knu.ac.kr, E-mail: hr@kasi.re.kr, E-mail: fabris@pq.cnpq.br, E-mail: oliver.piattella@pq.cnpq.br, E-mail: winfried.zimdahl@pq.cnpq.br [Departamento de Fisica, Universidade Federal do Espirito Santo, Vitória (Brazil)

    2016-07-01

    We present a new approximation to include fully general relativistic pressure and velocity in Newtonian hydrodynamics. The energy conservation, momentum conservation and two Poisson's equations are consistently derived from Einstein's gravity in the zero-shear gauge assuming weak gravity and action-at-a-distance limit. The equations show proper special relativity limit in the absence of gravity. Our approximation is complementary to the post-Newtonian approximation and the equations are valid in fully nonlinear situations.

  12. Einstein gravity with torsion induced by the scalar field

    Özçelik, H. T.; Kaya, R.; Hortaçsu, M.

    2018-06-01

    We couple a conformal scalar field in (2+1) dimensions to Einstein gravity with torsion. The field equations are obtained by a variational principle. We could not solve the Einstein and Cartan equations analytically. These equations are solved numerically with 4th order Runge-Kutta method. From the numerical solution, we make an ansatz for the rotation parameter in the proposed metric, which gives an analytical solution for the scalar field for asymptotic regions.

  13. Neutron stars structure in the context of massive gravity

    Hendi, S.H.; Bordbar, G.H.; Panah, B. Eslam; Panahiyan, S., E-mail: hendi@shirazu.ac.ir, E-mail: ghbordbar@shirazu.ac.ir, E-mail: behzad.eslampanah@gmail.com, E-mail: sh.panahiyan@gmail.com [Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz 71454 (Iran, Islamic Republic of)

    2017-07-01

    Motivated by the recent interests in spin−2 massive gravitons, we study the structure of neutron star in the context of massive gravity. The modifications of TOV equation in the presence of massive gravity are explored in 4 and higher dimensions. Next, by considering the modern equation of state for the neutron star matter (which is extracted by the lowest order constrained variational (LOCV) method with the AV18 potential), different physical properties of the neutron star (such as Le Chatelier's principle, stability and energy conditions) are investigated. It is shown that consideration of the massive gravity has specific contributions into the structure of neutron star and introduces new prescriptions for the massive astrophysical objects. The mass-radius relation is examined and the effects of massive gravity on the Schwarzschild radius, average density, compactness, gravitational redshift and dynamical stability are studied. Finally, a relation between mass and radius of neutron star versus the Planck mass is extracted.

  14. Neutron stars structure in the context of massive gravity

    Hendi, S. H.; Bordbar, G. H.; Eslam Panah, B.; Panahiyan, S.

    2017-07-01

    Motivated by the recent interests in spin-2 massive gravitons, we study the structure of neutron star in the context of massive gravity. The modifications of TOV equation in the presence of massive gravity are explored in 4 and higher dimensions. Next, by considering the modern equation of state for the neutron star matter (which is extracted by the lowest order constrained variational (LOCV) method with the AV18 potential), different physical properties of the neutron star (such as Le Chatelier's principle, stability and energy conditions) are investigated. It is shown that consideration of the massive gravity has specific contributions into the structure of neutron star and introduces new prescriptions for the massive astrophysical objects. The mass-radius relation is examined and the effects of massive gravity on the Schwarzschild radius, average density, compactness, gravitational redshift and dynamical stability are studied. Finally, a relation between mass and radius of neutron star versus the Planck mass is extracted.

  15. Neutron stars structure in the context of massive gravity

    Hendi, S.H.; Bordbar, G.H.; Panah, B. Eslam; Panahiyan, S.

    2017-01-01

    Motivated by the recent interests in spin−2 massive gravitons, we study the structure of neutron star in the context of massive gravity. The modifications of TOV equation in the presence of massive gravity are explored in 4 and higher dimensions. Next, by considering the modern equation of state for the neutron star matter (which is extracted by the lowest order constrained variational (LOCV) method with the AV18 potential), different physical properties of the neutron star (such as Le Chatelier's principle, stability and energy conditions) are investigated. It is shown that consideration of the massive gravity has specific contributions into the structure of neutron star and introduces new prescriptions for the massive astrophysical objects. The mass-radius relation is examined and the effects of massive gravity on the Schwarzschild radius, average density, compactness, gravitational redshift and dynamical stability are studied. Finally, a relation between mass and radius of neutron star versus the Planck mass is extracted.

  16. Modified teleparallel gravity: Inflation without an inflaton

    Ferraro, Rafael; Fiorini, Franco

    2007-01-01

    The Born-Infeld strategy to smooth theories having divergent solutions is applied to the teleparallel equivalent of general relativity. Differing from other theories of modified gravity, modified teleparallelism leads to second order equations, since the teleparallel Lagrangian only contains first derivatives of the vierbein. We show that the Born-Infeld-modified teleparallelism solves the particle horizon problem in a spatially flat Friedmann-Robertson-Walker (FRW) universe by providing an initial exponential expansion without resorting to an inflaton field

  17. Bouncing cosmologies from quantum gravity condensates

    Oriti, Daniele; Sindoni, Lorenzo; Wilson-Ewing, Edward

    2017-02-01

    We show how the large-scale cosmological dynamics can be obtained from the hydrodynamics of isotropic group field theory condensate states in the Gross-Pitaevskii approximation. The correct Friedmann equations are recovered in the classical limit for some choices of the parameters in the action for the group field theory, and quantum gravity corrections arise in the high-curvature regime causing a bounce which generically resolves the big-bang and big-crunch singularities.

  18. Classical gravity with higher derivatives

    Stelle, K.S.

    1978-01-01

    Inclusion of the four-derivative terms ∫Rsub(μν) Rsup(μν)(-g)sup(1/2) and ∫R 2 (-g)sup(1/2) into the gravitational action gives a class of effectively multimass models of gravity. In addition to the usual massless excitations of the field, there are now, for general amounts of the two new terms, massive spin-two and massive scalar excitations, with a total of eight degrees of freedom. The massive spin-two part of the field has negative energy. Specific ration of the two new terms give models with either the massive tensor or the massive scalar missing, with correspondingly fewer degrees of freedom. The static, linearized solutions of the field equations are combinations of Newtonian and Yukawa potentials. Owing to the Yukawa form of the corrections, observational evidence sets only very weak restrictions on the new masses. The acceptable static metric solutions in the full nonlinear theory are regular at the origin. The dynamical content of the linearized field is analyzed by reducing the fourth-order field equations to separated second-order equations, related by coupling to external sources in a fixed ratio. This analysis is carried out into the various helicity components using the transverse-traceless decomposition of the metric. (author)

  19. Finding Horndeski theories with Einstein gravity limits

    McManus, Ryan; Lombriser, Lucas; Peñarrubia, Jorge, E-mail: ryanm@roe.ac.uk, E-mail: llo@roe.ac.uk, E-mail: jorpega@roe.ac.uk [Institute for Astronomy, University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9 3HJ (United Kingdom)

    2016-11-01

    The Horndeski action is the most general scalar-tensor theory with at most second-order derivatives in the equations of motion, thus evading Ostrogradsky instabilities and making it of interest when modifying gravity at large scales. To pass local tests of gravity, these modifications predominantly rely on nonlinear screening mechanisms that recover Einstein's Theory of General Relativity in regions of high density. We derive a set of conditions on the four free functions of the Horndeski action that examine whether a specific model embedded in the action possesses an Einstein gravity limit or not. For this purpose, we develop a new and surprisingly simple scaling method that identifies dominant terms in the equations of motion by considering formal limits of the couplings that enter through the new terms in the modified action. This enables us to find regimes where nonlinear terms dominate and Einstein's field equations are recovered to leading order. Together with an efficient approximation of the scalar field profile, one can then further evaluate whether these limits can be attributed to a genuine screening effect. For illustration, we apply the analysis to both a cubic galileon and a chameleon model as well as to Brans-Dicke theory. Finally, we emphasise that the scaling method also provides a natural approach for performing post-Newtonian expansions in screened regimes.

  20. Lattice gravity and strings

    Jevicki, A.; Ninomiya, M.

    1985-01-01

    We are concerned with applications of the simplicial discretization method (Regge calculus) to two-dimensional quantum gravity with emphasis on the physically relevant string model. Beginning with the discretization of gravity and matter we exhibit a discrete version of the conformal trace anomaly. Proceeding to the string problem we show how the direct approach of (finite difference) discretization based on Nambu action corresponds to unsatisfactory treatment of gravitational degrees. Based on the Regge approach we then propose a discretization corresponding to the Polyakov string. In this context we are led to a natural geometric version of the associated Liouville model and two-dimensional gravity. (orig.)

  1. The Future of Gravity

    CERN. Geneva

    2007-01-01

    Of the four fundamental forces, gravity has been studied the longest, yet gravitational physics is one of the most rapidly developing areas of science today. This talk will give a broad brush survey of the past achievements and future prospects of general relativistic gravitational physics. Gravity is a two frontier science being important on both the very largest and smallest length scales considered in contemporary physics. Recent advances and future prospects will be surveyed in precision tests of general relativity, gravitational waves, black holes, cosmology and quantum gravity. The aim will be an overview of a subject that is becoming increasingly integrated with experiment and other branches of physics.

  2. Scaling in quantum gravity

    J. Ambjørn

    1995-07-01

    Full Text Available The 2-point function is the natural object in quantum gravity for extracting critical behavior: The exponential falloff of the 2-point function with geodesic distance determines the fractal dimension dH of space-time. The integral of the 2-point function determines the entropy exponent γ, i.e. the fractal structure related to baby universes, while the short distance behavior of the 2-point function connects γ and dH by a quantum gravity version of Fisher's scaling relation. We verify this behavior in the case of 2d gravity by explicit calculation.

  3. Generalized Einstein’s Equations from Wald Entropy

    Maulik Parikh

    2016-03-01

    Full Text Available We derive the gravitational equations of motion of general theories of gravity from thermodynamics applied to a local Rindler horizon through any point in spacetime. Specifically, for a given theory of gravity, we substitute the corresponding Wald entropy into the Clausius relation. Our approach works for all diffeomorphism-invariant theories of gravity in which the Lagrangian is a polynomial in the Riemann tensor.

  4. Cosmology of Horava-Lifshitz f(R) gravity

    Chakrabarti, Sayan K.; Sen, Anjan A.

    2011-08-01

    We discuss the cosmology of recently proposed Horava-Lifshitz f(R) gravity. In particular, we derive the modified Hubble equation that reduces to the standard HL gravity case in appropriate limit. We show how the bounce solutions in this theory are modified due to nonlinear effect of f(R) gravity. In addition we find that the solutions exist when the Universe can make turn around for large scale-factor. Therefore, in principle, the Universe in this set-up can show cyclic behavior. (orig.)

  5. Cosmology of Horava-Lifshitz f(R) gravity

    Chakrabarti, Sayan K. [Univ. Tecnica de Lisboa (Portugal). Inst. Superior Tecnico; Dutta, Koushik [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Sen, Anjan A. [Centre of Theoretical Physics, Jamia Millia Islamia, New Dehli (India)

    2011-08-15

    We discuss the cosmology of recently proposed Horava-Lifshitz f(R) gravity. In particular, we derive the modified Hubble equation that reduces to the standard HL gravity case in appropriate limit. We show how the bounce solutions in this theory are modified due to nonlinear effect of f(R) gravity. In addition we find that the solutions exist when the Universe can make turn around for large scale-factor. Therefore, in principle, the Universe in this set-up can show cyclic behavior. (orig.)

  6. Weak lensing: Dark Matter, Dark Energy and Dark Gravity

    Heavens, Alan

    2009-01-01

    In this non-specialist review I look at how weak lensing can provide information on the dark sector of the Universe. The review concentrates on what can be learned about Dark Matter, Dark Energy and Dark Gravity, and why. On Dark Matter, results on the confrontation of theoretical profiles with observation are reviewed, and measurements of neutrino masses discussed. On Dark Energy, the interest is whether this could be Einstein's cosmological constant, and prospects for high-precision studies of the equation of state are considered. On Dark Gravity, we consider the exciting prospects for future weak lensing surveys to distinguish General Relativity from extra-dimensional or other gravity theories.

  7. Gravity and Zero Point Energy

    Massie, U. W.

    When Planck introduced the 1/2 hv term to his 1911 black body equation he showed that there is a residual energy remaining at zero degree K after all thermal energy ceased. Other investigators, including Lamb, Casimir, and Dirac added to this information. Today zero point energy (ZPE) is accepted as an established condition. The purpose of this paper is to demonstrate that the density of the ZPE is given by the gravity constant (G) and the characteristics of its particles are revealed by the cosmic microwave background (CMB). Eddies of ZPE particles created by flow around mass bodies reduce the pressure normal to the eddy flow and are responsible for the force of gravity. Helium atoms resonate with ZPE particles at low temperature to produce superfluid helium. High velocity micro vortices of ZPE particles about a basic particle or particles are responsible for electromagnetic forces. The speed of light is the speed of the wave front in the ZPE and its value is a function of the temperature and density of the ZPE.

  8. Cosmological attractors in massive gravity

    Dubovsky, S; Tkachev, I I

    2005-01-01

    We study Lorentz-violating models of massive gravity which preserve rotations and are invariant under time-dependent shifts of the spatial coordinates. In the linear approximation the Newtonian potential in these models has an extra ``confining'' term proportional to the distance from the source. We argue that during cosmological expansion the Universe may be driven to an attractor point with larger symmetry which includes particular simultaneous dilatations of time and space coordinates. The confining term in the potential vanishes as one approaches the attractor. In the vicinity of the attractor the extra contribution is present in the Friedmann equation which, in a certain range of parameters, gives rise to the cosmic acceleration.

  9. Gravity where do we stand ?

    Colpi, Monica; Gorini, Vittorio; Moschella, Ugo

    2016-01-01

    This book presents an overview of the current understanding of gravitation, with a focus on the current efforts to test its theories, especially general relativity. It shows how the quest for a deeper understanding, which would possibly incorporate gravity in the quantum realm, is more than ever an open field. The majority of the contributions deals with the manifold facets of “experimental gravitation”, but the book goes beyond this and covers a broad range of subjects from the foundations of gravitational theories to astrophysics and cosmology. The book is divided into three parts. The first part deals with foundations and Solar System tests. An introductory pedagogical chapter reviews first Newtonian gravitational theory, special relativity, the equivalence principle and the basics of general relativity. Then it focuses on approximation methods, mainly the post-Newtonian formalism and the relaxed Einstein equations, with a discussion on how they are used in treating experimental tests and in the proble...

  10. Gravity induced wave function collapse

    Gasbarri, G.; Toroš, M.; Donadi, S.; Bassi, A.

    2017-11-01

    Starting from an idea of S. L. Adler [in Quantum Nonlocality and Reality: 50 Years of Bell's Theorem, edited by M. Bell and S. Gao (Cambridge University Press, Cambridge, England 2016)], we develop a novel model of gravity induced spontaneous wave function collapse. The collapse is driven by complex stochastic fluctuations of the spacetime metric. After deriving the fundamental equations, we prove the collapse and amplification mechanism, the two most important features of a consistent collapse model. Under reasonable simplifying assumptions, we constrain the strength ξ of the complex metric fluctuations with available experimental data. We show that ξ ≥10-26 in order for the model to guarantee classicality of macro-objects, and at the same time ξ ≤10-20 in order not to contradict experimental evidence. As a comparison, in the recent discovery of gravitational waves in the frequency range 35 to 250 Hz, the (real) metric fluctuations reach a peak of ξ ˜10-21.

  11. Dirac fields in loop quantum gravity and big bang nucleosynthesis

    Bojowald, Martin; Das, Rupam; Scherrer, Robert J.

    2008-01-01

    Big bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions. Several corrections to equation of state parameters arise from classical and quantum physics, which are derived here from a canonical perspective. In particular, loop quantum gravity allows one to compute quantum gravity corrections for Maxwell and Dirac fields. Although the classical actions are very different, quantum corrections to the equation of state are remarkably similar. To lowest order, these corrections take the form of an overall expansion-dependent multiplicative factor in the total density. We use these results, along with the predictions of big bang nucleosynthesis, to place bounds on these corrections and especially the patch size of discrete quantum gravity states.

  12. Gravity Data for Egypt

    National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data (71 records) were gathered by various governmental organizations (and academia) using a variety of methods. This data base was received in...

  13. New massive gravity

    Bergshoeff, Eric A.; Hohm, Olaf; Townsend, Paul K.

    2012-01-01

    We present a brief review of New Massive Gravity, which is a unitary theory of massive gravitons in three dimensions obtained by considering a particular combination of the Einstein-Hilbert and curvature squared terms.

  14. DMA Antarctic Gravity Data

    National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data (65,164 records) were gathered by various governmental organizations (and academia) using a variety of methods. The data base was received...

  15. Gravity Data for Minnesota

    National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data (55,907 records) were gathered by various governmental organizations (and academia) using a variety of methods. This data base was received...

  16. Stability in designer gravity

    Hertog, Thomas; Hollands, Stefan

    2005-01-01

    We study the stability of designer gravity theories, in which one considers gravity coupled to a tachyonic scalar with anti-de Sitter (AdS) boundary conditions defined by a smooth function W. We construct Hamiltonian generators of the asymptotic symmetries using the covariant phase space method of Wald et al and find that they differ from the spinor charges except when W = 0. The positivity of the spinor charge is used to establish a lower bound on the conserved energy of any solution that satisfies boundary conditions for which W has a global minimum. A large class of designer gravity theories therefore have a stable ground state, which the AdS/CFT correspondence indicates should be the lowest energy soliton. We make progress towards proving this by showing that minimum energy solutions are static. The generalization of our results to designer gravity theories in higher dimensions involving several tachyonic scalars is discussed

  17. Discrete quantum gravity

    Williams, Ruth M

    2006-01-01

    A review is given of a number of approaches to discrete quantum gravity, with a restriction to those likely to be relevant in four dimensions. This paper is dedicated to Rafael Sorkin on the occasion of his sixtieth birthday

  18. Integral equations

    Moiseiwitsch, B L

    2005-01-01

    Two distinct but related approaches hold the solutions to many mathematical problems--the forms of expression known as differential and integral equations. The method employed by the integral equation approach specifically includes the boundary conditions, which confers a valuable advantage. In addition, the integral equation approach leads naturally to the solution of the problem--under suitable conditions--in the form of an infinite series.Geared toward upper-level undergraduate students, this text focuses chiefly upon linear integral equations. It begins with a straightforward account, acco

  19. Streaming gravity mode instability

    Wang Shui.

    1989-05-01

    In this paper, we study the stability of a current sheet with a sheared flow in a gravitational field which is perpendicular to the magnetic field and plasma flow. This mixing mode caused by a combined role of the sheared flow and gravity is named the streaming gravity mode instability. The conditions of this mode instability are discussed for an ideal four-layer model in the incompressible limit. (author). 5 refs

  20. What Is Gravity?

    Nelson, George

    2004-01-01

    Gravity is the name given to the phenomenon that any two masses, like you and the Earth, attract each other. One pulls on the Earth and the Earth pulls on one the same amount. And one does not have to be touching. Gravity acts over vast distances, like the 150 million kilometers (93 million miles) between the Earth and the Sun or the billions of…

  1. Automated borehole gravity meter system

    Lautzenhiser, Th.V.; Wirtz, J.D.

    1984-01-01

    An automated borehole gravity meter system for measuring gravity within a wellbore. The gravity meter includes leveling devices for leveling the borehole gravity meter, displacement devices for applying forces to a gravity sensing device within the gravity meter to bring the gravity sensing device to a predetermined or null position. Electronic sensing and control devices are provided for (i) activating the displacement devices, (ii) sensing the forces applied to the gravity sensing device, (iii) electronically converting the values of the forces into a representation of the gravity at the location in the wellbore, and (iv) outputting such representation. The system further includes electronic control devices with the capability of correcting the representation of gravity for tidal effects, as well as, calculating and outputting the formation bulk density and/or porosity

  2. Gravity Before Einstein and Schwinger Before Gravity

    Trimble, Virginia L.

    2012-05-01

    Julian Schwinger was a child prodigy, and Albert Einstein distinctly not; Schwinger had something like 73 graduate students, and Einstein very few. But both thought gravity was important. They were not, of course, the first, nor is the disagreement on how one should think about gravity that is being highlighted here the first such dispute. The talk will explore, first, several of the earlier dichotomies: was gravity capable of action at a distance (Newton), or was a transmitting ether required (many others). Did it act on everything or only on solids (an odd idea of the Herschels that fed into their ideas of solar structure and sunspots)? Did gravitational information require time for its transmission? Is the exponent of r precisely 2, or 2 plus a smidgeon (a suggestion by Simon Newcomb among others)? And so forth. Second, I will try to say something about Scwinger's lesser known early work and how it might have prefigured his "source theory," beginning with "On the Interaction of Several Electrons (the unpublished, 1934 "zeroth paper," whose title somewhat reminds one of "On the Dynamics of an Asteroid," through his days at Berkeley with Oppenheimer, Gerjuoy, and others, to his application of ideas from nuclear physics to radar and of radar engineering techniques to problems in nuclear physics. And folks who think good jobs are difficult to come by now might want to contemplate the couple of years Schwinger spent teaching elementary physics at Purdue before moving on to the MIT Rad Lab for war work.

  3. General Relativity solutions in modified gravity

    Motohashi, Hayato; Minamitsuji, Masato

    2018-06-01

    Recent gravitational wave observations of binary black hole mergers and a binary neutron star merger by LIGO and Virgo Collaborations associated with its optical counterpart constrain deviation from General Relativity (GR) both on strong-field regime and cosmological scales with high accuracy, and further strong constraints are expected by near-future observations. Thus, it is important to identify theories of modified gravity that intrinsically possess the same solutions as in GR among a huge number of theories. We clarify the three conditions for theories of modified gravity to allow GR solutions, i.e., solutions with the metric satisfying the Einstein equations in GR and the constant profile of the scalar fields. Our analysis is quite general, as it applies a wide class of single-/multi-field scalar-tensor theories of modified gravity in the presence of matter component, and any spacetime geometry including cosmological background as well as spacetime around black hole and neutron star, for the latter of which these conditions provide a necessary condition for no-hair theorem. The three conditions will be useful for further constraints on modified gravity theories as they classify general theories of modified gravity into three classes, each of which possesses i) unique GR solutions (i.e., no-hair cases), ii) only hairy solutions (except the cases that GR solutions are realized by cancellation between singular coupling functions in the Euler-Lagrange equations), and iii) both GR and hairy solutions, for the last of which one of the two solutions may be selected dynamically.

  4. Extended Theories of Gravity

    Capozziello, Salvatore; De Laurentis, Mariafelicia

    2011-01-01

    Extended Theories of Gravity can be considered as a new paradigm to cure shortcomings of General Relativity at infrared and ultraviolet scales. They are an approach that, by preserving the undoubtedly positive results of Einstein’s theory, is aimed to address conceptual and experimental problems recently emerged in astrophysics, cosmology and High Energy Physics. In particular, the goal is to encompass, in a self-consistent scheme, problems like inflation, dark energy, dark matter, large scale structure and, first of all, to give at least an effective description of Quantum Gravity. We review the basic principles that any gravitational theory has to follow. The geometrical interpretation is discussed in a broad perspective in order to highlight the basic assumptions of General Relativity and its possible extensions in the general framework of gauge theories. Principles of such modifications are presented, focusing on specific classes of theories like f(R)-gravity and scalar–tensor gravity in the metric and Palatini approaches. The special role of torsion is also discussed. The conceptual features of these theories are fully explored and attention is paid to the issues of dynamical and conformal equivalence between them considering also the initial value problem. A number of viability criteria are presented considering the post-Newtonian and the post-Minkowskian limits. In particular, we discuss the problems of neutrino oscillations and gravitational waves in extended gravity. Finally, future perspectives of extended gravity are considered with possibility to go beyond a trial and error approach.

  5. On the Specification of the Gravity Model of Trade: Zeros, Excess Zeros and Zero-Inflated Estimation

    M.J. Burger (Martijn); F.G. van Oort (Frank); G.J.M. Linders (Gert-Jan)

    2009-01-01

    textabstractConventional studies of bilateral trade patterns specify a log-normal gravity equation for empirical estimation. However, the log-normal gravity equation suffers from three problems: the bias created by the logarithmic transformation, the failure of the homoscedasticity assumption, and

  6. Gravity and Heater Size Effects on Pool Boiling Heat Transfer

    Kim, Jungho; Raj, Rishi

    2014-01-01

    The current work is based on observations of boiling heat transfer over a continuous range of gravity levels between 0g to 1.8g and varying heater sizes with a fluorinert as the test liquid (FC-72/n-perfluorohexane). Variable gravity pool boiling heat transfer measurements over a wide range of gravity levels were made during parabolic flight campaigns as well as onboard the International Space Station. For large heaters and-or higher gravity conditions, buoyancy dominated boiling and heat transfer results were heater size independent. The power law coefficient for gravity in the heat transfer equation was found to be a function of wall temperature under these conditions. Under low gravity conditions and-or for smaller heaters, surface tension forces dominated and heat transfer results were heater size dependent. A pool boiling regime map differentiating buoyancy and surface tension dominated regimes was developed along with a unified framework that allowed for scaling of pool boiling over a wide range of gravity levels and heater sizes. The scaling laws developed in this study are expected to allow performance quantification of phase change based technologies under variable gravity environments eventually leading to their implementation in space based applications.

  7. Solution of equations of electric power networks in multiprocessor computers; Solucao de equacoes de redes de energia eletrica em computadores multiprocessadores

    Feltrin, Antonio Padilha

    1991-05-01

    This thesis describes a methodology for decomposing the repeat solution process the equation Ax = b independent tasks to be done in parallel, based on the matrix inverse factors (W-matrix) with partitions. The partitioning scheme proposed in this thesis consists of breaking up the W-matrix according the depths of the factorization path tree. In this scheme, all the information needed to generate the partitions can be obtained straightforward from the network factorization path tree. The partitioning algorithm is simple and ease to implement. The elements of W, matrices, except the last partition, can be obtained directly from L-matrix elements, not requiring extra work. The proposed scheme guarantees that additional fills be only created in the last partition. The forward and backward solutions are performed by rows, and the strategy proposed is to schedule on beach processor the operations corresponding to a row of each partition. It should be kept in mind that the multiprocessor environments are equipped with powerful unit processor and then it seems a sound strategy to perform the multi-add elementary operations inside the hardware in order to exploit its computing efficiency. This strategy seeks to match the parallel algorithm to the parallel architecture. The precedent relations - that give rise to delays - are replaced by multi-add operations performed inside the processor mode without external communication. In the partition, the forward, diagonal and backward solutions may be gathered, and so all the operations can be expressed as the product of matrix W{sub lp} by the update components of vector b. The performance results show that the potential speedup of the solution time is essentially bounded by the floating point operation capability of each processor, denoting that the methodology is a suitable way to exploit the growing power of the computing technology. 46 figs, 40 refs, 49 tabs.

  8. Quantum gravity in three dimensions, Witten spinors and the quantisation of length

    Wieland, Wolfgang

    2018-05-01

    In this paper, I investigate the quantisation of length in euclidean quantum gravity in three dimensions. The starting point is the classical hamiltonian formalism in a cylinder of finite radius. At this finite boundary, a counter term is introduced that couples the gravitational field in the interior to a two-dimensional conformal field theory for an SU (2) boundary spinor, whose norm determines the conformal factor between the fiducial boundary metric and the physical metric in the bulk. The equations of motion for this boundary spinor are derived from the boundary action and turn out to be the two-dimensional analogue of the Witten equations appearing in Witten's proof of the positive mass theorem. The paper concludes with some comments on the resulting quantum theory. It is shown, in particular, that the length of a one-dimensional cross section of the boundary turns into a number operator on the Fock space of the theory. The spectrum of this operator is discrete and matches the results from loop quantum gravity in the spin network representation.

  9. Quasi-topological Ricci polynomial gravities

    Li, Yue-Zhou; Liu, Hai-Shan; Lü, H.

    2018-02-01

    Quasi-topological terms in gravity can be viewed as those that give no contribution to the equations of motion for a special subclass of metric ansätze. They therefore play no rôle in constructing these solutions, but can affect the general perturbations. We consider Einstein gravity extended with Ricci tensor polynomial invariants, which admits Einstein metrics with appropriate effective cosmological constants as its vacuum solutions. We construct three types of quasi-topological gravities. The first type is for the most general static metrics with spherical, toroidal or hyperbolic isometries. The second type is for the special static metrics where g tt g rr is constant. The third type is the linearized quasitopological gravities on the Einstein metrics. We construct and classify results that are either dependent on or independent of dimensions, up to the tenth order. We then consider a subset of these three types and obtain Lovelock-like quasi-topological gravities, that are independent of the dimensions. The linearized gravities on Einstein metrics on all dimensions are simply Einstein and hence ghost free. The theories become quasi-topological on static metrics in one specific dimension, but non-trivial in others. We also focus on the quasi-topological Ricci cubic invariant in four dimensions as a specific example to study its effect on holography, including shear viscosity, thermoelectric DC conductivities and butterfly velocity. In particular, we find that the holographic diffusivity bounds can be violated by the quasi-topological terms, which can induce an extra massive mode that yields a butterfly velocity unbound above.

  10. McVittie solution in f(T) gravity

    Bejarano, Cecilia; Jose Guzman, Maria [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Ferraro, Rafael [Instituto de Astronomia y Fisica del Espacio (IAFE, CONICET-UBA), Buenos Aires (Argentina); Universidad de Buenos Aires, Departamento de Fisica, Facultad de Ciencias Exactas y Naturales, Buenos Aires (Argentina)

    2017-12-15

    We show that McVittie geometry, which describes a black hole embedded in a FLRW universe, not only solves the Einstein equations but also remains as a non-deformable solution of f(T) gravity. This search for GR solutions that survive in f(T) gravity is facilitated by a null tetrad approach. We also show that flat FLRW geometry is a consistent solution of f(T) dynamical equations not only for T = -6H{sup 2} but also for T = 0, which could be a manifestation of the additional degrees of freedom involved in f(T) theories. (orig.)

  11. McVittie solution in f(T) gravity

    Bejarano, Cecilia; Jose Guzman, Maria; Ferraro, Rafael

    2017-01-01

    We show that McVittie geometry, which describes a black hole embedded in a FLRW universe, not only solves the Einstein equations but also remains as a non-deformable solution of f(T) gravity. This search for GR solutions that survive in f(T) gravity is facilitated by a null tetrad approach. We also show that flat FLRW geometry is a consistent solution of f(T) dynamical equations not only for T = -6H 2 but also for T = 0, which could be a manifestation of the additional degrees of freedom involved in f(T) theories. (orig.)

  12. Some aspects of reconstruction using a scalar field in f(T) gravity

    Chakrabarti, Soumya [Indian Institute of Technology, Centre for Theoretical Studies, Kharagpur (India); Said, Jackson Levi [University of Malta, Institute of Space Sciences and Astronomy, Msida, MSD (Malta); Farrugia, Gabriel [University of Malta, Department of Physics, Msida, MSD (Malta)

    2017-12-15

    General relativity characterizes gravity as a geometric property exhibited on spacetime by massive objects, while teleparallel gravity achieves the same results at the level of equations, by taking a torsional perspective of gravity. Similar to the f(R) theory teleparallel gravity can also be generalized to f(T), with the resulting field equations being inherently distinct from f(R) gravity in that they are second order, while in the former case they turn out to be fourth order. In the present case, a minimally coupled scalar field is investigated in the f(T) gravity context for several forms of the scalar field potential. A number of new f(T) solutions are found for these potentials. Their respective state parameters are also being examined. (orig.)

  13. Method and Apparatus for Predicting Unsteady Pressure and Flow Rate Distribution in a Fluid Network

    Majumdar, Alok K. (Inventor)

    2009-01-01

    A method and apparatus for analyzing steady state and transient flow in a complex fluid network, modeling phase changes, compressibility, mixture thermodynamics, external body forces such as gravity and centrifugal force and conjugate heat transfer. In some embodiments, a graphical user interface provides for the interactive development of a fluid network simulation having nodes and branches. In some embodiments, mass, energy, and specific conservation equations are solved at the nodes, and momentum conservation equations are solved in the branches. In some embodiments, contained herein are data objects for computing thermodynamic and thermophysical properties for fluids. In some embodiments, the systems of equations describing the fluid network are solved by a hybrid numerical method that is a combination of the Newton-Raphson and successive substitution methods.

  14. A gauge-theoretic approach to gravity.

    Krasnov, Kirill

    2012-08-08

    Einstein's general relativity (GR) is a dynamical theory of the space-time metric. We describe an approach in which GR becomes an SU(2) gauge theory. We start at the linearized level and show how a gauge-theoretic Lagrangian for non-interacting massless spin two particles (gravitons) takes a much more simple and compact form than in the standard metric description. Moreover, in contrast to the GR situation, the gauge theory Lagrangian is convex. We then proceed with a formulation of the full nonlinear theory. The equivalence to the metric-based GR holds only at the level of solutions of the field equations, that is, on-shell. The gauge-theoretic approach also makes it clear that GR is not the only interacting theory of massless spin two particles, in spite of the GR uniqueness theorems available in the metric description. Thus, there is an infinite-parameter class of gravity theories all describing just two propagating polarizations of the graviton. We describe how matter can be coupled to gravity in this formulation and, in particular, how both the gravity and Yang-Mills arise as sectors of a general diffeomorphism-invariant gauge theory. We finish by outlining a possible scenario of the ultraviolet completion of quantum gravity within this approach.

  15. Ultrasonic hydrometer. [Specific gravity of electrolyte

    Swoboda, C.A.

    1982-03-09

    The disclosed ultrasonic hydrometer determines the specific gravity (density) of the electrolyte of a wet battery, such as a lead-acid battery. The hydrometer utilizes a transducer that when excited emits an ultrasonic impulse that traverses through the electrolyte back and forth between spaced sonic surfaces. The transducer detects the returning impulse, and means measures the time t between the initial and returning impulses. Considering the distance d between the spaced sonic surfaces and the measured time t, the sonic velocity V is calculated with the equation V = 2d/t. The hydrometer also utilizes a thermocouple to measure the electrolyte temperature. A hydrometer database correlates three variable parameters including sonic velocity in and temperature and specific gravity of the electrolyte, for temperature values between 0 and 40/sup 0/C and for specific gravity values between 1.05 and 1.30. Upon knowing two parameters (the calculated sonic velocity and the measured temperature), the third parameter (specific gravity) can be uniquely found in the database. The hydrometer utilizes a microprocessor for data storage and manipulation.

  16. Relic gravity waves from braneworld inflation

    Sahni, Varun; Sami, M.; Souradeep, Tarun

    2002-01-01

    We discuss a scenario in which extra dimensional effects allow a scalar field with a steep potential to play the dual role of the inflaton as well as dark energy (quintessence). The post-inflationary evolution of the universe in this scenario is generically characterized by a 'kinetic regime' during which the kinetic energy of the scalar field greatly exceeds its potential energy resulting in a 'stiff' equation of state for scalar field matter P φ ≅ρ φ . The kinetic regime precedes the radiation dominated epoch and introduces an important new feature into the spectrum of relic gravity waves created quantum mechanically during inflation. The amplitude of the gravity wave spectrum increases with the wave number for wavelengths shorter than the comoving horizon scale at the commencement of the radiative regime. This 'blue tilt' is a generic feature of models with steep potentials and imposes strong constraints on a class of inflationary braneworld models. Prospects for detection of the gravity wave background by terrestrial and space-borne gravity wave observatories such as LIGO II and LISA are discussed

  17. Loop quantum gravity and black hole entropy quantization

    2009-01-01

    Using the spin networks and the asymptotic quasinormal mode frequencies of black holes given by loop quantum gravity,the minimum horizon area gap is obtained.Then the quantum area spectrum of black holes is derived and the black hole entropy is a realized quantization.The results show that the black hole entropy given by loop quantum gravity is in full accord with the Bekenstein-Hawking entropy with a suitable Immirzi.

  18. Differential equations

    Tricomi, FG

    2013-01-01

    Based on his extensive experience as an educator, F. G. Tricomi wrote this practical and concise teaching text to offer a clear idea of the problems and methods of the theory of differential equations. The treatment is geared toward advanced undergraduates and graduate students and addresses only questions that can be resolved with rigor and simplicity.Starting with a consideration of the existence and uniqueness theorem, the text advances to the behavior of the characteristics of a first-order equation, boundary problems for second-order linear equations, asymptotic methods, and diff

  19. Weak lensing in generalized gravity theories

    Acquaviva, Viviana; Baccigalupi, Carlo; Perrotta, Francesca

    2004-01-01

    We extend the theory of weak gravitational lensing to cosmologies with generalized gravity, described in the Lagrangian by a generic function depending on the Ricci scalar and a nonminimal coupled scalar field. We work out the generalized Poisson equations relating the dynamics of the fluctuating components to the two gauge-invariant scalar gravitational potentials, fixing the contributions from the modified background expansion and fluctuations. We show how the lensing equation gets modified by the cosmic expansion as well as by the presence of anisotropic stress, which is non-null at the linear level both in scalar-tensor gravity and in theories where the gravitational Lagrangian term features a nonminimal dependence on the Ricci scalar. Starting from the geodesic deviation, we derive the generalized expressions for the shear tensor and projected lensing potential, encoding the spacetime variation of the effective gravitational constant and isolating the contribution of the anisotropic stress, which introduces a correction due to the spatial correlation between the gravitational potentials. Finally, we work out the expressions of the lensing convergence power spectrum as well as the correlation between the lensing potential and the integrated Sachs-Wolfe effect affecting cosmic microwave background total intensity and polarization anisotropies. To illustrate phenomenologically the effects, we work out approximate expressions for the quantities above in extended quintessence scenarios where the scalar field coupled to gravity plays the role of the dark energy

  20. The soliton content of classical Jackiw-Teitelboim gravity

    Reyes, Enrique G [Departamento de Matematicas y Ciencia de la Computacion, Universidad de Santiago de Chile, Casilla 307 Correo 2, Santiago, Chile (Chile)

    2006-01-13

    It is pointed out that every generic-in a sense to be made precise in section 2-solution to an arbitrary equation describing pseudo-spherical surfaces (or, equivalently, an arbitrary equation which is the integrability condition of a sl(2, R)-valued linear problem) determines pseudo-Riemannian surfaces of constant scalar curvature, and therefore, classical solutions to the Jackiw-Teitelboim field equations for two-dimensional gravity. In particular, this observation explains why some standard soliton equations appear in this theory. (letter to the editor)

  1. Simulation of sediment settling in reduced gravity

    Kuhn, Nikolaus; Kuhn, Brigitte; Rüegg, Hans-Rudolf; Gartmann, Andres

    2015-04-01

    Gravity has a non-linear effect on the settling velocity of sediment particles in liquids and gases due to the interdependence of settling velocity, drag and friction. However, Stokes' Law or similar empirical models, the common way of estimating the terminal velocity of a particle settling in a gas or liquid, carry the notion of a drag as a property of a particle, rather than a force generated by the flow around the particle. For terrestrial applications, this simplifying assumption is not relevant, but it may strongly influence the terminal velocity achieved by settling particles on other planetary bodies. False estimates of these settling velocities will, in turn, affect the interpretation of particle sizes observed in sedimentary rocks, e.g. on Mars and the search for traces of life. Simulating sediment settling velocities on other planets based on a numeric simulation using Navier-Stokes equations and Computational Fluid Dynamics requires a prohibitive amount of time and lacks measurements to test the quality of the results. The aim of the experiments presented in this study was therefore to quantify the error incurred by using settling velocity models calibrated on Earth at reduced gravities, such as those on the Moon and Mars. In principle, the effect of lower gravity on settling velocity can be achieved by reducing the difference in density between particle and liquid. However, the use of such analogues creates other problems because the properties (i.e. viscosity) and interaction of the liquids and sediment (i.e. flow around the boundary layer between liquid and particle) differ from those of water and mineral particles. An alternative for measuring the actual settling velocities of particles under reduced gravity, on Earth, is offered by placing a settling tube on a reduced gravity flight and conduct settling velocity measurements within the 20 to 25 seconds of Martian gravity that can be simulated during such a flight. In this presentation, the results

  2. Networking

    Rauno Lindholm, Daniel; Boisen Devantier, Lykke; Nyborg, Karoline Lykke; Høgsbro, Andreas; Fries, de; Skovlund, Louise

    2016-01-01

    The purpose of this project was to examine what influencing factor that has had an impact on the presumed increasement of the use of networking among academics on the labour market and how it is expressed. On the basis of the influence from globalization on the labour market it can be concluded that the globalization has transformed the labour market into a market based on the organization of networks. In this new organization there is a greater emphasis on employees having social qualificati...

  3. Differential equations

    Barbu, Viorel

    2016-01-01

    This textbook is a comprehensive treatment of ordinary differential equations, concisely presenting basic and essential results in a rigorous manner. Including various examples from physics, mechanics, natural sciences, engineering and automatic theory, Differential Equations is a bridge between the abstract theory of differential equations and applied systems theory. Particular attention is given to the existence and uniqueness of the Cauchy problem, linear differential systems, stability theory and applications to first-order partial differential equations. Upper undergraduate students and researchers in applied mathematics and systems theory with a background in advanced calculus will find this book particularly useful. Supplementary topics are covered in an appendix enabling the book to be completely self-contained.

  4. Gravity and strings

    Ortín, Tomás

    2015-01-01

    Self-contained and comprehensive, this definitive new edition of Gravity and Strings is a unique resource for graduate students and researchers in theoretical physics. From basic differential geometry through to the construction and study of black-hole and black-brane solutions in quantum gravity - via all the intermediate stages - this book provides a complete overview of the intersection of gravity, supergravity, and superstrings. Now fully revised, this second edition covers an extensive array of topics, including new material on non-linear electric-magnetic duality, the electric-tensor formalism, matter-coupled supergravity, supersymmetric solutions, the geometries of scalar manifolds appearing in 4- and 5-dimensional supergravities, and much more. Covering reviews of important solutions and numerous solution-generating techniques, and accompanied by an exhaustive index and bibliography, this is an exceptional reference work.

  5. Stochastic quantum gravity

    Rumpf, H.

    1987-01-01

    We begin with a naive application of the Parisi-Wu scheme to linearized gravity. This will lead into trouble as one peculiarity of the full theory, the indefiniteness of the Euclidean action, shows up already at this level. After discussing some proposals to overcome this problem, Minkowski space stochastic quantization will be introduced. This will still not result in an acceptable quantum theory of linearized gravity, as the Feynman propagator turns out to be non-causal. This defect will be remedied only after a careful analysis of general covariance in stochastic quantization has been performed. The analysis requires the notion of a metric on the manifold of metrics, and a natural candidate for this is singled out. With this a consistent stochastic quantization of Einstein gravity becomes possible. It is even possible, at least perturbatively, to return to the Euclidean regime. 25 refs. (Author)

  6. No slip gravity

    Linder, Eric V.

    2018-03-01

    A subclass of the Horndeski modified gravity theory we call No Slip Gravity has particularly interesting properties: 1) a speed of gravitational wave propagation equal to the speed of light, 2) equality between the effective gravitational coupling strengths to matter and light, Gmatter and Glight, hence no slip between the metric potentials, yet difference from Newton's constant, and 3) suppressed growth to give better agreement with galaxy clustering observations. We explore the characteristics and implications of this theory, and project observational constraints. We also give a simple expression for the ratio of the gravitational wave standard siren distance to the photon standard candle distance, in this theory and others, and enable a direct comparison of modified gravity in structure growth and in gravitational waves, an important crosscheck.

  7. Application of Newtonian Physics to Predict the Speed of a Gravity Racer

    Driscoll, H. F.; Bullas, A. M.; King, C. E.; Senior, T.; Haake, S. J.; Hart, J.

    2016-01-01

    Gravity racing can be studied using numerical solutions to the equations of motion derived from Newton's second law. This allows students to explore the physics of gravity racing and to understand how design and course selection influences vehicle speed. Using Euler's method, we have developed a spreadsheet application that can be used to predict…

  8. Airborne Gravity: NGS' Gravity Data for EN08 (2013)

    National Oceanic and Atmospheric Administration, Department of Commerce — Airborne gravity data for New York, Vermont, New Hampshire, Massachusettes, Maine, and Canada collected in 2013 over 1 survey. This data set is part of the Gravity...

  9. Airborne Gravity: NGS' Gravity Data for TS01 (2014)

    National Oceanic and Atmospheric Administration, Department of Commerce — Airborne gravity data for Puerto Rico and the Virgin Islands collected in 2009 over 1 survey. This data set is part of the Gravity for the Re-definition of the...

  10. Airborne Gravity: NGS' Gravity Data for AN08 (2016)

    National Oceanic and Atmospheric Administration, Department of Commerce — Airborne gravity data for Alaska collected in 2016 over one survey. This data set is part of the Gravity for the Re-definition of the American Vertical Datum...

  11. Airborne Gravity: NGS' Gravity Data for CN02 (2013 & 2014)

    National Oceanic and Atmospheric Administration, Department of Commerce — Airborne gravity data for Nebraska collected in 2013 & 2014 over 3 surveys. This data set is part of the Gravity for the Re-definition of the American Vertical...

  12. Airborne Gravity: NGS' Gravity Data for EN01 (2011)

    National Oceanic and Atmospheric Administration, Department of Commerce — Airborne gravity data for New York, Canada, and Lake Ontario collected in 2011 over 1 survey. This data set is part of the Gravity for the Re-definition of the...

  13. Airborne Gravity: NGS' Gravity Data for AN03 (2010)

    National Oceanic and Atmospheric Administration, Department of Commerce — Airborne gravity data for Alaska collected in 2010 and 2012 over 2 surveys. This data set is part of the Gravity for the Re-definition of the American Vertical Datum...

  14. Airborne Gravity: NGS' Gravity Data for EN06 (2016)

    National Oceanic and Atmospheric Administration, Department of Commerce — Airborne gravity data for Maine, Canada, and the Atlantic Ocean collected in 2012 over 2 surveys. This data set is part of the Gravity for the Re-definition of the...

  15. Airborne Gravity: NGS' Gravity Data for ES01 (2013)

    National Oceanic and Atmospheric Administration, Department of Commerce — Airborne gravity data for Florida, the Bahamas, and the Atlantic Ocean collected in 2013 over 1 survey. This data set is part of the Gravity for the Re-definition of...

  16. Towards a quantum gravity

    Romney, B.; Barrau, A.; Vidotto, F.; Le Meur, H.; Noui, K.

    2011-01-01

    The loop quantum gravity is the only theory that proposes a quantum description of space-time and therefore of gravitation. This theory predicts that space is not infinitely divisible but that is has a granular structure at the Planck scale (10 -35 m). Another feature of loop quantum gravity is that it gets rid of the Big-Bang singularity: our expanding universe may come from the bouncing of a previous contracting universe, in this theory the Big-Bang is replaced with a big bounce. The loop quantum theory predicts also the huge number of quantum states that accounts for the entropy of large black holes. (A.C.)

  17. General proof of the entropy principle for self-gravitating fluid in f(R) gravity

    Fang, Xiongjun [Department of Physics and Key Laboratory of Low Dimensional Quantum Structures andQuantum Control of Ministry of Education, Hunan Normal University,Changsha, Hunan 410081 (China); Guo, Minyong [Department of Physics, Beijing Normal University,Beijing 100875 (China); Jing, Jiliang [Department of Physics and Key Laboratory of Low Dimensional Quantum Structures andQuantum Control of Ministry of Education, Hunan Normal University,Changsha, Hunan 410081 (China)

    2016-08-29

    The discussions on the connection between gravity and thermodynamics attract much attention recently. We consider a static self-gravitating perfect fluid system in f(R) gravity, which is an important theory could explain the accelerated expansion of the universe. We first show that the Tolman-Oppenheimer-Volkoff equation of f(R) theories can be obtained by thermodynamical method in spherical symmetric spacetime. Then we prove that the maximum entropy principle is also valid for f(R) gravity in general static spacetimes beyond spherical symmetry. The result shows that if the constraint equation is satisfied and the temperature of fluid obeys Tolmans law, the extrema of total entropy implies other components of gravitational equations. Conversely, if f(R) gravitational equation hold, the total entropy of the fluid should be extremum. Our work suggests a general and solid connection between f(R) gravity and thermodynamics.

  18. An unusual cosmological solution in the context of higher-derivative gravity

    Accioly, A.J.

    1988-01-01

    A general vacuum solution to the higher-derivative gravity field equations is presented in case of a model that exhibits symmetries of the Goedel-type. The solution possesses unusual properties. (author) [pt

  19. n  +  1 formalism of f (Lovelock) gravity

    Lachaume, Xavier

    2018-06-01

    In this note we perform the n  +  1 decomposition, or Arnowitt–Deser–Misner (ADM) formulation of gravity theory. The Hamiltonian form of Lovelock gravity was known since the work of Teitelboim and Zanelli in 1987, but this result had not yet been extended to gravity. Besides, field equations of have been recently computed by Bueno et al, though without ADM decomposition. We focus on the non-degenerate case, i.e. when the Hessian of f is invertible. Using the same Legendre transform as for theories, we can identify the partial derivatives of f as scalar fields, and consider the theory as a generalised scalar‑tensor theory. We then derive the field equations, and project them along a n  +  1 decomposition. We obtain an original system of constraint equations for gravity, as well as dynamical equations. We give explicit formulas for the case.

  20. Lanczos-Lovelock gravity from a thermodynamic perspective

    Chakraborty, Sumanta

    2015-01-01

    The deep connection between gravitational dynamics and horizon thermodynamics leads to several intriguing features both in general relativity and in Lanczos-Lovelock theories of gravity. Recently in http://arxiv.org/abs/1312.3253 several additional results strengthening the above connection have been established within the framework of general relativity. In this work we provide a generalization of the above setup to Lanczos-Lovelock gravity as well. To our expectation it turns out that most of the results obtained in the context of general relativity generalize to Lanczos-Lovelock gravity in a straightforward but non-trivial manner. First, we provide an alternative and more general derivation of the connection between Noether charge for a specific time evolution vector field and gravitational heat density of the boundary surface. This will lead to holographic equipartition for static spacetimes in Lanczos-Lovelock gravity as well. Taking a cue from this, we have introduced naturally defined four-momentum current associated with gravity and matter energy momentum tensor for both Lanczos-Lovelock Lagrangian and its quadratic part. Then, we consider the concepts of Noether charge for null boundaries in Lanczos-Lovelock gravity by providing a direct generalization of previous results derived in the context of general relativity. Another very interesting feature for gravity is that gravitational field equations for arbitrary static and spherically symmetric spacetimes with horizon can be written as a thermodynamic identity in the near horizon limit. This result holds in both general relativity and in Lanczos-Lovelock gravity as well. In a previous work [http://arxiv.org/abs/1505.05297] we have shown that, for an arbitrary spacetime, the gravitational field equations near any null surface generically leads to a thermodynamic identity. In this work, we have also generalized this result to Lanczos-Lovelock gravity by showing that gravitational field equations for Lanczos

  1. Exact solutions in three-dimensional gravity

    Garcia-Diaz, Alberto A

    2017-01-01

    A self-contained text, systematically presenting the determination and classification of exact solutions in three-dimensional Einstein gravity. This book explores the theoretical framework and general physical and geometrical characteristics of each class of solutions, and includes information on the researchers responsible for their discovery. Beginning with the physical character of the solutions, these are identified and ordered on the basis of their geometrical invariant properties, symmetries, and algebraic classifications, or from the standpoint of their physical nature, for example electrodynamic fields, fluid, scalar field, or dilaton. Consequently, this text serves as a thorough catalogue on 2+1 exact solutions to the Einstein equations coupled to matter and fields, and on vacuum solutions of topologically massive gravity with a cosmological constant. The solutions are also examined from different perspectives, enabling a conceptual bridge between exact solutions of three- and four-dimensional gravit...

  2. Geometric flows in Horava-Lifshitz gravity

    Bakas, Ioannis; Lust, Dieter; Petropoulos, Marios

    2010-01-01

    We consider instanton solutions of Euclidean Horava-Lifshitz gravity in four dimensions satisfying the detailed balance condition. They are described by geometric flows in three dimensions driven by certain combinations of the Cotton and Ricci tensors as well as the cosmological-constant term. The deformation curvature terms can have competing behavior leading to a variety of fixed points. The instantons interpolate between any two fixed points, which are vacua of topologically massive gravity with Lambda > 0, and their action is finite. Special emphasis is placed on configurations with SU(2) isometry associated with homogeneous but generally non-isotropic Bianchi IX model geometries. In this case, the combined Ricci-Cotton flow reduces to an autonomous system of ordinary differential equations whose properties are studied in detail for different couplings. The occurrence and stability of isotropic and anisotropic fixed points are investigated analytically and some exact solutions are obtained. The correspond...

  3. Numerical simulations of convectively excited gravity waves

    Glatzmaier, G.A.

    1983-01-01

    Magneto-convection and gravity waves are numerically simulated with a nonlinear, three-dimensional, time-dependent model of a stratified, rotating, spherical fluid shell heated from below. A Solar-like reference state is specified while global velocity, magnetic field, and thermodynamic perturbations are computed from the anelastic magnetohydrodynamic equations. Convective overshooting from the upper (superadiabatic) part of the shell excites gravity waves in the lower (subadiabatic) part. Due to differential rotation and Coriolis forces, convective cell patterns propagate eastward with a latitudinally dependent phase velocity. The structure of the excited wave motions in the stable region is more time-dependent than that of the convective motions above. The magnetic field tends to be concentrated over giant-cell downdrafts in the convective zone but is affected very little by the wave motion in the stable region

  4. Quantum Gravity (2nd edn)

    Husain, Viqar

    2008-01-01

    There has been a flurry of books on quantum gravity in the past few years. The first edition of Kiefer's book appeared in 2004, about the same time as Carlo Rovelli's book with the same title. This was soon followed by Thomas Thiemann's 'Modern Canonical Quantum General Relativity'. Although the main focus of each of these books is non-perturbative and non-string approaches to the quantization of general relativity, they are quite orthogonal in temperament, style, subject matter and mathematical detail. Rovelli and Thiemann focus primarily on loop quantum gravity (LQG), whereas Kiefer attempts a broader introduction and review of the subject that includes chapters on string theory and decoherence. Kiefer's second edition attempts an even wider and somewhat ambitious sweep with 'new sections on asymptotic safety, dynamical triangulation, primordial black holes, the information-loss problem, loop quantum cosmology, and other topics'. The presentation of these current topics is necessarily brief given the size of the book, but effective in encapsulating the main ideas in some cases. For instance the few pages devoted to loop quantum cosmology describe how the mini-superspace reduction of the quantum Hamiltonian constraint of LQG becomes a difference equation, whereas the discussion of 'dynamical triangulations', an approach to defining a discretized Lorentzian path integral for quantum gravity, is less detailed. The first few chapters of the book provide, in a roughly historical sequence, the covariant and canonical metric variable approach to the subject developed in the 1960s and 70s. The problem(s) of time in quantum gravity are nicely summarized in the chapter on quantum geometrodynamics, followed by a detailed and effective introduction of the WKB approach and the semi-classical approximation. These topics form the traditional core of the subject. The next three chapters cover LQG, quantization of black holes, and quantum cosmology. Of these the chapter on LQG is

  5. Energy, momentum and angular momentum conservations in de Sitter gravity

    Lu, Jia-An

    2016-01-01

    In de Sitter (dS) gravity, where gravity is a gauge field introduced to realize the local dS invariance of the matter field, two kinds of conservation laws are derived. The first kind is a differential equation for a dS-covariant current, which unites the canonical energy-momentum (EM) and angular momentum (AM) tensors. The second kind presents a dS-invariant current which is conserved in the sense that its torsion-free divergence vanishes. The dS-invariant current unites the total (matter plus gravity) EM and AM currents. It is well known that the AM current contains an inherent part, called the spin current. Here it is shown that the EM tensor also contains an inherent part, which might be observed by its contribution to the deviation of the dust particle’s world line from a geodesic. All the results are compared to the ordinary Lorentz gravity. (paper)

  6. Shear waves in inhomogeneous, compressible fluids in a gravity field.

    Godin, Oleg A

    2014-03-01

    While elastic solids support compressional and shear waves, waves in ideal compressible fluids are usually thought of as compressional waves. Here, a class of acoustic-gravity waves is studied in which the dilatation is identically zero, and the pressure and density remain constant in each fluid particle. These shear waves are described by an exact analytic solution of linearized hydrodynamics equations in inhomogeneous, quiescent, inviscid, compressible fluids with piecewise continuous parameters in a uniform gravity field. It is demonstrated that the shear acoustic-gravity waves also can be supported by moving fluids as well as quiescent, viscous fluids with and without thermal conductivity. Excitation of a shear-wave normal mode by a point source and the normal mode distortion in realistic environmental models are considered. The shear acoustic-gravity waves are likely to play a significant role in coupling wave processes in the ocean and atmosphere.

  7. Numerical study of gravity currents in a channel

    Wang, D.

    1985-01-01

    A three-dimensional, primitive-equation model was used to study gravity currents produced by instantaneous releases of a buoyant fluid in a rectangular channel. Without rotation, the gravity current passes through two distinct phases: an initial adjustment phase in which the front speed is constant, and an eventual self-similar phase in which the front speed decreases with time. With rotation, the gravity current is confined to the right-hand wall, forming a coastal jet. The initial front-speed is constant; however, the front speed decreases rapidly due to strong mixing at the horizontal edge of the gravity current. Also, with rotation, part of the buoyant fluid is trapped near the source region, forming an anticyclonic vortex

  8. Quark stars in f(T, T)-gravity

    Pace, Mark; Said, Jackson Levi [University of Malta, Department of Physics, Msida (Malta); University of Malta, Institute of Space Sciences and Astronomy, Msida (Malta)

    2017-02-15

    We derive a working model for the Tolman-Oppenheimer-Volkoff equation for quark star systems within the modified f(T, T)-gravity class of models. We consider f(T, T)-gravity for a static spherically symmetric space-time. In this instance the metric is built from a more fundamental tetrad vierbein from which the metric tensor can be derived. We impose a linear f(T) parameter, namely taking f = αT(r) + βT(r) + φ and investigate the behaviour of a linear energy-momentum tensor trace, T. We also outline the restrictions which modified f(T, T)-gravity imposes upon the coupling parameters. Finally we incorporate the MIT bag model in order to derive the mass-radius and mass-central density relations of the quark star within f(T, T)-gravity. (orig.)

  9. Holographic dark energy and f(R) gravity

    Aghamohammadi, A [Faculty of Science, Islamic Azad University of Sanandaj, Sanandaj (Iran, Islamic Republic of); Saaidi, Kh, E-mail: ksaaidi@uok.ac.ir, E-mail: agha35484@yahoo.com [Department of Physics, Faculty of Science, University of Kurdistan, Sanandaj (Iran, Islamic Republic of)

    2011-02-15

    We investigate the corresponding relation between f(R) gravity and holographic dark energy. We introduce a type of energy density from f(R) that has the same role as holographic dark energy. We obtain the differential equation that specifies the evolution of the introduced energy density parameter based on a varying gravitational constant. We discover the relation for the equation of state parameter for low redshifts that contains varying G correction.

  10. Gravity Data for South America

    National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data (152,624 records) were compiled by the University of Texas at Dallas. This data base was received in June 1992. Principal gravity parameters...

  11. Interior Alaska Gravity Station Data

    National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data total 9416 records. This data base was received in March 1997. Principal gravity parameters include Free-air Anomalies which have been...

  12. Gravity Station Data for Spain

    National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data total 28493 records. This data base was received in April 1997. Principal gravity parameters include Free-air Anomalies which have been...

  13. Gravity Station Data for Portugal

    National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data total 3064 records. This data base was received in April 1997. Principal gravity parameters include Free-air Anomalies which have been...

  14. De Sitter space in gauge/gravity duality

    Lilia Anguelova

    2015-10-01

    Full Text Available We investigate gauge/gravity duality for gauge theories in de Sitter space. More precisely, we study a five-dimensional consistent truncation of type IIB supergravity, which encompasses a wide variety of gravity duals of strongly coupled gauge theories, including the Maldacena–Nunez solution and its walking deformations. We find several solutions of the 5d theory with dS4 spacetime and nontrivial profiles for (some of the scalars along the fifth (radial direction. In the process, we prove that one of the equations of motion becomes dependent on the others, for nontrivial warp factor. This dependence reduces the number of field equations and, thus, turns out to be crucial for the existence of solutions with (AdS4 spacetime. Finally, we comment on the implications of our dS4 solutions for building gravity duals of Glueball Inflation.

  15. Holographically viable extensions of topologically massive and minimal massive gravity?

    Altas, Emel; Tekin, Bayram

    2016-01-01

    Recently [E. Bergshoeff et al., Classical Quantum Gravity 31, 145008 (2014)], an extension of the topologically massive gravity (TMG) in 2 +1 dimensions, dubbed as minimal massive gravity (MMG), which is free of the bulk-boundary unitarity clash that inflicts the former theory and all the other known three-dimensional theories, was found. Field equations of MMG differ from those of TMG at quadratic terms in the curvature that do not come from the variation of an action depending on the metric alone. Here we show that MMG is a unique theory and there does not exist a deformation of TMG or MMG at the cubic and quartic order (and beyond) in the curvature that is consistent at the level of the field equations. The only extension of TMG with the desired bulk and boundary properties having a single massive degree of freedom is MMG.

  16. Brazilian international and inter-state trade flows: an exploratory analysis using the gravity model

    Paz, Lourenço Senne

    2003-01-01

    Recent efforts toward a world with freer trade, like WTO/GATT or regional Preferential Trade Agreements(PTAs), were put in doubt after McCallum's(1995) finding of a large border effect between US and Canadian provinces. Since then, there has been a great amount of research on this topic employing the gravity equation. This dissertation has two goals. The first goal is to review comprehensively the recent literature about the gravity equation, including its usages, econometric s...

  17. Stoneley waves in a non-homogeneous orthotropic granular medium under the influence of gravity

    S. M. Ahmed

    2005-01-01

    Full Text Available The aim of this paper is to investigate the Stoneley waves in a non-homogeneous orthotropic granular medium under the influence of a gravity field. The frequency equation obtained, in the form of a sixth-order determinantal expression, is in agreement with the corresponding result when both media are elastic. The frequency equation when the gravity field is neglected has been deduced as a particular case.

  18. FIA's volume-to-biomass conversion method (CRM) generally underestimates biomass in comparison to published equations

    David. C. Chojnacky

    2012-01-01

    An update of the Jenkins et al. (2003) biomass estimation equations for North American tree species resulted in 35 generalized equations developed from published equations. These 35 equations, which predict aboveground biomass of individual species grouped according to a taxa classification (based on genus or family and sometimes specific gravity), generally predicted...

  19. Colossal creations of gravity

    Skielboe, Andreas

    Gravity governs the evolution of the universe on the largest scales, and powers some of the most extreme objects at the centers of galaxies. Determining the masses and kinematics of galaxy clusters provides essential constraints on the large-scale structure of the universe, and act as direct probes...

  20. Discrete Lorentzian quantum gravity

    Loll, R.

    2000-01-01

    Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and that therefore also the lattice theory must be formulated

  1. Loop quantum gravity

    Pullin, J.

    2015-01-01

    Loop quantum gravity is one of the approaches that are being studied to apply the rules of quantum mechanics to the gravitational field described by the theory of General Relativity . We present an introductory summary of the main ideas and recent results. (Author)

  2. A finite quantum gravity

    Meszaros, A.

    1984-05-01

    In case the graviton has a very small non-zero mass, the existence of six additional massive gravitons with very big masses leads to a finite quantum gravity. There is an acausal behaviour on the scales that is determined by the masses of additional gravitons. (author)

  3. Venus - Ishtar gravity anomaly

    Sjogren, W. L.; Bills, B. G.; Mottinger, N. A.

    1984-01-01

    The gravity anomaly associated with Ishtar Terra on Venus is characterized, comparing line-of-sight acceleration profiles derived by differentiating Pioneer Venus Orbiter Doppler residual profiles with an Airy-compensated topographic model. The results are presented in graphs and maps, confirming the preliminary findings of Phillips et al. (1979). The isostatic compensation depth is found to be 150 + or - 30 km.

  4. Torsion induces gravity

    Aros, Rodrigo; Contreras, Mauricio

    2006-01-01

    In this work the Poincare-Chern-Simons and anti-de Sitter-Chern-Simons gravities are studied. For both, a solution that can be cast as a black hole with manifest torsion is found. Those solutions resemble Schwarzschild and Schwarzschild-AdS solutions, respectively

  5. Discrete quantum gravity

    Williams, J.W.

    1992-01-01

    After a brief introduction to Regge calculus, some examples of its application is quantum gravity are described in this paper. In particular, the earliest such application, by Ponzano and Regge, is discussed in some detail and it is shown how this leads naturally to current work on invariants of three-manifolds

  6. Loop Quantum Gravity

    Rovelli Carlo

    1998-01-01

    Full Text Available The problem of finding the quantum theory of the gravitational field, and thus understanding what is quantum spacetime, is still open. One of the most active of the current approaches is loop quantum gravity. Loop quantum gravity is a mathematically well-defined, non-perturbative and background independent quantization of general relativity, with its conventional matter couplings. Research in loop quantum gravity today forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained are: (i The computation of the physical spectra of geometrical quantities such as area and volume, which yields quantitative predictions on Planck-scale physics. (ii A derivation of the Bekenstein-Hawking black hole entropy formula. (iii An intriguing physical picture of the microstructure of quantum physical space, characterized by a polymer-like Planck scale discreteness. This discreteness emerges naturally from the quantum theory and provides a mathematically well-defined realization of Wheeler's intuition of a spacetime ``foam''. Long standing open problems within the approach (lack of a scalar product, over-completeness of the loop basis, implementation of reality conditions have been fully solved. The weak part of the approach is the treatment of the dynamics: at present there exist several proposals, which are intensely debated. Here, I provide a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

  7. Stochastic gravity: a primer with applications

    Hu, B L; Verdaguer, E

    2003-01-01

    Stochastic semiclassical gravity of the 1990s is a theory naturally evolved from semiclassical gravity of the 1970s and 1980s. It improves on the semiclassical Einstein equation with source given by the expectation value of the stress-energy tensor of quantum matter fields in curved spacetime by incorporating an additional source due to their fluctuations. In stochastic semiclassical gravity the main object of interest is the noise kernel, the vacuum expectation value of the (operator-valued) stress-energy bi-tensor, and the centrepiece is the (semiclassical) Einstein-Langevin equation. We describe this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the energy-momentum tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open system concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise and decoherence. We then describe the applications of stochastic gravity to the backreaction problems in cosmology and black-hole physics. In the first problem, we study the backreaction of conformally coupled quantum fields in a weakly inhomogeneous cosmology. In the second problem, we study the backreaction of a thermal field in the gravitational background of a quasi-static black hole (enclosed in a box) and its fluctuations. These examples serve to illustrate closely the ideas and techniques presented in the first part. This topical review is intended as a first introduction providing readers with some basic ideas and working knowledge. Thus, we place more emphasis here on pedagogy than completeness. (Further discussions of ideas, issues and ongoing research topics can be found

  8. Stochastic gravity: a primer with applications

    Hu, B L [Department of Physics, University of Maryland, College Park, MD 20742-4111 (United States); Verdaguer, E [Departament de Fisica Fonamental and CER en Astrofisica Fisica de Particules i Cosmologia, Universitat de Barcelona, Av. Diagonal 647, 08028 Barcelona (Spain)

    2003-03-21

    Stochastic semiclassical gravity of the 1990s is a theory naturally evolved from semiclassical gravity of the 1970s and 1980s. It improves on the semiclassical Einstein equation with source given by the expectation value of the stress-energy tensor of quantum matter fields in curved spacetime by incorporating an additional source due to their fluctuations. In stochastic semiclassical gravity the main object of interest is the noise kernel, the vacuum expectation value of the (operator-valued) stress-energy bi-tensor, and the centrepiece is the (semiclassical) Einstein-Langevin equation. We describe this new theory via two approaches: the axiomatic and the functional. The axiomatic approach is useful to see the structure of the theory from the framework of semiclassical gravity, showing the link from the mean value of the energy-momentum tensor to their correlation functions. The functional approach uses the Feynman-Vernon influence functional and the Schwinger-Keldysh closed-time-path effective action methods which are convenient for computations. It also brings out the open system concepts and the statistical and stochastic contents of the theory such as dissipation, fluctuations, noise and decoherence. We then describe the applications of stochastic gravity to the backreaction problems in cosmology and black-hole physics. In the first problem, we study the backreaction of conformally coupled quantum fields in a weakly inhomogeneous cosmology. In the second problem, we study the backreaction of a thermal field in the gravitational background of a quasi-static black hole (enclosed in a box) and its fluctuations. These examples serve to illustrate closely the ideas and techniques presented in the first part. This topical review is intended as a first introduction providing readers with some basic ideas and working knowledge. Thus, we place more emphasis here on pedagogy than completeness. (Further discussions of ideas, issues and ongoing research topics can be found

  9. Further stable neutron star models from f(R) gravity

    Astashenok, Artyom V. [I. Kant Baltic Federal University, Institute of Physics and Technology, Nevskogo st. 14, Kaliningrad, 236041 (Russian Federation); Capozziello, Salvatore [Dipartimento di Fisica, Università di Napoli ' ' Federico II' ' , Via Cinthia, 9, Napoli, I–80126 (Italy); Odintsov, Sergei D., E-mail: artyom.art@gmail.com, E-mail: capozziello@na.infn.it, E-mail: odintsov@ieec.uab.es [Instituciò Catalana de Recerca i Estudis Avançats (ICREA), Barcelona (Spain)

    2013-12-01

    Neutron star models in perturbative f(R) gravity are considered with realistic equations of state. In particular, we consider the FPS, SLy and other equations of state and a case of piecewise equation of state for stars with quark cores. The mass-radius relations for f(R) = R+R(e{sup −R/R{sub 0}}−1) model and for R{sup 2} models with logarithmic and cubic corrections are obtained. In the case of R{sup 2} gravity with cubic corrections, we obtain that at high central densities (ρ > 10ρ{sub ns}, where ρ{sub ns} = 2.7 × 10{sup 14} g/cm{sup 3} is the nuclear saturation density), stable star configurations exist. The minimal radius of such stars is close to 9 km with maximal mass ∼ 1.9M{sub ⊙} (SLy equation). A similar situation takes place for AP4 and BSK20 EoS. Such an effect can give rise to more compact stars than in General Relativity. If observationally identified, such objects could constitute a formidable signature for modified gravity at astrophysical level. Another interesting result can be achieved in modified gravity with only a cubic correction. For some EoS, the upper limit of neutron star mass increases and therefore these EoS can describe realistic star configurations (although, in General Relativity, these EoS are excluded by observational constraints)

  10. A rotating charged black hole solution in f (R) gravity

    Abstract. In the context of f (R) theories of gravity, we address the problem of finding a rotating charged black hole solution in the case of constant curvature. A new metric is obtained by solving the field equations and we show that its behaviour is typical of a rotating charged source. In addition, we analyse the ...

  11. The Coupling of Gravity to Spin and Electromagnetism

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    The coupled Einstein-Dirac-Maxwell equations are considered for a static, spherically symmetric system of two fermions in a singlet spinor state. Stable soliton-like solutions are shown to exist, and we discuss the regularizing effect of gravity from a Feynman diagram point of view.

  12. Further stable neutron star models from f(R) gravity

    Astashenok, Artyom V.; Capozziello, Salvatore; Odintsov, Sergei D.

    2013-01-01

    Neutron star models in perturbative f(R) gravity are considered with realistic equations of state. In particular, we consider the FPS, SLy and other equations of state and a case of piecewise equation of state for stars with quark cores. The mass-radius relations for f(R) = R+R(e −R/R 0 −1) model and for R 2 models with logarithmic and cubic corrections are obtained. In the case of R 2 gravity with cubic corrections, we obtain that at high central densities (ρ > 10ρ ns , where ρ ns = 2.7 × 10 14 g/cm 3 is the nuclear saturation density), stable star configurations exist. The minimal radius of such stars is close to 9 km with maximal mass ∼ 1.9M ⊙ (SLy equation). A similar situation takes place for AP4 and BSK20 EoS. Such an effect can give rise to more compact stars than in General Relativity. If observationally identified, such objects could constitute a formidable signature for modified gravity at astrophysical level. Another interesting result can be achieved in modified gravity with only a cubic correction. For some EoS, the upper limit of neutron star mass increases and therefore these EoS can describe realistic star configurations (although, in General Relativity, these EoS are excluded by observational constraints)

  13. Quantum Gravity Effects in Cosmology

    Gu Je-An

    2018-01-01

    Full Text Available Within the geometrodynamic approach to quantum cosmology, we studied the quantum gravity effects in cosmology. The Gibbons-Hawking temperature is corrected by quantum gravity due to spacetime fluctuations and the power spectrum as well as any probe field will experience the effective temperature, a quantum gravity effect.

  14. Even-dimensional topological gravity from Chern-Simons gravity

    Merino, N.; Perez, A.; Salgado, P.

    2009-01-01

    It is shown that the topological action for gravity in 2n-dimensions can be obtained from the (2n+1)-dimensional Chern-Simons gravity genuinely invariant under the Poincare group. The 2n-dimensional topological gravity is described by the dynamics of the boundary of a (2n+1)-dimensional Chern-Simons gravity theory with suitable boundary conditions. The field φ a , which is necessary to construct this type of topological gravity in even dimensions, is identified with the coset field associated with the non-linear realizations of the Poincare group ISO(d-1,1).

  15. Gravity-driven granular flow in a silo: Characterizing local forces and rearrangements

    Thackray Emma

    2017-01-01

    Full Text Available While the gravity-driven flow of a granular material in a silo geometry can be modeled by the Beverloo equation, the mesoscale-level particle rearrangements and interactions that drive this flow are not wellunderstood. We have constructed a quasi-two-dimensional system of bidisperse, millimeter-scale disks with photoelastic properties that make force networks within the material visible. The system is contained in an acrylic box with an adjustable bottom opening. We can approach the clogging transition by adjusting this opening. By placing the system between cross-polarizers, we can obtain high-speed video of this system during flow, and extract intensity signals that can be used to identify and quantify localized, otherwise indeterminate forces. We can simultaneously track individual particle motions, which can be used to identify shear transformation zones in the system. In this paper, we present our results thus far.

  16. Cosmology of modified Gauss-Bonnet gravity

    Li Baojiu; Barrow, John D.; Mota, David F.

    2007-01-01

    We consider the cosmology where some function f(G) of the Gauss-Bonnet term G is added to the gravitational action to account for the late-time accelerating expansion of the universe. The covariant and gauge invariant perturbation equations are derived with a method which could also be applied to general f(R,R ab R ab ,R abcd R abcd ) gravitational theories. It is pointed out that, despite their fourth-order character, such f(G) gravity models generally cannot reproduce arbitrary background cosmic evolutions; for example, the standard ΛCDM paradigm with Ω DE =0.76 cannot be realized in f(G) gravity theories unless f is a true cosmological constant because it imposes exclusionary constraints on the form of f(G). We analyze the perturbation equations and find that, as in the f(R) model, the stability of early-time perturbation growth puts some constraints on the functional form of f(G), in this case ∂ 2 f/∂G 2 <0. Furthermore, the stability of small-scale perturbations also requires that f not deviate significantly from a constant. These analyses are illustrated by numerically propagating the perturbation equations with a specific model reproducing a representative ΛCDM cosmic history. Our results show how the f(G) models are highly constrained by cosmological data

  17. GEODYNAMIC WAVES AND GRAVITY

    A. V. Vikulin

    2014-01-01

    Full Text Available  Gravity phenomena related to the Earth movements in the Solar System and through the Galaxy are reviewed. Such movements are manifested by geological processes on the Earth and correlate with geophysical fields of the Earth. It is concluded that geodynamic processes and the gravity phenomena (including those of cosmic nature are related.  The state of the geomedium composed of blocks is determined by stresses with force moment and by slow rotational waves that are considered as a new type of movements [Vikulin, 2008, 2010]. It is shown that the geomedium has typical rheid properties [Carey, 1954], specifically an ability to flow while being in the solid state [Leonov, 2008]. Within the framework of the rotational model with a symmetric stress tensor, which is developed by the authors [Vikulin, Ivanchin, 1998; Vikulin et al., 2012a, 2013], such movement of the geomedium may explain the energy-saturated state of the geomedium and a possibility of its movements in the form of vortex geological structures [Lee, 1928]. The article discusses the gravity wave detection method based on the concept of interactions between gravity waves and crustal blocks [Braginsky et al., 1985]. It is concluded that gravity waves can be recorded by the proposed technique that detects slow rotational waves. It is shown that geo-gravitational movements can be described by both the concept of potential with account of gravitational energy of bodies [Kondratyev, 2003] and the nonlinear physical acoustics [Gurbatov et al., 2008]. Based on the combined description of geophysical and gravitational wave movements, the authors suggest a hypothesis about the nature of spin, i.e. own moment as a demonstration of the space-time ‘vortex’ properties.  

  18. Measuring the Change in Water Table with Gravity Methods - a Controlled Experiment

    Lund, S; Christiansen, Lars; Andersen, O. B.

    2009-01-01

    Gravity changes linearly with the change in soil water content. With the GRACE satellite mission the interest for ground-based gravity methods in hydrology has gained new attention. Time-lapse gravity data have the potential to constrain hydrological model parameters in a calibration scheme....... The greatest potential is seen for specific yield. The gravity signal from hydrology is small (10^-8 m/s^2 level) and the application of ground-based methods is mainly limited by the sensitivity of available instruments. In order to demonstrate the ability of the Scintrex CG-5 gravity meter to detect a change...... in water content, a controlled experiment was set up in 30 m by 20 m basin. The water table was lowered 0.69 m within 1½ hours and the corresponding gravity signal measured using two different approaches: a time series measurements at one location and a gravity network measurement including four points...

  19. Gravity measurement, processing and evaluation: Test cases de Peel and South Limburg

    Nohlmans, Ron

    1990-05-01

    A general overview of the process of the measurement and the adjustment of a gravity network and the computation of some output parameters of gravimetry, gravity values, gravity anomalies and mean block anomalies, is given. An overview of developments in gravimetry, globally and in the Netherlands, until now is given. The basic theory of relative gravity measurements is studied and a description of the most commonly used instrument, the LaCoste and Romberg gravimeter is given. The surveys done in the scope of this study are descibed. A more detailed impression of the adjustment procedure and the results of the adjustment are given. A closer look is taken at the more geophysical side of gravimetry: gravity reduction, the computation of anomalies and the correlation with elevation. The interpolation of gravity and the covariance of gravity anomalies are addressed.

  20. Effect of Numerical Error on Gravity Field Estimation for GRACE and Future Gravity Missions

    McCullough, Christopher; Bettadpur, Srinivas

    2015-04-01

    In recent decades, gravity field determination from low Earth orbiting satellites, such as the Gravity Recovery and Climate Experiment (GRACE), has become increasingly more effective due to the incorporation of high accuracy measurement devices. Since instrumentation quality will only increase in the near future and the gravity field determination process is computationally and numerically intensive, numerical error from the use of double precision arithmetic will eventually become a prominent error source. While using double-extended or quadruple precision arithmetic will reduce these errors, the numerical limitations of current orbit determination algorithms and processes must be accurately identified and quantified in order to adequately inform the science data processing techniques of future gravity missions. The most obvious numerical limitation in the orbit determination process is evident in the comparison of measured observables with computed values, derived from mathematical models relating the satellites' numerically integrated state to the observable. Significant error in the computed trajectory will corrupt this comparison and induce error in the least squares solution of the gravitational field. In addition, errors in the numerically computed trajectory propagate into the evaluation of the mathematical measurement model's partial derivatives. These errors amalgamate in turn with numerical error from the computation of the state transition matrix, computed using the variational equations of motion, in the least squares mapping matrix. Finally, the solution of the linearized least squares system, computed using a QR factorization, is also susceptible to numerical error. Certain interesting combinations of each of these numerical errors are examined in the framework of GRACE gravity field determination to analyze and quantify their effects on gravity field recovery.

  1. Bernoulli's Equation

    regarding nature of forces hold equally for liquids, even though the ... particle. Figure A. A fluid particle is a very small imaginary blob of fluid, here shown sche- matically in .... picture gives important information about the flow field. ... Bernoulli's equation is derived assuming ideal flow, .... weight acting in the flow direction S is.

  2. Relativistic equations

    Gross, F.

    1986-01-01

    Relativistic equations for two and three body scattering are discussed. Particular attention is paid to relativistic three body kinetics because of recent form factor measurements of the Helium 3 - Hydrogen 3 system recently completed at Saclay and Bates and the accompanying speculation that relativistic effects are important for understanding the three nucleon system. 16 refs., 4 figs

  3. Metastable gravity on classical defects

    Ringeval, Christophe; Rombouts, Jan-Willem

    2005-01-01

    We discuss the realization of metastable gravity on classical defects in infinite-volume extra dimensions. In dilatonic Einstein gravity, it is found that the existence of metastable gravity on the defect core requires violation of the dominant energy condition for codimension N c =2 defects. This is illustrated with a detailed analysis of a six-dimensional hyperstring minimally coupled to dilaton gravity. We present the general conditions under which a codimension N c >2 defect admits metastable modes, and find that they differ from lower codimensional models in that, under certain conditions, they do not require violation of energy conditions to support quasilocalized gravity

  4. An analysis of the dynamics of activity and travel needs in response to social network and life-cycle dynamics : a structural equation model

    Sharmeen, F.; Arentze, T.A.; Timmermans, H.J.P.

    2014-01-01

    Several studies in transportation literature have shown that in the short-term social networks play an important role in discretionary activity and travel decisions of an individual. However, social networks may not remain unchanged in the long term, particularly in response to life-cycle events

  5. Halo scale predictions of symmetron modified gravity

    Clampitt, Joseph; Jain, Bhuvnesh; Khoury, Justin, E-mail: clampitt@sas.upenn.edu, E-mail: bjain@physics.upenn.edu, E-mail: jkhoury@sas.upenn.edu [Center for Particle Cosmology and Department of Physics and Astronomy, University of Pennsylvania, 209 South 33rd St., Philadelphia, PA 19104 (United States)

    2012-01-01

    We offer predictions of symmetron modified gravity in the neighborhood of realistic dark matter halos. The predictions for the fifth force are obtained by solving the nonlinear symmetron equation of motion in the spherical NFW approximation. In addition, we compare the three major known screening mechanisms: Vainshtein, Chameleon, and Symmetron around such dark matter halos, emphasizing the significant differences between them and highlighting observational tests which exploit these differences. Finally, we demonstrate the host halo environmental screening effect (''blanket screening'') on smaller satellite halos by solving for the modified forces around a density profile which is the sum of satellite and approximate host components.

  6. Scaling solutions for dilaton quantum gravity

    Henz, T.; Pawlowski, J.M., E-mail: j.pawlowski@thphys.uni-heidelberg.de; Wetterich, C.

    2017-06-10

    Scaling solutions for the effective action in dilaton quantum gravity are investigated within the functional renormalization group approach. We find numerical solutions that connect ultraviolet and infrared fixed points as the ratio between scalar field and renormalization scale k is varied. In the Einstein frame the quantum effective action corresponding to the scaling solutions becomes independent of k. The field equations derived from this effective action can be used directly for cosmology. Scale symmetry is spontaneously broken by a non-vanishing cosmological value of the scalar field. For the cosmology corresponding to our scaling solutions, inflation arises naturally. The effective cosmological constant becomes dynamical and vanishes asymptotically as time goes to infinity.

  7. Constraining inverse-curvature gravity with supernovae.

    Mena, Olga; Santiago, José; Weller, Jochen

    2006-02-03

    We show that models of generalized modified gravity, with inverse powers of the curvature, can explain the current accelerated expansion of the Universe without resorting to dark energy and without conflicting with solar system experiments. We have solved the Friedmann equations for the full dynamical range of the evolution of the Universe and performed a detailed analysis of supernovae data in the context of such models that results in an excellent fit. If we further include constraints on the current expansion of the Universe and on its age, we obtain that the matter content of the Universe is 0.07baryonic matter component.

  8. On gravitational energy in conformal teleparallel gravity

    da Silva, J. G.; Ulhoa, S. C.

    2017-07-01

    The paper deals with the definition of gravitational energy in conformal teleparallel gravity. The total energy is defined by means of the field equations which allow a local conservation law. Then such an expression is analyzed for a homogeneous and isotropic Universe. This model is implemented by the Friedmann-Robertson-Walker (FRW) line element. The energy of the Universe in the absence of matter is identified with the dark energy, however it can be expanded for curved models defining such an energy as the difference between the total energy and the energy of the perfect fluid which is the matter field in the FRW model.

  9. Electrodynamics in scale-covariant gravity theory

    Mansfield, V.N.; Malin, S.

    1980-01-01

    Utilizing the inherent scale-invariance of Maxwell's Equations, classical electrodynamics is incorporated into the theory of scale-invariant gravity. In this incorporation the gravitational constant G is shown to transform like β -2 (β is the gauge function), the generalized Lorentz Force Law is derived, the electric charge is shown to be invariant under gauge transformation, and matter creation is shown to be a necessity. In all nontrivial gauges a modified version of QED is obtained. The deviation from standard QED, however, is shown to be beyond the range of experimental detection when G α β -2 . (orig.)

  10. Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact ...

    Combined Sinh-Cosh-Gordon equation: Symmetry reductions, exact solutions and conservation laws. ... In this paper we study the combined sinh-cosh-Gordon equation, which arises in mathematical physics and has a wide range of scientific applications that range from chemical reactions to water surface gravity waves.

  11. Quantum gravity from noncommutative spacetime

    Lee, Jungjai; Yang, Hyunseok

    2014-01-01

    We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.

  12. Quantum gravity from noncommutative spacetime

    Lee, Jungjai [Daejin University, Pocheon (Korea, Republic of); Yang, Hyunseok [Korea Institute for Advanced Study, Seoul (Korea, Republic of)

    2014-12-15

    We review a novel and authentic way to quantize gravity. This novel approach is based on the fact that Einstein gravity can be formulated in terms of a symplectic geometry rather than a Riemannian geometry in the context of emergent gravity. An essential step for emergent gravity is to realize the equivalence principle, the most important property in the theory of gravity (general relativity), from U(1) gauge theory on a symplectic or Poisson manifold. Through the realization of the equivalence principle, which is an intrinsic property in symplectic geometry known as the Darboux theorem or the Moser lemma, one can understand how diffeomorphism symmetry arises from noncommutative U(1) gauge theory; thus, gravity can emerge from the noncommutative electromagnetism, which is also an interacting theory. As a consequence, a background-independent quantum gravity in which the prior existence of any spacetime structure is not a priori assumed but is defined by using the fundamental ingredients in quantum gravity theory can be formulated. This scheme for quantum gravity can be used to resolve many notorious problems in theoretical physics, such as the cosmological constant problem, to understand the nature of dark energy, and to explain why gravity is so weak compared to other forces. In particular, it leads to a remarkable picture of what matter is. A matter field, such as leptons and quarks, simply arises as a stable localized geometry, which is a topological object in the defining algebra (noncommutative *-algebra) of quantum gravity.

  13. The gravity field and GGOS

    Forsberg, René; Sideris, M.G.; Shum, C.K.

    2005-01-01

    The gravity field of the earth is a natural element of the Global Geodetic Observing System (GGOS). Gravity field quantities are like spatial geodetic observations of potential very high accuracy, with measurements, currently at part-per-billion (ppb) accuracy, but gravity field quantities are also...... unique as they can be globally represented by harmonic functions (long-wavelength geopotential model primarily from satellite gravity field missions), or based on point sampling (airborne and in situ absolute and superconducting gravimetry). From a GGOS global perspective, one of the main challenges...... is to ensure the consistency of the global and regional geopotential and geoid models, and the temporal changes of the gravity field at large spatial scales. The International Gravity Field Service, an umbrella "level-2" IAG service (incorporating the International Gravity Bureau, International Geoid Service...

  14. New experimental proposals for testing Dirac equation

    Camacho, Abel; Macias, Alfredo

    2004-01-01

    The advent of phenomenological quantum gravity has ushered us in the search for experimental tests of the deviations from general relativity predicted by quantum gravity or by string theories, and as a by-product of this quest the possible modifications that some field equations, for instance, the motion equation of spin-1/2-particles, have already been considered. In the present Letter a modified Dirac equation, whose extra term embraces a second-order time derivative, is taken as mainstay, and three different experimental proposals to detect it are put forward. The novelty in these ideas is that two of them do not fall within the extant approaches in this context, to wit, red-shift, atomic interferometry, or Hughes-Drever type-like experiments

  15. Inverse dualization and non-local dualities between Einstein gravity and supergravities

    Chen Chiangmei; Gal'tsov, Dmitri V; Sharakin, Sergei A

    2002-01-01

    We investigate non-local dualities between suitably compactified higher dimensional Einstein gravity and supergravities which can be revealed if one reinterprets the dualized Kaluza-Klein 2-forms in D>4 as antisymmetric forms belonging to supergravities. We find several examples of such a correspondence including one between the six-dimensional Einstein gravity and the four-dimensional Einstein-Maxwell-dilaton-axion theory (truncated N=4 supergravity), and others between the compactified eleven- and ten-dimensional supergravities and the eight- or ten-dimensional pure gravity. The Killing spinor equation of the D=11 supergravity is shown to be equivalent to the geometric Killing spinor equation in the dual gravity. We give several examples of using new dualities for solution generation and demonstrate how p-branes can be interpreted as non-local duals of pure gravity solutions. New supersymmetric solutions are presented including M2 subset of 5-brane with two rotation parameters

  16. Upper atmospheric planetary-wave and gravity-wave observations

    Justus, C. G.; Woodrum, A.

    1973-01-01

    Previously collected data on atmospheric pressure, density, temperature and winds between 25 and 200 km from sources including Meteorological Rocket Network data, ROBIN falling sphere data, grenade release and pitot tube data, meteor winds, chemical release winds, satellite data, and others were analyzed by a daily-difference method, and results on the magnitude of atmospheric perturbations interpreted as gravity waves and planetary waves are presented. Traveling planetary-wave contributions in the 25-85 km range were found to have significant height and latitudinal variation. It was found that observed gravity-wave density perturbations and wind are related to one another in the manner predicted by gravity-wave theory. It was determined that, on the average, gravity-wave energy deposition or reflection occurs at all altitudes except the 55-75 km region of the mesosphere.

  17. The behavior of surface tension on steady-state rotating fluids in the low gravity environments

    Hung, R. J.; Leslie, Fred W.

    1987-01-01

    The effect of surface tension on steady-state rotating fluids in a low gravity environment is studied. All the values of the physical parameters used in these calculations, except in the low gravity environments, are based on the measurements carried out by Leslie (1985) in the low gravity environment of a free-falling aircraft. The profile of the interface of two fluids is derived from Laplace's equation relating the pressure drop across an interface to the radii of curvature which has been applied to a low gravity rotating bubble that contacts the container boundary. The interface shape depends on the ratio of gravity to surface tension forces, the ratio of centrifugal to surface tension forces, the contact radius of the interface to the boundary, and the contact angle. The shape of the bubble is symmetric about its equator in a zero-gravity environment. This symmetry disappears and gradually shifts to parabolic profiles as the gravity environment becomes non-zero. The location of the maximum radius of the bubble moves upward from the center of the depth toward the top boundary of the cylinder as gravity increases. The contact radius of interface to the boundary r0 at the top side of cylinder increases and r0 at the bottom side of the cylinder decreases as the gravity environment increases from zero to 1 g.

  18. Non Newtonian gravity creeping flow

    Gratton, J.; Mahajan, S.M.; Minotti, F.

    1988-11-01

    We derive the governing equations for creeping gravity currents of non Newtonian liquids having a power law rheology, using a lubrication approximation. We consider unidirectional and axisymmetric currents. The equations differ from those for Newtonian liquids, being nonlinear in the spatial derivative of the thickness of the current. However, many solutions are closely analogous to those for Newtonian rheology; in particular the spreading relations can also be expressed as power laws of time, with exponents that depend on the rheological index. Similarity solutions for currents whose volume varies as a power of time are obtained. For the spread of a constant volume of liquid, analytic solutions are found. We also derive solutions of the waiting-time type, as well as the ones describing steady flows from a constant source to a sink. General travelling wave solutions are given, and analytic formulae for a simple case are derived. A phase plane formalism, that allows the systematic derivation of self similar solutions, is introduced. The application of the Boltzmann transform is briefly discussed. Present results are closely analogous to those for Newtonian liquids; all the solutions obtained here have their counterparts in Newtonian flows. This happens because the power law rheology, like the Newtonian constitutive relation, involves a single dimensional parameter. Thus one finds similarity solutions whenever the analogous Newtonian problem is self similar. Although the spreading relations are rheology-dependent, in most cases the dependence is rather weak. The present results may be of interest for geophysics since the lithosphere deforms according to an average power law rheology. (author). 17 refs

  19. Cosmological Tests of Gravity

    CERN. Geneva

    2017-01-01

    Extensions of Einstein’s theory of General Relativity are under investigation as a potential explanation of the accelerating expansion rate of the universe. I’ll present a cosmologist’s overview of attempts to test these ideas in an efficient and unbiased manner. I’ll start by introducing the bestiary of alternative gravity theories that have been put forwards. This proliferation of models motivates us to develop model-independent, agnostic tools for comparing the theory space to cosmological data. I’ll introduce the effective field theory for cosmological perturbations, a framework designed to unify modified gravity theories in terms of a manageable set of parameters. Having outlined the formalism, I’ll talk about the current constraints on this framework, and the improvements expected from the next generation of large galaxy clustering, weak lensing and intensity mapping experiments.

  20. The relativistic gravity train

    Seel, Max

    2018-05-01

    The gravity train that takes 42.2 min from any point A to any other point B that is connected by a straight-line tunnel through Earth has captured the imagination more than most other applications in calculus or introductory physics courses. Brachystochron and, most recently, nonlinear density solutions have been discussed. Here relativistic corrections are presented. It is discussed how the corrections affect the time to fall through Earth, the Sun, a white dwarf, a neutron star, and—the ultimate limit—the difference in time measured by a moving, a stationary and the fiducial observer at infinity if the density of the sphere approaches the density of a black hole. The relativistic gravity train can serve as a problem with approximate and exact analytic solutions and as numerical exercise in any introductory course on relativity.

  1. Antimatter gravity experiment

    Brown, R.E.; Camp, J.B.; Darling, T.W.

    1990-01-01

    An experiment is being developed to measure the acceleration of the antiproton in the gravitational field of the earth. Antiprotons of a few MeV from the LEAR facility at CERN will be slowed, captured, cooled to a temperature of about 10 K, and subsequently launched a few at a time into a drift tube where the effect of gravity on their motion will be determined by a time-of-flight method. Development of the experiment is proceeding at Los Alamos using normal matter. The fabrication of a drift tube that will produce a region of space in which gravity is the dominant force on moving ions is of major difficulty. This involves a study of methods of minimizing the electric fields produced by spatially varying work functions on conducting surfaces. Progress in a number of areas is described, with stress on the drift-tube development

  2. Lectures on Quantum Gravity

    Gomberoff, Andres

    2006-01-01

    The 2002 Pan-American Advanced Studies Institute School on Quantum Gravity was held at the Centro de Estudios Cientificos (CECS),Valdivia, Chile, January 4-14, 2002. The school featured lectures by ten speakers, and was attended by nearly 70 students from over 14 countries. A primary goal was to foster interaction and communication between participants from different cultures, both in the layman’s sense of the term and in terms of approaches to quantum gravity. We hope that the links formed by students and the school will persist throughout their professional lives, continuing to promote interaction and the essential exchange of ideas that drives research forward. This volume contains improved and updated versions of the lectures given at the School. It has been prepared both as a reminder for the participants, and so that these pedagogical introductions can be made available to others who were unable to attend. We expect them to serve students of all ages well.

  3. Simplicial quantum gravity

    Hartle, J.B.

    1985-01-01

    Simplicial approximation and the ideas associated with the Regge calculus provide a concrete way of implementing a sum over histories formulation of quantum gravity. A simplicial geometry is made up of flat simplices joined together in a prescribed way together with an assignment of lengths to their edges. A sum over simplicial geometries is a sum over the different ways the simplices can be joined together with an integral over their edge lengths. The construction of the simplicial Euclidean action for this approach to quantum general relativity is illustrated. The recovery of the diffeomorphism group in the continuum limit is discussed. Some possible classes of simplicial complexes with which to define a sum over topologies are described. In two dimensional quantum gravity it is argued that a reasonable class is the class of pseudomanifolds

  4. Gravity, Time, and Lagrangians

    Huggins, Elisha

    2010-01-01

    Feynman mentioned to us that he understood a topic in physics if he could explain it to a college freshman, a high school student, or a dinner guest. Here we will discuss two topics that took us a while to get to that level. One is the relationship between gravity and time. The other is the minus sign that appears in the Lagrangian. (Why would one…

  5. Spontaneously generated gravity

    Zee, A.

    1981-01-01

    We show, following a recent suggestion of Adler, that gravity may arise as a consequence of dynamical symmetry breaking in a scale- and gauge-invariant world. Our calculation is not tied to any specific scheme of dynamical symmetry breaking. A representation for Newton's coupling constant in terms of flat-space quantities is derived. The sign of Newton's coupling constant appears to depend on infrared details of the symmetry-breaking mechanism

  6. Can dark energy be a bonus in Horava gravity?

    Park, Mu-In

    2010-01-01

    Recently, Horava proposed a renormalizable gravity theory with higher spatial derivatives in four dimensions which reduces to Einstein gravity with a non-vanishing cosmological constant in IR but with improved UV behaviors. Here, I consider a non-trivial test of the new gravity theory in a Friedmann-Robertson-Walker (FRW) universe by considering an IR modification which breaks 'softly' the detailed balance condition in the original Horava model. I separate the dark energy parts from the usual Einstein gravity parts in the Friedman equations and obtain the formula of the equations of the state parameters. The IR-modified Horava gravity seems to be consistent with the current observational data, but we need some more refined data sets to see whether the theory is really consistent with our universe. From the consistency of our theory, I obtain some constraints on the allowed values of w 0 and w a in Chevallier, Polarski, and Linder's parametrization, and this may be tested in the near future, by sharpening the data sets.

  7. Electrovacuum solutions in nonlocal gravity

    Fernandes, Karan; Mitra, Arpita

    2018-05-01

    We consider the coupling of the electromagnetic field to a nonlocal gravity theory comprising of the Einstein-Hilbert action in addition to a nonlocal R □-2R term associated with a mass scale m . We demonstrate that in the case of the minimally coupled electromagnetic field, real corrections about the Reissner-Nordström background only exist between the inner Cauchy horizon and the event horizon of the black hole. This motivates us to consider the modified coupling of electromagnetism to this theory via the Kaluza ansatz. The Kaluza reduction introduces nonlocal terms involving the electromagnetic field to the pure gravitational nonlocal theory. An iterative approach is provided to perturbatively solve the equations of motion to arbitrary order in m2 about any known solution of general relativity. We derive the first-order corrections and demonstrate that the higher order corrections are real and perturbative about the external background of a Reissner-Nordström black hole. We also discuss how the Kaluza reduced action, through the inclusion of nonlocal electromagnetic fields, could also be relevant in quantum effects on curved backgrounds with horizons.

  8. Gravity localization on hybrid branes

    D.F.S. Veras

    2016-03-01

    Full Text Available This work deals with gravity localization on codimension-1 brane worlds engendered by compacton-like kinks, the so-called hybrid branes. In such scenarios, the thin brane behavior is manifested when the extra dimension is outside the compact domain, where the energy density is non-trivial, instead of asymptotically as in the usual thick brane models. The zero mode is trapped in the brane, as required. The massive modes, although not localized in the brane, have important phenomenological implications such as corrections to the Newton's law. We study such corrections in the usual thick domain wall and in the hybrid brane scenarios. By means of suitable numerical methods, we attain the mass spectrum for the graviton and the corresponding wavefunctions. The spectra possess the usual linearly increasing behavior from the Kaluza–Klein theories. Further, we show that the 4D gravitational force is slightly increased at short distances. The first eigenstate contributes highly for the correction to the Newton's law. The subsequent normalized solutions have diminishing contributions. Moreover, we find out that the phenomenology of the hybrid brane is not different from the usual thick domain wall. The use of numerical techniques for solving the equations of the massive modes is useful for matching possible phenomenological measurements in the gravitational law as a probe to warped extra dimensions.

  9. Absolute Gravity Datum in the Age of Cold Atom Gravimeters

    Childers, V. A.; Eckl, M. C.

    2014-12-01

    The international gravity datum is defined today by the International Gravity Standardization Net of 1971 (IGSN-71). The data supporting this network was measured in the 1950s and 60s using pendulum and spring-based gravimeter ties (plus some new ballistic absolute meters) to replace the prior protocol of referencing all gravity values to the earlier Potsdam value. Since this time, gravimeter technology has advanced significantly with the development and refinement of the FG-5 (the current standard of the industry) and again with the soon-to-be-available cold atom interferometric absolute gravimeters. This latest development is anticipated to provide improvement in the range of two orders of magnitude as compared to the measurement accuracy of technology utilized to develop ISGN-71. In this presentation, we will explore how the IGSN-71 might best be "modernized" given today's requirements and available instruments and resources. The National Geodetic Survey (NGS), along with other relevant US Government agencies, is concerned about establishing gravity control to establish and maintain high order geodetic networks as part of the nation's essential infrastructure. The need to modernize the nation's geodetic infrastructure was highlighted in "Precise Geodetic Infrastructure, National Requirements for a Shared Resource" National Academy of Science, 2010. The NGS mission, as dictated by Congress, is to establish and maintain the National Spatial Reference System, which includes gravity measurements. Absolute gravimeters measure the total gravity field directly and do not involve ties to other measurements. Periodic "intercomparisons" of multiple absolute gravimeters at reference gravity sites are used to constrain the behavior of the instruments to ensure that each would yield reasonably similar measurements of the same location (i.e. yield a sufficiently consistent datum when measured in disparate locales). New atomic interferometric gravimeters promise a significant

  10. Granular Superconductors and Gravity

    Noever, David; Koczor, Ron

    1999-01-01

    As a Bose condensate, superconductors provide novel conditions for revisiting previously proposed couplings between electromagnetism and gravity. Strong variations in Cooper pair density, large conductivity and low magnetic permeability define superconductive and degenerate condensates without the traditional density limits imposed by the Fermi energy (approx. 10(exp -6) g cu cm). Recent experiments have reported anomalous weight loss for a test mass suspended above a rotating Type II, YBCO superconductor, with a relatively high percentage change (0.05-2.1%) independent of the test mass' chemical composition and diamagnetic properties. A variation of 5 parts per 104 was reported above a stationary (non-rotating) superconductor. In experiments using a sensitive gravimeter, bulk YBCO superconductors were stably levitated in a DC magnetic field and exposed without levitation to low-field strength AC magnetic fields. Changes in observed gravity signals were measured to be less than 2 parts in 108 of the normal gravitational acceleration. Given the high sensitivity of the test, future work will examine variants on the basic magnetic behavior of granular superconductors, with particular focus on quantifying their proposed importance to gravity.

  11. Venus gravity fields

    Sjogren, W. L.; Ananda, M.; Williams, B. G.; Birkeland, P. W.; Esposito, P. S.; Wimberly, R. N.; Ritke, S. J.

    1981-01-01

    Results of Pioneer Venus Orbiter observations concerning the gravity field of Venus are presented. The gravitational data was obtained from reductions of Doppler radio tracking data for the Orbiter, which is in a highly eccentric orbit with periapsis altitude varying from 145 to 180 km and nearly fixed periapsis latitude of 15 deg N. The global gravity field was obtained through the simultaneous estimation of the orbit state parameters and gravity coefficients from long-period variations in orbital element rates. The global field has been described with sixth degree and order spherical harmonic coefficients, which are capable of resolving the three major topographical features on Venus. Local anomalies have been mapped using line-of-sight accelerations derived from the Doppler residuals between 40 deg N and 10 deg S latitude at approximately 300 km spatial resolution. Gravitational data is observed to correspond to topographical data obtained by radar altimeter, with most of the gravitational anomalies about 20-30 milligals. Simulations evaluating the isostatic states of two topographic features indicate that at least partial isostasy prevails, with the possibility of complete compensation.

  12. Thickenings and conformal gravity

    Lebrun, Claude

    1991-07-01

    A twistor correspondence is given for complex conformal space-times with vanishing Bach and Eastwood-Dighton tensors; when the Weyl curvature is algebraically general, these equations are precisely the conformal version of Einstein's vacuum equations with cosmological constant. This gives a fully curved version of the linearized correspondence of Baston and Mason [B-M].

  13. Thickenings and conformal gravity

    LeBrun, C. (State Univ. of New York, Stony Brook, NY (USA). Dept. of Mathematics)

    1991-07-01

    A twistor correspondence is given for complex conformal space-times with vanishing Bach and Eastwood-Dighton tensors; when the Weyl curvature is algebraically general, these equations are precisely the conformal version of Einstein's vacuum equations with cosmological constant. This gives a fully curved version of the linearized correspondence of Baston and Mason (B-M). (orig.).

  14. Thickenings and conformal gravity

    LeBrun, C.

    1991-01-01

    A twistor correspondence is given for complex conformal space-times with vanishing Bach and Eastwood-Dighton tensors; when the Weyl curvature is algebraically general, these equations are precisely the conformal version of Einstein's vacuum equations with cosmological constant. This gives a fully curved version of the linearized correspondence of Baston and Mason [B-M]. (orig.)

  15. Unraveling gravity beyond Einstein with extended test bodies

    Puetzfeld, Dirk; Obukhov, Yuri N.

    2013-01-01

    The motion of test bodies in gravity is tightly linked to the conservation laws. This well-known fact in the context of General Relativity is also valid for gravitational theories which go beyond Einstein's theory. Here we derive the equations of motion for test bodies for a very large class of gravitational theories with a general nonminimal coupling to matter. These equations form the basis for future systematic tests of alternative gravity theories. Our treatment is covariant and generalizes the classic Mathisson–Papapetrou–Dixon result for spinning (extended) test bodies. The equations of motion for structureless test bodies turn out to be surprisingly simple, despite the very general nature of the theories considered.

  16. Constraining inverse curvature gravity with supernovae

    Mena, Olga; Santiago, Jose; /Fermilab; Weller, Jochen; /University Coll., London /Fermilab

    2005-10-01

    We show that the current accelerated expansion of the Universe can be explained without resorting to dark energy. Models of generalized modified gravity, with inverse powers of the curvature can have late time accelerating attractors without conflicting with solar system experiments. We have solved the Friedman equations for the full dynamical range of the evolution of the Universe. This allows us to perform a detailed analysis of Supernovae data in the context of such models that results in an excellent fit. Hence, inverse curvature gravity models represent an example of phenomenologically viable models in which the current acceleration of the Universe is driven by curvature instead of dark energy. If we further include constraints on the current expansion rate of the Universe from the Hubble Space Telescope and on the age of the Universe from globular clusters, we obtain that the matter content of the Universe is 0.07 {le} {omega}{sub m} {le} 0.21 (95% Confidence). Hence the inverse curvature gravity models considered can not explain the dynamics of the Universe just with a baryonic matter component.

  17. Cosmology in general massive gravity theories

    Comelli, D.; Nesti, F.; Pilo, L.

    2014-01-01

    We study the cosmological FRW flat solutions generated in general massive gravity theories. Such a model are obtained adding to the Einstein General Relativity action a peculiar non derivative potentials, function of the metric components, that induce the propagation of five gravitational degrees of freedom. This large class of theories includes both the case with a residual Lorentz invariance as well as the case with rotational invariance only. It turns out that the Lorentz-breaking case is selected as the only possibility. Moreover it turns out that that perturbations around strict Minkowski or dS space are strongly coupled. The upshot is that even though dark energy can be simply accounted by massive gravity modifications, its equation of state w eff has to deviate from -1. Indeed, there is an explicit relation between the strong coupling scale of perturbations and the deviation of w eff from -1. Taking into account current limits on w eff and submillimiter tests of the Newton's law as a limit on the possible strong coupling scale, we find that it is still possible to have a weakly coupled theory in a quasi dS background. Future experimental improvements on short distance tests of the Newton's law may be used to tighten the deviation of w eff form -1 in a weakly coupled massive gravity theory

  18. QCD ghost f(T)-gravity model

    Karami, K.; Abdolmaleki, A.; Asadzadeh, S. [University of Kurdistan, Department of Physics, Sanandaj (Iran, Islamic Republic of); Safari, Z. [Research Institute for Astronomy and Astrophysics of Maragha (RIAAM), Maragha (Iran, Islamic Republic of)

    2013-09-15

    Within the framework of modified teleparallel gravity, we reconstruct a f(T) model corresponding to the QCD ghost dark energy scenario. For a spatially flat FRW universe containing only the pressureless matter, we obtain the time evolution of the torsion scalar T (or the Hubble parameter). Then, we calculate the effective torsion equation of state parameter of the QCD ghost f(T)-gravity model as well as the deceleration parameter of the universe. Furthermore, we fit the model parameters by using the latest observational data including SNeIa, CMB and BAO data. We also check the viability of our model using a cosmographic analysis approach. Moreover, we investigate the validity of the generalized second law (GSL) of gravitational thermodynamics for our model. Finally, we point out the growth rate of matter density perturbation. We conclude that in QCD ghost f(T)-gravity model, the universe begins a matter dominated phase and approaches a de Sitter regime at late times, as expected. Also this model is consistent with current data, passes the cosmographic test, satisfies the GSL and fits the data of the growth factor well as the {Lambda}CDM model. (orig.)

  19. Testing quantum gravity through dumb holes

    Pourhassan, Behnam, E-mail: b.pourhassan@du.ac.ir [School of Physics, Damghan University, Damghan (Iran, Islamic Republic of); Faizal, Mir, E-mail: f2mir@uwaterloo.ca [Department of Physics and Astronomy, University of Lethbridge, Lethbridge, AB T1K 3M4 (Canada); Irving K. Barber School of Arts and Sciences, University of British Columbia - Okanagan, Kelowna, BC V1V 1V7 (Canada); Capozziello, Salvatore, E-mail: capozzie@na.infn.it [Dipartimento di Fisica, Università di Napoli ”Frederico II” Complesso Universitario di Monte S. Angelo, Edificio G, Via Cinthia, I-80126 Napoli (Italy); Gran Sasso Science Institute (INFN), Via F. Crispi 7, I-67100 L’ Aquila (Italy)

    2017-02-15

    We propose a method to test the effects of quantum fluctuations on black holes by analyzing the effects of thermal fluctuations on dumb holes, the analogs for black holes. The proposal is based on the Jacobson formalism, where the Einstein field equations are viewed as thermodynamical relations, and so the quantum fluctuations are generated from the thermal fluctuations. It is well known that all approaches to quantum gravity generate logarithmic corrections to the entropy of a black hole and the coefficient of this term varies according to the different approaches to the quantum gravity. It is possible to demonstrate that such logarithmic terms are also generated from thermal fluctuations in dumb holes. In this paper, we claim that it is possible to experimentally test such corrections for dumb holes, and also obtain the correct coefficient for them. This fact can then be used to predict the effects of quantum fluctuations on realistic black holes, and so it can also be used, in principle, to experimentally test the different approaches to quantum gravity.

  20. Cosmography in f(T) gravity

    Capozziello, S.; Cardone, V. F.; Farajollahi, H.; Ravanpak, A.

    2011-01-01

    Based only on the assumption that the Universe is homogenous and isotropic on large scales, cosmography is an ideal tool to investigate the cosmic expansion history in an almost model-independent way. Fitting the data on the luminosity distance and baryon acoustic oscillations allows to determine the confidence ranges for the cosmographic parameters hence giving some quantitative constraints that at whatever theory has to fulfill. As an application, we consider here the case of teleparallel gravity also referred to as f(T) gravity. To this end, we first work out analytical expressions to express the present day values of f(T) derivatives as a function of the cosmographic parameters, which hold under quite general and physically motivated conditions. We then use the constraints coming from cosmography to find out the confidence ranges for f(T) derivatives up to the fifth order and show how these can be used to check the viability of given teleparallel gravity models without the need to explicitly solve the second order dynamic equations.

  1. Scattering of Ricci scalar perturbations from Schwarzschild black holes in modified gravity

    Sibandze, Dan B.; Goswami, Rituparno; Maharaj, Sunil D.; Nzioki, Anne Marie [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics Statistics and Computer Science, Private Bag X54001, Durban (South Africa); Dunsby, Peter K.S. [University of Cape Town, Department of Mathematics and Applied Mathematics and ACGC, Cape Town (South Africa)

    2017-06-15

    It has already been shown that the gravitational waves emitted from a Schwarzschild black hole in f(R) gravity have no signatures of the modification of gravity from General Relativity, as the Regge-Wheeler equation remains invariant. In this paper we consider the perturbations of Ricci scalar in a vacuum Schwarzschild spacetime, which is unique to higher order theories of gravity and is absent in General Relativity. We show that the equation that governs these perturbations can be reduced to a Volterra integral equation. We explicitly calculate the reflection coefficients for the Ricci scalar perturbations, when they are scattered by the black hole potential barrier. Our analysis shows that a larger fraction of these Ricci scalar waves are reflected compared to the gravitational waves. This may provide a novel observational signature for fourth order gravity. (orig.)

  2. The Imperfect Fluid behind Kinetic Gravity Braiding

    Pujolas, Oriol; Vikman, Alexander

    2011-01-01

    We present a standard hydrodynamical description for non-canonical scalar field theories with kinetic gravity braiding. In particular, this picture applies to the simplest galileons and k-essence. The fluid variables not only have a clear physical meaning but also drastically simplify the analysis of the system. The fluid carries charges corresponding to shifts in field space. This shift-charge current contains a spatial part responsible for diffusion of the charges. Moreover, in the incompressible limit, the equation of motion becomes the standard diffusion equation. The fluid is indeed imperfect because the energy flows neither along the field gradient nor along the shift current. The fluid has zero vorticity and is not dissipative: there is no entropy production, the energy-momentum is exactly conserved, the temperature vanishes and there is no shear viscosity. Still, in an expansion around a perfect fluid one can identify terms which correct the pressure in the manner of bulk viscosity. We close by formul...

  3. First order formalism for quantum gravity

    Gleiser, M.; Holman, R.; Neto, N.P.

    1987-05-01

    We develop a first order formalism for the quantization of gravity. We take as canonical variables both the induced metric and the extrinsic curvature of the (d - 1) -dimensional hypersurfaces obtained by the foliation of the d - dimensional spacetime. After solving the constraint algebra we use the Dirac formalism to quantize the theory and obtain a new representation for the Wheeler-DeWitt equation, defined in the functional space of the extrinsic curvature. We also show how to obtain several different representations of the Wheeler-DeWitt equation by considering actions differing by a total divergence. In particular, the intrinsic and extrinsic time approaches appear in a natural way, as do equivalent representations obtained by functional Fourier transforms of appropriate variables. We conclude with some remarks about the construction of the Hilbert space within the first order formalism. 10 refs

  4. Polar gravity fields from GOCE and airborne gravity

    Forsberg, René; Olesen, Arne Vestergaard; Yidiz, Hasan

    2011-01-01

    Airborne gravity, together with high-quality surface data and ocean satellite altimetric gravity, may supplement GOCE to make consistent, accurate high resolution global gravity field models. In the polar regions, the special challenge of the GOCE polar gap make the error characteristics...... of combination models especially sensitive to the correct merging of satellite and surface data. We outline comparisons of GOCE to recent airborne gravity surveys in both the Arctic and the Antarctic. The comparison is done to new 8-month GOCE solutions, as well as to a collocation prediction from GOCE gradients...... in Antarctica. It is shown how the enhanced gravity field solutions improve the determination of ocean dynamic topography in both the Arctic and in across the Drake Passage. For the interior of Antarctica, major airborne gravity programs are currently being carried out, and there is an urgent need...

  5. Gravity signatures of terrane accretion

    Franco, Heather; Abbott, Dallas

    1999-01-01

    In modern collisional environments, accreted terranes are bracketed by forearc gravity lows, a gravitational feature which results from the abandonment of the original trench and the initiation of a new trench seaward of the accreted terrane. The size and shape of the gravity low depends on the type of accreted feature and the strength of the formerly subducting plate. Along the Central American trench, the accretion of Gorgona Island caused a seaward trench jump of 48 to 66 km. The relict trench axes show up as gravity lows behind the trench with minimum values of -78 mgal (N of Gorgona) and -49 mgal (S of Gorgona) respectively. These forearc gravity lows have little or no topographic expression. The active trench immediately seaward of these forearc gravity lows has minimum gravity values of -59 mgal (N of Gorgona) and -58 mgal (S of Gorgona), respectively. In the north, the active trench has a less pronounced gravity low than the sediment covered forearc. In the Mariana arc, two Cretaceous seamounts have been accreted to the Eocene arc. The northern seamount is most likely a large block, the southern seamount may be a thrust slice. These more recent accretion events have produced modest forearc topographic and gravity lows in comparison with the topographic and gravity lows within the active trench. However, the minimum values of the Mariana forearc gravity lows are modest only by comparison to the Mariana Trench (-216 mgal); their absolute values are more negative than at Gorgona Island (-145 to -146 mgal). We speculate that the forearc gravity lows and seaward trench jumps near Gorgona Island were produced by the accretion of a hotspot island from a strong plate. The Mariana gravity lows and seaward trench jumps (or thrust slices) were the result of breaking a relatively weak plate close to the seamount edifice. These gravity lows resulting from accretion events should be preserved in older accreted terranes.

  6. A structure-based constitutive equation for filler-reinforced rubber-like networks and for the description of the Mullins effect

    Meissner, Bohumil; Matějka, Libor

    2006-01-01

    Roč. 47, č. 23 (2006), s. 7997-8012 ISSN 0032-3861 R&D Projects: GA ČR GA203/05/2252 Institutional research plan: CEZ:AV0Z40500505 Keywords : elastomers * fillers * constitutive equation Subject RIV: CD - Macromolecular Chemistry Impact factor: 2.773, year: 2006

  7. Black hole production in particle collisions and higher curvature gravity

    Rychkov, Vyacheslav S.

    2004-01-01

    The problem of black hole production in trans-Planckian particle collisions is revisited, in the context of large extra dimensions scenarios of TeV-scale gravity. The validity of the standard description of this process (two colliding Aichelburg-Sexl shock waves in classical Einstein gravity) is questioned. It is observed that the classical spacetime has large curvature along the transverse collision plane, as signaled by the curvature invariant (R μνλσ ) 2 . Thus quantum gravity effects, and in particular higher curvature corrections to the Einstein gravity, cannot be ignored. To give a specific example of what may happen, the collision is reanalyzed in the Einstein-Lanczos-Lovelock gravity theory, which modifies the Einstein-Hilbert Lagrangian by adding a particular 'Gauss-Bonnet' combination of curvature squared terms. The analysis uses a series of approximations, which reduce the field equations to a tractable second order nonlinear PDE of the Monge-Ampere type. It is found that the resulting spacetime is significantly different from the pure Einstein case in the future of the transverse collision plane. These considerations cast serious doubts on the geometric cross section estimate, which is based on the classical Einstein gravity description of the black hole production process

  8. Cosmological stability bound in massive gravity and bigravity

    Fasiello, Matteo; Tolley, Andrew J.

    2013-01-01

    We give a simple derivation of a cosmological bound on the graviton mass for spatially flat FRW solutions in massive gravity with an FRW reference metric and for bigravity theories. This bound comes from the requirement that the kinetic term of the helicity zero mode of the graviton is positive definite. The bound is dependent only on the parameters in the massive gravity potential and the Hubble expansion rate for the two metrics. We derive the decoupling limit of bigravity and FRW massive gravity, and use this to give an independent derivation of the cosmological bound. We recover our previous results that the tension between satisfying the Friedmann equation and the cosmological bound is sufficient to rule out all observationally relevant FRW solutions for massive gravity with an FRW reference metric. In contrast, in bigravity this tension is resolved due to different nature of the Vainshtein mechanism. We find that in bigravity theories there exists an FRW solution with late-time self-acceleration for which the kinetic terms for the helicity-2, helicity-1 and helicity-0 are generically nonzero and positive making this a compelling candidate for a model of cosmic acceleration. We confirm that the generalized bound is saturated for the candidate partially massless (bi)gravity theories but the existence of helicity-1/helicity-0 interactions implies the absence of the conjectured partially massless symmetry for both massive gravity and bigravity

  9. Critical gravity on AdS2 spacetimes

    Myung, Yun Soo; Kim, Yong-Wan; Park, Young-Jai

    2011-01-01

    We study the critical gravity in two-dimensional anti-de Sitter (AdS 2 ) spacetimes, which was obtained from the cosmological topologically massive gravity (TMG Λ ) in three dimensions by using the Kaluza-Klein dimensional reduction. We perform the perturbation analysis around AdS 2 , which may correspond to the near-horizon geometry of the extremal Banados, Teitelboim, and Zanelli (BTZ) black hole obtained from the TMG Λ with identification upon uplifting three dimensions. A massive propagating scalar mode δF satisfies the second-order differential equation away from the critical point of K=l, whose solution is given by the Bessel functions. On the other hand, δF satisfies the fourth-order equation at the critical point. We exactly solve the fourth-order equation, and compare it with the log gravity in two dimensions. Consequently, the critical gravity in two dimensions could not be described by a massless scalar δF ml and its logarithmic partner δF log 4th .

  10. Regularization ambiguities in loop quantum gravity

    Perez, Alejandro

    2006-01-01

    One of the main achievements of loop quantum gravity is the consistent quantization of the analog of the Wheeler-DeWitt equation which is free of ultraviolet divergences. However, ambiguities associated to the intermediate regularization procedure lead to an apparently infinite set of possible theories. The absence of an UV problem--the existence of well-behaved regularization of the constraints--is intimately linked with the ambiguities arising in the quantum theory. Among these ambiguities is the one associated to the SU(2) unitary representation used in the diffeomorphism covariant 'point-splitting' regularization of the nonlinear functionals of the connection. This ambiguity is labeled by a half-integer m and, here, it is referred to as the m ambiguity. The aim of this paper is to investigate the important implications of this ambiguity. We first study 2+1 gravity (and more generally BF theory) quantized in the canonical formulation of loop quantum gravity. Only when the regularization of the quantum constraints is performed in terms of the fundamental representation of the gauge group does one obtain the usual topological quantum field theory as a result. In all other cases unphysical local degrees of freedom arise at the level of the regulated theory that conspire against the existence of the continuum limit. This shows that there is a clear-cut choice in the quantization of the constraints in 2+1 loop quantum gravity. We then analyze the effects of the ambiguity in 3+1 gravity exhibiting the existence of spurious solutions for higher representation quantizations of the Hamiltonian constraint. Although the analysis is not complete in 3+1 dimensions - due to the difficulties associated to the definition of the physical inner product - it provides evidence supporting the definitions quantum dynamics of loop quantum gravity in terms of the fundamental representation of the gauge group as the only consistent possibilities. If the gauge group is SO(3) we find

  11. Mimicking the effect of gravity using an elastic membrane

    Wu, Yecun; Zhu, Changqing; Wang, Yijun; Shi, Qingfan

    2014-01-01

    Comparing astrospace with an elastic membrane is an interesting analogy but it lacks a theoretical basis and experimental support. We develop a theoretical model that brings to light the relationship between the conceptual model of a gravity well and an elastic deformation equation of a membrane supporting a heavy ball, and further derive the ‘gravitational constant’ for such a small ‘elastic space’. The experimental data obtained are consistent with the prediction of our model, in mimicking the revolution of a small planet. Teaching practice shows that using an elastic membrane is a simple, intuitive and reliable method to enhance the quality of learning about the effect of gravity. (paper)

  12. Astrophysical flows near [Formula: see text] gravity black holes.

    Ahmed, Ayyesha K; Azreg-Aïnou, Mustapha; Bahamonde, Sebastian; Capozziello, Salvatore; Jamil, Mubasher

    In this paper, we study the accretion process for fluids flowing near a black hole in the context of f ( T ) teleparallel gravity. Specifically, by performing a dynamical analysis by a Hamiltonian system, we are able to find the sonic points. After that, we consider different isothermal test fluids in order to study the accretion process when they are falling onto the black hole. We find that these flows can be classified according to the equation of state and the black hole features. Results are compared in f ( T ) and f ( R ) gravity.

  13. A note on the geometric unification of gravity and electromagnetism

    Coley, A.

    1984-01-01

    In recent years there have been many authors that have sought a geometrically unified theory of gravity and electromagnetism. It will be argued that the motivation behind the search for such a unified theory on geometric grounds alone is both erroneous and misleading. It is felt that any new unified theory of gravity and electromagnetism must include an explanation of why the existing theory is inadequate, and should provide clear physical reasons for introducing new fields (or field equations) that appear in the theory. (author)

  14. Astrophysical flows near f(T) gravity black holes

    Ahmed, Ayyesha K.; Jamil, Mubasher [National University of Sciences and Technology (NUST), Department of Mathematics, School of Natural Sciences (SNS), Islamabad (Pakistan); Azreg-Ainou, Mustapha [Baskent University, Baglica Campus, Engineering Faculty, Ankara (Turkey); Bahamonde, Sebastian [University College London, Department of Mathematics, London (United Kingdom); Capozziello, Salvatore [Universita di Napoli ' ' Federico II' ' , Dipartimento di Fisica, Naples (Italy); Gran Sasso Science Institute (INFN), L' Aquila (Italy); INFN Sezione di Napoli, Naples (Italy)

    2016-05-15

    In this paper, we study the accretion process for fluids flowing near a black hole in the context of f(T) teleparallel gravity. Specifically, by performing a dynamical analysis by a Hamiltonian system, we are able to find the sonic points. After that, we consider different isothermal test fluids in order to study the accretion process when they are falling onto the black hole. We find that these flows can be classified according to the equation of state and the black hole features. Results are compared in f(T) and f(R) gravity. (orig.)

  15. Propagating Degrees of Freedom in f(R Gravity

    Yun Soo Myung

    2016-01-01

    Full Text Available We have computed the number of polarization modes of gravitational waves propagating in the Minkowski background in f(R gravity. These are three of two from transverse-traceless tensor modes and one from a massive trace mode, which confirms the results found in the literature. There is no massless breathing mode and the massive trace mode corresponds to the Ricci scalar. A newly defined metric tensor in f(R gravity satisfies the transverse-traceless (TT condition as well as the TT wave equation.

  16. Geometric scalar theory of gravity beyond spherical symmetry

    Moschella, U.; Novello, M.

    2017-04-01

    We construct several exact solutions for a recently proposed geometric scalar theory of gravity. We focus on a class of axisymmetric geometries and a big-bang-like geometry and discuss their Lorentzian character. The axisymmetric solutions are parametrized by an integer angular momentum l . The l =0 (spherical) case gives rise to the Schwarzschild geometry. The other solutions have naked singular surfaces. While not a priori obvious, all the solutions that we present here are globally Lorentzian. The Lorentzian signature appears to be a robust property of the disformal geometries solving the vacuum geometric scalar theory of gravity equations.

  17. Linear network theory

    Sander, K F

    1964-01-01

    Linear Network Theory covers the significant algebraic aspect of network theory, with minimal reference to practical circuits. The book begins the presentation of network analysis with the exposition of networks containing resistances only, and follows it up with a discussion of networks involving inductance and capacity by way of the differential equations. Classification and description of certain networks, equivalent networks, filter circuits, and network functions are also covered. Electrical engineers, technicians, electronics engineers, electricians, and students learning the intricacies

  18. A 70th Degree Lunar Gravity Model (GLGM-2) from Clementine and other tracking data

    Lemonie, Frank G. R.; Smith, David E.; Zuber, Maria T.; Neumann, Gregory A.

    1997-01-01

    A spherical harmonic model of the lunar gravity field complete to degree and order 70 has been developed from S band Doppler tracking data from the Clementine mission, as well as historical tracking data from Lunar Orbiters 1-5 and the Apollo 15 and 16 subsatellites. The model combines 361,000 Doppler observations from Clementine with 347,000 historical observations. The historical data consist of mostly 60-s Doppler with a noise of 0.25 to several mm/s. The Clementine data consist of mostly 10-s Doppler data, with a data noise of 0.25 mm/s for the observations from the Deep Space Network, and 2.5 mm/s for the data from a naval tracking station at Pomonkey, Maryland. Observations provided Clementine, provide the strongest satellite constraint on the Moon's low-degree field. In contrast the historical data, collected by spacecraft that had lower periapsis altitudes, provide distributed regions of high-resolution coverage within +/- 29 deg of the nearside lunar equator. To obtain the solution for a high-degree field in the absence of a uniform distribution of observations, we applied an a priori power law constraint of the form 15 x 10(exp -5)/sq l which had the effect of limiting the gravitational power and noise at short wavelengths. Coefficients through degree and order 18 are not significantly affected by the constraint, and so the model permits geophysical analysis of effects of the major basins at degrees 10-12. The GLGM-2 model confirms major features of the lunar gravity field shown in previous gravitational field models but also reveals significantly more detail, particularly at intermediate wavelengths (10(exp 3) km). Free-air gravity anomaly maps derived from the new model show the nearside and farside highlands to be gravitationally smooth, reflecting a state of isostatic compensation. Mascon basins (including Imbrium, Serenitatis, Crisium, Smythii, and Humorum) are denoted by gravity highs first recognized from Lunar Orbiter tracking. All of the major

  19. Entropic Phase Maps in Discrete Quantum Gravity

    Benjamin F. Dribus

    2017-06-01

    Full Text Available Path summation offers a flexible general approach to quantum theory, including quantum gravity. In the latter setting, summation is performed over a space of evolutionary pathways in a history configuration space. Discrete causal histories called acyclic directed sets offer certain advantages over similar models appearing in the literature, such as causal sets. Path summation defined in terms of these histories enables derivation of discrete Schrödinger-type equations describing quantum spacetime dynamics for any suitable choice of algebraic quantities associated with each evolutionary pathway. These quantities, called phases, collectively define a phase map from the space of evolutionary pathways to a target object, such as the unit circle S 1 ⊂ C , or an analogue such as S 3 or S 7 . This paper explores the problem of identifying suitable phase maps for discrete quantum gravity, focusing on a class of S 1 -valued maps defined in terms of “structural increments” of histories, called terminal states. Invariants such as state automorphism groups determine multiplicities of states, and induce families of natural entropy functions. A phase map defined in terms of such a function is called an entropic phase map. The associated dynamical law may be viewed as an abstract combination of Schrödinger’s equation and the second law of thermodynamics.

  20. Scalar fields and higher-derivative gravity in brane worlds

    Pichler, S.

    2004-01-01

    We consider the brane world picture in the context of higher-derivative theories of gravity and tackle the problematic issues fine-tuning and brane-embedding. First, we give an overview of extra-dimensional physics, from the Kaluza-Klein picture up to modern brane worlds with large extra dimensions. We describe the different models and their physical impact on future experiments. We work within the framework of Randall-Sundrum models in which the brane is a gravitating object, which warps the background metric. We add scalar fields to the original model and find new and self-consistent solutions for quadratic potentials of the fields. This gives us the tools to investigate higher-derivative gravity theories in brane world models. Specifically, we take gravitational Lagrangians that depend on an arbitrary function of the Ricci scalar only, so-called f(R)-gravity. We make use of the conformal equivalence between f(R)-gravity and Einstein-Hilbert gravity with an auxiliary scalar field. We find that the solutions in the higher-derivative gravity framework behave very differently from the original Randall-Sundrum model: the metric functions do not have the typical kink across the brane. Furthermore, we present solutions that do not rely on a cosmological constant in the bulk and so avoid the fine-tuning problem. We address the issue of brane-embedding, which is important in perturbative analyses. We consider the embedding of codimension one hypersurfaces in general and derive a new equation of motion with which the choice for the embedding has to comply. In particular, this allows for a consistent consideration of brane world perturbations in the case of higher-derivative gravity. We use the newly found background solutions for quadratic potentials and find that gravity is still effectively localized on the brane, i.e that the Newtonian limit holds

  1. Spin foam models of Yang-Mills theory coupled to gravity

    Mikovic, A

    2003-01-01

    We construct a spin foam model of Yang-Mills theory coupled to gravity by using a discretized path integral of the BF theory with polynomial interactions and the Barrett-Crane ansatz. In the Euclidean gravity case, we obtain a vertex amplitude which is determined by a vertex operator acting on a simple spin network function. The Euclidean gravity results can be straightforwardly extended to the Lorentzian case, so that we propose a Lorentzian spin foam model of Yang-Mills theory coupled to gravity

  2. Geodetic and geophysical results from a Taiwan airborne gravity survey: Data reduction and accuracy assessment

    Hwang, C.W.; Hsiao, Y.S.; Shih, H.C.

    2007-01-01

    [ 1] An airborne gravity survey was conducted over Taiwan using a LaCoste and Romberg (LCR) System II air-sea gravimeter with gravity and global positioning system (GPS) data sampled at 1 Hz. The aircraft trajectories were determined using a GPS network kinematic adjustment relative to eight GPS ...... using airborne and surface gravity data and the other using surface data only, and the former yields a better agreement with the GPS-derived geoidal heights. Bouguer anomalies derived from airborne gravity by a rigorous numerical integration reveal important tectonic features....

  3. Temporal gravity changes before the 2008 Yutian Ms7.3 earthquake

    Chongyang, Shen; Hui, Li; Shaoan, Sun; Guangliang, Yang; Songbai, Xuan; Hongbo, Tan; Shaoming, Liu

    2012-01-01

    Based on the data of the repeated gravity observation network in Chinese mainland since 1998, we analyzed the temporal changes of regional gravity field before the 2008 Yutian Ms7. 3 earthquake. The result shows some mid-to-long term (two to ten years) changes during the earthquake’s preparation. Notable features are a gravity increase lasting several years and a relatively large-scaled gradient zone of gravity change, the former indicating a continuous energy accumulation and the latter a po...

  4. Joint Military Operations: Centers of Gravity and the War in Kosovo

    Milley, Mark

    2000-01-01

    ... and not throw the baby out with the bathwater. Even in this age of networked warfare, precision strike munitions and real time intelligence, Clausewitz's discussions of centers of gravity still provide fundamental insight into the conduct of war...

  5. Cosmological tests of modified gravity.

    Koyama, Kazuya

    2016-04-01

    We review recent progress in the construction of modified gravity models as alternatives to dark energy as well as the development of cosmological tests of gravity. Einstein's theory of general relativity (GR) has been tested accurately within the local universe i.e. the Solar System, but this leaves the possibility open that it is not a good description of gravity at the largest scales in the Universe. This being said, the standard model of cosmology assumes GR on all scales. In 1998, astronomers made the surprising discovery that the expansion of the Universe is accelerating, not slowing down. This late-time acceleration of the Universe has become the most challenging problem in theoretical physics. Within the framework of GR, the acceleration would originate from an unknown dark energy. Alternatively, it could be that there is no dark energy and GR itself is in error on cosmological scales. In this review, we first give an overview of recent developments in modified gravity theories including f(R) gravity, braneworld gravity, Horndeski theory and massive/bigravity theory. We then focus on common properties these models share, such as screening mechanisms they use to evade the stringent Solar System tests. Once armed with a theoretical knowledge of modified gravity models, we move on to discuss how we can test modifications of gravity on cosmological scales. We present tests of gravity using linear cosmological perturbations and review the latest constraints on deviations from the standard [Formula: see text]CDM model. Since screening mechanisms leave distinct signatures in the non-linear structure formation, we also review novel astrophysical tests of gravity using clusters, dwarf galaxies and stars. The last decade has seen a number of new constraints placed on gravity from astrophysical to cosmological scales. Thanks to on-going and future surveys, cosmological tests of gravity will enjoy another, possibly even more, exciting ten years.

  6. Measured and modelled absolute gravity changes in Greenland

    Nielsen, Jens Emil; Forsberg, René; Strykowski, Gabriel

    2014-01-01

    in Greenland. Theresult is compared with the initial measurements of absolute gravity (AG) change at selected GreenlandNetwork (GNET) sites.We find that observations are highly influenced by the direct attraction from the ice and ocean. Thisis especially evident in the measurements conducted at the GNET...

  7. Compact objects in relativistic theories of gravity

    Okada da Silva, Hector

    2017-05-01

    In this dissertation we discuss several aspects of compact objects, i.e. neutron stars and black holes, in relativistic theories of gravity. We start by studying the role of nuclear physics (encoded in the so-called equation of state) in determining the properties of neutron stars in general relativity. We show that low-mass neutron stars are potentially useful astrophysical laboratories that can be used to constrain the properties of the equation of state. More specifically, we show that various bulk properties of these objects, such as their quadrupole moment and tidal deformability, are tightly correlated. Next, we develop a formalism that aims to capture how generic modifications from general relativity affect the structure of neutron stars, as predicted by a broad class of gravity theories, in the spirit of the parametrized post-Newtonian formalism (PPN). Our "post-Tolman-Oppenheimer-Volkoff" formalism provides a toolbox to study both stellar structure and the interior/exterior geometries of static, spherically symmetric relativistic stars. We also apply the formalism to parametrize deviations from general relativity in various astrophysical observables related with neutron stars, including surface redshift, apparent radius, Eddington luminosity. We then turn our attention to what is arguably the most well-motivated and well-investigated generalization of general relativity: scalar-tensor theory. We start by considering theories where gravity is mediated by a single extra scalar degree of freedom (in addition to the metric tensor). An interesting class of scalar-tensor theories passes all experimental tests in the weak-field regime of gravity, yet considerably deviates from general relativity in the strong-field regime in the presence of matter. A common assumption in modeling neutron stars is that the pressure within these object is spatially isotropic. We relax this assumption and examine how pressure anisotropy affects the mass, radius and moment of inertia

  8. Bringing Gravity to Space

    Norsk, P.; Shelhamer, M.

    2016-01-01

    This panel will present NASA's plans for ongoing and future research to define the requirements for Artificial Gravity (AG) as a countermeasure against the negative health effects of long-duration weightlessness. AG could mitigate the gravity-sensitive effects of spaceflight across a host of physiological systems. Bringing gravity to space could mitigate the sensorimotor and neuro-vestibular disturbances induced by G-transitions upon reaching a planetary body, and the cardiovascular deconditioning and musculoskeletal weakness induced by weightlessness. Of particular interest for AG during deep-space missions is mitigation of the Visual Impairment Intracranial Pressure (VIIP) syndrome that the majority of astronauts exhibit in space to varying degrees, and which presumably is associated with weightlessness-induced fluid shift from lower to upper body segments. AG could be very effective for reversing the fluid shift and thus help prevent VIIP. The first presentation by Dr. Charles will summarize some of the ground-based and (very little) space-based research that has been conducted on AG by the various space programs. Dr. Paloski will address the use of AG during deep-space exploration-class missions and describe the different AG scenarios such as intra-vehicular, part-of-vehicle, or whole-vehicle centrifugations. Dr. Clement will discuss currently planned NASA research as well as how to coordinate future activities among NASA's international partners. Dr. Barr will describe some possible future plans for using space- and ground-based partial-G analogs to define the relationship between physiological responses and G levels between 0 and 1. Finally, Dr. Stenger will summarize how the human cardiovascular system could benefit from intermittent short-radius centrifugations during long-duration missions.

  9. Is Gravity an Entropic Force?

    Shan Gao

    2011-04-01

    Full Text Available The remarkable connections between gravity and thermodynamics seem to imply that gravity is not fundamental but emergent, and in particular, as Verlinde suggested, gravity is probably an entropic force. In this paper, we will argue that the idea of gravity as an entropic force is debatable. It is shown that there is no convincing analogy between gravity and entropic force in Verlinde’s example. Neither holographic screen nor test particle satisfies all requirements for the existence of entropic force in a thermodynamics system. Furthermore, we show that the entropy increase of the screen is not caused by its statistical tendency to increase entropy as required by the existence of entropic force, but in fact caused by gravity. Therefore, Verlinde’s argument for the entropic origin of gravity is problematic. In addition, we argue that the existence of a minimum size of spacetime, together with the Heisenberg uncertainty principle in quantum theory, may imply the fundamental existence of gravity as a geometric property of spacetime. This may provide a further support for the conclusion that gravity is not an entropic force.

  10. Active Response Gravity Offload System

    Valle, Paul; Dungan, Larry; Cunningham, Thomas; Lieberman, Asher; Poncia, Dina

    2011-01-01

    The Active Response Gravity Offload System (ARGOS) provides the ability to simulate with one system the gravity effect of planets, moons, comets, asteroids, and microgravity, where the gravity is less than Earth fs gravity. The system works by providing a constant force offload through an overhead hoist system and horizontal motion through a rail and trolley system. The facility covers a 20 by 40-ft (approximately equals 6.1 by 12.2m) horizontal area with 15 ft (approximately equals4.6 m) of lifting vertical range.

  11. Teleparallel equivalent of Lovelock gravity

    González, P. A.; Vásquez, Yerko

    2015-12-01

    There is a growing interest in modified gravity theories based on torsion, as these theories exhibit interesting cosmological implications. In this work inspired by the teleparallel formulation of general relativity, we present its extension to Lovelock gravity known as the most natural extension of general relativity in higher-dimensional space-times. First, we review the teleparallel equivalent of general relativity and Gauss-Bonnet gravity, and then we construct the teleparallel equivalent of Lovelock gravity. In order to achieve this goal, we use the vielbein and the connection without imposing the Weitzenböck connection. Then, we extract the teleparallel formulation of the theory by setting the curvature to null.

  12. Field-theoretic approach to gravity in the flat space-time

    Cavalleri, G [Centro Informazioni Studi Esperienze, Milan (Italy); Milan Univ. (Italy). Ist. di Fisica); Spinelli, G [Istituto di Matematica del Politecnico di Milano, Milano (Italy)

    1980-01-01

    In this paper it is discussed how the field-theoretical approach to gravity starting from the flat space-time is wider than the Einstein approach. The flat approach is able to predict the structure of the observable space as a consequence of the behaviour of the particle proper masses. The field equations are formally equal to Einstein's equations without the cosmological term.

  13. The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

    Finster, Felix E-mail: felix.finster@mis.mpg.de; Smoller, Joel E-mail: smoller@umich.edu; Yau, S.-T. E-mail: yau@math.harvard.edu

    2000-09-18

    We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

  14. The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

    Finster, Felix; Smoller, Joel; Yau, Shing-Tung

    2000-09-01

    We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling.

  15. The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

    Finster, Felix; Smoller, Joel; Yau, S.-T.

    2000-01-01

    We consider a spherically symmetric, static system of a Dirac particle interacting with classical gravity and an SU(2) Yang-Mills field. The corresponding Einstein-Dirac-Yang-Mills equations are derived. Using numerical methods, we find different types of soliton-like solutions of these equations and discuss their properties. Some of these solutions are stable even for arbitrarily weak gravitational coupling

  16. Comparative Study on Theoretical and Machine Learning Methods for Acquiring Compressed Liquid Densities of 1,1,1,2,3,3,3-Heptafluoropropane (R227ea via Song and Mason Equation, Support Vector Machine, and Artificial Neural Networks

    Hao Li

    2016-01-01

    Full Text Available 1,1,1,2,3,3,3-Heptafluoropropane (R227ea is a good refrigerant that reduces greenhouse effects and ozone depletion. In practical applications, we usually have to know the compressed liquid densities at different temperatures and pressures. However, the measurement requires a series of complex apparatus and operations, wasting too much manpower and resources. To solve these problems, here, Song and Mason equation, support vector machine (SVM, and artificial neural networks (ANNs were used to develop theoretical and machine learning models, respectively, in order to predict the compressed liquid densities of R227ea with only the inputs of temperatures and pressures. Results show that compared with the Song and Mason equation, appropriate machine learning models trained with precise experimental samples have better predicted results, with lower root mean square errors (RMSEs (e.g., the RMSE of the SVM trained with data provided by Fedele et al. [1] is 0.11, while the RMSE of the Song and Mason equation is 196.26. Compared to advanced conventional measurements, knowledge-based machine learning models are proved to be more time-saving and user-friendly.

  17. A distinguishing gravitational property for gravitational equation in higher dimensions

    Dadhich, Naresh

    2016-01-01

    It is well known that Einstein gravity is kinematic (meaning that there is no non-trivial vacuum solution; i.e. the Riemann tensor vanishes whenever the Ricci tensor does so) in 3 dimension because the Riemann tensor is entirely given in terms of the Ricci tensor. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one Nth order term in the action) gravity for which the Nth order Lovelock-Riemann tensor is indeed given in terms of the corresponding Ricci tensor for all odd, d = 2N + 1, dimensions. This feature of gravity is realized only in higher dimensions and it uniquely picks out pure Lovelock gravity from all other generalizations of Einstein gravity. It serves as a good distinguishing and guiding criterion for the gravitational equation in higher dimensions. (orig.)

  18. A distinguishing gravitational property for gravitational equation in higher dimensions

    Dadhich, Naresh

    2016-03-01

    It is well known that Einstein gravity is kinematic (meaning that there is no non-trivial vacuum solution; i.e. the Riemann tensor vanishes whenever the Ricci tensor does so) in 3 dimension because the Riemann tensor is entirely given in terms of the Ricci tensor. Could this property be universalized for all odd dimensions in a generalized theory? The answer is yes, and this property uniquely singles out pure Lovelock (it has only one Nth order term in the action) gravity for which the Nth order Lovelock-Riemann tensor is indeed given in terms of the corresponding Ricci tensor for all odd, d=2N+1, dimensions. This feature of gravity is realized only in higher dimensions and it uniquely picks out pure Lovelock gravity from all other generalizations of Einstein gravity. It serves as a good distinguishing and guiding criterion for the gravitational equation in higher dimensions.

  19. The gravity apple tree

    Aldama, Mariana Espinosa

    2015-01-01

    The gravity apple tree is a genealogical tree of the gravitation theories developed during the past century. The graphic representation is full of information such as guides in heuristic principles, names of main proponents, dates and references for original articles (See under Supplementary Data for the graphic representation). This visual presentation and its particular classification allows a quick synthetic view for a plurality of theories, many of them well validated in the Solar System domain. Its diachronic structure organizes information in a shape of a tree following similarities through a formal concept analysis. It can be used for educational purposes or as a tool for philosophical discussion. (paper)

  20. Differential Equations Compatible with KZ Equations

    Felder, G.; Markov, Y.; Tarasov, V.; Varchenko, A.

    2000-01-01

    We define a system of 'dynamical' differential equations compatible with the KZ differential equations. The KZ differential equations are associated to a complex simple Lie algebra g. These are equations on a function of n complex variables z i taking values in the tensor product of n finite dimensional g-modules. The KZ equations depend on the 'dual' variable in the Cartan subalgebra of g. The dynamical differential equations are differential equations with respect to the dual variable. We prove that the standard hypergeometric solutions of the KZ equations also satisfy the dynamical equations. As an application we give a new determinant formula for the coordinates of a basis of hypergeometric solutions