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

Science.gov (United States)

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.

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

Science.gov (United States)

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

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

Directory of Open Access Journals (Sweden)

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.

Massive gravity from bimetric gravity

International Nuclear Information System (INIS)

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)

NGS Gravity Network Data for the U.S.

Data.gov (United States)

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.

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

DEFF Research Database (Denmark)

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...

The electrical network of maize root apex is gravity dependent.

Science.gov (United States)

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.

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

Directory of Open Access Journals (Sweden)

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.

Semigroup methods for evolution equations on networks

CERN Document Server

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...

Equations of motion in linearised gravity

International Nuclear Information System (INIS)

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)

Equations of motion in relativistic gravity

CERN Document Server

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 ...

Equations of motion for massive spin 2 field coupled to gravity

International Nuclear Information System (INIS)

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

Equations of motion for massive spin 2 field coupled to gravity

Energy Technology Data Exchange (ETDEWEB)

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.

A dynamic ventilation model for gravity sewer networks.

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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

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

Directory of Open Access Journals (Sweden)

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.

Minimal Liouville gravity on the torus via the Douglas string equation

International Nuclear Information System (INIS)

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)

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

Energy Technology Data Exchange (ETDEWEB)

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.

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

International Nuclear Information System (INIS)

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)

Chiral gravity, log gravity, and extremal CFT

International Nuclear Information System (INIS)

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.

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

International Nuclear Information System (INIS)

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.

An introduction to neural network methods for differential equations

CERN Document Server

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...

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

Energy Technology Data Exchange (ETDEWEB)

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.

Optimization of a Time-Lapse Gravity Network for Carbon Sequestration

Science.gov (United States)

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

influence of gravity

Directory of Open Access Journals (Sweden)

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.

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

Directory of Open Access Journals (Sweden)

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.

Stochastic analysis of complex reaction networks using binomial moment equations.

Science.gov (United States)

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.

Terrestrial gravity data analysis for interim gravity model improvement

Science.gov (United States)

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.

Generalized master equations for non-Poisson dynamics on networks.

Science.gov (United States)

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.

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

Directory of Open Access Journals (Sweden)

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.

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

Directory of Open Access Journals (Sweden)

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.

Solitons in Newtonian gravity

International Nuclear Information System (INIS)

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)

Horizon thermodynamics in fourth-order gravity

Directory of Open Access Journals (Sweden)

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.

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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)

Gravity with Intermediate Goods Trade

Directory of Open Access Journals (Sweden)

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.

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

Science.gov (United States)

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.

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

DEFF Research Database (Denmark)

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...

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

International Nuclear Information System (INIS)

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)

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

International Nuclear Information System (INIS)

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.

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

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

Contravariant gravity on Poisson manifolds and Einstein gravity

International Nuclear Information System (INIS)

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)

Stochastic Gravity: Theory and Applications

Directory of Open Access Journals (Sweden)

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

Network Reconstruction From High-Dimensional Ordinary Differential Equations.

Science.gov (United States)

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.

Carroll versus Galilei gravity

Energy Technology Data Exchange (ETDEWEB)

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.

Quintic quasi-topological gravity

Energy Technology Data Exchange (ETDEWEB)

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.

Constructing general partial differential equations using polynomial and neural networks.

Science.gov (United States)

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.

Superconducting gravity gradiometer for sensitive gravity measurements. I. Theory

International Nuclear Information System (INIS)

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

Solving differential equations with unknown constitutive relations as recurrent neural networks

Energy Technology Data Exchange (ETDEWEB)

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.

Critical gravity on AdS2 spacetimes

International Nuclear Information System (INIS)

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 .

The earth's shape and gravity

CERN Document Server

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

Exact Solutions in 3D New Massive Gravity

Science.gov (United States)

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.

2D higher spin gravity and the multimatrix models

International Nuclear Information System (INIS)

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.)

Epidemics in networks: a master equation approach

International Nuclear Information System (INIS)

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)

Epidemics in networks: a master equation approach

Science.gov (United States)

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.

Newtonian hydrodynamic equations with relativistic pressure and velocity

Energy Technology Data Exchange (ETDEWEB)

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.

Solution of weakly compressible isothermal flow in landfill gas collection networks

Science.gov (United States)

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.

Constraints on modified gravity models from white dwarfs

Energy Technology Data Exchange (ETDEWEB)

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.

General relativity and gauge gravity theories of higher order

International Nuclear Information System (INIS)

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

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

African Journals Online (AJOL)

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 ...

On 3D Minimal Massive Gravity

CERN Document Server

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.

n  +  1 formalism of f (Lovelock) gravity

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

International Nuclear Information System (INIS)

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

The quantization of gravity

CERN Document Server

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 ...

Solution of weakly compressible isothermal flow in landfill gas collection networks

Energy Technology Data Exchange (ETDEWEB)

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)

Solution of weakly compressible isothermal flow in landfill gas collection networks

International Nuclear Information System (INIS)

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)

Gravity interpretation via EULDPH

International Nuclear Information System (INIS)

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

Equivalence of two-dimensional gravities

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Neural network error correction for solving coupled ordinary differential equations

Science.gov (United States)

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.

Radion and holographic brane gravity

International Nuclear Information System (INIS)

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

Singularity: Raychaudhuri equation once again

Indian Academy of Sciences (India)

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.

Measuring Gravity in International Trade Flows

Directory of Open Access Journals (Sweden)

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

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

Directory of Open Access Journals (Sweden)

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.

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

International Nuclear Information System (INIS)

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

Lanczos-Lovelock gravity from a thermodynamic perspective

International Nuclear Information System (INIS)

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

On higher derivative gravity

International Nuclear Information System (INIS)

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

Phase space of modified Gauss-Bonnet gravity

Energy Technology Data Exchange (ETDEWEB)

Carloni, Sante [Universidade de Lisboa-UL, Centro Multidisciplinar de Astrofisica-CENTRA, Instituto Superior Tecnico-IST, Lisbon (Portugal); Mimoso, Jose P. [Instituto de Astrofisica e Ciencias do Espaco, Universidade de Lisboa, Departamento de Fisica, Faculdade de Ciencias, Lisbon (Portugal)

2017-08-15

We investigate the evolution of non-vacuum Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetimes with any spatial curvature in the context of Gauss-Bonnet gravity. The analysis employs a new method which enables us to explore the phase space of any specific theory of this class. We consider several examples, discussing the transition from a decelerating into an acceleration universe within these theories. We also deduce from the dynamical equations some general conditions on the form of the action which guarantee the presence of specific behaviours like the emergence of accelerated expansion. As in f(R) gravity, our analysis shows that there is a set of initial conditions for which these models have a finite time singularity which can be an attractor. The presence of this instability also in the Gauss-Bonnet gravity is to be ascribed to the fourth-order derivative in the field equations, i.e., is the direct consequence of the higher order of the equations. (orig.)

Dirac fields in loop quantum gravity and big bang nucleosynthesis

International Nuclear Information System (INIS)

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.

Generalized Vaidya spacetime for cubic gravity

Science.gov (United States)

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.

Black holes in pure Lovelock gravities

International Nuclear Information System (INIS)

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

Lovelock-Brans-Dicke gravity

Science.gov (United States)

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 }{{{\

Stochastic differential equations for quantum dynamics of spin-boson networks

International Nuclear Information System (INIS)

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)

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

Science.gov (United States)

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.

Tensor Galileons and gravity

Energy Technology Data Exchange (ETDEWEB)

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.

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

Energy Technology Data Exchange (ETDEWEB)

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.)

Image recovery using diffusion equation embedded neural network

International Nuclear Information System (INIS)

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

Classical Weyl transverse gravity

Energy Technology Data Exchange (ETDEWEB)

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.)

Lanczos–Lovelock models of gravity

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

Polytropic and Chaplygin f(T)-gravity models

International Nuclear Information System (INIS)

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.

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

Science.gov (United States)

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.

Variation of the gravity acceleration with the latitude and altitude

Directory of Open Access Journals (Sweden)

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.

Late-time cosmological approach in mimetic f(R, T) gravity

Energy Technology Data Exchange (ETDEWEB)

Baffou, E.H. [Institut de Mathematiques et de Sciences Physiques (IMSP), Porto-Novo (Benin); Houndjo, M.J.S. [Institut de Mathematiques et de Sciences Physiques (IMSP), Porto-Novo (Benin); Faculte des Sciences et Techniques de Natitingou, Natitingou (Benin); Hamani-Daouda, M. [Universite de Niamey, Departement de Physique, Niamey (Niger); Alvarenga, F.G. [Universidade Federal do Espirito Santo, Departamento de Engenharia e Ciencias Naturais, CEUNES, Sao Mateus, ES (Brazil)

2017-10-15

In this paper, we investigate the late-time cosmic acceleration in mimetic f(R, T) gravity with the Lagrange multiplier and potential in a Universe containing, besides radiation and dark energy, a self-interacting (collisional) matter. We obtain through the modified Friedmann equations the main equation that can describe the cosmological evolution. Then, with several models from Q(z) and the well-known particular model f(R, T), we perform an analysis of the late-time evolution. We examine the behavior of the Hubble parameter, the dark energy equation of state and the total effective equation of state and in each case we compare the resulting picture with the non-collisional matter (assumed as dust) and also with the collisional matter in mimetic f(R, T) gravity. The results obtained are in good agreement with the observational data and show that in the presence of the collisional matter the dark energy oscillations in mimetic f(R, T) gravity can be damped. (orig.)

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

Science.gov (United States)

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.

McVittie solution in f(T) gravity

Energy Technology Data Exchange (ETDEWEB)

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.)

McVittie solution in f(T) gravity

International Nuclear Information System (INIS)

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.)

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

Energy Technology Data Exchange (ETDEWEB)

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.

De Sitter space in gauge/gravity duality

Directory of Open Access Journals (Sweden)

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.

Scattering of Ricci scalar perturbations from Schwarzschild black holes in modified gravity

Energy Technology Data Exchange (ETDEWEB)

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.)

Unraveling gravity beyond Einstein with extended test bodies

International Nuclear Information System (INIS)

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.

Equivalent equations of motion for gravity and entropy

International Nuclear Information System (INIS)

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.

Antigravity: Spin-gravity coupling in action

Science.gov (United States)

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.

A perturbative approach to neutron stars in f(T, T)-gravity

Energy Technology Data Exchange (ETDEWEB)

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

2017-05-15

We derive a Tolman-Oppenheimer-Volkoff equation in neutron star systems within the modified f(T, T)-gravity class of models using a perturbative approach. In our approach f(T, T)-gravity is considered to be a static spherically symmetric space-time. In this instance the metric is built from a more fundamental vierbein which can be used to relate inertial and global coordinates. A linear function f = T(r) + T(r) + χh(T, T) + O(χ{sup 2}) is taken as the Lagrangian density for the gravitational action. Finally we impose the polytropic equation of state of neutron star upon the derived equations in order to derive the mass profile and mass-central density relations of the neutron star in f(T, T)-gravity. (orig.)

Cosmology of Horava-Lifshitz f(R) gravity

International Nuclear Information System (INIS)

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.)

Cosmology of Horava-Lifshitz f(R) gravity

Energy Technology Data Exchange (ETDEWEB)

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.)

Algorithms for optimization of branching gravity-driven water networks

Directory of Open Access Journals (Sweden)

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

Algorithms for optimization of branching gravity-driven water networks

Science.gov (United States)

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.

Alternative Hamiltonian representation for gravity

International Nuclear Information System (INIS)

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

Population equations for degree-heterogenous neural networks

Science.gov (United States)

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.

Exploring plane-symmetric solutions in f(R) gravity

Energy Technology Data Exchange (ETDEWEB)

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.

Further stable neutron star models from f(R) gravity

Energy Technology Data Exchange (ETDEWEB)

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)

Further stable neutron star models from f(R) gravity

International Nuclear Information System (INIS)

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)

Gravity as Quantum Entanglement Force

OpenAIRE

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...

The Schrödinger–Newton equation and its foundations

International Nuclear Information System (INIS)

Bahrami, Mohammad; Großardt, André; Donadi, Sandro; Bassi, Angelo

2014-01-01

The necessity of quantising the gravitational field is still subject to an open debate. In this paper we compare the approach of quantum gravity, with that of a fundamentally semi-classical theory of gravity, in the weak-field non-relativistic limit. We show that, while in the former case the Schrödinger equation stays linear, in the latter case one ends up with the so-called Schrödinger–Newton equation, which involves a nonlinear, non-local gravitational contribution. We further discuss that the Schrödinger–Newton equation does not describe the collapse of the wave-function, although it was initially proposed for exactly this purpose. Together with the standard collapse postulate, fundamentally semi-classical gravity gives rise to superluminal signalling. A consistent fundamentally semi-classical theory of gravity can therefore only be achieved together with a suitable prescription of the wave-function collapse. We further discuss, how collapse models avoid such superluminal signalling and compare the nonlinearities appearing in these models with those in the Schrödinger–Newton equation. (paper)

Stochastic Gravity: Theory and Applications

Directory of Open Access Journals (Sweden)

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

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

International Nuclear Information System (INIS)

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)

Circulation-based Modeling of Gravity Currents

Science.gov (United States)

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

Massive Conformal Gravity

International Nuclear Information System (INIS)

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.

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

Science.gov (United States)

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.

Alternative Hamiltonian representation for gravity

Energy Technology Data Exchange (ETDEWEB)

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.

f(Lovelock) theories of gravity

Science.gov (United States)

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.

f(Lovelock) theories of gravity

International Nuclear Information System (INIS)

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.

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

Science.gov (United States)

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.

Can dark energy be a bonus in Horava gravity?

International Nuclear Information System (INIS)

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.

Quantum Gravity Experiments

Directory of Open Access Journals (Sweden)

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.

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

Science.gov (United States)

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.

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

DEFF Research Database (Denmark)

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....

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

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

Noether symmetry approach in f(G,T) gravity

Energy Technology Data Exchange (ETDEWEB)

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.)

Neutron stars structure in the context of massive gravity

Energy Technology Data Exchange (ETDEWEB)

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.

Neutron stars structure in the context of massive gravity

Science.gov (United States)

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.

Neutron stars structure in the context of massive gravity

International Nuclear Information System (INIS)

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.

Minimal theory of massive gravity

International Nuclear Information System (INIS)

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.

Surfing surface gravity waves

Science.gov (United States)

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.

Gauge-invariant flow equation

Science.gov (United States)

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.

What goes up... gravity and scientific method

CERN Document Server

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.

2D gravity and random matrices

International Nuclear Information System (INIS)

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

Violation of causality in f(T) gravity

Energy Technology Data Exchange (ETDEWEB)

Otalora, G. [Pontificia Universidad Catolica de Valparaiso, Instituto de Fisica, Valparaiso (Chile); Reboucas, M.J. [Centro Brasileiro de Pesquisas Fisicas, Rio de Janeiro, RJ (Brazil)

2017-11-15

In the standard formulation, the f(T) field equations are not invariant under local Lorentz transformations, and thus the theory does not inherit the causal structure of special relativity. Actually, even locally violation of causality can occur in this formulation of f(T) gravity. A locally Lorentz covariant f(T) gravity theory has been devised recently, and this local causality problem seems to have been overcome. The non-locality question, however, is left open. If gravitation is to be described by this covariant f(T) gravity theory there are a number of issues that ought to be examined in its context, including the question as to whether its field equations allow homogeneous Goedel-type solutions, which necessarily leads to violation of causality on non-local scale. Here, to look into the potentialities and difficulties of the covariant f(T) theories, we examine whether they admit Goedel-type solutions. We take a combination of a perfect fluid with electromagnetic plus a scalar field as source, and determine a general Goedel-type solution, which contains special solutions in which the essential parameter of Goedel-type geometries, m{sup 2}, defines any class of homogeneous Goedel-type geometries. We show that solutions of the trigonometric and linear classes (m{sup 2} < 0 and m = 0) are permitted only for the combined matter sources with an electromagnetic field matter component. We extended to the context of covariant f(T) gravity a theorem which ensures that any perfect-fluid homogeneous Goedel-type solution defines the same set of Goedel tetrads h{sub A}{sup μ} up to a Lorentz transformation. We also showed that the single massless scalar field generates Goedel-type solution with no closed time-like curves. Even though the covariant f(T) gravity restores Lorentz covariance of the field equations and the local validity of the causality principle, the bare existence of the Goedel-type solutions makes apparent that the covariant formulation of f(T) gravity

Generalized Einstein’s Equations from Wald Entropy

Directory of Open Access Journals (Sweden)

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.

An Einstein equation for discrete quantum gravity

OpenAIRE

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...

Gravity Field Parameter Estimation Using QR Factorization

Science.gov (United States)

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.

Estimating Janka hardness from specific gravity for tropical and temperate species

Science.gov (United States)

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...

The Schroedinger-Newton equation as model of self-gravitating quantum systems

International Nuclear Information System (INIS)

Grossardt, Andre

2013-01-01

The Schroedinger-Newton equation (SN equation) describes a quantummechanical one-particle-system with gravitational self-interaction and might play a role answering the question if gravity must be quantised. As non-relativistic limit of semi-classical gravity, it provides testable predictions of the effects that classical gravity has on genuinely quantum mechanical systems in the mass regime between a few thousand proton masses and the Planck mass, which is experimentally unexplored. In this thesis I subsume the mathematical properties of the SN equation and justify it as a physical model. I will give a short outline of the controversial debate around semi-classical gravity as a fundamental theory, along with the idea of the SN equation as a model of quantum state reduction. Subsequently, I will respond to frequent objections against nonlinear Schrodinger equations. I will show how the SN equation can be obtained from Einstein's General Relativity coupled to either a KleinGordon or a Dirac equation, in the same sense as the linear Schroedinger equation can be derived in flat Minkowski space-time. The equation is, to this effect, a non-relativistic approximation of the semi-classical Einstein equations. Additionally, I will discuss, first by means of analytic estimations and later numerically, in which parameter range effects of gravitational selfinteraction - e.g. in molecular-interferometry experiments - should be expected. Besides the one-particle SN equation I will provide justification for a modified equation describing the centre-of-mass wave-function of a many-particle system. Furthermore, for this modified equation, I will examine, numerically, the consequences for experiments. Although one arrives at the conclusion that no effects of the SN equation can be expected for masses up to six or seven orders of magnitude above those considered in contemporary molecular interferometry experiments, tests of the equation, for example in satellite experiments, seem

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

NARCIS (Netherlands)

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

Innovation diffusion equations on correlated scale-free networks

Energy Technology Data Exchange (ETDEWEB)

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.

Innovation diffusion equations on correlated scale-free networks

International Nuclear Information System (INIS)

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.

Compact stars in f(R, T) gravity

Energy Technology Data Exchange (ETDEWEB)

Das, Amit; Guha, B.K. [Indian Institute of Engineering Science and Technology, Department of Physics, Howrah, West Bengal (India); Rahaman, Farook [Jadavpur University, Department of Mathematics, Kolkata, West Bengal (India); Ray, Saibal [Government College of Engineering and Ceramic Technology, Department of Physics, Kolkata, West Bengal (India)

2016-12-15

In the present paper we generate a set of solutions describing the interior of a compact star under f(R, T) theory of gravity which admits conformal motion. An extension of general relativity, the f(R, T) gravity is associated to Ricci scalar R and the trace of the energy-momentum tensor T. To handle the Einstein field equations in the form of differential equations of second order, first of all we adopt the Lie algebra with conformal Killing vectors (CKV) which enable one to get a solvable form of such equations and second we consider the equation of state (EOS) p = ωρ with 0 < ω < 1 for the fluid distribution consisting of normal matter, ω being the EOS parameter. We therefore analytically explore several physical aspects of the model to represent behavior of the compact stars such as - energy conditions, TOV equation, stability of the system, Buchdahl condition, compactness and redshift. It is checked that the physical validity and the acceptability of the present model within the specified observational constraint in connection to a dozen of the compact star candidates are quite satisfactory. (orig.)

The covariant formulation of f ( T ) gravity

International Nuclear Information System (INIS)

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)

Neutron Star Models in Alternative Theories of Gravity

Science.gov (United States)

Manolidis, Dimitrios

We study the structure of neutron stars in a broad class of alternative theories of gravity. In particular, we focus on Scalar-Tensor theories and f(R) theories of gravity. We construct static and slowly rotating numerical star models for a set of equations of state, including a polytropic model and more realistic equations of state motivated by nuclear physics. Observable quantities such as masses, radii, etc are calculated for a set of parameters of the theories. Specifically for Scalar-Tensor theories, we also calculate the sensitivities of the mass and moment of inertia of the models to variations in the asymptotic value of the scalar field at infinity. These quantities enter post-Newtonian equations of motion and gravitational waveforms of two body systems that are used for gravitational-wave parameter estimation, in order to test these theories against observations. The construction of numerical models of neutron stars in f(R) theories of gravity has been difficult in the past. Using a new formalism by Jaime, Patino and Salgado we were able to construct models with high interior pressure, namely pc > rho c/3, both for constant density models and models with a polytropic equation of state. Thus, we have shown that earlier objections to f(R) theories on the basis of the inability to construct viable neutron star models are unfounded.

General Relativity solutions in modified gravity

Science.gov (United States)

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.

Minimal theory of massive gravity

Directory of Open Access Journals (Sweden)

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.

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

DEFF Research Database (Denmark)

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...

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

NARCIS (Netherlands)

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

Unified Framework for Deriving Simultaneous Equation Algorithms for Water Distribution Networks

Science.gov (United States)

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 ...

A Immirzi-like parameter for 3D quantum gravity

International Nuclear Information System (INIS)

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

Emergent universe with wormholes in massive gravity

Science.gov (United States)

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.

Power-law and intermediate inflationary models in f(T)-gravity

Energy Technology Data Exchange (ETDEWEB)

Rezazadeh, K. [Department of Physics, University of Kurdistan,Pasdaran St., Sanandaj (Iran, Islamic Republic of); Abdolmaleki, A. [Research Institute for Astronomy Astrophysics of Maragha (RIAAM),P.O. Box 55134-441, Maragha (Iran, Islamic Republic of); Karami, K. [Department of Physics, University of Kurdistan,Pasdaran St., Sanandaj (Iran, Islamic Republic of)

2016-01-21

We study inflation in the framework of f(T)-gravity in the presence of a canonical scalar field. After reviewing the basic equations governing the background cosmology in f(T)-gravity, we turn to study the cosmological perturbations and obtain the evolutionary equations for the scalar and tensor perturbations. Solving those equations, we find the power spectra for the scalar and tensor perturbations. Then, we consider a power-law f(T) function and investigate the inflationary models with the power-law and intermediate scale factors. We see that in contrast with the standard inflationary scenario based on the Einstein gravity, the power-law and intermediate inflationary models in f(T)-gravity can be compatible with the observational results of Planck 2015 at 68% CL. We find that in our f(T) setting, the potentials responsible for the both power-law and intermediate inflationary models have the power-law form V(ϕ)∝ϕ{sup m} but the power m is different for them. Therefore, we can refine some of power-law inflationary potentials in the framework of f(T)-gravity while they are disfavored by the observational data in the standard inflationary scenario. Interestingly enough, is that the self-interacting quartic potential V(ϕ)∝ϕ{sup 4} which has special reheating properties, can be consistent with the Planck 2015 data in our f(T) scenario while it is ruled out in the standard inflationary scenario.

Power-law and intermediate inflationary models in f(T)-gravity

International Nuclear Information System (INIS)

Rezazadeh, K.; Abdolmaleki, A.; Karami, K.

2016-01-01

We study inflation in the framework of f(T)-gravity in the presence of a canonical scalar field. After reviewing the basic equations governing the background cosmology in f(T)-gravity, we turn to study the cosmological perturbations and obtain the evolutionary equations for the scalar and tensor perturbations. Solving those equations, we find the power spectra for the scalar and tensor perturbations. Then, we consider a power-law f(T) function and investigate the inflationary models with the power-law and intermediate scale factors. We see that in contrast with the standard inflationary scenario based on the Einstein gravity, the power-law and intermediate inflationary models in f(T)-gravity can be compatible with the observational results of Planck 2015 at 68% CL. We find that in our f(T) setting, the potentials responsible for the both power-law and intermediate inflationary models have the power-law form V(ϕ)∝ϕ m but the power m is different for them. Therefore, we can refine some of power-law inflationary potentials in the framework of f(T)-gravity while they are disfavored by the observational data in the standard inflationary scenario. Interestingly enough, is that the self-interacting quartic potential V(ϕ)∝ϕ 4 which has special reheating properties, can be consistent with the Planck 2015 data in our f(T) scenario while it is ruled out in the standard inflationary scenario.

A Trick of Gravity

Science.gov (United States)

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.

Instantons and gravity

International Nuclear Information System (INIS)

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

Numerical study of gravity currents in a channel

International Nuclear Information System (INIS)

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

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

Science.gov (United States)

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.

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

Science.gov (United States)

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.

Spin foam models of matter coupled to gravity

International Nuclear Information System (INIS)

Mikovic, A

2002-01-01

We construct a class of spin foam models describing matter coupled to gravity, such that the gravitational sector is described by the unitary irreducible representations of the appropriate symmetry group, while the matter sector is described by the finite-dimensional irreducible representations of that group. The corresponding spin foam amplitudes in the four-dimensional gravity case are expressed in terms of the spin network amplitudes for pentagrams with additional external and internal matter edges. We also give a quantum field theory formulation of the model, where the matter degrees of freedom are described by spin network fields carrying the indices from the appropriate group representation. In the non-topological Lorentzian gravity case, we argue that the matter representations should be appropriate SO(3) or SO(2) representations contained in a given Lorentz matter representation, depending on whether one wants to describe a massive or a massless matter field. The corresponding spin network amplitudes are given as multiple integrals of propagators which are matrix spherical functions

Initial value formulation of higher derivative gravity

International Nuclear Information System (INIS)

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

Distribution Function of the Atoms of Spacetime and the Nature of Gravity

Directory of Open Access Journals (Sweden)

Thanu Padmanabhan

2015-10-01

Full Text Available The fact that the equations of motion for matter remain invariant when a constant is added to the Lagrangian suggests postulating that the field equations of gravity should also respect this symmetry. This principle implies that: (1 the metric cannot be varied in any extremum principle to obtain the field equations; and (2 the stress-tensor of matter should appear in the variational principle through the combination Tabnanb where na is an auxiliary null vector field, which could be varied to get the field equations. This procedure uniquely selects the Lanczos–Lovelock models of gravity in D-dimensions and Einstein’s theory in D = 4. Identifying na with the normals to the null surfaces in the spacetime in the macroscopic limit leads to a thermodynamic interpretation for gravity. Several geometrical variables and the equation describing the spacetime evolution acquire a thermodynamic interpretation. Extending these ideas one level deeper, we can obtain this variational principle from a distribution function for the “atoms of spacetime”, which counts the number of microscopic degrees of freedom of the geometry. This is based on the curious fact that the renormalized spacetime endows each event with zero volume, but finite area!

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

Science.gov (United States)

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.

Anomaly freedom in perturbative loop quantum gravity

International Nuclear Information System (INIS)

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.

Loop equations in the theory of gravitation

International Nuclear Information System (INIS)

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

Quark stars in f(T, T)-gravity

Energy Technology Data Exchange (ETDEWEB)

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.)

Characteristics of gravity fields in the Jinggu M6.6 earthquake

Directory of Open Access Journals (Sweden)

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.

New experimental proposals for testing Dirac equation

International Nuclear Information System (INIS)

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

Finding Horndeski theories with Einstein gravity limits

Energy Technology Data Exchange (ETDEWEB)

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.

Capillary-gravity waves and the Navier-Stokes equation

International Nuclear Information System (INIS)

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)

Stochastic solution of population balance equations for reactor networks

International Nuclear Information System (INIS)

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

Gravity across Space and Time

NARCIS (Netherlands)

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

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

Science.gov (United States)

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

Quaternion wave equations in curved space-time

Science.gov (United States)

Edmonds, J. D., Jr.

1974-01-01

The quaternion formulation of relativistic quantum theory is extended to include curvilinear coordinates and curved space-time in order to provide a framework for a unified quantum/gravity theory. Six basic quaternion fields are identified in curved space-time, the four-vector basis quaternions are identified, and the necessary covariant derivatives are obtained. Invariant field equations are derived, and a general invertable coordinate transformation is developed. The results yield a way of writing quaternion wave equations in curvilinear coordinates and curved space-time as well as a natural framework for solving the problem of second quantization for gravity.

Newton-Cartan gravity and torsion

Science.gov (United States)

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.

The soliton content of classical Jackiw-Teitelboim gravity

Energy Technology Data Exchange (ETDEWEB)

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)

Energy conditions in f(G,T) gravity

Energy Technology Data Exchange (ETDEWEB)

Sharif, M.; Ikram, Ayesha [University of the Punjab, Department of Mathematics, Lahore (Pakistan)

2016-11-15

The aim of this paper is to introduce a new modified gravity theory named f(G,T) gravity (G and T are the Gauss-Bonnet invariant and trace of the energy-momentum tensor, respectively) and investigate energy conditions for two reconstructed models in the context of FRW universe. We formulate general field equations, divergence of energy-momentum tensor, equation of motion for test particles as well as corresponding energy conditions. The massive test particles follow non-geodesic lines of geometry due to the presence of an extra force. We express the energy conditions in terms of cosmological parameters like the deceleration, jerk, and snap parameters. The reconstruction technique is applied to this theory using de Sitter and power-law cosmological solutions. We analyze the energy bounds and obtain feasible constraints on the free parameters. (orig.)

Higher-order gravity in higher dimensions: geometrical origins of four-dimensional cosmology?

Energy Technology Data Exchange (ETDEWEB)

Troisi, Antonio [Universita degli Studi di Salerno, Dipartimento di Fisica ' ' E.R. Caianiello' ' , Salerno (Italy)

2017-03-15

Determining the cosmological field equations is still very much debated and led to a wide discussion around different theoretical proposals. A suitable conceptual scheme could be represented by gravity models that naturally generalize Einstein theory like higher-order gravity theories and higher-dimensional ones. Both of these two different approaches allow one to define, at the effective level, Einstein field equations equipped with source-like energy-momentum tensors of geometrical origin. In this paper, the possibility is discussed to develop a five-dimensional fourth-order gravity model whose lower-dimensional reduction could provide an interpretation of cosmological four-dimensional matter-energy components. We describe the basic concepts of the model, the complete field equations formalism and the 5-D to 4-D reduction procedure. Five-dimensional f(R) field equations turn out to be equivalent, on the four-dimensional hypersurfaces orthogonal to the extra coordinate, to an Einstein-like cosmological model with three matter-energy tensors related with higher derivative and higher-dimensional counter-terms. By considering the gravity model with f(R) = f{sub 0}R{sup n} the possibility is investigated to obtain five-dimensional power law solutions. The effective four-dimensional picture and the behaviour of the geometrically induced sources are finally outlined in correspondence to simple cases of such higher-dimensional solutions. (orig.)

Quantum Gravity

International Nuclear Information System (INIS)

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)

Infinite degeneracy of states in quantum gravity

International Nuclear Information System (INIS)

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.

Gravity Effect on Two-Phase Immiscible Flows in Communicating Layered Reservoirs

DEFF Research Database (Denmark)

Zhang, Xuan; Shapiro, Alexander; Stenby, Erling Halfdan

2012-01-01

An upscaling method is developed for two-phase immiscible incompressible flows in layered reservoirs with good communication between the layers. It takes the effect of gravity into consideration. Waterflooding of petroleum reservoirs is used as a basic example for application of this method....... An asymptotic analysis is applied to a system of 2D flow equations for incompressible fluids at high-anisotropy ratios, but low to moderate gravity ratios, which corresponds to the most often found reservoir conditions. The 2D Buckley–Leverett problem is reduced to a system of 1D parabolic equations...

Hot Carcass Specific Gravity: Could Be Used Accurately for In-vivo Body Composition Determination

International Nuclear Information System (INIS)

Fekry, A.E.; Shebaita, M.K.

1998-01-01

Twelve mature male goats (Bucks) of Egyptian Baladi breed aged 4 years old and body weight of 30.5 kg were used to verify the validation of predicting equations by which carcass specific gravity and body weight can be used to estimate body composition. Live body weight, TOH-space, Blood and plasma volume were determined. Two weeks later, all bucks were slaughtered and each of empty body weight, hot carcass weight, hot carcass specific gravity, offals, along with separating carcass components (muscle, fat, bone) and chemical components (water, protein, fat, ash) of the whole body, empty body and carcass were determined. Step-wise regression analyses of the relationships among hot carcass specific gravity, body and carcass weight (as independent variables) and body composition parameters were performed. The validation of the obtained predicting equations was examined by calculating the intercept and the slope of the regression of the predicted parameter on the observed parameter. The valid equation should have an insignificant intercept from zero and insignificant slope from one. The data revealed that hot carcass specific gravity has not any valid equation to predict body and carcass composition. Live body weight can be used to predict empty body weight and red blood cells volume. Empty body weight has a valid equation to estimate empty body water. However, hot carcass weight can be used to estimate carcass water, muscle and edible portion

The Juno Gravity Science Instrument

Science.gov (United States)

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.

Born-Infeld gravity in Weitzenboeck spacetime

International Nuclear Information System (INIS)

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.

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

KAUST Repository

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.

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

KAUST Repository

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.

A Non-Polynomial Gravity Formulation for Loop Quantum Cosmology Bounce

Directory of Open Access Journals (Sweden)

Stefano Chinaglia

2017-09-01

Full Text Available Recently the so-called mimetic gravity approach has been used to obtain corrections to the Friedmann equation of General Relativity similar to the ones present in loop quantum cosmology. In this paper, we propose an alternative way to derive this modified Friedmann equation via the so-called non-polynomial gravity approach, which consists of adding geometric non-polynomial higher derivative terms to Hilbert–Einstein action, which are nonetheless polynomials and lead to a second-order differential equation in Friedmann–Lemaître–Robertson–Walker space-times. Our explicit action turns out to be a realization of the Helling proposal of effective action with an infinite number of terms. The model is also investigated in the presence of a non-vanishing cosmological constant, and a new exact bounce solution is found and studied.

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

Directory of Open Access Journals (Sweden)

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.

Holographic dark energy and f(R) gravity

Energy Technology Data Exchange (ETDEWEB)

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.

Unimodular Einstein-Cartan gravity: Dynamics and conservation laws

Science.gov (United States)

Bonder, Yuri; Corral, Cristóbal

2018-04-01

Unimodular gravity is an interesting approach to address the cosmological constant problem, since the vacuum energy density of quantum fields does not gravitate in this framework, and the cosmological constant appears as an integration constant. These features arise as a consequence of considering a constrained volume element 4-form that breaks the diffeomorphisms invariance down to volume preserving diffeomorphisms. In this work, the first-order formulation of unimodular gravity is presented by considering the spin density of matter fields as a source of spacetime torsion. Even though the most general matter Lagrangian allowed by the symmetries is considered, dynamical restrictions arise on their functional dependence. The field equations are obtained and the conservation laws associated with the symmetries are derived. It is found that, analogous to torsion-free unimodular gravity, the field equation for the vierbein is traceless; nevertheless, torsion is algebraically related to the spin density as in standard Einstein-Cartan theory. The particular example of massless Dirac spinors is studied, and comparisons with standard Einstein-Cartan theory are shown.

Neutron stars in screened modified gravity: Chameleon versus dilaton

Science.gov (United States)

Brax, Philippe; Davis, Anne-Christine; Jha, Rahul

2017-04-01

We consider the scalar field profile around relativistic compact objects such as neutron stars for a range of modified gravity models with screening mechanisms of the chameleon and Damour-Polyakov types. We focus primarily on inverse power law chameleons and the environmentally dependent dilaton as examples of both mechanisms. We discuss the modified Tolman-Oppenheimer-Volkoff equation and then implement a relaxation algorithm to solve for the scalar profiles numerically. We find that chameleons and dilatons behave in a similar manner and that there is a large degeneracy between the modified gravity parameters and the neutron star equation of state. This is exemplified by the modifications to the mass-radius relationship for a variety of model parameters.

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

NARCIS (Netherlands)

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

Allowance for influence of gravity field nonuniformity

Science.gov (United States)

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.

Acoustic-gravity modons in the atmosphere

Directory of Open Access Journals (Sweden)

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.

Holographically viable extensions of topologically massive and minimal massive gravity?

Science.gov (United States)

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.

Spin foam models of Yang-Mills theory coupled to gravity

International Nuclear Information System (INIS)

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

The Approach to Defining Gravity Factors of Influence on the Foreign Trade Relations of Countries

Directory of Open Access Journals (Sweden)

Kalyuzhna Nataliya G.

2017-03-01

Full Text Available The aim of the article is to determine the gravity factors of influence on the foreign trade relations of countries on the basis of the results of the comparative analysis of the classical specifications of the gravity model of foreign trade and the domestic experience in gravity modeling. It is substantiated that a gravity model is one of the tools of economic and mathematical modeling, the use of which is characterized by a high level of adequacy and ensures prediction of foreign trade conditions. The main approaches to the definition of explanatory variables in the gravity equation of foreign trade are analyzed, and the author’s approach to the selection of the factors of the gravity model is proposed. As the first explanatory variable in the specification of the gravity model of foreign trade and the characteristics of the importance of economies of foreign trade partners, it is proposed to use the GDP calculated at purchasing power parity with the expected positive and statistically significant coefficient. As the second explanatory variable of the gravity equation of foreign trade, it is proposed to use a complex characteristic of the “trade distance” between countries, which reflects the current conditions of bilateral trade and depends on factors influencing the foreign trade turnover between countries — both directly (static proportionality of transport costs of geographical remoteness, and indirectly (dynamic institutional conditions of bilateral relations. The expediency of using the world average annual price for oil as the quantitative equivalent of the “trading distance” index is substantiated. Prospects for further research in this direction are identifying the form and force of influence of certain basic gravity variables on the foreign trade relations of certain partner countries and determining the appropriateness of including additional factors in the composition of the gravity equation of foreign trade.

Topological aspects of classical and quantum (2+1)-dimensional gravity

International Nuclear Information System (INIS)

Soda, Jiro.

1990-03-01

In order to understand (3+1)-dimensional gravity, (2+1)-dimensional gravity is studied as a toy model. Our emphasis is on its topological aspects, because (2+1)-dimensional gravity without matter fields has no local dynamical degrees of freedom. Starting from a review of the canonical ADM formalism and York's formalism for the initial value problem, we will solve the evolution equations of (2+1)-dimensional gravity with a cosmological constant in the case of g=0 and g=1, where g is the genus of Riemann surface. The dynamics of it is understood as the geodesic motion in the moduli space. This remarkable fact is the same with the case of (2+1)-dimensional pure gravity and seen more apparently from the action level. Indeed we will show the phase space reduction of (2+1)-dimensional gravity in the case of g=1. For g ≥ 2, unfortunately we are not able to explicitly perform the phase space reduction of (2+1)-dimensional gravity due to the complexity of the Hamiltonian constraint equation. Based on this result, we will attempt to incorporate matter fields into (2+1)-dimensional pure gravity. The linearization and mini-superspace methods are used for this purpose. By using the linearization method, we conclude that the transverse-traceless part of the energy-momentum tensor affects the geodesic motion. In the case of the Einstein-Maxwell theory, we observe that the Wilson lines interact with the geometry to bend the geodesic motion. We analyze the mini-superspace model of (2+1)-dimensional gravity with the matter fields in the case of g=0 and g=1. For g=0, a wormhole solution is found but for g=1 we can not find an analogous solution. Quantum gravity is also considered and we succeed to perform the phase space reduction of (2+1)-dimensional gravity in the case of g=1 at the quantum level. From this analysis we argue that the conformal rotation is not necessary in the sense that the Euclidean quantum gravity is inappropriate for the full gravity. (author)

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

International Nuclear Information System (INIS)

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.

Einstein gravity with torsion induced by the scalar field

Science.gov (United States)

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.

GRIM5-C1: Combination solution of the global gravity field to degree and order 120

Science.gov (United States)

Gruber, Thomas; Bode, Albert; Reigber, Christoph; Schwintzer, Peter; Balmino, Georges; Biancale, Richard; Lemoine, Jean-Michel

2000-12-01

The new satellite Earth gravity field model GRIM5-S1 was recently prepared in a joint GFZ and GRGS effort. Based on this satellite solution and terrestrial and altimetric gravity anomalies from NIMA, a combined model GRIM5-C1, with full variance-covariance matrix up to degree and order 120, was computed. Surface gravity and altimetric gravity data are corrected for several systematic effects, such as ellipsoidal corrections and aliasing. A weighting scheme for gravity anomalies, according to their given standard deviations was developed. From each data set full normal equations were set up and finally combined with the GRIM5-S1 normals. To take into account good information from the satellite-only model a procedure was developed to identify such coefficients and appropriately weighed them in the final normal equation system. Internal error propagation and comparisons to external data sets show, that the GRIM5-C1 model represents the best state of long wavelength gravity field models.

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

OpenAIRE

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...

Kinetic theory of Jean instability in Eddington-inspired Born-Infeld gravity

Energy Technology Data Exchange (ETDEWEB)

Martino, Ivan de [University of the Basque Country UPV/EHU, Department of Theoretical Physics and History of Science, Faculty of Science and Technology, Leioa (Spain); Capolupo, Antonio [Universita di Salerno, Dipartimento di Fisica E.R. Caianiello, Fisciano (Italy); INFN Gruppo Collegato di Salerno, Fisciano (Italy)

2017-10-15

We analyze the stability of self-gravitating systems which dynamics is investigated using the collisionless Boltzmann equation, and the modified Poisson equation of Eddington-inspired Born-Infield gravity. These equations provide a description of the Jeans paradigm used to determine the critical scale above which such systems collapse. At equilibrium, the systems are described using the time-independent Maxwell-Boltzmann distribution function f{sub 0}(v). Considering small perturbations to this equilibrium state, we obtain a modified dispersion relation, and we find a new characteristic scale length. Our results indicate that the dynamics of self-gravitating astrophysical systems can be fully addressed in the Eddington-inspired Born-Infeld gravity. The latter modifies the Jeans instability in high densities environments, while its effects become negligible in star formation regions. (orig.)

The QCD mass gap and quark deconfinement scales as mass bounds in strong gravity

Energy Technology Data Exchange (ETDEWEB)

Burikham, Piyabut [Chulalongkorn University, High Energy Physics Theory Group, Department of Physics, Faculty of Science, Bangkok (Thailand); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom); Lake, Matthew J. [Sun Yat-Sen University, School of Physics, Guangzhou (China); Nanyang Technological University, School of Physical and Mathematical Sciences, Singapore (Singapore); Naresuan University, The Institute for Fundamental Study, ' ' The Tah Poe Academia Institute' ' , Phitsanulok (Thailand); Thailand Center of Excellence in Physics, Ministry of Education, Bangkok (Thailand)

2017-11-15

Though not a part of mainstream physics, Salam's theory of strong gravity remains a viable effective model for the description of strong interactions in the gauge singlet sector of QCD, capable of producing particle confinement and asymptotic freedom, but not of reproducing interactions involving SU(3) color charge. It may therefore be used to explore the stability and confinement of gauge singlet hadrons, though not to describe scattering processes that require color interactions. It is a two-tensor theory of both strong interactions and gravity, in which the strong tensor field is governed by equations formally identical to the Einstein equations, apart from the coupling parameter, which is of order 1 GeV{sup -1}. We revisit the strong gravity theory and investigate the strong gravity field equations in the presence of a mixing term which induces an effective strong cosmological constant, Λ{sub f}. This introduces a strong de Sitter radius for strongly interacting fermions, producing a confining bubble, which allows us to identify Λ{sub f} with the 'bag constant' of the MIT bag model, B ≅ 2 x 10{sup 14} g cm{sup -3}. Assuming a static, spherically symmetric geometry, we derive the strong gravity TOV equation, which describes the equilibrium properties of compact hadronic objects. From this, we determine the generalized Buchdahl inequalities for a strong gravity 'particle', giving rise to upper and lower bounds on the mass/radius ratio of stable, compact, strongly interacting objects. We show, explicitly, that the existence of the lower mass bound is induced by the presence of Λ{sub f}, producing a mass gap, and that the upper bound corresponds to a deconfinement phase transition. The physical implications of our results for holographic duality in the context of the AdS/QCD and dS/QCD correspondences are also discussed. (orig.)

Ultrasonic hydrometer. [Specific gravity of electrolyte

Science.gov (United States)

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.

Relic gravity waves from braneworld inflation

International Nuclear Information System (INIS)

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

The Bach equations in spin-coefficient form

Science.gov (United States)

Forbes, Hamish

2018-06-01

Conformal gravity theories are defined by field equations that determine only the conformal structure of the spacetime manifold. The Bach equations represent an early example of such a theory, we present them here in component form in terms of spin- and boost-weighted spin-coefficients using the compacted spin-coefficient formalism. These equations can be used as an efficient alternative to the standard tensor form. As a simple application we solve the Bach equations for pp-wave and static spherically symmetric spacetimes.

Covariant formulation of scalar-torsion gravity

Science.gov (United States)

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.

Using structural equation modeling for network meta-analysis.

Science.gov (United States)

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

Supersoft Symmetry Energy Encountering Non-Newtonian Gravity in Neutron Stars

International Nuclear Information System (INIS)

Wen Dehua; Li Baoan; Chen Liewen

2009-01-01

Considering the non-Newtonian gravity proposed in grand unification theories, we show that the stability and observed global properties of neutron stars cannot rule out the supersoft nuclear symmetry energies at suprasaturation densities. The degree of possible violation of the inverse-square law of gravity in neutron stars is estimated using an equation of state of neutron-rich nuclear matter consistent with the available terrestrial laboratory data.

BRS invariant stochastic quantization of Einstein gravity

International Nuclear Information System (INIS)

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)

Cosmological implications of modified gravity induced by quantum metric fluctuations

Energy Technology Data Exchange (ETDEWEB)

Liu, Xing [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, Yat Sen School, Guangzhou (China); Harko, Tiberiu [Babes-Bolyai University, Department of Physics, Cluj-Napoca (Romania); University College London, Department of Mathematics, London (United Kingdom); Liang, Shi-Dong [Sun Yat-Sen University, School of Physics, Guangzhou (China); Sun Yat-Sen University, State Key Laboratory of Optoelectronic Material and Technology, Guangdong Province Key Laboratory of Display Material and Technology, School of Physics, Guangzhou (China)

2016-08-15

We investigate the cosmological implications of modified gravities induced by the quantum fluctuations of the gravitational metric. If the metric can be decomposed as the sum of the classical and of a fluctuating part, of quantum origin, then the corresponding Einstein quantum gravity generates at the classical level modified gravity models with a non-minimal coupling between geometry and matter. As a first step in our study, after assuming that the expectation value of the quantum correction can be generally expressed in terms of an arbitrary second order tensor constructed from the metric and from the thermodynamic quantities characterizing the matter content of the Universe, we derive the (classical) gravitational field equations in their general form. We analyze in detail the cosmological models obtained by assuming that the quantum correction tensor is given by the coupling of a scalar field and of a scalar function to the metric tensor, and by a term proportional to the matter energy-momentum tensor. For each considered model we obtain the gravitational field equations, and the generalized Friedmann equations for the case of a flat homogeneous and isotropic geometry. In some of these models the divergence of the matter energy-momentum tensor is non-zero, indicating a process of matter creation, which corresponds to an irreversible energy flow from the gravitational field to the matter fluid, and which is direct consequence of the non-minimal curvature-matter coupling. The cosmological evolution equations of these modified gravity models induced by the quantum fluctuations of the metric are investigated in detail by using both analytical and numerical methods, and it is shown that a large variety of cosmological models can be constructed, which, depending on the numerical values of the model parameters, can exhibit both accelerating and decelerating behaviors. (orig.)

Weak lensing in generalized gravity theories

International Nuclear Information System (INIS)

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

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

African Journals Online (AJOL)

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.

Entropy of Egypt's virtual water trade gravity field

Science.gov (United States)

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

The Kadomtsev endash Petviashvili equation under rapid forcing

International Nuclear Information System (INIS)

Moroz, I.M.

1997-01-01

We consider the initial value problem for the forced Kadomtsev endash Petviashvili equation (KP) when the forcing is assumed to be fast compared to the evolution of the unforced equation. This suggests the introduction of two time scales. Solutions to the forced KP are sought by expanding the dependent variable in powers of a small parameter, which is inversely related to the forcing time scale. The unforced system describes weakly nonlinear, weakly dispersive, weakly two-dimensional wave propagation and is studied in two forms, depending upon whether gravity dominates surface tension or vice versa. We focus on the effect that the forcing has on the one-lump solution to the KPI equation (where surface tension dominates) and on the one- and two-line soliton solutions to the KPII equation (when gravity dominates). Solutions to second order in the expansion are computed analytically for some specific choices of the forcing function, which are related to the choice of initial data. copyright 1997 American Institute of Physics

Gravity and the Spin-2 Planar Schrödinger Equation

Science.gov (United States)

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.

Earthquake precursors: spatial-temporal gravity changes before the great earthquakes in the Sichuan-Yunnan area

Science.gov (United States)

Zhu, Yi-Qing; Liang, Wei-Feng; Zhang, Song

2018-01-01

Using multiple-scale mobile gravity data in the Sichuan-Yunnan area, we systematically analyzed the relationships between spatial-temporal gravity changes and the 2014 Ludian, Yunnan Province Ms6.5 earthquake and the 2014 Kangding Ms6.3, 2013 Lushan Ms7.0, and 2008 Wenchuan Ms8.0 earthquakes in Sichuan Province. Our main results are as follows. (1) Before the occurrence of large earthquakes, gravity anomalies occur in a large area around the epicenters. The directions of gravity change gradient belts usually agree roughly with the directions of the main fault zones of the study area. Such gravity changes might reflect the increase of crustal stress, as well as the significant active tectonic movements and surface deformations along fault zones, during the period of gestation of great earthquakes. (2) Continuous significant changes of the multiple-scale gravity fields, as well as greater gravity changes with larger time scales, can be regarded as medium-range precursors of large earthquakes. The subsequent large earthquakes always occur in the area where the gravity changes greatly. (3) The spatial-temporal gravity changes are very useful in determining the epicenter of coming large earthquakes. The large gravity networks are useful to determine the general areas of coming large earthquakes. However, the local gravity networks with high spatial-temporal resolution are suitable for determining the location of epicenters. Therefore, denser gravity observation networks are necessary for better forecasts of the epicenters of large earthquakes. (4) Using gravity changes from mobile observation data, we made medium-range forecasts of the Kangding, Ludian, Lushan, and Wenchuan earthquakes, with especially successful forecasts of the location of their epicenters. Based on the above discussions, we emphasize that medium-/long-term potential for large earthquakes might exist nowadays in some areas with significant gravity anomalies in the study region. Thus, the monitoring

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

Directory of Open Access Journals (Sweden)

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.

Temporal gravity changes before the 2008 Yutian Ms7.3 earthquake

OpenAIRE

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...

Observational tests of modified gravity

International Nuclear Information System (INIS)

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).

Quasi-topological Ricci polynomial gravities

Science.gov (United States)

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.

Weak lensing: Dark Matter, Dark Energy and Dark Gravity

International Nuclear Information System (INIS)

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.

Asymptomatic freedom in renormalisable gravity and supergravity

International Nuclear Information System (INIS)

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

Clustering of galaxies with f(R) gravity

Science.gov (United States)

Capozziello, Salvatore; Faizal, Mir; Hameeda, Mir; Pourhassan, Behnam; Salzano, Vincenzo; Upadhyay, Sudhaker

2018-02-01

Based on thermodynamics, we discuss the galactic clustering of expanding Universe by assuming the gravitational interaction through the modified Newton's potential given by f(R) gravity. We compute the corrected N-particle partition function analytically. The corrected partition function leads to more exact equations of state of the system. By assuming that the system follows quasi-equilibrium, we derive the exact distribution function that exhibits the f(R) correction. Moreover, we evaluate the critical temperature and discuss the stability of the system. We observe the effects of correction of f(R) gravity on the power-law behaviour of particle-particle correlation function also. In order to check the feasibility of an f(R) gravity approach to the clustering of galaxies, we compare our results with an observational galaxy cluster catalogue.

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

Science.gov (United States)

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.

Stochastic gravity: a primer with applications

International Nuclear Information System (INIS)

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

Stochastic gravity: a primer with applications

Energy Technology Data Exchange (ETDEWEB)

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

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

Science.gov (United States)

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.

Propagating Degrees of Freedom in f(R Gravity

Directory of Open Access Journals (Sweden)

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.

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

Science.gov (United States)

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…

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

Directory of Open Access Journals (Sweden)

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

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

Science.gov (United States)

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.

A family of metric gravities

Science.gov (United States)

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

Semiclassical unimodular gravity

International Nuclear Information System (INIS)

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

Constraints on perturbative f(R) gravity via neutron stars

Energy Technology Data Exchange (ETDEWEB)

Arapoğlu, Savaş; Ekşi, K. Yavuz [İstanbul Technical University, Faculty of Science and Letters, Physics Engineering Department, Maslak 34469, İstanbul (Turkey); Deliduman, Cemsinan, E-mail: arapoglu@itu.edu.tr, E-mail: cemsinan@msgsu.edu.tr, E-mail: eksi@itu.edu.tr [Mimar Sinan Fine Arts University, Department of Physics, Beşiktaş 34349, İstanbul (Turkey)

2011-07-01

We study the structure of neutron stars in perturbative f(R) gravity models with realistic equations of state. We obtain mass-radius relations in a gravity model of the form f(R) = R+αR{sup 2}. We find that deviations from the results of general relativity, comparable to the variations due to using different equations of state (EoS'), are induced for |α| ∼ 10{sup 9} cm{sup 2}. Some of the soft EoS' that are excluded within the framework of general relativity can be reconciled with the 2 solar mass neutron star recently observed for certain values of α within this range. For some of the EoS' we find that a new solution branch, which allows highly massive neutron stars, exists for values of α greater than a few 10{sup 9} cm{sup 2}. We find constraints on α for a variety of EoS' using the recent observational constraints on the mass-radius relation. These are all 5 orders of magnitude smaller than the recent constraint obtained via Gravity Probe B for this gravity model. The associated length scale √(alpha)approx 10{sup 5} cm is only an order of magnitude smaller than the typical radius of a neutron star, the probe used in this test. This implies that real deviations from general relativity can be even smaller.

Loop quantum gravity and black hole entropy quantization

Institute of Scientific and Technical Information of China (English)

无

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.

Gravity and Heater Size Effects on Pool Boiling Heat Transfer

Science.gov (United States)

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.

Astrophysical flows near f(T) gravity black holes

Energy Technology Data Exchange (ETDEWEB)

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.)

Cosmological and black hole brane-world universes in higher derivative gravity

International Nuclear Information System (INIS)

Nojiri, Shin'ichi; Odintsov, Sergei D.; Ogushi, Sachiko

2002-01-01

A general model of multidimensional R 2 gravity including a Riemann tensor square term (nonzero c case) is considered. The number of brane-worlds in such a model is constructed (mainly in five dimensions) and their properties are discussed. The thermodynamics of a Schwarzschild-anti-deSitter (S-AdS) BH (with boundary) is presented when perturbation on c is used. The entropy, free energy, and energy are calculated. For a nonzero c the entropy (energy) is not proportional to the area (mass). The equation of motion of the brane in a BH background is presented as a FRW equation. Using a dual CFT description it is shown that the dual field theory is not a conformal one when c is not zero. In this case the holographic entropy does not coincide with the BH entropy (they coincide for Einstein gravity or c=0 HD gravity where the AdS/CFT description is well applied). An asymmetrically warped background (an analogue of a charged AdS BH) where Lorentz invariance violation occurs is found. The cosmological 4D dS brane connecting two dS bulk spaces is formulated in terms of the parameters of R 2 gravity. Within the proposed dS/CFT correspondence the holographic conformal anomaly from five-dimensional higher derivative gravity in a de Sitter background is evaluated

Equilibrium and stability of relativistic stars in extended theories of gravity

Energy Technology Data Exchange (ETDEWEB)

Wojnar, Aneta [Maria Curie-Sklodowska University, Institute of Physics, Lublin (Poland); Univ. di Monte S. Angelo, Napoli (Italy); Universita' di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica ' ' E. Pancini' ' , Naples (Italy); INFN, Napoli (Italy); Velten, Hermano [Universidade Federal do Espirito Santo (UFES), Vitoria (Brazil)

2016-12-15

We study static, spherically symmetric equilibrium configurations in extended theories of gravity (ETG) following the notation introduced by Capozziello et al. We calculate the differential equations for the stellar structure in such theories in a very generic form i.e., the Tolman-Oppenheimer-Volkoff generalization for any ETG is introduced. Stability analysis is also investigated with special focus on the particular example of scalar-tensor gravity. (orig.)

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

International Nuclear Information System (INIS)

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

Gravity localization in non-minimally coupled scalar thick braneworlds with a Gauss-Bonnet term

International Nuclear Information System (INIS)

Malagon-Morejon, D; Quiros, I; Herrera-Aguilar, A

2011-01-01

We consider a warped five-dimensional thick braneworld with a four-dimensional Poincare invariant space-time in the framework of scalar matter non-minimally coupled to gravity plus a Gauss-Bonnet term in the bulk. Scalar field and higher curvature corrections to the background equations as well as the perturbed equations are shown. A relationship between 4-dimensional and 5-dimensional Planck masses is studied in general terms. By imposing finiteness of the 4-dimensional Planck mass and regularity of the geometry, the localization properties of the tensor modes of the first order perturbed geometry are analized for an important class of solutions motivated by models with scalar fields which are minimally coupled to gravity. In order to study the gravity localization properties for this model, the normalizability condition for the lowest level of the tensor fluctuations is analized. We see that for the class of solutions examined, gravity in 4 dimensions is recovered if the curvature invariants are regular and Planck masses are finite.

High-precision gravity measurements using absolute and relative gravimeters at Mount Etna (Sicily, Italy

Directory of Open Access Journals (Sweden)

Ciro Del Negro

2011-12-01

Full Text Available Accurate detection of time gravity changes attributable to the dynamics of volcanoes requires high-precision gravity measurements. With the aim of improving the quality of data from the Mount Etna gravity network, we used both absolute and relative gravimeters in a hybrid method. In this report, some of the techniques for gravity surveys are reviewed, and the results related to each method are compared. We show how the total uncertainty estimated for the gravity measurements performed with this combined use of absolute and relative gravimeters is roughly comparable to that calculated when the measurements are acquired using only relative gravimeters (the traditional method. However, the data highlight how the hybrid approach improves the measurement capabilities for surveying the Mount Etna volcanic area. This approach enhances the accuracy of the data, and then of the four-dimensional surveying, which minimizes ambiguities inherent in the gravity measurements. As a case study, we refer to two gravity datasets acquired in 2005 and 2010 from the western part of the Etna volcano, which included five absolute and 13 relative stations of the Etna gravity network.

Cosmography in f(T) gravity

International Nuclear Information System (INIS)

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.

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

DEFF Research Database (Denmark)

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...

New Class of Quasinormal Modes of Neutron Stars in Scalar-Tensor Gravity

Science.gov (United States)

Mendes, Raissa F. P.; Ortiz, Néstor

2018-05-01

Detection of the characteristic spectrum of pulsating neutron stars can be a powerful tool not only to probe the nuclear equation of state but also to test modifications to general relativity. However, the shift in the oscillation spectrum induced by modified theories of gravity is often small and degenerate with our ignorance of the equation of state. In this Letter, we show that the coupling to additional degrees of freedom present in modified theories of gravity can give rise to new families of modes, with no counterpart in general relativity, which could be sufficiently well resolved in frequency space to allow for clear detection. We present a realization of this idea by performing a thorough study of radial oscillations of neutron stars in massless scalar-tensor theories of gravity. We anticipate astrophysical scenarios where the presence of this class of quasinormal modes could be probed with electromagnetic and gravitational wave measurements.

Cosmology of modified Gauss-Bonnet gravity

International Nuclear Information System (INIS)

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

Field-theoretic approach to gravity in the flat space-time

Energy Technology Data Exchange (ETDEWEB)

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.

Modified gravity in Arnowitt-Deser-Misner formalism

Science.gov (United States)

Gao, Changjun

2010-02-01

Motivated by Hořava-Lifshitz gravity theory, we propose and investigate two kinds of modified gravity theories, the f(R) kind and the K-essence kind, in the Arnowitt-Deser-Misner (ADM) formalism. The f(R) kind includes one ultraviolet (UV) term and one infrared (IR) term together with the Einstein-Hilbert action. We find that these two terms naturally present the ultraviolet and infrared modifications to the Friedmann equation. The UV and IR modifications can avoid the past Big-Bang singularity and the future Big-Rip singularity, respectively. Furthermore, the IR modification can naturally account for the current acceleration of the Universe. The Lagrangian of K-essence kind modified gravity is made up of the three-dimensional Ricci scalar and an arbitrary function of the extrinsic curvature term. We find the cosmic acceleration can also be naturally interpreted without invoking any kind of dark energy. The static, spherically symmetry and vacuum solutions of both theories are Schwarzschild or Schwarzschild-de Sitter solution. Thus these modified gravity theories are viable for solar system tests.

Modified gravity in Arnowitt-Deser-Misner formalism

International Nuclear Information System (INIS)

Gao Changjun

2010-01-01

Motivated by Horava-Lifshitz gravity theory, we propose and investigate two kinds of modified gravity theories, the f(R) kind and the K-essence kind, in the Arnowitt-Deser-Misner (ADM) formalism. The f(R) kind includes one ultraviolet (UV) term and one infrared (IR) term together with the Einstein-Hilbert action. We find that these two terms naturally present the ultraviolet and infrared modifications to the Friedmann equation. The UV and IR modifications can avoid the past Big-Bang singularity and the future Big-Rip singularity, respectively. Furthermore, the IR modification can naturally account for the current acceleration of the Universe. The Lagrangian of K-essence kind modified gravity is made up of the three-dimensional Ricci scalar and an arbitrary function of the extrinsic curvature term. We find the cosmic acceleration can also be naturally interpreted without invoking any kind of dark energy. The static, spherically symmetry and vacuum solutions of both theories are Schwarzschild or Schwarzschild-de Sitter solution. Thus these modified gravity theories are viable for solar system tests.

Upper atmospheric planetary-wave and gravity-wave observations

Science.gov (United States)

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.

The Coupling of Gravity to Spin and Electromagnetism

Science.gov (United States)

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.

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

Science.gov (United States)

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.

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

Energy Technology Data Exchange (ETDEWEB)

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.

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

International Nuclear Information System (INIS)

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

Noncommutative geometry inspired black holes in Rastall gravity

Energy Technology Data Exchange (ETDEWEB)

Ma, Meng-Sen [Shanxi Datong University, Institute of Theoretical Physics, Datong (China); Shanxi Datong University, Department of Physics, Datong (China); Zhao, Ren [Shanxi Datong University, Institute of Theoretical Physics, Datong (China)

2017-09-15

Under two different metric ansatzes, the noncommutative geometry inspired black holes (NCBH) in the framework of Rastall gravity are derived and analyzed. We consider the fluid-type matter with the Gaussian-distribution smeared mass density. Taking a Schwarzschild-like metric ansatz, it is shown that the noncommutative geometry inspired Schwarzschild black hole (NCSBH) in Rastall gravity, unlike its counterpart in general relativity (GR), is not a regular black hole. It has at most one event horizon. After showing a finite maximal temperature, the black hole will leave behind a point-like massive remnant at zero temperature. Considering a more general metric ansatz and a special equation of state of the matter, we also find a regular NCBH in Rastall gravity, which has a similar geometric structure and temperature to that of NCSBH in GR. (orig.)

Eddington's theory of gravity and its progeny.

Science.gov (United States)

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.

Thin accretion disk signatures in dynamical Chern-Simons-modified gravity

International Nuclear Information System (INIS)

Harko, Tiberiu; Kovacs, Zoltan; Lobo, Francisco S N

2010-01-01

A promising extension of general relativity is Chern-Simons (CS)-modified gravity, in which the Einstein-Hilbert action is modified by adding a parity-violating CS term, which couples to gravity via a scalar field. In this work, we consider the interesting, yet relatively unexplored, dynamical formulation of CS-modified gravity, where the CS coupling field is treated as a dynamical field, endowed with its own stress-energy tensor and evolution equation. We consider the possibility of observationally testing dynamical CS-modified gravity by using the accretion disk properties around slowly rotating black holes. The energy flux, temperature distribution, the emission spectrum as well as the energy conversion efficiency are obtained, and compared to the standard general relativistic Kerr solution. It is shown that the Kerr black hole provides a more efficient engine for the transformation of the energy of the accreting mass into radiation than their slowly rotating counterparts in CS-modified gravity. Specific signatures appear in the electromagnetic spectrum, thus leading to the possibility of directly testing CS-modified gravity by using astrophysical observations of the emission spectra from accretion disks.

Expectation values in quantum gravity

International Nuclear Information System (INIS)

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

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

International Nuclear Information System (INIS)

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

New Spin Foam Models of Quantum Gravity

Science.gov (United States)

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.

Universal Property of Quantum Gravity implied by Bekenstein-Hawking Entropy and Boltzmann formula

International Nuclear Information System (INIS)

Saida, Hiromi

2013-01-01

We search for a universal property of quantum gravity. By u niversal , we mean the independence from any existing model of quantum gravity (such as the super string theory, loop quantum gravity, causal dynamical triangulation, and so on). To do so, we try to put the basis of our discussion on theories established by some experiments. Thus, we focus our attention on thermodynamical and statistical-mechanical basis of the black hole thermodynamics: Let us assume that the Bekenstein-Hawking entropy is given by the Boltzmann formula applied to the underlying theory of quantum gravity. Under this assumption, the conditions justifying Boltzmann formula together with uniqueness of Bekenstein-Hawking entropy imply a reasonable universal property of quantum gravity. The universal property indicates a repulsive gravity at Planck length scale, otherwise stationary black holes can not be regarded as thermal equilibrium states of gravity. Further, in semi-classical level, we discuss a possible correction of Einstein equation which generates repulsive gravity at Planck length scale.

Physics on all scales. Scalar-tensor theories of quantum gravity in particle physics and cosmology

Energy Technology Data Exchange (ETDEWEB)

Henz, Tobias

2016-05-10

In this thesis, we investigate dilaton quantum gravity using a functional renormalization group approach. We derive and discuss flow equations both in the background field approximation and using a vertex expansion as well as solve the fixed point equations globally to show how realistic gravity, connecting ultraviolet and infrared physics, can be realized on a pure fixed point trajectory by virtue of spontaneous breaking of scale invariance. The emerging physical system features a dynamically generated moving Planck scale resembling the Newton coupling as well as slow roll inflation with an exponentially decreasing effective cosmological constant that vanishes completely in the infrared. The moving Planck scale might make quantum gravity experimentally accessible at a different energy scale than previously believed. We therefore not only provide further evidence for the existence of a consistent quantum theory of gravity based on general relativity, but also offer potential solutions towards the hierarchy and cosmological constant problems, thereby opening up exciting opportunities for further research.

Four-dimensional gravity as an almost-Poisson system

Science.gov (United States)

Ita, Eyo Eyo

2015-04-01

In this paper, we examine the phase space structure of a noncanonical formulation of four-dimensional gravity referred to as the Instanton representation of Plebanski gravity (IRPG). The typical Hamiltonian (symplectic) approach leads to an obstruction to the definition of a symplectic structure on the full phase space of the IRPG. We circumvent this obstruction, using the Lagrange equations of motion, to find the appropriate generalization of the Poisson bracket. It is shown that the IRPG does not support a Poisson bracket except on the vector constraint surface. Yet there exists a fundamental bilinear operation on its phase space which produces the correct equations of motion and induces the correct transformation properties of the basic fields. This bilinear operation is known as the almost-Poisson bracket, which fails to satisfy the Jacobi identity and in this case also the condition of antisymmetry. We place these results into the overall context of nonsymplectic systems.

Focus on quantum Einstein gravity Focus on quantum Einstein gravity

Science.gov (United States)

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

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

Science.gov (United States)

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.

Geometric scalar theory of gravity beyond spherical symmetry

Science.gov (United States)

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.

Structural equation models from paths to networks

CERN Document Server

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...

Gravity Matching Aided Inertial Navigation Technique Based on Marginal Robust Unscented Kalman Filter

Directory of Open Access Journals (Sweden)

Ming Liu

2015-01-01

Full Text Available This paper is concerned with the topic of gravity matching aided inertial navigation technology using Kalman filter. The dynamic state space model for Kalman filter is constructed as follows: the error equation of the inertial navigation system is employed as the process equation while the local gravity model based on 9-point surface interpolation is employed as the observation equation. The unscented Kalman filter is employed to address the nonlinearity of the observation equation. The filter is refined in two ways as follows. The marginalization technique is employed to explore the conditionally linear substructure to reduce the computational load; specifically, the number of the needed sigma points is reduced from 15 to 5 after this technique is used. A robust technique based on Chi-square test is employed to make the filter insensitive to the uncertainties in the above constructed observation model. Numerical simulation is carried out, and the efficacy of the proposed method is validated by the simulation results.

On the Mechanism for a Gravity Effect Using Type 2 Superconductors

Science.gov (United States)

Robertson, Glen A.

1999-01-01

In this paper, we formulate a percent mass change equation based on Woodward's transient mass shift and the Cavendish balance equations applied to superconductor Josephson junctions, A correction to the transient mass shift equation is presented due to the emission of the mass energy from the superconductor. The percentage of mass change predicted by the equation was estimated against the maximum percent mass change reported by Podkletnov in his gravity shielding experiments. An experiment is then discussed, which could shed light on the transient mass shift near superconductor and verify the corrected gravitational potential.

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

International Nuclear Information System (INIS)

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

Gravity variation before the Akto Ms6.7 earthquake, Xinjiang

Directory of Open Access Journals (Sweden)

Hongtao Hao

2017-03-01

Full Text Available The relationship between gravity variation and the Akto Ms6.7 earthquake on November 11, 2016, was studied by use of mobile gravity observation data from the China continental structural environmental monitoring network. The result revealed that before the Akto earthquake, a high positive gravity variation was observed in the Pamir tectonic knots region (within a maximum magnitude of approximately +80 microgal, which was consistent with the existing knowledge of gravity abnormality and the locations of strong earthquakes. In view of the recent strong seismic activities in the Pamir tectonic knots region, as well as the strong upward crust movement and compressive strain, it is believed that gravity change in the Pamir tectonic knots region reflects the recent strong seismic activities and crust movement.

Astrophysical flows near [Formula: see text] gravity black holes.

Science.gov (United States)

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.

A gauge-theoretic approach to gravity.

Science.gov (United States)

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.

A GOCE only gravity model GOSG01S and the validation of GOCE related satellite gravity models

Directory of Open Access Journals (Sweden)

Xinyu Xu

2017-07-01

Full Text Available We compile the GOCE-only satellite model GOSG01S complete to spherical harmonic degree of 220 using Satellite Gravity Gradiometry (SGG data and the Satellite-to-Satellite Tracking (SST observations along the GOCE orbit based on applying a least-squares analysis. The diagonal components (Vxx, Vyy, Vzz of the gravitational gradient tensor are used to form the system of observation equations with the band-pass ARMA filter. The point-wise acceleration observations (ax, ay, az along the orbit are used to form the system of observation equations up to the maximum spherical harmonic degree/order 130. The analysis of spectral accuracy characteristics of the newly derived gravitational model GOSG01S and the existing models GOTIM04S, GODIR04S, GOSPW04S and JYY_GOCE02S based on their comparison with the ultra-high degree model EIGEN-6C2 reveals a significant consistency at the spectral window approximately between 80 and 190 due to the same period SGG data used to compile these models. The GOCE related satellite gravity models GOSG01S, GOTIM05S, GODIR05S, GOTIM04S, GODIR04S, GOSPW04S, JYY_GOCE02S, EIGEN-6C2 and EGM2008 are also validated by using GPS-leveling data in China and USA. According to the truncation at degree 200, the statistic results show that all GGMs have very similar differences at GPS-leveling points in USA, and all GOCE related gravity models have better performance than EGM2008 in China. This suggests that all these models provide much more information on the gravity field than EGM2008 in areas with low terrestrial gravity coverage. And STDs of height anomaly differences in China for the selected truncation degrees show that GOCE has improved the accuracy of the global models beyond degree 90 and the accuracies of the models improve from 24 cm to 16 cm. STDs of geoid height differences in USA show that GOSG01S model has best consistency comparing with GPS-leveling data for the frequency band of the degree between 20 and 160.

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

International Nuclear Information System (INIS)

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

Loop Quantum Gravity.

Science.gov (United States)

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.

Aspects of Quadratic Gravity

CERN Document Server

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-...

The Raychaudhuri equation in homogeneous cosmologies

International Nuclear Information System (INIS)

Albareti, F.D.; Cembranos, J.A.R.; Cruz-Dombriz, A. de la; Dobado, A.

2014-01-01

In this work we address the issue of studying the conditions required to guarantee the Focusing Theorem for both null and timelike geodesic congruences by using the Raychaudhuri equation. In particular we study the case of Friedmann-Robertson-Walker as well as more general Bianchi Type I spacetimes. The fulfillment of the Focusing Theorem is mandatory in small scales since it accounts for the attractive character of gravity. However, the Focusing Theorem is not satisfied at cosmological scales due to the measured negative deceleration parameter. The study of the conditions needed for congruences convergence is not only relevant at the fundamental level but also to derive the viability conditions to be imposed on extended theories of gravity describing the different expansion regimes of the universe. We illustrate this idea for f(R) gravity theories

Solar System constraints to general f(R) gravity

International Nuclear Information System (INIS)

Chiba, Takeshi; Smith, Tristan L.; Erickcek, Adrienne L.

2007-01-01

It has been proposed that cosmic acceleration or inflation can be driven by replacing the Einstein-Hilbert action of general relativity with a function f(R) of the Ricci scalar R. Such f(R) gravity theories have been shown to be equivalent to scalar-tensor theories of gravity that are incompatible with Solar System tests of general relativity, as long as the scalar field propagates over Solar System scales. Specifically, the parameterized post-Newtonian (PPN) parameter in the equivalent scalar-tensor theory is γ=1/2, which is far outside the range allowed by observations. In response to a flurry of papers that questioned the equivalence of f(R) theory to scalar-tensor theories, it was recently shown explicitly, without resorting to the scalar-tensor equivalence, that the vacuum field equations for 1/R gravity around a spherically symmetric mass also yield γ=1/2. Here we generalize this analysis to f(R) gravity and enumerate the conditions that, when satisfied by the function f(R), lead to the prediction that γ=1/2

Covariant approach of perturbations in Lovelock type brane gravity

Science.gov (United States)

Bagatella-Flores, Norma; Campuzano, Cuauhtemoc; Cruz, Miguel; Rojas, Efraín

2016-12-01

We develop a covariant scheme to describe the dynamics of small perturbations on Lovelock type extended objects propagating in a flat Minkowski spacetime. The higher-dimensional analogue of the Jacobi equation in this theory becomes a wave type equation for a scalar field Φ . Whithin this framework, we analyse the stability of membranes with a de Sitter geometry where we find that the Jacobi equation specializes to a Klein-Gordon (KG) equation for Φ possessing a tachyonic mass. This shows that, to some extent, these types of extended objects share the symmetries of the Dirac-Nambu-Goto (DNG) action which is by no means coincidental because the DNG model is the simplest included in this type of gravity.

Search for a correlation between Josephson junctions and gravity

International Nuclear Information System (INIS)

Robertson, Glen A.

2000-01-01

Woodward's transient mass shift (TMS) formula has commonality with Modanese's anomalous coupling theory (ACT) and Woodward's capacitor experiment has commonality with Podkletnov's layered superconductor disk experiment. The TMS formula derives a mass fluctuation from a time-varying energy density. The ACT suggests that the essential ingredient for the gravity phenomenon is the presence of strong variations or fluctuations of the Cooper pair density (a time-varying energy density). Woodward's experiment used a small array of capacitors whose energy density was varied by an applied 11 kHz signal. Podkletnov's superconductor disk contained many Josephson junctions (small capacitive like interfaces), which were radiated with a 3-4 MHz signal. This paper formulates a TMS for superconductor Josephson junctions. The equation was compared to the 2% mass change claimed by Podkletnov in his gravity shielding experiments. The TMS is calculated to be 2% for a 2-kg superconductor with an induced total power to the multiple Josephson junctions of about 3.3-watts. A percent mass change equation is then formulated based on the Cavendish balance equation where the superconductor TMS is used for the delta change in mass. An experiment using a Cavendish balance is then discussed

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

International Nuclear Information System (INIS)

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

Constraining inverse curvature gravity with supernovae

Energy Technology Data Exchange (ETDEWEB)

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.

Testing quantum gravity through dumb holes

Energy Technology Data Exchange (ETDEWEB)

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.

Late time acceleration of the universe in f(R) gravity model

International Nuclear Information System (INIS)

Mukherjee, Ankan

2014-01-01

In this work, a new way to look at the nature of late time dynamics of the universe for f(R) gravity models using the contracted Bianchi Identity has been proposed. As the Einstein field equations contain derivatives of the curvature scalar R, the contracted Bianchi identity yields a second order nonlinear differential equation in H, the Hubble parameter. This equation is studied for two particular forms of f(R), and the late time behaviour of the model is discussed. (author)

R 2 inflation to probe non-perturbative quantum gravity

Science.gov (United States)

Koshelev, Alexey S.; Sravan Kumar, K.; Starobinsky, Alexei A.

2018-03-01

It is natural to expect a consistent inflationary model of the very early Universe to be an effective theory of quantum gravity, at least at energies much less than the Planck one. For the moment, R + R 2, or shortly R 2, inflation is the most successful in accounting for the latest CMB data from the PLANCK satellite and other experiments. Moreover, recently it was shown to be ultra-violet (UV) complete via an embedding into an analytic infinite derivative (AID) non-local gravity. In this paper, we derive a most general theory of gravity that contributes to perturbed linear equations of motion around maximally symmetric space-times. We show that such a theory is quadratic in the Ricci scalar and the Weyl tensor with AID operators along with the Einstein-Hilbert term and possibly a cosmological constant. We explicitly demonstrate that introduction of the Ricci tensor squared term is redundant. Working in this quadratic AID gravity framework without a cosmological term we prove that for a specified class of space homogeneous space-times, a space of solutions to the equations of motion is identical to the space of backgrounds in a local R 2 model. We further compute the full second order perturbed action around any background belonging to that class. We proceed by extracting the key inflationary parameters of our model such as a spectral index ( n s ), a tensor-to-scalar ratio ( r) and a tensor tilt ( n t ). It appears that n s remains the same as in the local R 2 inflation in the leading slow-roll approximation, while r and n t get modified due to modification of the tensor power spectrum. This class of models allows for any value of r complete R 2 gravity a natural target for future CMB probes.

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

Science.gov (United States)

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.

First law of thermodynamics and Friedmann-like equations in braneworld cosmology

International Nuclear Information System (INIS)

Ge Xianhui

2007-01-01

We derive the Friedmann-like equations in braneworld cosmology by imposing the first law of thermodynamics and Bekenstein's area-entropy formula on the apparent horizon of a Friedmann-Robertson-Walker universe in both Randall-Sundrum II gravity and Dvali-Gabadadze-Porrati gravity models. Israel's boundary condition plays an important role in our calculations in both cases, besides the first law of thermodynamics and Bekenstein's area-entropy formula. The results indicate that thermodynamics on the brane world knows the behaviors of gravity

Gravity data from the Sierra Vista Subwatershed, Upper San Pedro Basin, Arizona

Science.gov (United States)

Kennedy, Jeffrey R.

2015-01-01

Observations of very small changes of Earth’s gravitational field (time-lapse gravity) provide a direct, non-invasive method for measuring changes in aquifer storage change. An existing network of gravity stations in the Sierra Vista Subwatershed was revised in 2014 to better understand the spatial distribution of changes in aquifer storage, especially with relation to ephemeral channel recharge and a groundwater cone of depression associated with pumping in the greater Sierra Vista area. In addition, the network was extended to provide baseline data for possible future enhanced-recharge projects.

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

Directory of Open Access Journals (Sweden)

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.

The metric on field space, functional renormalization, and metric–torsion quantum gravity

International Nuclear Information System (INIS)

Reuter, Martin; Schollmeyer, Gregor M.

2016-01-01

Searching for new non-perturbatively renormalizable quantum gravity theories, functional renormalization group (RG) flows are studied on a theory space of action functionals depending on the metric and the torsion tensor, the latter parameterized by three irreducible component fields. A detailed comparison with Quantum Einstein–Cartan Gravity (QECG), Quantum Einstein Gravity (QEG), and “tetrad-only” gravity, all based on different theory spaces, is performed. It is demonstrated that, over a generic theory space, the construction of a functional RG equation (FRGE) for the effective average action requires the specification of a metric on the infinite-dimensional field manifold as an additional input. A modified FRGE is obtained if this metric is scale-dependent, as it happens in the metric–torsion system considered.

A note on the geometric unification of gravity and electromagnetism

International Nuclear Information System (INIS)

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)

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

Science.gov (United States)

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.

Gravity modulation of thermal instability in a viscoelastic fluid saturated anisotropic porous medium

Energy Technology Data Exchange (ETDEWEB)

Bhadauria, Beer S. [Babasaheb Bhimrao Ambedkar Univ., Lucknow (India). Dept. of Applied Mathematics and Statistics; Banaras Hindu Univ., Varanasi (India). Dept. of Mathematics; Srivastava, Atul K. [Banaras Hindu Univ., Varanasi (India). Dept. of Mathematics; Sacheti, Nirmal C.; Chandran, Pallath [Sultan Qaboos Univ., Muscat (Oman). Dept. of Mathematics

2012-01-15

The present paper deals with a thermal instability problem in a viscoelastic fluid saturating an anisotropic porous medium under gravity modulation. To find the gravity modulation effect, the gravity field is considered in two parts: a constant part and an externally imposed time-dependent periodic part. The time-dependent part of the gravity field, which can be realized by shaking the fluid, has been represented by a sinusoidal function. Using Hill's equation and the Floquet theory, the convective threshold has been obtained. It is found that gravity modulation can significantly affect the stability limits of the system. Further, we find that there is a competition between the synchronous and subharmonic modes of convection at the onset of instability. Effects of various parameters on the onset of instability have also been discussed. (orig.)

New effective coupled F((4)R, φ) modified gravity from f((5)R) gravity in five dimensions

International Nuclear Information System (INIS)

Madriz Aguilar, Jose Edgar

2015-01-01

Using some ideas of the Wesson induced matter theory, we obtain a new kind of F( (4) R, φ) modified gravity theory as an effective four-dimensional (4D) theory derived from f( (5) R) gravity in five dimensions (5D). This new theory exhibits a different matter coupling than the one in BBHL theory. We show that the field equations of the Wesson induced matter theory and of some brane-world scenarios can be obtained as maximally symmetric solutions of the same f( (5) R) theory. We found criteria for the Dolgov-Kawasaki instabilities for both the f( (5) R) and the F( (4) R, φ) theories. We demonstrate that under certain conditions imposed on the 5D geometry it is possible to interpret the F( (4) R, φ) theory as a modified gravity theory with dynamical coefficients, making this new theory a viable candidate to address the present accelerating cosmic expansion issue. Matter sources in the F( (4) R, φ) case appear induced by the 5D geometry without the necessity of the introduction of matter sources in 5D. (orig.)

Warped, anisotropic wormhole/soliton configurations in vacuum 5D gravity

International Nuclear Information System (INIS)

Vacaru, Sergiu I; Singleton, D

2002-01-01

In this paper we apply the anholonomic frames method developed in previous work to construct and study anisotropic vacuum field configurations in 5D gravity. Starting with an off-diagonal 5D metric, parametrized in terms of several ansatz functions, we show that using anholonomic frames greatly simplifies the resulting Einstein field equations. These simplified equations contain an interesting freedom in that one can choose one of the ansatz functions and then determine the remaining ansatz functions in terms of this choice. As examples we take one of the ansatz functions to be a solitonic solution of either the Kadomtsev-Petviashvili equation or the sine-Gordon equation. There are several interesting physical consequences of these solutions. First, a certain subclass of the solutions discussed in this paper has an exponential warp factor similar to that of the Randall-Sundrum model. However, the warp factor depends on more than just the fifth coordinate. In addition the warp factor arises from anisotropic vacuum solutions rather than from any explicit matter. Second, the solitonic character of these solutions might allow them to be interpreted either as gravitational models for particles (i.e. analogous to the 't Hooft-Polyakov monopole, but in the context of gravity), or as nonlinear, anisotropic gravitational waves

Assessing Hypothetical Gravity Control Propulsion

OpenAIRE

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...

Stability Analysis and Internal Heating Effect on Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium Under Gravity Modulation

Science.gov (United States)

Bhadauria, B. S.; Singh, M. K.; Singh, A.; Singh, B. K.; Kiran, P.

2016-12-01

In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

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

Science.gov (United States)

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.

Mass Redistribution in the Core and Time-varying Gravity at the Earth's Surface

Science.gov (United States)

Kuang, Wei-Jia; Chao, Benjamin F.; Fang, Ming

2003-01-01

The Earth's liquid outer core is in convection, as suggested by the existence of the geomagnetic field in much of the Earth's history. One consequence of the convection is the redistribution of mass resulting from relative motion among fluid parcels with slightly different densities. This time dependent mass redistribution inside the core produces a small perturbation on the gravity field of the Earth. With our numerical dynamo solutions, we find that the mass redistribution (and the resultant gravity field) symmetric about the equator is much stronger than that anti-symmetric about the equator. In particular, J(sub 2) component is the strongest. In addition, the gravity field variation increases with the Rayleigh number that measures the driving force for the geodynamo in the core. With reasonable scaling from the current dynamo solutions, we could expect that at the surface of the Earth, the J(sub 2) variation from the core is on the order of l0(exp -16)/year relative to the mean (i.e. spherically symmetric) gravity field of the Earth. The possible shielding effect due to core-mantle boundary pressure variation loading is likely much smaller and is therefore negligible. Our results suggest that time-varying gravity field perturbation due to core mass redistribution may be measured with modem space geodetic observations, which will result a new means of detecting dynamical processes in the Earth's deep interior.

Constraining f(T) gravity in the Solar System

Energy Technology Data Exchange (ETDEWEB)

Iorio, Lorenzo [Ministero dell' Istruzione dell' Università e della Ricerca (M.I.U.R), Viale Unità di Italia 68, 70125 Bari (Italy); Radicella, Ninfa [Dipartimento di Fisica E.R. Caianiello, Università di Salerno, Via Giovanni Paolo II 132, Fisciano (Italy); Ruggiero, Matteo Luca, E-mail: lorenzo.iorio@libero.it, E-mail: ninfa.radicella@sa.infn.it, E-mail: matteo.ruggiero@polito.it [DISAT, Politecnico di Torino, Corso Duca degli Abruzzi 24, Torino (Italy)

2015-08-01

In the framework of f(T) theories of gravity, we solve the field equations for f(T)=T+α T{sup n} in the weak-field approximation and for spherical symmetry spacetime. Since f(T)=T corresponds to Teleparallel Gravity, which is equivalent to General Relativity, the non linearity of the Lagrangian are expected to produce perturbations of the general relativistic solutions, parameterized by α. Hence, we use the f(T) solutions to model the gravitational field of the Sun and exploit data from accurate radio-tracking of spacecrafts orbiting Mercury and Saturn to infer preliminary bounds on the model parameter α and on the cosmological constant Λ.

Holography as a highly efficient renormalization group flow. I. Rephrasing gravity

Science.gov (United States)

Behr, Nicolas; Kuperstein, Stanislav; Mukhopadhyay, Ayan

2016-07-01

We investigate how the holographic correspondence can be reformulated as a generalization of Wilsonian renormalization group (RG) flow in a strongly interacting large-N quantum field theory. We first define a highly efficient RG flow as one in which the Ward identities related to local conservation of energy, momentum and charges preserve the same form at each scale. To achieve this, it is necessary to redefine the background metric and external sources at each scale as functionals of the effective single-trace operators. These redefinitions also absorb the contributions of the multitrace operators to these effective Ward identities. Thus, the background metric and external sources become effectively dynamical, reproducing the dual classical gravity equations in one higher dimension. Here, we focus on reconstructing the pure gravity sector as a highly efficient RG flow of the energy-momentum tensor operator, leaving the explicit constructive field theory approach for generating such RG flows to the second part of the work. We show that special symmetries of the highly efficient RG flows carry information through which we can decode the gauge fixing of bulk diffeomorphisms in the corresponding gravity equations. We also show that the highly efficient RG flow which reproduces a given classical gravity theory in a given gauge is unique provided the endpoint can be transformed to a nonrelativistic fixed point with a finite number of parameters under a universal rescaling. The results obtained here are used in the second part of this work, where we do an explicit field-theoretic construction of the RG flow and obtain the dual classical gravity theory.

Compact objects in relativistic theories of gravity

Science.gov (United States)

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

Gravity's rainbow: A bridge between LQC and DSR

Directory of Open Access Journals (Sweden)

M.A. Gorji

2017-02-01

Full Text Available The doubly special relativity (DSR theories are constructed in order to take into account an observer-independent length scale in special relativity framework. Gravity's rainbow is a simple generalization of DSR theories to incorporate gravity. In this paper, we show that the effective Friedmann equations that are suggested by loop quantum cosmology (LQC can be exactly reobtained in rainbow cosmology setup. The deformed geometry of LQC then fixes the modified dispersion relation and results in a unique DSR model. In comparison with standard LQC scenario where only the geometry is modified, both geometry and matter parts get modified in our setup. In this respect, we show that the total number of microstates for the universe is finite which suggests the statistical origin of the energy and entropy density bounds. These results explicitly show that the DSR theories are appropriate candidates for the flat limit of loop quantum gravity.

New 'phase' of quantum gravity.

Science.gov (United States)

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.

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

DEFF Research Database (Denmark)

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...

Loop Quantum Gravity

Directory of Open Access Journals (Sweden)

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.

Geodynamical behavior of some active area in Egypt, as deduced from geodetic and gravity data

Science.gov (United States)

Issawy, E.; Mrlina, J.; Radwan, A.; Mahmoud, S.; Rayan, A.

2009-04-01

Temporal gravity variation in parallel with the space geodetic technique (GPS) had been started in Egypt for real campaigns in 1997. The geodetic networks around the High Dam, Aswan area was the first net to be measured. More than five measurement epochs were performed. The results had a considerable limit of coincidence between gravity and GPS observations. The trend of gravity changes indicated a positive stress and had the vertical displacement observed for leveling points. The lowest gravity changes along Kalabsha fault reflect extensional and/or strike component of the stress field. Also, the areas around Cairo (Greater Cairo) and due to the occurrence of an earthquake of 1992, such type of measurements were useful for monitoring the recent activity. The data of the geodetic network around Cairo after 5 campaigns showed that, the estimated horizontal velocities for almost all points are 5.5± mm/year in approximately NW-SE direction. The non-tidal changes can explain the dynamic process within the upper crust related to the development of local stress conditions. The trends of gravity changes are more or less coincident with that deduced from GPS deformation analysis and the occurrence of the main shocks in the area. In additions, in 2005 the geodetic network around the southern part of Sinai and the Gulf of Suez were established. One campaign of measurements had been performed and the gravity values were obtained.

Pan tropical biomass equations for Mexico's dry forests

Directory of Open Access Journals (Sweden)

José Návar

2014-12-01

Full Text Available This study reports a set of robust regional M-tree allometric equations for Mexico's tropical dry forests and their application to a forest inventory dataset for the States of Durango and Sinaloa, Mexico. Calculated M data from 15 reported equations were fitted, applied and validated for regional and global models. Proposed theoretical models, empirically derived equations, as well as global and local reported equations were fitted and applied to calculated M-tree data using wood specific gravity, diameter at breast height, and top height as exogenous variables. Empirically-derived, computer-based equations assessed the M-tree evaluations slightly better than the theoretical, the global and the local models. However, the theoretical models projected compatible M-tree values and deserve further attention once wood specific gravity data are collected in the field. Using the best fit equation, mean M plot density values of 30, 41 and 35 Mg ha-1 were estimated from 57 plots (1,600 m² each, 217 plots (1,000 m² each and 166 plots (1,000 m² each in the tropical dry forests of the States of Durango, Tiniaquis and Vado Hondo (Sinaloa, respectively. The large sample size, the richness of the tested allometric models, the economic and ecological importance of this data-source, and the spatial coverage of these equations made this dataset uniquely useful for biomass, charcoal, and other bio-energy estimations, as well as for understanding the inherent heterogeneity of the stand-structure in dynamic tropical forest environments.

Cosmological stability bound in massive gravity and bigravity

International Nuclear Information System (INIS)

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

Stability Analysis and Internal Heating Effect on Oscillatory Convection in a Viscoelastic Fluid Saturated Porous Medium Under Gravity Modulation

Directory of Open Access Journals (Sweden)

Bhadauria B.S.

2016-12-01

Full Text Available In this paper, we investigate the combined effect of internal heating and time periodic gravity modulation in a viscoelastic fluid saturated porous medium by reducing the problem into a complex non-autonomous Ginzgburg-Landau equation. Weak nonlinear stability analysis has been performed by using power series expansion in terms of the amplitude of gravity modulation, which is assumed to be small. The Nusselt number is obtained in terms of the amplitude for oscillatory mode of convection. The influence of viscoelastic parameters on heat transfer has been discussed. Gravity modulation is found to have a destabilizing effect at low frequencies and a stabilizing effect at high frequencies. Finally, it is found that overstability advances the onset of convection, more with internal heating. The conditions for which the complex Ginzgburg-Landau equation undergoes Hopf bifurcation and the amplitude equation undergoes supercritical pitchfork bifurcation are studied.

Energy, momentum and angular momentum conservations in de Sitter gravity

International Nuclear Information System (INIS)

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)

Absolute Gravity Datum in the Age of Cold Atom Gravimeters

Science.gov (United States)

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

Accelerated FRW solutions in Chern-Simons gravity

International Nuclear Information System (INIS)

Cataldo, Mauricio; Crisostomo, Juan; Gomez, Fernando; Salgado, Patricio; Campo, Sergio del; Quinzacara, Cristian C.

2014-01-01

We consider a five-dimensional Einstein-Chern-Simons action which is composed of a gravitational sector and a sector of matter where the gravitational sector is given by a Chern-Simons gravity action instead of the Einstein-Hilbert action and where the matter sector is given by the so-called perfect fluid. It is shown that (i) the Einstein-Chern-Simons (EChS) field equations subject to suitable conditions can be written in a similar way to the Einstein-Maxwell field equations; (ii) these equations have solutions that describe an accelerated expansion for the three possible cosmological models of the universe, namely, spherical expansion, flat expansion, and hyperbolic expansion when α a parameter of the theory, is greater than zero. This result allows us to conjecture that these solutions are compatible with the era of dark energy and that the energy-momentum tensor for the field h a , a bosonic gauge field from the Chern-Simons gravity action, corresponds to a form of positive cosmological constant. It is also shown that the EChS field equations have solutions compatible with the era of matter: (i) In the case of an open universe, the solutions correspond to an accelerated expansion (α > 0) with a minimum scale factor at initial time that, when time goes to infinity, the scale factor behaves as a hyperbolic sine function. (ii) In the case of a flat universe, the solutions describe an accelerated expansion whose scale factor behaves as an exponential function of time. (iii) In the case of a closed universe there is found only one solution for a universe in expansion, which behaves as a hyperbolic cosine function of time. (orig.)

Cosmology of f(R) gravity in the metric variational approach

Science.gov (United States)

Li, Baojiu; Barrow, John D.

2007-04-01

We consider the cosmologies that arise in a subclass of f(R) gravity with f(R)=R+μ2n+2/(-R)n and n∈(-1,0) in the metric (as opposed to the Palatini) variational approach to deriving the gravitational field equations. The calculations of the isotropic and homogeneous cosmological models are undertaken in the Jordan frame and at both the background and the perturbation levels. For the former, we also discuss the connection to the Einstein frame in which the extra degree of freedom in the theory is associated with a scalar field sharing some of the properties of a “chameleon” field. For the latter, we derive the cosmological perturbation equations in general theories of f(R) gravity in covariant form and implement them numerically to calculate the cosmic microwave background (CMB) temperature and matter power spectra of the cosmological model. The CMB power is shown to reduce at low l’s, and the matter power spectrum is almost scale independent at small scales, thus having a similar shape to that in standard general relativity. These are in stark contrast with what was found in the Palatini f(R) gravity, where the CMB power is largely amplified at low l’s and the matter spectrum is strongly scale dependent at small scales. These features make the present model more adaptable than that arising from the Palatini f(R) field equations, and none of the data on background evolution, CMB power spectrum, or matter power spectrum currently rule it out.

a method of gravity and seismic sequential inversion and its GPU implementation

Science.gov (United States)

Liu, G.; Meng, X.

2011-12-01

In this abstract, we introduce a gravity and seismic sequential inversion method to invert for density and velocity together. For the gravity inversion, we use an iterative method based on correlation imaging algorithm; for the seismic inversion, we use the full waveform inversion. The link between the density and velocity is an empirical formula called Gardner equation, for large volumes of data, we use the GPU to accelerate the computation. For the gravity inversion method , we introduce a method based on correlation imaging algorithm,it is also a interative method, first we calculate the correlation imaging of the observed gravity anomaly, it is some value between -1 and +1, then we multiply this value with a little density ,this value become the initial density model. We get a forward reuslt with this initial model and also calculate the correaltion imaging of the misfit of observed data and the forward data, also multiply the correaltion imaging result a little density and add it to the initial model, then do the same procedure above , at last ,we can get a inversion density model. For the seismic inveron method ,we use a mothod base on the linearity of acoustic wave equation written in the frequency domain,with a intial velociy model, we can get a good velocity result. In the sequential inversion of gravity and seismic , we need a link formula to convert between density and velocity ,in our method , we use the Gardner equation. Driven by the insatiable market demand for real time, high-definition 3D images, the programmable NVIDIA Graphic Processing Unit (GPU) as co-processor of CPU has been developed for high performance computing. Compute Unified Device Architecture (CUDA) is a parallel programming model and software environment provided by NVIDIA designed to overcome the challenge of using traditional general purpose GPU while maintaining a low learn curve for programmers familiar with standard programming languages such as C. In our inversion processing

Breaking the EOS-gravity degeneracy with masses and pulsating frequencies of neutron stars

International Nuclear Information System (INIS)

Lin, Weikang; Li, Bao-An; Chen, Lie-Wen; Wen, De-Hua; Xu, Jun

2014-01-01

A thorough understanding of many astrophysical phenomena associated with compact objects requires reliable knowledge about both the equation of state (EOS) of super-dense nuclear matter and the theory of strong-field gravity simultaneously because of the EOS-gravity degeneracy. Currently, variations of the neutron star (NS) mass–radius correlation from using alternative gravity theories are much larger than those from changing the NS matter EOS within known constraints. At least two independent observables are required to break the EOS-gravity degeneracy. Using model EOSs for hybrid stars and a Yukawa-type non-Newtonian gravity, we investigate both the mass–radius correlation and pulsating frequencies of NSs. While the maximum mass of NSs increases, the frequencies of the f, p 1 , p 2 , and w I pulsating modes are found to decrease with the increasing strength of the Yukawa-type non-Newtonian gravity, providing a useful reference for future determination simultaneously of both the strong-field gravity and the supranuclear EOS by combining data of x-ray and gravitational wave emissions of NSs. (paper)

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

Science.gov (United States)

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...

Bouncing cosmologies from quantum gravity condensates

Science.gov (United States)

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.

Towards systems biology of the gravity response of higher plants -multiscale analysis of Arabidopsis thaliana root growth

Science.gov (United States)

Palme, Klaus; Aubry, D.; Bensch, M.; Schmidt, T.; Ronneberger, O.; Neu, C.; Li, X.; Wang, H.; Santos, F.; Wang, B.; Paponov, I.; Ditengou, F. A.; Teale, W. T.; Volkmann, D.; Baluska, F.; Nonis, A.; Trevisan, S.; Ruperti, B.; Dovzhenko, A.

Gravity plays a fundamental role in plant growth and development. Up to now, little is known about the molecular organisation of the signal transduction cascades and networks which co-ordinate gravity perception and response. By using an integrated systems biological approach, a systems analysis of gravity perception and the subsequent tightly-regulated growth response is planned in the model plant Arabidopsis thaliana. This approach will address questions such as: (i) what are the components of gravity signal transduction pathways? (ii) what are the dynamics of these components? (iii) what is their spatio-temporal regulation in different tis-sues? Using Arabidopsis thaliana as a model-we use root growth to obtain insights in the gravity response. New techniques enable identification of the individual genes affected by grav-ity and further integration of transcriptomics and proteomics data into interaction networks and cell communication events that operate during gravitropic curvature. Using systematic multiscale analysis we have identified regulatory networks consisting of transcription factors, the protein degradation machinery, vesicle trafficking and cellular signalling during the gravire-sponse. We developed approach allowing to incorporate key features of the root system across all relevant spatial and temporal scales to describe gene-expression patterns and correlate them with individual gene and protein functions. Combination of high-resolution microscopy and novel computational tools resulted in development of the root 3D model in which quantitative descriptions of cellular network properties and of multicellular interactions important in root growth and gravitropism can be integrated for the first time.

Quantum Gravity (Cambridge Monographs on Mathematical Physics)

International Nuclear Information System (INIS)

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

Initial value formulation of dynamical Chern-Simons gravity

Science.gov (United States)

Delsate, Térence; Hilditch, David; Witek, Helvi

2015-01-01

We derive an initial value formulation for dynamical Chern-Simons gravity, a modification of general relativity involving parity-violating higher derivative terms. We investigate the structure of the resulting system of partial differential equations thinking about linearization around arbitrary backgrounds. This type of consideration is necessary if we are to establish well-posedness of the Cauchy problem. Treating the field equations as an effective field theory we find that weak necessary conditions for hyperbolicity are satisfied. For the full field equations we find that there are states from which subsequent evolution is not determined. Generically the evolution system closes, but is not hyperbolic in any sense that requires a first order pseudodifferential reduction. In a cursory mode analysis we find that the equations of motion contain terms that may cause ill-posedness of the initial value problem.

Cosmic strings in f(R,L{sub m}) gravity

Energy Technology Data Exchange (ETDEWEB)

Harko, Tiberiu [University College London, Department of Mathematics, London (United Kingdom); Lake, Matthew J. [Naresuan University, The Institute for Fundamental Study, ' ' The Tah Poe Academia Institute' ' , Phitsanulok (Thailand); Ministry of Education, Thailand Center of Excellence in Physics, Bangkok (Thailand)

2015-02-01

We consider Kasner-type static, cylindrically symmetric interior string solutions in the f(R,L{sub m}) theory of modified gravity. The physical properties of the string are described by an anisotropic energy-momentum tensor satisfying the condition T{sub t}{sup t} = T{sub z}{sup z}; that is, the energy density of the string along the z-axis is equal to minus the string tension. As a first step in our study we obtain the gravitational field equations in the f(R,L{sub m}) theory for a general static, cylindrically symmetric metric, and then for a Kasner-type metric, in which the metric tensor components have a power law dependence on the radial coordinate r. String solutions in two particular modified gravity models are investigated in detail. The first is the so-called ''exponential'' modified gravity, in which the gravitational action is proportional to the exponential of the sum of the Ricci scalar and matter Lagrangian, and the second is the ''self-consistent model'', obtained by explicitly determining the gravitational action from the field equations under the assumption of a power law dependent matter Lagrangian. In each case, the thermodynamic parameters of the string, as well as the precise form of the matter Lagrangian, are explicitly obtained. (orig.)

Physical renormalization schemes and asymptotic safety in quantum gravity

Science.gov (United States)

Falls, Kevin

2017-12-01

The methods of the renormalization group and the ɛ -expansion are applied to quantum gravity revealing the existence of an asymptotically safe fixed point in spacetime dimensions higher than two. To facilitate this, physical renormalization schemes are exploited where the renormalization group flow equations take a form which is independent of the parameterisation of the physical degrees of freedom (i.e. the gauge fixing condition and the choice of field variables). Instead the flow equation depends on the anomalous dimensions of reference observables. In the presence of spacetime boundaries we find that the required balance between the Einstein-Hilbert action and Gibbons-Hawking-York boundary term is preserved by the beta functions. Exploiting the ɛ -expansion near two dimensions we consider Einstein gravity coupled to matter. Scheme independence is generically obscured by the loop-expansion due to breaking of two-dimensional Weyl invariance. In schemes which preserve two-dimensional Weyl invariance we avoid the loop expansion and find a unique ultraviolet (UV) fixed point. At this fixed point the anomalous dimensions are large and one must resum all loop orders to obtain the critical exponents. Performing the resummation a set of universal scaling dimensions are found. These scaling dimensions show that only a finite number of matter interactions are relevant. This is a strong indication that quantum gravity is renormalizable.

Black hole production in particle collisions and higher curvature gravity

International Nuclear Information System (INIS)

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

Warm inflation in f(G) theory of gravity

Energy Technology Data Exchange (ETDEWEB)

Sharif, M., E-mail: msharif.math@pu.edu.pk; Ikram, A., E-mail: ayeshamaths91@gmail.com [University of the Punjab, Quaid-e-Azam Campus, Department of Mathematics (Pakistan)

2016-07-15

The aim of this paper is to explore warm inflation in the background of f(G) theory of gravity using scalar fields for the FRW universe model. We construct the field equations under slow-roll approximations and evaluate the slow-roll parameters, scalar and tensor power spectra and their corresponding spectral indices using viable power-law model. These parameters are evaluated for a constant as well as variable dissipation factor during intermediate and logamediate inflationary epochs. We also find the number of e-folds and tensor- scalar ratio for each case. The graphical behavior of these parameters proves that the isotropic model in f(G) gravity is compatible with observational Planck data.

Exact solutions in three-dimensional gravity

CERN Document Server

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...

QCD ghost f(T)-gravity model

Energy Technology Data Exchange (ETDEWEB)

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.)

Magnetic vortices in gauge/gravity duality

Energy Technology Data Exchange (ETDEWEB)

Strydom, Migael

2014-07-18

We study strongly-coupled phenomena using gauge/gravity duality, with a particular focus on vortex solutions produced by magnetic field and time-dependent problems in holographic models. The main result is the discovery of a counter-intuitive effect where a strong non-abelian magnetic field induces the formation of a triangular vortex lattice ground state in a simple holographic model. Gauge/gravity duality is a powerful theoretical tool that has been used to study strongly-coupled systems ranging from the quark-gluon plasma produced at particle colliders to condensed matter theories. The most important idea is that of duality: a strongly coupled quantum field theory can be studied by investigating the properties of a particular gravity background described by Einstein's equations. One gravity background we study in this dissertation is AdS-Schwarzschild with an SU(2) gauge field. We switch on the gauge field component that gives the field theory an external magnetic field. When the magnetic field is above a critical value, we find that the system is unstable, indicating a superconducting phase transition. We find the instability in two ways. Firstly, we do a quasinormal mode analysis, studying fluctuations about the background. Secondly, we rewrite the equations in Schroedinger form and numerically find that, as the magnetic field is increased, the potential deepens until it is capable of supporting a bound state. Next we show that the resulting superconducting ground state is a triangular vortex lattice. This is done by performing a perturbative expansion in a small parameter proportional to the condensate size. After solving the equations to third order, we use the holographic dictionary to calculate the total energy of different lattice solutions and identify the minimum energy state. In addition, we show that the result holds in an AdS-hard wall model as well, which is dual to a confining theory. Next we extend the simple gravity model to include a

The quantum cosmological wavefunction at very early times for a quadratic gravity theory

International Nuclear Information System (INIS)

Davis, Simon

2003-01-01

The quantum cosmological wavefunction for a quadratic gravity theory derived from the heterotic string effective action is obtained near the inflationary epoch and during the initial Planck era. Neglecting derivatives with respect to the scalar field, the wavefunction would satisfy a third-order differential equation near the inflationary epoch which has a solution that is singular in the scale factor limit a(t) → 0. When scalar field derivatives are included, a sixth-order differential equation is obtained for the wavefunction and the solution by Mellin transform is regular in the a → 0 limit. It follows that inclusion of the scalar field in the quadratic gravity action is necessary for consistency of the quantum cosmology of the theory at very early times

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

Directory of Open Access Journals (Sweden)

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.

Space-time philosophy reconstructed via massive Nordström scalar gravities? Laws vs. geometry, conventionality, and underdetermination

Science.gov (United States)

Pitts, J. Brian

2016-02-01

What if gravity satisfied the Klein-Gordon equation? Both particle physics from the 1920-30s and the 1890s Neumann-Seeliger modification of Newtonian gravity with exponential decay suggest considering a "graviton mass term" for gravity, which is algebraic in the potential. Unlike Nordström's "massless" theory, massive scalar gravity is strictly special relativistic in the sense of being invariant under the Poincaré group but not the 15-parameter Bateman-Cunningham conformal group. It therefore exhibits the whole of Minkowski space-time structure, albeit only indirectly concerning volumes. Massive scalar gravity is plausible in terms of relativistic field theory, while violating most interesting versions of Einstein's principles of general covariance, general relativity, equivalence, and Mach. Geometry is a poor guide to understanding massive scalar gravity(s): matter sees a conformally flat metric due to universal coupling, but gravity also sees the rest of the flat metric (barely or on long distances) in the mass term. What is the 'true' geometry, one might wonder, in line with Poincaré's modal conventionality argument? Infinitely many theories exhibit this bimetric 'geometry,' all with the total stress-energy's trace as source; thus geometry does not explain the field equations. The irrelevance of the Ehlers-Pirani-Schild construction to a critique of conventionalism becomes evident when multi-geometry theories are contemplated. Much as Seeliger envisaged, the smooth massless limit indicates underdetermination of theories by data between massless and massive scalar gravities-indeed an unconceived alternative. At least one version easily could have been developed before General Relativity; it then would have motivated thinking of Einstein's equations along the lines of Einstein's newly re-appreciated "physical strategy" and particle physics and would have suggested a rivalry from massive spin 2 variants of General Relativity (massless spin 2, Pauli and Fierz

Universality of isothermal fluid spheres in Lovelock gravity

Science.gov (United States)

Dadhich, Naresh; Hansraj, Sudan; Maharaj, Sunil D.

2016-02-01

We show universality of isothermal fluid spheres in pure Lovelock gravity where the equation of motion has only one N th order term coming from the corresponding Lovelock polynomial action of degree N . Isothermality is characterized by the equation of state, p =α ρ and the property, ρ ˜1 /r2 N . Then the solution describing isothermal spheres, which exist only for the pure Lovelock equation, is of the same form for the general Lovelock degree N in all dimensions d ≥2 N +2 . We further prove that the necessary and sufficient condition for the isothermal sphere is that its metric is conformal to the massless global monopole or the solid angle deficit metric, and this feature is also universal.

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

Science.gov (United States)

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.

Speeding up N-body simulations of modified gravity: chameleon screening models

Science.gov (United States)

Bose, Sownak; Li, Baojiu; Barreira, Alexandre; He, Jian-hua; Hellwing, Wojciech A.; Koyama, Kazuya; Llinares, Claudio; Zhao, Gong-Bo

2017-02-01

We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f(R) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f(R) simulations. For example, a test simulation with 5123 particles in a box of size 512 Mpc/h is now 5 times faster than before, while a Millennium-resolution simulation for f(R) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.

Speeding up N -body simulations of modified gravity: chameleon screening models

International Nuclear Information System (INIS)

Bose, Sownak; Li, Baojiu; He, Jian-hua; Llinares, Claudio; Barreira, Alexandre; Hellwing, Wojciech A.; Koyama, Kazuya; Zhao, Gong-Bo

2017-01-01

We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f ( R ) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f ( R ) simulations. For example, a test simulation with 512 3 particles in a box of size 512 Mpc/ h is now 5 times faster than before, while a Millennium-resolution simulation for f ( R ) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.

Speeding up N -body simulations of modified gravity: chameleon screening models

Energy Technology Data Exchange (ETDEWEB)

Bose, Sownak; Li, Baojiu; He, Jian-hua; Llinares, Claudio [Institute for Computational Cosmology, Department of Physics, Durham University, Durham DH1 3LE (United Kingdom); Barreira, Alexandre [Max-Planck-Institut für Astrophysik, Karl-Schwarzschild-Str. 1, 85741 Garching (Germany); Hellwing, Wojciech A.; Koyama, Kazuya [Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 3FX (United Kingdom); Zhao, Gong-Bo, E-mail: sownak.bose@durham.ac.uk, E-mail: baojiu.li@durham.ac.uk, E-mail: barreira@mpa-garching.mpg.de, E-mail: jianhua.he@durham.ac.uk, E-mail: wojciech.hellwing@port.ac.uk, E-mail: kazuya.koyama@port.ac.uk, E-mail: claudio.llinares@durham.ac.uk, E-mail: gbzhao@nao.cas.cn [National Astronomy Observatories, Chinese Academy of Science, Beijing, 100012 (China)

2017-02-01

We describe and demonstrate the potential of a new and very efficient method for simulating certain classes of modified gravity theories, such as the widely studied f ( R ) gravity models. High resolution simulations for such models are currently very slow due to the highly nonlinear partial differential equation that needs to be solved exactly to predict the modified gravitational force. This nonlinearity is partly inherent, but is also exacerbated by the specific numerical algorithm used, which employs a variable redefinition to prevent numerical instabilities. The standard Newton-Gauss-Seidel iterative method used to tackle this problem has a poor convergence rate. Our new method not only avoids this, but also allows the discretised equation to be written in a form that is analytically solvable. We show that this new method greatly improves the performance and efficiency of f ( R ) simulations. For example, a test simulation with 512{sup 3} particles in a box of size 512 Mpc/ h is now 5 times faster than before, while a Millennium-resolution simulation for f ( R ) gravity is estimated to be more than 20 times faster than with the old method. Our new implementation will be particularly useful for running very high resolution, large-sized simulations which, to date, are only possible for the standard model, and also makes it feasible to run large numbers of lower resolution simulations for covariance analyses. We hope that the method will bring us to a new era for precision cosmological tests of gravity.

Newtonian gravity in loop quantum gravity

OpenAIRE

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.

No-go theorem for bimetric gravity with positive and negative mass

International Nuclear Information System (INIS)

Hohmann, Manuel; Wohlfarth, Mattias N. R.

2009-01-01

We argue that the most conservative geometric extension of Einstein gravity describing both positive and negative mass sources and observers is bimetric gravity and contains two copies of standard model matter which interact only gravitationally. Matter fields related to one of the metrics then appear dark from the point of view of an observer defined by the other metric, and so may provide a potential explanation for the dark universe. In this framework we consider the most general form of linearized field equations compatible with physically and mathematically well-motivated assumptions. Using gauge-invariant linear perturbation theory, we prove a no-go theorem ruling out all bimetric gravity theories that, in the Newtonian limit, lead to precisely opposite forces on positive and negative test masses.

Mimicking the effect of gravity using an elastic membrane

International Nuclear Information System (INIS)

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)

Particle creation phenomenology, Dirac sea and the induced Weyl and Einstein-dilaton gravity

Energy Technology Data Exchange (ETDEWEB)

Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N., E-mail: berezin@inr.ac.ru, E-mail: dokuchaev@inr.ac.ru, E-mail: eroshenko@inr.ac.ru [Institute for Nuclear Research, Russian Academy of Sciences, 60th October Anniversary Prospect 7a, 117312 Moscow (Russian Federation)

2017-01-01

We constructed the conformally invariant model for scalar particle creation induced by strong gravitational fields. Starting from the 'usual' hydrodynamical description of the particle motion written in the Eulerian coordinates we substituted the particle number conservation law (which enters the formalism) by 'the particle creation law', proportional to the square of the Weyl tensor (following the famous result by Ya.B. Zel'dovich and A.A. Starobinsky). Then, demanding the conformal invariance of the whole dynamical system, we have got both the (Weyl)-conformal gravity and the Einstein-Hilbert gravity action integral with dilaton field. Thus, we obtained something like the induced gravity suggested first by A.D. Sakharov. It is shown that the resulting system is self-consistent. We considered also the vacuum equations. It is shown that, beside the 'empty vacuum', there may exist the 'dynamical vacuum', which is nothing more but the Dirac sea. The latter is described by the unexpectedly elegant equation which includes both the Bach and Einstein tensors and the cosmological terms.

Brane-Localized Gravity

International Nuclear Information System (INIS)

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

A distinguishing gravitational property for gravitational equation in higher dimensions

International Nuclear Information System (INIS)

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.)

A distinguishing gravitational property for gravitational equation in higher dimensions

Science.gov (United States)

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.

Higher Curvature Gravity from Entanglement in Conformal Field Theories

Science.gov (United States)

Haehl, Felix M.; Hijano, Eliot; Parrikar, Onkar; Rabideau, Charles

2018-05-01

By generalizing different recent works to the context of higher curvature gravity, we provide a unifying framework for three related results: (i) If an asymptotically anti-de Sitter (AdS) spacetime computes the entanglement entropies of ball-shaped regions in a conformal field theory using a generalized Ryu-Takayanagi formula up to second order in state deformations around the vacuum, then the spacetime satisfies the correct gravitational equations of motion up to second order around the AdS background. (ii) The holographic dual of entanglement entropy in higher curvature theories of gravity is given by the Wald entropy plus a particular correction term involving extrinsic curvatures. (iii) Conformal field theory relative entropy is dual to gravitational canonical energy (also in higher curvature theories of gravity). Especially for the second point, our novel derivation of this previously known statement does not involve the Euclidean replica trick.

The Bouguer Correction Algorithm for Gravity with Limited Range

Directory of Open Access Journals (Sweden)

MA Jian

2017-01-01

Full Text Available The Bouguer correction is an important item in gravity reduction, while the traditional Bouguer correction, whether the plane Bouguer correction or the spherical Bouguer correction, exists approximation error because of far-zone virtual terrain. The error grows as the calculation point gets higher. Therefore gravity reduction using the Bouguer correction with limited range, which was in accordance with the scope of the topographic correction, was researched in this paper. After that, a simplified formula to calculate the Bouguer correction with limited range was proposed. The algorithm, which is innovative and has the value of mathematical theory to some extent, shows consistency with the equation evolved from the strict integral algorithm for topographic correction. The interpolation experiment shows that gravity reduction based on the Bouguer correction with limited range is prior to unlimited range when the calculation point is taller than 1000 m.

Interpretation of f(R,T) gravity in terms of a conserved effective fluid

Science.gov (United States)

Shabani, Hamid; Ziaie, Amir Hadi

2018-03-01

In the present work, we introduce a novel approach to study f(R,T) gravity theory from a different perspective. Here, T denotes the trace of energy-momentum tensor (EMT) of matter fluids. The usual method (as discussed in the literature) is to choose an h(T) function and then solve for the resulted Friedman equations. Nevertheless, our aim here is, without loss of generality, to reformulate a particular class of f(R,T) gravity models in which the Einstein-Hilbert action is promoted by an arbitrary function of the trace of EMT. The strategy is the redefinition of the equation of motion in terms of the components of an effective fluid. We show that in this case the EMT is automatically conserved. As we shall see, adopting such a point of view (at least) in f(R,T) gravity is accompanied by two significant points. On one hand, h(T) function is chosen based upon a physical concept and on the other, we clearly understand the overall or effective behavior of matter in terms of a conserved effective fluid. To illustrate the idea, we study some models in which different physical properties for the effective fluid is attributed to each model. Particularly, we discuss models with constant effective density, constant effective pressure and constant effective equation of state (EoS) parameter. Moreover, two models with a relation between the effective density and the effective pressure will be considered. An elegant result is that in f(R,T) gravity, there is a possibility that a perfect fluid could effectively behave as a modified Chaplygin gas with four free parameters.

Numerical simulations of convectively excited gravity waves

International Nuclear Information System (INIS)

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

A classical approach to higher-derivative gravity

International Nuclear Information System (INIS)

Accioly, A.J.

1988-01-01

Two classical routes towards higher-derivative gravity theory are described. The first one is a geometrical route, starting from first principles. The second route is a formal one, and is based on a recent theorem by Castagnino et.al. [J. Math. Phys. 28 (1987) 1854]. A cosmological solution of the higher-derivative field equations is exhibited which in a classical framework singles out this gravitation theory. (author) [pt

Stability of the Kasner universe in f (T ) gravity

Science.gov (United States)

Paliathanasis, Andronikos; Said, Jackson Levi; Barrow, John D.

2018-02-01

f (T ) gravity theory offers an alternative context in which to consider gravitational interactions where torsion, rather than curvature, is the mechanism by which gravitation is communicated. We investigate the stability of the Kasner solution with several forms of the arbitrary Lagrangian function examined within the f (T ) context. This is a Bianchi type-I vacuum solution with anisotropic expansion factors. In the f (T ) gravity setting, the solution must conform to a set of conditions in order to continue to be a vacuum solution of the generalized field equations. With this solution in hand, the perturbed field equations are determined for power-law and exponential forms of the f (T ) function. We find that the point which describes the Kasner solution is a saddle point which means that the singular solution is unstable. However, we find the de Sitter universe is a late-time attractor. In general relativity, the cosmological constant drives the isotropization of the spacetime while in this setting the extra f (T ) contributions now provide this impetus.

On the structure of Poincare gauge Langrangians for gravity

International Nuclear Information System (INIS)

Wallner, R.P.

1980-01-01

As in translational gauge theories of gravity the pure gauge field Lagrangian Lsub(transl) approximately (translational field strength) 2 approximately (torsion) 2 does not work in its standard form THETA sup(a) Λ *THETAsub(a) because of the lack of any correct Newtonian limit, one has to replace it by a suitable linear combination of other invariants squared in torsion. The appearance of unphysical solutions in full Poincare-gauge theories of gravity due to the standard Lsub(rot) approximately (curvature) 2 -term Ω sub(ab) Λ*Ω sub(ab) now suggests an analogous procedure for Lsub(rot). Here, the various invariants squared in curvature are listed and the number of those coming into question is reduced to two by a formal argument. In addtion, the field equations to all translational and rotational squared invariants are given and a certain combination, which will exclude massive gauge field solutions of the linearized equations, is proposed. For the purpose of rotational and calculational economy, the calculus of exterior forms is used throughout. (Author)

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

International Nuclear Information System (INIS)

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

Geodetic and geophysical results from a Taiwan airborne gravity survey: Data reduction and accuracy assessment

DEFF Research Database (Denmark)

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....

Effects of Low Anisotropy on Generalized Ghost Dark Energy in Galileon Gravity

Science.gov (United States)

Hossienkhani, H.; Fayaz, V.; Jafari, A.; Yousefi, H.

2018-04-01

The definition of the Galileon gravity form is extended to the Brans-Dicke theory. Given, the framework of the Galileon theory, the generalized ghost dark energy model in an anisotropic universe is investigated. We study the cosmological implications of this model. In particular, we obtain the equation of state and the deceleration parameters and a differential equation governing the evolution of this dark energy in Bianchi type I model. We also probe observational constraints by using the latest observational data on the generalized ghost dark energy models as the unification of dark matter and dark energy. In order to do so, we focus on observational determinations of the Hubble expansion rate (namely, the expansion history) H(z). As a result, we show the influence of the anisotropy (although low) on the evolution of the universe in the statefinder diagrams for Galileon gravity.

Flipped spinfoam vertex and loop gravity

Energy Technology Data Exchange (ETDEWEB)

Engle, Jonathan; Pereira, Roberto [CPT, CNRS Case 907, Universite de la Mediterranee, F-13288 Marseille (France); Rovelli, Carlo [CPT, CNRS Case 907, Universite de la Mediterranee, F-13288 Marseille (France)], E-mail: rovelli@cpt.univ-mrs.fr

2008-07-21

We introduce a vertex amplitude for 4d loop quantum gravity. We derive it from a conventional quantization of a Regge discretization of euclidean general relativity. This yields a spinfoam sum that corrects some difficulties of the Barrett-Crane theory. The second class simplicity constraints are imposed weakly, and not strongly as in Barrett-Crane theory. Thanks to a flip in the quantum algebra, the boundary states turn out to match those of SO(3) loop quantum gravity-the two can be identified as eigenstates of the same physical quantities-providing a solution to the problem of connecting the covariant SO(4) spinfoam formalism with the canonical SO(3) spin-network one. The vertex amplitude is SO(3) and SO(4)-covariant. It rectifies the triviality of the intertwiner dependence of the Barrett-Crane vertex, which is responsible for its failure to yield the correct propagator tensorial structure. The construction provides also an independent derivation of the kinematics of loop quantum gravity and of the result that geometry is quantized.

The International Trade Network: weighted network analysis and modelling

International Nuclear Information System (INIS)

Bhattacharya, K; Mukherjee, G; Manna, S S; Saramäki, J; Kaski, K

2008-01-01

Tools of the theory of critical phenomena, namely the scaling analysis and universality, are argued to be applicable to large complex web-like network structures. Using a detailed analysis of the real data of the International Trade Network we argue that the scaled link weight distribution has an approximate log-normal distribution which remains robust over a period of 53 years. Another universal feature is observed in the power-law growth of the trade strength with gross domestic product, the exponent being similar for all countries. Using the 'rich-club' coefficient measure of the weighted networks it has been shown that the size of the rich-club controlling half of the world's trade is actually shrinking. While the gravity law is known to describe well the social interactions in the static networks of population migration, international trade, etc, here for the first time we studied a non-conservative dynamical model based on the gravity law which excellently reproduced many empirical features of the ITN

Influence of the inertia and gravity on the boiling flows stability

International Nuclear Information System (INIS)

Delmastro, D.F.; Clausse, A.

1987-01-01

A study of boiling flows stability on the basis of a linear analysis is presented. From the homogeneous flows' conservation equations, a distributed parameters model, which allows to deal with the frequency field system, is obtained. The adimensional parameters which characterize the inertia effects and the gravity on the impulse equation, are identified. On the other hand, a mean volumes model which permits to gather analytic criteria helpful for the design and comprehension of the problem is developed. (Author)

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

Science.gov (United States)

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

Measured and modelled absolute gravity changes in Greenland

DEFF Research Database (Denmark)

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...

Spherically Symmetric Solutions of the Einstein-Bach Equations and a Consistent Spin-2 Field Theory

International Nuclear Information System (INIS)

Janda, A.

2006-01-01

We briefly present a relationship between General Relativity coupled to certain spin-0 and spin-2 field theories and higher derivatives metric theories of gravity. In a special case, described by the Einstein-Bach equations, the spin-0 field drops out from the theory and we obtain a consistent spin-two field theory interacting gravitationally, which overcomes a well known inconsistency of the theory for a linear spin-two field coupled to the Einstein's gravity. Then we discuss basic properties of static spherically symmetric solutions of the Einstein-Bach equations. (author)

Geometric flows in Horava-Lifshitz gravity

CERN Document Server

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...

The matter Lagrangian and the energy-momentum tensor in modified gravity with nonminimal coupling between matter and geometry

International Nuclear Information System (INIS)

Harko, T.

2010-01-01

We show that in modified f(R) type gravity models with nonminimal coupling between matter and geometry, both the matter Lagrangian and the energy-momentum tensor are completely and uniquely determined by the form of the coupling. This result is obtained by using the variational formulation for the derivation of the equations of motion in the modified gravity models with geometry-matter coupling, and the Newtonian limit for a fluid obeying a barotropic equation of state. The corresponding energy-momentum tensor of the matter in modified gravity models with nonminimal coupling is more general than the usual general-relativistic energy-momentum tensor for perfect fluids, and it contains a supplementary, equation of state dependent term, which could be related to the elastic stresses in the body, or to other forms of internal energy. Therefore, the extra force induced by the coupling between matter and geometry never vanishes as a consequence of the thermodynamic properties of the system, or for a specific choice of the matter Lagrangian, and it is nonzero in the case of a fluid of dust particles.

Comparison of the Effect of Horizontal Vibrations on Interfacial Waves in a Two-Layer System of Inviscid Liquids to Effective Gravity Inversion

Science.gov (United States)

Pimenova, Anastasiya V.; Goldobin, Denis S.; Lyubimova, Tatyana P.

2018-02-01

We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and arbitrary ratio of layer thicknesses. The derivation is performed within the framework of the long-wavelength approximation, which is relevant as the linear instability of a thin-layers system is long-wavelength. The dynamics of equations is integrable and the equations themselves can be compared to the Boussinesq equation for the gravity waves in shallow water, which allows one to compare the action of the vibrational field to the action of the gravity and its possible effective inversion.

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

Science.gov (United States)

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.

Disentangling dark energy and cosmic tests of gravity from weak lensing systematics

Science.gov (United States)

Laszlo, Istvan; Bean, Rachel; Kirk, Donnacha; Bridle, Sarah

2012-06-01

We consider the impact of key astrophysical and measurement systematics on constraints on dark energy and modifications to gravity on cosmic scales. We focus on upcoming photometric ‘stage III’ and ‘stage IV’ large-scale structure surveys such as the Dark Energy Survey (DES), the Subaru Measurement of Images and Redshifts survey, the Euclid survey, the Large Synoptic Survey Telescope (LSST) and Wide Field Infra-Red Space Telescope (WFIRST). We illustrate the different redshift dependencies of gravity modifications compared to intrinsic alignments, the main astrophysical systematic. The way in which systematic uncertainties, such as galaxy bias and intrinsic alignments, are modelled can change dark energy equation-of-state parameter and modified gravity figures of merit by a factor of 4. The inclusion of cross-correlations of cosmic shear and galaxy position measurements helps reduce the loss of constraining power from the lensing shear surveys. When forecasts for Planck cosmic microwave background and stage IV surveys are combined, constraints on the dark energy equation-of-state parameter and modified gravity model are recovered, relative to those from shear data with no systematic uncertainties, provided fewer than 36 free parameters in total are used to describe the galaxy bias and intrinsic alignment models as a function of scale and redshift. While some uncertainty in the intrinsic alignment (IA) model can be tolerated, it is going to be important to be able to parametrize IAs well in order to realize the full potential of upcoming surveys. To facilitate future investigations, we also provide a fitting function for the matter power spectrum arising from the phenomenological modified gravity model we consider.

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

International Nuclear Information System (INIS)

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

Scalar fields and higher-derivative gravity in brane worlds

International Nuclear Information System (INIS)

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

A test of Newton's Law of Gravity using the BREN Tower, Nevada

International Nuclear Information System (INIS)

Kasameyer, P.; Thomas, J.; Fackler, O.; Mugge, M.; Kammeraad, J.; Millett, M.; Harris, B.; Felske, D.

1989-01-01

We predicted gravity values on a tower by upward continuing an extensive set of surface data in order to test the 1/r 2 dependence of Newton's Law of Universal Gravitation. We measured gravity at 12 heights up to 454 m on a tower at the Nevada Test Site, and at 91 locations on the surface of the earth within 2.5 kilometers of the tower. These data have been combined with 60,000 surface gravity measurements within 300 kilometers of the tower and have been used to predict the gravitational field on the tower via a solution of Laplace's equation. A discrepancy between the observed gravity values and the prediction could suggest a breakdown of Newtonian Gravity, but we observe none. Our preliminary results are consistent with the Newtonian hypothesis to within 93 +- 95 μgals at the top of the tower, a result which conflicts with the previously reported 500 μgal non-Newtonian signal seen at 562 meters above the earth. 24 refs., 2 figs

Characteristics of gravity signal and loading effect in China

Directory of Open Access Journals (Sweden)

Shuang Yi

2015-07-01

Full Text Available The complex geographical environment in China makes its gravity signals miscellaneous. This work gives a comprehensive representation and explanation in secular trend of gravity change in different regions, the key features of which include positive trend in inner Tibet Plateau and South China and negative trend in North China plain and high mountain Asia (HMA. We also present the patterns of amplitudes and phases of annual and semiannual change. The mechanism underlying the semiannual period is explicitly discussed. The displacement in three directions expressed in terms of geo-potential spherical coefficients and load Love numbers are given. A case study applied with these equations is presented. The results show that Global Positioning System (GPS observations can be used to compare with Gravity Recovery and Climate Experiment (GRACE derived displacement and the vertical direction has a signal-noise-ratio of about one order of magnitude larger than the horizontal directions.

Regularization ambiguities in loop quantum gravity

International Nuclear Information System (INIS)

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

Topology and dark energy: testing gravity in voids.

Science.gov (United States)

Spolyar, Douglas; Sahlén, Martin; Silk, Joe

2013-12-13

Modified gravity has garnered interest as a backstop against dark matter and dark energy (DE). As one possible modification, the graviton can become massive, which introduces a new scalar field--here with a Galileon-type symmetry. The field can lead to a nontrivial equation of state of DE which is density and scale dependent. Tension between type Ia supernovae and Planck could be reduced. In voids, the scalar field dramatically alters the equation of state of DE, induces a soon-observable gravitational slip between the two metric potentials, and develops a topological defect (domain wall) due to a nontrivial vacuum structure for the field.

The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

Energy Technology Data Exchange (ETDEWEB)

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.

The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

Science.gov (United 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.

The interaction of Dirac particles with non-abelian gauge fields and gravity - bound states

International Nuclear Information System (INIS)

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

Wormholes in a viable f(T) gravity

Energy Technology Data Exchange (ETDEWEB)

Jamil, Mubasher [National University of Sciences and Technology (NUST), Center for Advanced Mathematics and Physics (CAMP), Islamabad (Pakistan); Eurasian National University, Eurasian International Center for Theoretical Physics, Astana (Kazakstan (Kazakhstan)); Momeni, Davood; Myrzakulov, Ratbay [Eurasian National University, Eurasian International Center for Theoretical Physics, Astana (Kazakstan (Kazakhstan))

2013-01-15

In this paper, we derive some new exact solutions of static wormholes in f(T) gravity. We discuss independent cases of the pressure components including isotropic and anisotropic pressure. Lastly we consider radial pressure satisfying a barotropic equation of state. We also check the behavior of null energy condition (NEC) for each case and observe that it is violated for the anisotropic case, while it is satisfied for isotropic and barotropic cases. (orig.)

Astrophysical tests of scale-covariant gravity theories

International Nuclear Information System (INIS)

Mansfield, V.N.; Malin, S.

1980-01-01

Starting from the most general form of the conservation laws in scale-covariant gravitation theory, a conservation of energy equation appropriate for stars is derived. Applications to white dwarfs and neutron stars reveal serious difficulties for some choices of gauge that have been frequently employed in the literature on scale-covariant gravity. We also show how to restrict some of the possible gauges that result from theories which are independent of the Large Numbers Hypothesis

Quark–hadron phase transition in massive gravity

Energy Technology Data Exchange (ETDEWEB)

Atazadeh, K., E-mail: atazadeh@azaruniv.ac.ir

2016-11-15

We study the quark–hadron phase transition in the framework of massive gravity. We show that the modification of the FRW cosmological equations leads to the quark–hadron phase transition in the early massive Universe. Using numerical analysis, we consider that a phase transition based on the chiral symmetry breaking after the electroweak transition, occurred at approximately 10 μs after the Big Bang to convert a plasma of free quarks and gluons into hadrons.

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

Energy Technology Data Exchange (ETDEWEB)

Groh, Kai

2012-10-15

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement

Quantum Einstein gravity. Advancements of heat kernel-based renormalization group studies

International Nuclear Information System (INIS)

Groh, Kai

2012-10-01

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory. As its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained. The constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point. Finally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of

On Einsteinization of background curved space in the induced quantum gravity

International Nuclear Information System (INIS)

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

1989-09-01

It is shown within the induced quantum gravity approach that approximate invariance of the vacuum (up to topological terms) under rescaling of background tetrads requires that these tetrads should satisfy the Einstein equation with the Newton and cosmological constants defined by low energy parameters. (author). 7 refs

Quantum solitonic wave-packet of a meso-scopic system in singularity free gravity

Science.gov (United States)

Buoninfante, Luca; Lambiase, Gaetano; Mazumdar, Anupam

2018-06-01

In this paper we will discuss how to localise a quantum wave-packet due to self-gravitating meso-scopic object by taking into account gravitational self-interaction in the Schrödinger equation beyond General Relativity. In particular, we will study soliton-like solutions in infinite derivative ghost free theories of gravity, which resolves the gravitational 1 / r singularity in the potential. We will show a unique feature that the quantum spread of such a gravitational system is larger than that of the Newtonian gravity, therefore enabling us a window of opportunity to test classical and quantum properties of such theories of gravity in the near future at a table-top experiment.

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

Science.gov (United States)

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.

Traversable wormholes without exotic matter in multimetric repulsive gravity

Science.gov (United States)

Hohmann, Manuel

2014-04-01

We present a static, spherically symmetric, traversable wormhole solution to multimetric gravity which is sustained by only nonexotic matter, i.e., matter which satisfies all energy conditions. The possibility of this solution arises from the fact that under certain conditions the multimetric gravitational field equations reduce to the Einstein equations, but with a negative effective gravitational constant. We show that the Arnowitt-Deser-Misner mass of this wormhole vanishes, so that it appears massless to observers in the asymptotically flat spacetime. We finally speculate on the feasibility of creating and maintaining this type of wormhole by an advanced civilization.

Study of some chaotic inflationary models in f(R) gravity

Science.gov (United States)

Sharif, M.; Nawazish, Iqra

2018-04-01

In this paper, we discuss an inflationary scenario via scalar field and fluid cosmology for an anisotropic homogeneous universe model in f(R) gravity. We consider an equation of state which corresponds to a quasi-de Sitter expansion and investigate the effect of the anisotropy parameter for different values of the deviation parameter. We evaluate potential models like linear, quadratic and quartic models which correspond to chaotic inflation. We construct the observational parameters for a power-law model of f(R) gravity and construct the graphical analysis of tensor-scalar ratio and spectral index which indicates the consistency of these parameters with Planck 2015 data.

Classical aspects of higher spin topologically massive gravity

International Nuclear Information System (INIS)

Chen Bin; Long Jiang; Zhang Jiandong

2012-01-01

We study the classical solutions of three-dimensional topologically massive gravity (TMG) and its higher spin generalization, in the first-order formulation. The action of higher spin TMG has been proposed by Chen and Long (2011 J. High Energy Phys. JHEP12(2011)114) to be of a Chern–Simons-like form. The equations of motion are more complicated than the ones in pure higher spin AdS 3 gravity, but are still tractable. As all the solutions in higher spin gravity are automatically the solutions of higher spin TMG, we focus on other solutions. We manage to find the AdS pp-wave solutions with higher spin hair and find that the non-vanishing higher spin fields may or may not modify the pp-wave geometry. In order to discuss the warped spacetime, we introduce the notion of a special Killing vector, which is defined to be the symmetry on the frame-like fields. We reproduce various warped spacetimes of TMG in our framework, with the help of special Killing vectors. (paper)

Cosmological models in energy-momentum-squared gravity

Science.gov (United States)

Board, Charles V. R.; Barrow, John D.

2017-12-01

We study the cosmological effects of adding terms of higher order in the usual energy-momentum tensor to the matter Lagrangian of general relativity. This is in contrast to most studies of higher-order gravity which focus on generalizing the Einstein-Hilbert curvature contribution to the Lagrangian. The resulting cosmological theories give rise to field equations of similar form to several particular theories with different fundamental bases, including bulk viscous cosmology, loop quantum gravity, k -essence, and brane-world cosmologies. We find a range of exact solutions for isotropic universes, discuss their behaviors with reference to the early- and late-time evolution, accelerated expansion, and the occurrence or avoidance of singularities. We briefly discuss extensions to anisotropic cosmologies and delineate the situations where the higher-order matter terms will dominate over anisotropies on approach to cosmological singularities.

The speed of gravity in general relativity and theoretical interpretation of the Jovian deflection experiment

International Nuclear Information System (INIS)

Kopeikin, Sergei M

2004-01-01

According to Einstein, the notions of geodesic, parallel transport (affine connection) and curvature of the spacetime manifold have a pure geometric origin and do not correlate with any electromagnetic concepts. At the same time, curvature is generated by matter which is not affiliated with the spacetime geometric concepts. For this reason, the fundamental constant c entering the geometric and matter sectors of the general theory of relativity has different conceptual meanings. Specifically, the letter c on the left-hand side of the Einstein equations (geometric sector) entering the Christoffel symbols and its time derivatives is the ultimate speed of gravity characterizing the upper limit on the speed of its propagation as well as the maximal rate of change of time derivatives of the metric tensor, that is gravitational field. The letter c on the right-hand side of the Einstein equations (matter sector) is the maximal speed of propagation of any other field rather than gravity. Einstein's general principle of relativity extends his principle of special relativity and equates the numerical value of the ultimate speed of gravity to that of the speed of light in the special theory of relativity but this general principle must be tested experimentally. To this end, we work out the speed of gravity parametrization of the Einstein equations (c g -parametrization) to keep track of the time-dependent effects associated with the geometric sector of general relativity and to separate them from the time-dependent effects of the matter sector. Parametrized post-Newtonian (PPN) approximation of the Einstein equations is derived in order to explain the gravitational physics of the Jovian deflection VLBI experiment conducted on 8 September 2002. The post-Newtonian series expansion in the c g -parametrized general relativity is with respect to a small parameter that is proportional to the ratio of the characteristic velocity of the bodies to the speed of propagation of the

Simulation of sediment settling in reduced gravity

Science.gov (United States)

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

Even-dimensional topological gravity from Chern-Simons gravity

International Nuclear Information System (INIS)

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).

Recent findings on sinks for sulfide in gravity sewer networks

DEFF Research Database (Denmark)

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...

Gravity's rainbow: A bridge between LQC and DSR

Energy Technology Data Exchange (ETDEWEB)

Gorji, M.A., E-mail: m.gorji@stu.umz.ac.ir [Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar (Iran, Islamic Republic of); Nozari, K., E-mail: knozari@umz.ac.ir [Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar (Iran, Islamic Republic of); Vakili, B., E-mail: b.vakili@iauctb.ac.ir [Department of Physics, Central Tehran Branch, Islamic Azad University, Tehran (Iran, Islamic Republic of)

2017-02-10

The doubly special relativity (DSR) theories are constructed in order to take into account an observer-independent length scale in special relativity framework. Gravity's rainbow is a simple generalization of DSR theories to incorporate gravity. In this paper, we show that the effective Friedmann equations that are suggested by loop quantum cosmology (LQC) can be exactly reobtained in rainbow cosmology setup. The deformed geometry of LQC then fixes the modified dispersion relation and results in a unique DSR model. In comparison with standard LQC scenario where only the geometry is modified, both geometry and matter parts get modified in our setup. In this respect, we show that the total number of microstates for the universe is finite which suggests the statistical origin of the energy and entropy density bounds. These results explicitly show that the DSR theories are appropriate candidates for the flat limit of loop quantum gravity.

New effective coupled F({sup (4)}R, φ) modified gravity from f({sup (5)}R) gravity in five dimensions

Energy Technology Data Exchange (ETDEWEB)

Madriz Aguilar, Jose Edgar [Centro Universitario de Ciencias Exactas e ingenierias (CUCEI), Universidad de Guadalajara (UdG), Departamento de Matematicas, Guadalajara, Jalisco (Mexico)

2015-12-15

Using some ideas of the Wesson induced matter theory, we obtain a new kind of F({sup (4)}R, φ) modified gravity theory as an effective four-dimensional (4D) theory derived from f({sup (5)}R) gravity in five dimensions (5D). This new theory exhibits a different matter coupling than the one in BBHL theory. We show that the field equations of the Wesson induced matter theory and of some brane-world scenarios can be obtained as maximally symmetric solutions of the same f({sup (5)}R) theory. We found criteria for the Dolgov-Kawasaki instabilities for both the f({sup (5)}R) and the F({sup (4)}R, φ) theories. We demonstrate that under certain conditions imposed on the 5D geometry it is possible to interpret the F({sup (4)}R, φ) theory as a modified gravity theory with dynamical coefficients, making this new theory a viable candidate to address the present accelerating cosmic expansion issue. Matter sources in the F({sup (4)}R, φ) case appear induced by the 5D geometry without the necessity of the introduction of matter sources in 5D. (orig.)

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

International Nuclear Information System (INIS)

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

Rotating solutions in critical Lovelock gravities

Science.gov (United States)

Cvetič, M.; Feng, Xing-Hui; Lü, H.; Pope, C. N.

2017-02-01

For appropriate choices of the coupling constants, the equations of motion of Lovelock gravities up to order n in the Riemann tensor can be factorized such that the theories admit a single (A)dS vacuum. In this paper we construct two classes of exact rotating metrics in such critical Lovelock gravities of order n in d = 2 n + 1 dimensions. In one class, the n angular momenta in the n orthogonal spatial 2-planes are equal, and hence the metric is of cohomogeneity one. We construct these metrics in a Kerr-Schild form, but they can then be recast in terms of Boyer-Lindquist coordinates. The other class involves metrics with only a single non-vanishing angular momentum. Again we construct them in a Kerr-Schild form, but in this case it does not seem to be possible to recast them in Boyer-Lindquist form. Both classes of solutions have naked curvature singularities, arising because of the over rotation of the configurations.

Rotating solutions in critical Lovelock gravities

Directory of Open Access Journals (Sweden)

M. Cvetič

2017-02-01

Full Text Available For appropriate choices of the coupling constants, the equations of motion of Lovelock gravities up to order n in the Riemann tensor can be factorized such that the theories admit a single (AdS vacuum. In this paper we construct two classes of exact rotating metrics in such critical Lovelock gravities of order n in d=2n+1 dimensions. In one class, the n angular momenta in the n orthogonal spatial 2-planes are equal, and hence the metric is of cohomogeneity one. We construct these metrics in a Kerr–Schild form, but they can then be recast in terms of Boyer–Lindquist coordinates. The other class involves metrics with only a single non-vanishing angular momentum. Again we construct them in a Kerr–Schild form, but in this case it does not seem to be possible to recast them in Boyer–Lindquist form. Both classes of solutions have naked curvature singularities, arising because of the over rotation of the configurations.

Gravity and Zero Point Energy

Science.gov (United States)

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.

Nonlinear massive spin-2 field generated by higher derivative gravity

International Nuclear Information System (INIS)

Magnano, Guido; Sokolowski, Leszek M.

2003-01-01

We present a systematic exposition of the Lagrangian field theory for the massive spin-2 field generated in higher-derivative gravity upon reduction to a second-order theory by means of the appropriate Legendre transformation. It has been noticed by various authors that this nonlinear field overcomes the well-known inconsistency of the theory for a linear massive spin-2 field interacting with Einstein's gravity. Starting from a Lagrangian quadratically depending on the Ricci tensor of the metric, we explore the two possible second-order pictures usually called '(Helmholtz-)Jordan frame' and 'Einstein frame'. In spite of their mathematical equivalence, the two frames have different structural properties: in Einstein frame, the spin-2 field is minimally coupled to gravity, while in the other frame it is necessarily coupled to the curvature, without a separate kinetic term. We prove that the theory admits a unique and linearly stable ground state solution, and that the equations of motion are consistent, showing that these results can be obtained independently in either frame (each frame therefore provides a self-contained theory). The full equations of motion and the (variational) energy-momentum tensor for the spin-2 field in Einstein frame are given, and a simple but non-trivial exact solution to these equations is found. The comparison of the energy-momentum tensors for the spin-2 field in the two frames suggests that the Einstein frame is physically more acceptable. We point out that the energy-momentum tensor generated by the Lagrangian of the linearized theory is unrelated to the corresponding tensor of the full theory. It is then argued that the ghost-like nature of the nonlinear spin-2 field, found long ago in the linear approximation, may not be so harmful to classical stability issues, as has been expected

Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

International Nuclear Information System (INIS)

Schenkel, Alexander

2011-01-01

The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the noncommutative

Noncommutative gravity and quantum field theory on noncummutative curved spacetimes

Energy Technology Data Exchange (ETDEWEB)

Schenkel, Alexander

2011-10-24

The purpose of the first part of this thesis is to understand symmetry reduction in noncommutative gravity, which then allows us to find exact solutions of the noncommutative Einstein equations. We propose an extension of the usual symmetry reduction procedure, which is frequently applied to the construction of exact solutions of Einstein's field equations, to noncommutative gravity and show that this leads to preferred choices of noncommutative deformations of a given symmetric system. We classify in the case of abelian Drinfel'd twists all consistent deformations of spatially flat Friedmann-Robertson-Walker cosmologies and of the Schwarzschild black hole. The deformed symmetry structure allows us to obtain exact solutions of the noncommutative Einstein equations in many of our models, for which the noncommutative metric field coincides with the classical one. In the second part we focus on quantum field theory on noncommutative curved spacetimes. We develop a new formalism by combining methods from the algebraic approach to quantum field theory with noncommutative differential geometry. The result is an algebra of observables for scalar quantum field theories on a large class of noncommutative curved spacetimes. A precise relation to the algebra of observables of the corresponding undeformed quantum field theory is established. We focus on explicit examples of deformed wave operators and find that there can be noncommutative corrections even on the level of free field theories, which is not the case in the simplest example of the Moyal-Weyl deformed Minkowski spacetime. The convergent deformation of simple toy-models is investigated and it is shown that these quantum field theories have many new features compared to formal deformation quantization. In addition to the expected nonlocality, we obtain that the relation between the deformed and the undeformed quantum field theory is affected in a nontrivial way, leading to an improved behavior of the

Polar gravity fields from GOCE and airborne gravity

DEFF Research Database (Denmark)

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...

Ricci cubic gravity in d dimensions, gravitons and SAdS/Lifshitz black holes

Energy Technology Data Exchange (ETDEWEB)

Ghodsi, Ahmad; Najafi, Farzaneh [Ferdowsi University of Mashhad, Department of Physics, Mashhad (Iran, Islamic Republic of)

2017-08-15

A special class of higher curvature theories of gravity, Ricci cubic gravity (RCG), in general d dimensional space-time has been investigated in this paper. We have used two different approaches, the linearized equations of motion and the auxiliary field formalism to study the massive and massless graviton propagating modes of the AdS background. Using the auxiliary field formalism, we have found the renormalized boundary stress tensor to compute the mass of the Schwarzschild-AdS and Lifshitz black holes in RCG theory. (orig.)

Generalized Lagrangian Path Approach to Manifestly-Covariant Quantum Gravity Theory

Directory of Open Access Journals (Sweden)

Massimo Tessarotto

2018-03-01

Full Text Available A trajectory-based representation for the quantum theory of the gravitational field is formulated. This is achieved in terms of a covariant Generalized Lagrangian-Path (GLP approach which relies on a suitable statistical representation of Bohmian Lagrangian trajectories, referred to here as GLP-representation. The result is established in the framework of the manifestly-covariant quantum gravity theory (CQG-theory proposed recently and the related CQG-wave equation advancing in proper-time the quantum state associated with massive gravitons. Generally non-stationary analytical solutions for the CQG-wave equation with non-vanishing cosmological constant are determined in such a framework, which exhibit Gaussian-like probability densities that are non-dispersive in proper-time. As a remarkable outcome of the theory achieved by implementing these analytical solutions, the existence of an emergent gravity phenomenon is proven to hold. Accordingly, it is shown that a mean-field background space-time metric tensor can be expressed in terms of a suitable statistical average of stochastic fluctuations of the quantum gravitational field whose quantum-wave dynamics is described by GLP trajectories.

Modified teleparallel gravity: Inflation without an inflaton

International Nuclear Information System (INIS)

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

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

African Journals Online (AJOL)

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 ...

From Classical to Discrete Gravity through Exponential Non-Standard Lagrangians in General Relativity

Directory of Open Access Journals (Sweden)

Rami Ahmad El-Nabulsi

2015-08-01

Full Text Available Recently, non-standard Lagrangians have gained a growing importance in theoretical physics and in the theory of non-linear differential equations. However, their formulations and implications in general relativity are still in their infancies despite some advances in contemporary cosmology. The main aim of this paper is to fill the gap. Though non-standard Lagrangians may be defined by a multitude form, in this paper, we considered the exponential type. One basic feature of exponential non-standard Lagrangians concerns the modified Euler-Lagrange equation obtained from the standard variational analysis. Accordingly, when applied to spacetime geometries, one unsurprisingly expects modified geodesic equations. However, when taking into account the time-like paths parameterization constraint, remarkably, it was observed that mutually discrete gravity and discrete spacetime emerge in the theory. Two different independent cases were obtained: A geometrical manifold with new spacetime coordinates augmented by a metric signature change and a geometrical manifold characterized by a discretized spacetime metric. Both cases give raise to Einstein’s field equations yet the gravity is discretized and originated from “spacetime discreteness”. A number of mathematical and physical implications of these results were discussed though this paper and perspectives are given accordingly.

Propagation of acoustic-gravity waves in arctic zones with elastic ice-sheets

Science.gov (United States)

Kadri, Usama; Abdolali, Ali; Kirby, James T.

2017-04-01

We present an analytical solution of the boundary value problem of propagating acoustic-gravity waves generated in the ocean by earthquakes or ice-quakes in arctic zones. At the surface, we assume elastic ice-sheets of a variable thickness, and show that the propagating acoustic-gravity modes have different mode shape than originally derived by Ref. [1] for a rigid ice-sheet settings. Computationally, we couple the ice-sheet problem with the free surface model by Ref. [2] representing shrinking ice blocks in realistic sea state, where the randomly oriented ice-sheets cause inter modal transition at the edges and multidirectional reflections. We then derive a depth-integrated equation valid for spatially slowly varying thickness of ice-sheet and water depth. Surprisingly, and unlike the free-surface setting, here it is found that the higher acoustic-gravity modes exhibit a larger contribution. These modes travel at the speed of sound in water carrying information on their source, e.g. ice-sheet motion or submarine earthquake, providing various implications for ocean monitoring and detection of quakes. In addition, we found that the propagating acoustic-gravity modes can result in orbital displacements of fluid parcels sufficiently high that may contribute to deep ocean currents and circulation, as postulated by Refs. [1, 3]. References [1] U. Kadri, 2016. Generation of Hydroacoustic Waves by an Oscillating Ice Block in Arctic Zones. Advances in Acoustics and Vibration, 2016, Article ID 8076108, 7 pages http://dx.doi.org/10.1155/2016/8076108 [2] A. Abdolali, J. T. Kirby and G. Bellotti, 2015, Depth-integrated equation for hydro-acoustic waves with bottom damping, J. Fluid Mech., 766, R1 doi:10.1017/jfm.2015.37 [3] U. Kadri, 2014. Deep ocean water transportation by acoustic?gravity waves. J. Geophys. Res. Oceans, 119, doi:10.1002/ 2014JC010234

Calculation of gravity and magnetic anomalies along profiles with end corrections and inverse solutions for density and magnetization

Science.gov (United States)

Cady, John W.

1977-01-01

An equation derived for the vertical gravity field due to a body with polygonal cross section and finite strike length.  The equations consists of the 2-dimensional equation of Talwani, Worzel, and Landisman (1959), with the addition of end corrections.  Equations for the magnetic field due to a similar body were derived by Shuey and Pasquale (1973).  They coined the term "2 1/2-dimensional" to describe the geometry.

Thermodynamics and cosmological reconstruction in f(T , B) gravity

Science.gov (United States)

Bahamonde, Sebastian; Zubair, M.; Abbas, G.

2018-03-01

Recently, it was formulated a teleparallel theory called f(T , B) gravity which connects both f(T) and f(R) under suitable limits. In this theory, the function in the action is assumed to depend on the torsion scalar T and also on a boundary term related with the divergence of torsion, B = 2∇μTμ. In this work, we study different features of a flat Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology in this theory. First, we show that the FLRW equations can be transformed to the form of Clausius relation TˆhSeff = - dE + WdV, where Tˆh is the horizon temperature and Seff is the entropy which contains contributions both from horizon entropy and an additional entropy term introduced due to the non-equilibrium. We also formulate the constraint for the validity of the generalised second law of thermodynamics (GSLT). Additionally, using a cosmological reconstruction technique, we show that both f(T , B) and - T + F(B) gravity can mimic power-law, de-Sitter and ΛCDM models. Finally, we formulate the perturbed evolution equations and analyse the stability of some important cosmological solutions.

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

Indian Academy of Sciences (India)

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 ...

The hidden flat like universe. Starobinsky-like inflation induced by f(T) gravity

Energy Technology Data Exchange (ETDEWEB)

El Hanafy, W. [The British University in Egypt, Centre for Theoretical Physics, P.O. Box 43, El Sherouk (Egypt); Egyptian Relativity Group, Giza (Egypt); Nashed, G.G.L. [The British University in Egypt, Centre for Theoretical Physics, P.O. Box 43, El Sherouk (Egypt); Ain Shams University, Mathematics Department, Faculty of Science, Cairo (Egypt); Egyptian Relativity Group, Giza (Egypt)

2015-06-15

We study a single-fluid component in a flat like universe (FLU) governed by f(T) gravity theories, where T is the teleparallel torsion scalar. The FLU model, regardless of the value of the spatial curvature k, identifies a special class of f(T) gravity theories. Remarkably, FLU f(T) gravity does not reduce to teleparallel gravity theory. In large Hubble spacetime the theory is consistent with the inflationary universe scenario and respects the conservation principle. The equation of state evolves similarly in all models k = 0,±1. We study the case when the torsion tensor consists of a scalar field, which enables to derive a quintessence potential from the obtained f(T) gravity theory. The potential produces Starobinsky-like model naturally without using a conformal transformation, with higher orders continuously interpolate between Starobinsky and quadratic inflation models. The slow-roll analysis shows double solutions, so that for a single value of the scalar tilt (spectral index) n{sub s} the theory can predict double tensor-to-scalar ratios r of E-mode and B-mode polarizations. (orig.)

The hidden flat like universe. Starobinsky-like inflation induced by f(T) gravity

International Nuclear Information System (INIS)

El Hanafy, W.; Nashed, G.G.L.

2015-01-01

We study a single-fluid component in a flat like universe (FLU) governed by f(T) gravity theories, where T is the teleparallel torsion scalar. The FLU model, regardless of the value of the spatial curvature k, identifies a special class of f(T) gravity theories. Remarkably, FLU f(T) gravity does not reduce to teleparallel gravity theory. In large Hubble spacetime the theory is consistent with the inflationary universe scenario and respects the conservation principle. The equation of state evolves similarly in all models k = 0,±1. We study the case when the torsion tensor consists of a scalar field, which enables to derive a quintessence potential from the obtained f(T) gravity theory. The potential produces Starobinsky-like model naturally without using a conformal transformation, with higher orders continuously interpolate between Starobinsky and quadratic inflation models. The slow-roll analysis shows double solutions, so that for a single value of the scalar tilt (spectral index) n s the theory can predict double tensor-to-scalar ratios r of E-mode and B-mode polarizations. (orig.)

Heat transfer to liquid sodium in a straight duct in the presence of a transverse magnetic field and a gravity field

International Nuclear Information System (INIS)

Majid, A.

1998-01-01

Heat transfer to liquid sodium in the presence of a transverse magnetic field and gravity field was analyzed in a square cross section straight duct. The duct had conducting vanadium walls. Magnetohydrodynamic equations in three dimensions and energy equation in three dimensions in cartesian coordinate system were solved. Firstly Nusselt number was calculated with no magnetic field and gravity field. Secondly the Nusselt number was calculated for the case of transverse magnetic field acting on the fluid. Thirdly Nusselt number was calculated for the case of transverse magnetic field and gravity field acting on the fluid. Only one face of the channel was heated. It was found that Nusselt number is not sensitive to application of gravity field and is slightly sensitive to application of transverse magnetic field. The sensitivity of Nusselt number to magnetic field intensity becomes almost negligible after increasing the strength of magnetic field to 0.1 Tesla. (author)

Newtonian potential and geodesic completeness in infinite derivative gravity

Science.gov (United States)

Edholm, James; Conroy, Aindriú

2017-08-01

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

A perturbative solution for gravitational waves in quadratic gravity

International Nuclear Information System (INIS)

Neto, Edgard C de Rey; Aguiar, Odylio D; Araujo, Jose C N de

2003-01-01

We find a gravitational wave solution to the linearized version of quadratic gravity by adding successive perturbations to Einstein's linearized field equations. We show that only the Ricci-squared quadratic invariant contributes to give a different solution to those found in Einstein's general relativity. The perturbative solution is written as a power series in the β parameter, the coefficient of the Ricci-squared term in the quadratic gravitational action. We also show that, for monochromatic waves of a given angular frequency ω, the perturbative solution can be summed out to give an exact solution to the linearized version of quadratic gravity, for 0 1/2 . This result may lead to implications for the predictions for gravitational wave backgrounds of cosmological origin

Analyzing the uncertainties in use of forest-derived biomass equations for open-grown trees in agricultural land

Science.gov (United States)

Xinhua Zhou; Michele M. Schoeneberger; James R. Brandle; Tala N. Awada; Jianmin Chu; Derrel L. Martin; Jihong Li; Yuqiang Li; Carl W. Mize

2014-01-01

Quantifying carbon in agroforestry trees requires biomass equations that capture the growth differences (e.g., tree specific gravity and architecture) created in the more open canopies of agroforestry plantings compared with those generally encountered in forests. Whereas forest-derived equations are available, equations for open-grown trees are not. Data from...

Einstein’s gravity from a polynomial affine model

Science.gov (United States)

Castillo-Felisola, Oscar; Skirzewski, Aureliano

2018-03-01

We show that the effective field equations for a recently formulated polynomial affine model of gravity, in the sector of a torsion-free connection, accept general Einstein manifolds—with or without cosmological constant—as solutions. Moreover, the effective field equations are partially those obtained from a gravitational Yang–Mills theory known as Stephenson–Kilmister–Yang theory. Additionally, we find a generalization of a minimally coupled massless scalar field in General Relativity within a ‘minimally’ coupled scalar field in this affine model. Finally, we present a brief (perturbative) analysis of the propagators of the gravitational theory, and count the degrees of freedom. For completeness, we prove that a Birkhoff-like theorem is valid for the analyzed sector.

BOOK REVIEW: Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum Gravity Canonical Gravity and Applications: Cosmology, Black Holes, and Quantum Gravity

Science.gov (United States)

Husain, Viqar