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Journal articles on the topic 'Stochastic gravity'

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Published: 1 April 2023

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1

Moffat, J. W. "Stochastic gravity." Physical Review D 56, no. 10 (November 15, 1997): 6264–77. http://dx.doi.org/10.1103/physrevd.56.6264.

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2

Ross, D. K., and William Moreau. "Stochastic gravity." General Relativity and Gravitation 27, no. 8 (August 1995): 845–58. http://dx.doi.org/10.1007/bf02113067.

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3

Verdaguer, E. "Stochastic gravity: beyond semiclassical gravity." Journal of Physics: Conference Series 66 (May 1, 2007): 012006. http://dx.doi.org/10.1088/1742-6596/66/1/012006.

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4

Erlich, Joshua. "Stochastic emergent quantum gravity." Classical and Quantum Gravity 35, no. 24 (November 19, 2018): 245005. http://dx.doi.org/10.1088/1361-6382/aaeb55.

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5

Rumpf, Helmut. "Stochastic Quantum Gravity inDDimensions." Progress of Theoretical Physics Supplement 111 (1993): 63–81. http://dx.doi.org/10.1143/ptps.111.63.

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6

Baulieu, L. "Stochastic equations for gravity." Physics Letters B 175, no. 2 (July 1986): 133–37. http://dx.doi.org/10.1016/0370-2693(86)90702-1.

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7

Rumpf, Helmut. "Stochastic quantization of Einstein gravity." Physical Review D 33, no. 4 (February 15, 1986): 942–52. http://dx.doi.org/10.1103/physrevd.33.942.

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8

Salopek, D. S., and J. R. Bond. "Stochastic inflation and nonlinear gravity." Physical Review D 43, no. 4 (February 15, 1991): 1005–31. http://dx.doi.org/10.1103/physrevd.43.1005.

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9

Wang, Ya Jun, and Wo Hua Zhang. "Super Gravity Dam Generalized Damage Study." Advanced Materials Research 479-481 (February 2012): 421–25. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.421.

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Fuzzy sub-space, with analysis on generalized uncertainty of damage, is setup in this paper when topological consistency of damage fuzzy and randomness on [0,1] scale being demonstrated deeply. Furthermore, deduced under fuzzy characteristics translation are three fuzzy analytical models of damage functional, namely, half depressed distribution, swing distribution, combined swing distribution, by which, fuzzy extension territory on damage evolution is formulated here. With the representation of damage variable ß probabilistic distribution as well as formulation on stochastic sub-space of damage variable, expended on the basis of extension criterion and fuzzy probability is damage model defined within generalized uncertain space, by which, introduced is fuzzy probabilistic integral algorithm of generalized uncertain damage variable that could be simulated by the forthcoming fuzzy stochastic damage constitution model based on three fuzzy functional models before. Moreover, in order to realize the joint of fuzzy input and output procedure on generalized uncertain damage variable calculation, fuzzy self-adapting stochastic damage reliability algorithm is, with the update on fuzzy stochastic finite element method within standard normal distribution probabilistic space by the help of foregoing fuzzy stochastic damage constitution model, offered in this paper on the basis of equivalent-normalization and orthogonal design theory. 3-dimension fuzzy stochastic damage mechanical status of numerical model of Longtan Rolled-Concrete Dam is researched here by fuzzy stochastic damage finite element method program under property authority. Random field parameters’ statistical dependence and non-normality are considered comprehensively in fuzzy stochastic damage model of this paper, by which, damage uncertainty’s proper development and conception expansion as well as fuzzy and randomness of mechanics are hybridized overall in fuzzy stochastic damage analysis process.
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10

Shushi, Tomer. "Randomness in modified general relativity theory: The stochastic f(R) gravity model." Canadian Journal of Physics 96, no. 11 (November 2018): 1173–77. http://dx.doi.org/10.1139/cjp-2017-0938.

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We consider a stochastic modification of the f(R) gravity models, and provide its important properties, including the gravity field equations for the model. We show a prediction in which particles are localized by a system of random gravitational potentials. As an important special case, we investigate a gravity model in the presence of a small stochastic space–time perturbation and provide its gravity field equations. Using the proposed model we examine the stochastic quantum mechanics interpretation, and obtain a novel Schrödinger equation with gravitational potential that is based on diffusion in a gravitational field. Furthermore, we provide a new interpretation to the wavefunction collapse. It seems that the stochastic f(R) gravity model causes decoherence of the spatial superposition state of particles.
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11

Baulieu, Laurent, Luca Ciambelli, and Siye Wu. "Weyl symmetry in stochastic quantum gravity." Classical and Quantum Gravity 37, no. 4 (January 27, 2020): 045011. http://dx.doi.org/10.1088/1361-6382/ab6392.

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12

Hu, B. L., and E. Verdaguer. "Stochastic gravity: a primer with applications." Classical and Quantum Gravity 20, no. 6 (February 19, 2003): R1—R42. http://dx.doi.org/10.1088/0264-9381/20/6/201.

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13

Mattingly, James. "Emergence of spacetime in stochastic gravity." Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 44, no. 3 (August 2013): 329–37. http://dx.doi.org/10.1016/j.shpsb.2013.04.001.

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14

Prugovečki, Eduard. "Geometro-stochastic quantization of gravity. I." Foundations of Physics Letters 2, no. 1 (February 1989): 81–104. http://dx.doi.org/10.1007/bf00690081.

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15

Prugovečki, E. "Generally covariant geometro-stochastic quantum gravity." Il Nuovo Cimento A 102, no. 3 (September 1989): 881–923. http://dx.doi.org/10.1007/bf02730756.

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16

Prugovečki, Eduard. "Geometro-stochastic quantization of gravity. II." Foundations of Physics Letters 2, no. 2 (March 1989): 163–90. http://dx.doi.org/10.1007/bf00696111.

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17

NAKAZAWA, NAOHITO. "ON THE LANGEVIN EQUATION FOR STOCHASTIC QUANTIZATION OF GRAVITY." Modern Physics Letters A 05, no. 29 (November 20, 1990): 2407–12. http://dx.doi.org/10.1142/s0217732390002778.

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We study the Langevin equation for stochastic quantization of gravity. By introducing two independent variables with a second-class constraint for the gravitational field, we formulate a pair of Langevin equations for gravity which couples with white noises. After eliminating the multiplier field for the second-class constraint, we show that the equations lead to stochastic quantization of gravity including a unique superspace metric.
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18

Mathis, S., and C. Neiner. "Stochastic excitation of gravity waves in rapidly rotating massive stars." Proceedings of the International Astronomical Union 9, S307 (June 2014): 220–21. http://dx.doi.org/10.1017/s1743921314006784.

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AbstractStochastic gravity waves have been recently detected and characterised in stars thanks to space asteroseismology and they may play an important role in the evolution of stellar angular momentum. In this context, the observational study of the CoRoT hot Be star HD 51452 suggests a potentially strong impact of rotation on stochastic excitation of gravito-inertial waves in rapidly rotating stars. In this work, we present our results on the action of the Coriolis acceleration on stochastic wave excitation by turbulent convection. We study the change of efficiency of this mechanism as a function of the waves' Rossby number and we demonstrate that the excitation presents two different regimes for super-inertial and sub-inertial frequencies. Consequences for rapidly rotating early-type stars and the transport of angular momentum in their interiors are discussed.
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19

Baulieu, Laurent, Adel Bilal, and Marco Picco. "Stochastic quantization of 2D gravity and its link with 3D gravity and topological 4D gravity." Nuclear Physics B 346, no. 2-3 (December 1990): 507–26. http://dx.doi.org/10.1016/0550-3213(90)90290-t.

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20

Calcagni, Gianluca, and Sachiko Kuroyanagi. "Stochastic gravitational-wave background in quantum gravity." Journal of Cosmology and Astroparticle Physics 2021, no. 03 (March 9, 2021): 019. http://dx.doi.org/10.1088/1475-7516/2021/03/019.

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21

Nakazawa, N. "BRS Symmetry in Stochastic Quantization of Gravity." Progress of Theoretical Physics 86, no. 5 (November 1, 1991): 1053–75. http://dx.doi.org/10.1143/ptp/86.5.1053.

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22

Khalatnikov, Isaak M., and A. Yu Kamenshchik. "Stochastic cosmology, perturbation theories and Lifshitz gravity." Uspekhi Fizicheskih Nauk 185, no. 9 (2015): 948–63. http://dx.doi.org/10.3367/ufnr.0185.201509f.0948.

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23

Potapov, Alex, Jim R. Muirhead, Subhash R. Lele, and Mark A. Lewis. "Stochastic gravity models for modeling lake invasions." Ecological Modelling 222, no. 4 (February 2011): 964–72. http://dx.doi.org/10.1016/j.ecolmodel.2010.07.024.

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24

BORGMAN, J., and L. H. FORD. "STOCHASTIC GRAVITY AND THE LANGEVIN-RAYCHAUDHURI EQUATION." International Journal of Modern Physics A 20, no. 11 (April 30, 2005): 2364–73. http://dx.doi.org/10.1142/s0217751x05024638.

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We treat the gravitational effects of quantum stress tensor fluctuations. An operational approach is adopted in which these fluctuations produce fluctuations in the focusing of a bundle of geodesics. This can be calculated explicitly using the Raychaudhuri equation as a Langevin equation. The physical manifestation of these fluctuations are angular blurring and luminosity fluctuations of the images of distant sources.
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25

Souprayen, Claude, Jacques Vanneste, Albert Hertzog, and Alain Hauchecorne. "Atmospheric gravity wave spectra: A stochastic approach." Journal of Geophysical Research: Atmospheres 106, no. D20 (October 1, 2001): 24071–86. http://dx.doi.org/10.1029/2001jd900043.

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26

Khalatnikov, I. M., and A. Yu Kamenshchik. "Stochastic cosmology, perturbation theories, and Lifshitz gravity." Physics-Uspekhi 58, no. 9 (September 30, 2015): 878–91. http://dx.doi.org/10.3367/ufne.0185.201509f.0948.

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27

Tang, Wenbo, Jesse E. Taylor, and Alex Mahalov. "Lagrangian dynamics in stochastic inertia-gravity waves." Physics of Fluids 22, no. 12 (December 2010): 126601. http://dx.doi.org/10.1063/1.3518137.

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28

MILLET, Christophe, Bruno RIBSTEIN, and Francois LOTT. "Infrasound scattering from stochastic gravity wave packets." Journal of the Acoustical Society of America 141, no. 5 (May 2017): 3628. http://dx.doi.org/10.1121/1.4987800.

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29

Shamsipour, Pejman, Denis Marcotte, Michel Chouteau, Martine Rivest, and Abderrezak Bouchedda. "3D stochastic gravity inversion using nonstationary covariances." GEOPHYSICS 78, no. 2 (March 1, 2013): G15—G24. http://dx.doi.org/10.1190/geo2012-0122.1.

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The flexibility of geostatistical inversions in geophysics is limited by the use of stationary covariances, which, implicitly and mostly for mathematical convenience, assumes statistical homogeneity of the studied field. For fields showing sharp contrasts due, for example, to faults or folds, an approach based on the use of nonstationary covariances for cokriging inversion was developed. The approach was tested on two synthetic cases and one real data set. Inversion results based on the nonstationary covariance were compared to the results from the stationary covariance for two synthetic models. The nonstationary covariance better recovered the known synthetic models. With the real data set, the nonstationary assumption resulted in a better match with the known surface geology.
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30

Yawn, Kenneth R., Bruce N. Miller, and Willard Maier. "Stochastic dynamics of gravity in one dimension." Physical Review E 52, no. 4 (October 1, 1995): 3390–401. http://dx.doi.org/10.1103/physreve.52.3390.

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31

Eckermann, Stephen D. "Explicitly Stochastic Parameterization of Nonorographic Gravity Wave Drag." Journal of the Atmospheric Sciences 68, no. 8 (August 1, 2011): 1749–65. http://dx.doi.org/10.1175/2011jas3684.1.

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Abstract A straightforward methodology is presented for converting the deterministic multiwave parameterizations of nonorographic gravity wave drag, currently used in general circulation models (GCMs), to stochastic analogs that use fewer waves (in the example herein, a single wave) within each grid box. Deterministic discretizations of source-level momentum flux spectra using a fixed spectrum of many waves with predefined phase speeds are replaced by sampling these source spectra stochastically using waves with randomly assigned phase speeds. Using simple conversion formulas, it is shown that time-mean wave-induced drag, diffusion, and heating-rate profiles identical to those from the deterministic scheme are produced by the stochastic analog. Furthermore, in these examples the need for bulk intermittency factors of small value is largely obviated through the explicit incorporation of stochastic intermittency into the scheme. When implemented in a GCM, the single-wave stochastic analog of an existing deterministic scheme reproduces almost identical time-mean middle-atmosphere climate and drag as its deterministic antecedent but with an order of magnitude reduction in computational expense. The stochastically parameterized drag is also accompanied by inherent variability about the time-mean profile that forces the smallest space–time scales of the GCM. Studies of mean GCM kinetic energy spectra show that this additional stochastic forcing does not lead to excessive increases in dynamical variability at these smallest GCM scales. The results show that the expensive deterministic schemes currently used in GCMs are easily modified and replaced by cheap stochastic analogs without any obvious deleterious impacts on GCM climate or variability, while offering potential advantages of computational savings, reduction of systematic climate biases, and greater and more realistic ensemble spread.
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32

El-Nabulsi, Rami Ahmad, and Waranont Anukool. "Oscillating gravity, non-singularity and mass quantization from Moffat stochastic gravity arguments." Communications in Theoretical Physics 74, no. 10 (September 26, 2022): 105405. http://dx.doi.org/10.1088/1572-9494/ac841f.

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Abstract In Moffat stochastic gravity arguments, the spacetime geometry is assumed to be a fluctuating background and the gravitational constant is a control parameter due to the presence of a time-dependent Gaussian white noise ξ ( t ) . In such a surrounding, both the singularities of gravitational collapse and the Big Bang have a zero probability of occurring. In this communication, we generalize Moffat’s arguments by adding a random temporal tiny variable for a smoothing purpose and creating a white Gaussian noise process with a short correlation time. The Universe accordingly is found to be non-singular and is dominated by an oscillating gravity. A connection with a quantum oscillator was established and analyzed. Surprisingly, the Hubble mass which emerges in extended supergravity may be quantized.
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33

Kwon, Jay Hyoun, and Christopher Jekeli. "The effect of stochastic gravity models in airborne vector gravimetry." GEOPHYSICS 67, no. 3 (May 2002): 770–76. http://dx.doi.org/10.1190/1.1484520.

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Measurements of specific force using inertial measurement units (IMU) combined with Global Positioning System (GPS) accelerometry can be used on an airborne platform to determine the total gravitational vector. Traditional methods, originating with inertial surveying systems and based on Kalman filtering, rely on choosing an appropriate stochastic model for the gravity disturbance components included in the set of system error states. An alternative procedure that uses no a priori stochastic model has proven to be as effective, or moreso, in extracting the gravity vector from airborne IMU/GPS data. This method is based on inspecting acceleration residuals from a Kalman filter that estimates only sensor biases. Using actual data collected over the Canadian Rocky Mountains, this method was compared to the traditional approach adapted for different types of stochastic models for the gravity disturbance vector. In all test cases, the estimation filter without a gravitational model yielded better results—up to 50%. This implies that accurate gravity vector determination from airborne IMU/GPS need not rely on an a priori stochastic model of the field, even though the theory of optimal estimation requests it. However, no filter was able to remove all systematic errors from the data; these remaining errors could only be reduced by elementary methods such as endpoint matching and correlative processing of adjacent passes of the system over the gravity field. The final, best gravity estimates had standard deviations with respect to control data of 6 mGal in the horizontal components and 3–4 mGal in the vertical component.
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34

Lasser, Martin, Ulrich Meyer, Daniel Arnold, and Adrian Jäggi. "Stochastic noise modelling of kinematic orbit positions in the Celestial Mechanics Approach." Advances in Geosciences 50 (October 20, 2020): 101–13. http://dx.doi.org/10.5194/adgeo-50-101-2020.

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Abstract. Gravity field models may be derived from kinematic orbit positions of Low Earth Orbiting satellites equipped with onboard GPS (Global Positioning System) receivers. An accurate description of the stochastic behaviour of the kinematic positions plays a key role to calculate high quality gravity field solutions. In the Celestial Mechanics Approach (CMA) kinematic positions are used as pseudo-observations to estimate orbit parameters and gravity field coefficients simultaneously. So far, a simplified stochastic model based on epoch-wise covariance information, which may be efficiently derived in the kinematic point positioning process, has been applied. We extend this model by using the fully populated covariance matrix, covering correlations over 50 min. As white noise is generally assumed for the original GPS carrier phase observations, this purely formal variance propagation cannot describe the full noise characteristics introduced by the original observations. Therefore, we sophisticate our model by deriving empirical covariances from the residuals of an orbit fit of the kinematic positions. We process GRACE (Gravity Recovery And Climate Experiment) GPS data of April 2007 to derive gravity field solutions up to degree and order 70. Two different orbit parametrisations, a purely dynamic orbit and a reduced-dynamic orbit with constrained piecewise constant accelerations, are adopted. The resulting gravity fields are solved on a monthly basis using daily orbital arcs. Extending the stochastic model from utilising epoch-wise covariance information to an empirical model, leads to a – expressed in terms of formal errors – more realistic gravity field solution.
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35

Cremaschini, Claudio, and Massimo Tessarotto. "Quantum-Gravity Stochastic Effects on the de Sitter Event Horizon." Entropy 22, no. 6 (June 22, 2020): 696. http://dx.doi.org/10.3390/e22060696.

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The stochastic character of the cosmological constant arising from the non-linear quantum-vacuum Bohm interaction in the framework of the manifestly-covariant theory of quantum gravity (CQG theory) is pointed out. This feature is shown to be consistent with the axiomatic formulation of quantum gravity based on the hydrodynamic representation of the same CQG theory developed recently. The conclusion follows by investigating the indeterminacy properties of the probability density function and its representation associated with the quantum gravity state, which corresponds to a hydrodynamic continuity equation that satisfies the unitarity principle. As a result, the corresponding form of stochastic quantum-modified Einstein field equations is obtained and shown to admit a stochastic cosmological de Sitter solution for the space-time metric tensor. The analytical calculation of the stochastic averages of relevant physical observables is obtained. These include in particular the radius of the de Sitter sphere fixing the location of the event horizon and the expression of the Hawking temperature associated with the related particle tunneling effect. Theoretical implications for cosmology and field theories are pointed out.
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36

Shamsipour, Pejman, Denis Marcotte, Michel Chouteau, and Pierre Keating. "3D stochastic inversion of gravity data using cokriging and cosimulation." GEOPHYSICS 75, no. 1 (January 2010): I1—I10. http://dx.doi.org/10.1190/1.3295745.

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A new application has been developed, based on geostatistical techniques of cokriging and conditional simulation, for the 3D inversion of gravity data including geologic constraints. The necessary gravity, density, and gravity-density covariance matrices are estimated using the observed gravity data. Then the densities are cokriged or simulated using the gravity data as the secondary variable. The model allows noise to be included in the observations. The method is applied to two synthetic models: a short dipping dike and a stochastic distribution of densities. Then some geologic information is added as constraints to the cokriging system. The results show the ability of the method to integrate complex a priori information. The survey data of the Matagami mining camp are considered as a case study. The inversion method based on cokriging is applied to the residual anomaly to map the geology through the estimation of the density distribution in this region. The results of the inversion and simulation methods are in good agreement with the surface geology of the survey region.
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37

CAPOZZIELLO, SALVATORE, CHRISTIAN CORDA, and MARIAFELICIA DE LAURENTIS. "STOCHASTIC BACKGROUND OF GRAVITATIONAL WAVES "TUNED" BY f(R) GRAVITY." Modern Physics Letters A 22, no. 15 (May 20, 2007): 1097–104. http://dx.doi.org/10.1142/s0217732307023444.

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We show that the stochastic background of gravitational waves, produced in the early cosmological epochs, depends strictly on the assumed theory of gravity. In particular, the specific form of the function f(R), where R is the Ricci scalar, is related to the evolution and the production mechanism of gravitational waves. On the other hand, detecting the stochastic background by the forthcoming interferometric experiments (VIRGO, LIGO, LISA) could be a further tool to select the effective theory of gravity.
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38

Irhami, Milda. "Stochastic Gravity Model and Trade Efficiency for lndonesia." Economics and Finance in Indonesia 55, no. 2 (March 21, 2015): 177. http://dx.doi.org/10.7454/efi.v55i2.115.

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39

Sakamoto, J. "Generally Covariant Formulation in Stochastic Quantization of Gravity." Progress of Theoretical Physics 74, no. 4 (October 1, 1985): 842–51. http://dx.doi.org/10.1143/ptp.74.842.

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40

DIEGO, OSCAR. "NONPERTURBATIVE STOCHASTIC DEFINITIONS OF 2-D QUANTUM GRAVITY." Modern Physics Letters A 09, no. 26 (August 30, 1994): 2445–59. http://dx.doi.org/10.1142/s021773239400232x.

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I construct the ground state, up to first nonperturbative order, of the stochastic stabilization of the zero-dimensional matrix model which defines 2-D quantum gravity. It is given by the linear combination of a perturbative wave function and a nonperturbative one. The nonperturbative behavior which arise from the stabilized model and from the string equation are similar. I show the modification of the loop equation by nonperturbative contribution.
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41

Greensite, J. "Stabilized quantum gravity stochastic interpretation and numerical simulation." Nuclear Physics B 390, no. 2 (February 1993): 439–60. http://dx.doi.org/10.1016/0550-3213(93)90463-y.

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42

Chen, Gang. "Stochastic modeling of rock fragment flow under gravity." International Journal of Rock Mechanics and Mining Sciences 34, no. 2 (February 1997): 323–31. http://dx.doi.org/10.1016/s0148-9062(96)00051-4.

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43

Allen, B. "Stochastic gravity-wave background in inflationary-universe models." Physical Review D 37, no. 8 (April 15, 1988): 2078–85. http://dx.doi.org/10.1103/physrevd.37.2078.

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44

Williams, P. D., T. W. N. Haine, and P. L. Read. "Stochastic resonance in a nonlinear model of a rotating, stratified shear flow, with a simple stochastic inertia-gravity wave parameterization." Nonlinear Processes in Geophysics 11, no. 1 (February 25, 2004): 127–35. http://dx.doi.org/10.5194/npg-11-127-2004.

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Abstract. We report on a numerical study of the impact of short, fast inertia-gravity waves on the large-scale, slowly-evolving flow with which they co-exist. A nonlinear quasi-geostrophic numerical model of a stratified shear flow is used to simulate, at reasonably high resolution, the evolution of a large-scale mode which grows due to baroclinic instability and equilibrates at finite amplitude. Ageostrophic inertia-gravity modes are filtered out of the model by construction, but their effects on the balanced flow are incorporated using a simple stochastic parameterization of the potential vorticity anomalies which they induce. The model simulates a rotating, two-layer annulus laboratory experiment, in which we recently observed systematic inertia-gravity wave generation by an evolving, large-scale flow. We find that the impact of the small-amplitude stochastic contribution to the potential vorticity tendency, on the model balanced flow, is generally small, as expected. In certain circumstances, however, the parameterized fast waves can exert a dominant influence. In a flow which is baroclinically-unstable to a range of zonal wavenumbers, and in which there is a close match between the growth rates of the multiple modes, the stochastic waves can strongly affect wavenumber selection. This is illustrated by a flow in which the parameterized fast modes dramatically re-partition the probability-density function for equilibrated large-scale zonal wavenumber. In a second case study, the stochastic perturbations are shown to force spontaneous wavenumber transitions in the large-scale flow, which do not occur in their absence. These phenomena are due to a stochastic resonance effect. They add to the evidence that deterministic parameterizations in general circulation models, of subgrid-scale processes such as gravity wave drag, cannot always adequately capture the full details of the nonlinear interaction.
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45

Mathis, S., C. Neiner, and N. Tran Minh. "Impact of rotation on stochastic excitation of gravity and gravito-inertial waves in stars." Astronomy & Astrophysics 565 (May 2014): A47. http://dx.doi.org/10.1051/0004-6361/201321830.

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46

Cremaschini, Claudio, and Massimo Tessarotto. "Physical Properties of Schwarzschild–deSitter Event Horizon Induced by Stochastic Quantum Gravity." Entropy 23, no. 5 (April 23, 2021): 511. http://dx.doi.org/10.3390/e23050511.

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A new type of quantum correction to the structure of classical black holes is investigated. This concerns the physics of event horizons induced by the occurrence of stochastic quantum gravitational fields. The theoretical framework is provided by the theory of manifestly covariant quantum gravity and the related prediction of an exclusively quantum-produced stochastic cosmological constant. The specific example case of the Schwarzschild–deSitter geometry is looked at, analyzing the consequent stochastic modifications of the Einstein field equations. It is proved that, in such a setting, the black hole event horizon no longer identifies a classical (i.e., deterministic) two-dimensional surface. On the contrary, it acquires a quantum stochastic character, giving rise to a frame-dependent transition region of radial width δr between internal and external subdomains. It is found that: (a) the radial size of the stochastic region depends parametrically on the central mass M of the black hole, scaling as δr∼M3; (b) for supermassive black holes δr is typically orders of magnitude larger than the Planck length lP. Instead, for typical stellar-mass black holes, δr may drop well below lP. The outcome provides new insight into the quantum properties of black holes, with implications for the physics of quantum tunneling phenomena expected to arise across stochastic event horizons.
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47

Wang, Lei, James L. Davis, Emma M. Hill, and Mark E. Tamisiea. "Stochastic filtering for determining gravity variations for decade-long time series of GRACE gravity." Journal of Geophysical Research: Solid Earth 121, no. 4 (April 2016): 2915–31. http://dx.doi.org/10.1002/2015jb012650.

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48

VERDAGUER, ENRIC. "METRIC FLUCTUATIONS IN DE SITTER SPACETIME IN STOCHASTIC GRAVITY." International Journal of Modern Physics D 20, no. 05 (May 20, 2011): 851–60. http://dx.doi.org/10.1142/s0218271811019189.

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Stochastic gravity extends semiclassical gravity by allowing for a systematic and self-consistent description of the metric fluctuations produced by the quantum fluctuations of the stress tensor. The effect of minimally coupled scalar fields with arbitrary mass in de Sitter spacetime is discussed, assuming that these fields are in the Bunch–Davies de Sitter invariant vacuum. The matter field fluctuations are described by the noise kernel which is obtained from the symmetrized two-point correlation of the stress tensor operator. The noise kernel is computed in terms of de Sitter invariant bi-tensors. It turns out that in a de Sitter background the two-point function of the linearized Einstein tensor, which is gauge invariant, is directly related to the noise kernel.
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49

Shamsipour, Pejman, Denis Marcotte, and Michel Chouteau. "3D stochastic joint inversion of gravity and magnetic data." Journal of Applied Geophysics 79 (April 2012): 27–37. http://dx.doi.org/10.1016/j.jappgeo.2011.12.012.

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50

Cho, H. T., and B. L. Hu. "Noise kernels of stochastic gravity in conformally-flat spacetimes." Classical and Quantum Gravity 32, no. 5 (February 3, 2015): 055006. http://dx.doi.org/10.1088/0264-9381/32/5/055006.

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