scholarly journals A fast quadrature-based gravity model for the homogeneous polyhedron

2019 ◽  
Vol 492 (1) ◽  
pp. 420-430
Author(s):  
Jason M Pearl ◽  
Darren L Hitt
Keyword(s):  
Gravitational Field ◽  
Gravity Model ◽  
Approximate Model ◽  
Edge Length ◽  
Gravity Models ◽  
Surface Topology ◽  
Constant Density ◽  
Bulk Properties ◽  
Average Edge Length ◽  
Computationally Expensive

ABSTRACT To date several probes have been sent to explore the Solar system’s asteroids and comets. These bodies are often irregular in shape and to safely navigate probes in their vicinity accurate gravity models are required. For an arbitrarily shaped constant-density body, the gravitational field can be determined from the surface topology and bulk properties. This is achieved by replacing the body’s true geometry with a polyhedron that closely resembles it and for which analytic equations for the gravitational field exist. For some applications however, these equations are too computationally expensive and it can be beneficial to replace them with numerically amenable approximations. In this work, a numerical-quadrature-based model for the gravitational field of a polyhedron consisting of triangular facets is derived. The proposed approximate model is found to be faster than its analytic counterpart. The error of the approximation is found to be negligible for the potential and Laplacian calculations. The approximate model introduces singularities to the surface of the acceleration calculation degrading the solution at altitudes less than the average edge length of the polyhedron.

Facile Synthesis of Cu2O Nanocubes in Triblock Copolymer Solutions

2007 ◽  
Vol 121-123 ◽  
pp. 275-278
Author(s):  
Jin Hua Jiang ◽  
Qiu Ming Gao
Keyword(s):  
Triblock Copolymer ◽  
Solar Spectrum ◽  
Blue Shift ◽  
Edge Length ◽  
Promising Candidate ◽  
Organic Species ◽  
Transmission Electron ◽  
Ft Ir ◽  
Average Edge Length

Cuprous oxide and related materials in nanosizes are of much interest and investigated extensively recently. It is reported here that cubic Cu2O nanocubes were synthesized successfully in aqueous solutions at room temperature in air condition. Copper (II) salts in water were reduced with ascorbate acid in air, using the nonionic pluronic amphiphilic triblock copolymer EO20PO70EO20 (P123) as the template-directing and protecting agent. The average edge length of the cubes varied from 50 to 100 nm. Transmission electron microscopy (TEM) has been used for the shape and structural characterization of the obtained Cu2O nanocubes. The UV-Vis spectra showed an obvious blue-shift (0.53 eV), compared to the band gap of the bulk Cu2O crystal, which makes it a promising candidate in solar energy conversion since this sample can make use of higher energy visible rays of solar spectrum. In the FT-IR spectra the peak of Cu-O bond for the Cu2O is clearly distinguished and several weak peaks of the C-H, C-C and C=O bonds for the organic species can also be detectable, implying a little P123 residua in the products. The effect of the triblock copolymer P123 on the growth of the Cu2O nanocubes is discussed.

scholarly journals THE GRAVITY MODEL FORMALIZATION FOR THE INTERCITY PASSENGER’S CORRESPONDENCES PARAMETER’S ESTIMATION

2017 ◽  
Vol 16 (5) ◽  
pp. 437-443 ◽  
Author(s):  
C. V. Dolya
Keyword(s):  
Gravity Model ◽  
Transportation System ◽  
Gravity Models ◽  
Gravity Modeling ◽  
Passenger Transport ◽  
Passenger Transportation ◽  
The Given ◽  
Selection Of ◽  
Calibration Coefficients

he paper considers a possibility to apply gravity models for calculation of intercity passenger transport corres- pondences which are implemented with the help of public transport. The Ukraine transportation system has been selected as an object of investigation and this approach extends application possibilities of the obtained results. Calibration coefficients used in calculation of the indicated correspondences are rather important and significant in case of forecasting passenger transport correspondences. Formalization of these factors is necessary for every transportation system if a calculation of pas-senger transport correspondences has been made for it. In this case searching for actual calibration parameters and other coef-ficients as components of gravitational models is a relevant objective of the given paper. Selection of the gravity model va- riant plays rather significant role in solution of this problem. The developed methods for calculation of passenger transport correspondences are proposed for their application in respect of various transport and trip types. The executed research works have made it possible to investigate a process pertaining to providing of services for passenger transportation while using public routes. The obtained characteristics on functioning of the studied system have allowed to assess the possibility for ap-plication of the known methods for calculation of passenger correspondences and analyze the quality of their application. Calibration coefficients have been empirically selected for calculation of the indicated correspondences while using method of gravity modeling. Formalization of previously unexplored parameters of gravity model component provides the possibility to apply the considered approach for calculation of passenger correspondences within the framework of the investigated trans-portion system. This makes it possible to plan and arrange interaction of various transport types and provides new data and knowledge on the studied system.

scholarly journals Generalizing the coupling between geometry and matter: $$f\left( R,L_m,T\right) $$ gravity

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
Zahra Haghani ◽  
Tiberiu Harko
Keyword(s):  
Gravitational Field ◽  
Energy Momentum Tensor ◽  
Equations Of Motion ◽  
Momentum Tensor ◽  
Newtonian Limit ◽  
Gravity Models ◽  
Momentum Balance ◽  
Field Equations ◽  
Gravitational Fields ◽  
Generalized Poisson

AbstractWe generalize and unify the $$f\left( R,T\right) $$ f R , T and $$f\left( R,L_m\right) $$ f R , L m type gravity models by assuming that the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar R, of the trace of the energy–momentum tensor T, and of the matter Lagrangian $$L_m$$ L m , so that $$ L_{grav}=f\left( R,L_m,T\right) $$ L grav = f R , L m , T . We obtain the gravitational field equations in the metric formalism, the equations of motion for test particles, and the energy and momentum balance equations, which follow from the covariant divergence of the energy–momentum tensor. Generally, the motion is non-geodesic, and takes place in the presence of an extra force orthogonal to the four-velocity. The Newtonian limit of the equations of motion is also investigated, and the expression of the extra acceleration is obtained for small velocities and weak gravitational fields. The generalized Poisson equation is also obtained in the Newtonian limit, and the Dolgov–Kawasaki instability is also investigated. The cosmological implications of the theory are investigated for a homogeneous, isotropic and flat Universe for two particular choices of the Lagrangian density $$f\left( R,L_m,T\right) $$ f R , L m , T of the gravitational field, with a multiplicative and additive algebraic structure in the matter couplings, respectively, and for two choices of the matter Lagrangian, by using both analytical and numerical methods.

Randomness in modified general relativity theory: The stochastic f(R) gravity model

2018 ◽  
Vol 96 (11) ◽  
pp. 1173-1177
Author(s):  
Tomer Shushi
Keyword(s):  
Gravity Field ◽  
Gravity Model ◽  
Gravity Models ◽  
Relativity Theory ◽  
Field Equations ◽  
Important Special Case ◽  
Proposed Model ◽  
Stochastic Space ◽  
Wavefunction Collapse ◽  
New Interpretation

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.

scholarly journals A new f(R) gravity model and properties of gravitational waves in it

2020 ◽  
Vol 80 (12) ◽  
Author(s):  
Dhruba Jyoti Gogoi ◽  
Umananda Dev Goswami
Keyword(s):  
Gravitational Waves ◽  
Gravity Model ◽  
Longitudinal Mode ◽  
Mass Scale ◽  
Gravity Models ◽  
Jordan Frame ◽  
New Model ◽  
Existing Problems ◽  
Pulsar Timing ◽  
New Directions

AbstractIn this paper, we have introduced a new f(R) gravity model as an attempt to have a model with more parametric control, so that the model can be used to explain the existing problems as well as to explore new directions in physics of gravity, by properly constraining it with recent observational data. Here basic aim is to study the properties of Gravitational Waves (GWs) in this new model. In f(R) gravity metric formalism, the model shows the existence of scalar degree of freedom as like other f(R) gravity models. Due to this reason, there is a scalar mode of polarization of GWs present in the theory. This polarization mode exists in a mixed state, of which one is transverse massless breathing mode with non-vanishing trace and the other is massive longitudinal mode. The longitudinal mode being massive, travels at speed less than the usual tensor modes found in General Relativity (GR). Moreover, for a better understanding of the model, we have studied the potential and mass of scalar graviton in both Jordan frame and Einstein frame. This model can pass the solar system tests and can explain primordial and present dark energy. Also, we have put constraints on the model. It is found that the correlation function for the third mode of polarization under certain mass scale predicted by the model agrees well with the recent data of Pulsar Timing Arrays. It seems that this new model would be useful in dealing with different existing issues in the areas of astrophysics and cosmology.

scholarly journals A Gravity-Based Food Flow Model to Identify the Source of Foodborne Disease Outbreaks

2020 ◽  
Vol 17 (2) ◽  
pp. 444 ◽  
Author(s):  
Tim Schlaich ◽  
Abigail L. Horn ◽  
Marcel Fuhrmann ◽  
Hanno Friedrich
Keyword(s):  
Gravity Model ◽  
Food Supply ◽  
Food Item ◽  
Disease Outbreaks ◽  
Gravity Models ◽  
Shopping Behavior ◽  
Foodborne Disease ◽  
Inference Models ◽  
Computational Approaches ◽  
Home Location

Computational traceback methodologies are important tools for investigations of widespread foodborne disease outbreaks as they assist investigators to determine the causative outbreak location and food item. In modeling the entire food supply chain from farm to fork, however, these methodologies have paid little attention to consumer behavior and mobility, instead making the simplifying assumption that consumers shop in the area adjacent to their home location. This paper aims to fill this gap by introducing a gravity-based approach to model food-flows from supermarkets to consumers and demonstrating how models of consumer shopping behavior can be used to improve computational methodologies to infer the source of an outbreak of foodborne disease. To demonstrate our approach, we develop and calibrate a gravity model of German retail shopping behavior at the postal-code level. Modeling results show that on average about 70 percent of all groceries are sourced from non-home zip codes. The value of considering shopping behavior in computational approaches for inferring the source of an outbreak is illustrated through an application example to identify a retail brand source of an outbreak. We demonstrate a significant increase in the accuracy of a network-theoretic source estimator for the outbreak source when the gravity model is included in the food supply network compared with the baseline case when contaminated individuals are assumed to shop only in their home location. Our approach illustrates how gravity models can enrich computational inference models for identifying the source (retail brand, food item, location) of an outbreak of foodborne disease. More broadly, results show how gravity models can contribute to computational approaches to model consumer shopping interactions relating to retail food environments, nutrition, and public health.

scholarly journals Exact Solutions in Poincaré Gauge Gravity Theory

Universe ◽  
2019 ◽  
Vol 5 (5) ◽  
pp. 127 ◽  
Author(s):  
Yuri N. Obukhov
Keyword(s):  
Gravitational Field ◽  
Gravity Models ◽  
Field Potentials ◽  
De Sitter ◽  
Field Equations ◽  
Yang Mills ◽  
Gravitational Field Equations ◽  
Poincaré Symmetry ◽  
Gauge Gravity ◽  
Vacuum Solutions

In the framework of the gauge theory based on the Poincaré symmetry group, the gravitational field is described in terms of the coframe and the local Lorentz connection. Considered as gauge field potentials, they give rise to the corresponding field strength which are naturally identified with the torsion and the curvature on the Riemann–Cartan spacetime. We study the class of quadratic Poincaré gauge gravity models with the most general Yang–Mills type Lagrangian which contains all possible parity-even and parity-odd invariants built from the torsion and the curvature. Exact vacuum solutions of the gravitational field equations are constructed as a certain deformation of de Sitter geometry. They are black holes with nontrivial torsion.

On average edge length of minimum spanning trees

1999 ◽  
Vol 70 (5) ◽  
pp. 241-243
Author(s):  
Suman Kumar Nath ◽  
Rezaul Alam Chowdhury ◽  
M. Kaykobad
Keyword(s):  
Spanning Trees ◽  
Edge Length ◽  
Minimum Spanning Trees ◽  
Average Edge Length

Gravity model development for TOPEX/POSEIDON: Joint Gravity Models 1 and 2

1994 ◽  
Vol 99 (C12) ◽  
pp. 24421 ◽  
Author(s):  
R. S. Nerem ◽  
F. J. Lerch ◽  
J. A. Marshall ◽  
E. C. Pavlis ◽  
B. H. Putney ◽  
...  
Keyword(s):  
Gravity Model ◽  
Model Development ◽  
Gravity Models

New global marine gravity model from CryoSat-2 and Jason-1 reveals buried tectonic structure

Science ◽  
2014 ◽  
Vol 346 (6205) ◽  
pp. 65-67 ◽  
Author(s):  
David T. Sandwell ◽  
R. Dietmar Müller ◽  
Walter H. F. Smith ◽  
Emmanuel Garcia ◽  
Richard Francis
Keyword(s):  
Gravity Model ◽  
Deep Ocean ◽  
Gravity Models ◽  
Spreading Ridge ◽  
Radar Altimeter ◽  
Tectonic Structures ◽  
Tectonic Processes ◽  
Marine Gravity ◽  
Regional Tectonic ◽  
Slow Spreading

Gravity models are powerful tools for mapping tectonic structures, especially in the deep ocean basins where the topography remains unmapped by ships or is buried by thick sediment. We combined new radar altimeter measurements from satellites CryoSat-2 and Jason-1 with existing data to construct a global marine gravity model that is two times more accurate than previous models. We found an extinct spreading ridge in the Gulf of Mexico, a major propagating rift in the South Atlantic Ocean, abyssal hill fabric on slow-spreading ridges, and thousands of previously uncharted seamounts. These discoveries allow us to understand regional tectonic processes and highlight the importance of satellite-derived gravity models as one of the primary tools for the investigation of remote ocean basins.

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