Examples for Application of Gravitational Model in the Investigation of Spatial Structure

In this paper the authors wish to introduce an application of the gravitational model through two concrete examples. In their investigation the gravitational model was transformed to analyze the spatial structure of Europe, and the impact of accessibility in Hungary. In this analysis not only the size of gravitational forces but their direction can also be measured. Displacements were illustrated by a bi-dimensional regression, which gives a new perspective to the investigation of spatial structure.

Does Space Have a Gravitational Susceptibility? A Model for the ΛCDM Density Parameters in the Friedmann Equation

We propose a model for gravity based on the gravitational polarization of space. With this model, we can relate the density parameters within the Friedmann model, and show that dark matter is bound mass formed from massive dipoles set up within the vacuum surrounding ordinary matter. Aggregate matter induces a gravitational field within the surrounding space, which reinforces the original field. Dark energy, on the other hand, is the energy density associated with gravitational fields both for ordinary matter, and bound, or induced dipole matter. At high CBR temperatures, the cosmic susceptibility, induced by ordinary matter vanishes, as it is a smeared or average value for the cosmos as a whole. Even though gravitational dipoles do exist, no large-scale alignment or ordering is possible. Our model assumes that space, i.e., the vacuum, is filled with a vast assembly (sea) of positive and negative mass particles having Planck mass, called planckions, which is based on extensive work by Winterberg. These original particles form a very stiff two-component superfluid, where positive and negative mass species neutralize one another already at the submicroscopic level, leading to zero net mass, zero net gravitational pressure, and zero net entropy, for the undisturbed medium. It is theorized that the gravitational dipoles form from such material positive and negative particles, and moreover, this causes an intrinsic polarization of the vacuum for the universe as a whole. We calculate that in the present epoch, the smeared or average susceptibility of the cosmos equals, , and the overall resulting polarization equals, =2.396kg/m2. Moreover, due to all the ordinary mass in the universe, made up of quarks and leptons, we calculate a net gravitational field having magnitude, =3.771E-10m/s2. This smeared or average value permeates all of space, and can be deduced by any observer, irrespective of location within the universe. This net gravitational field is forced upon us by Gauss’s law, and although technically a surface gravitational field, it is argued that this surface, smeared value holds point for point in the observable universe. A complete theory of gravitational polarization is presented. In contrast to electrostatics, gravistatics leads to anti-screening of the original source field, increasing the original value, , to, , where is the induced or polarized field. In the present epoch, this leads to a bound mass, , where MF is the sum of all ordinary source matter in the universe, and equals the relative permittivity. A new radius, and new mass, for the observable universe is dictated by the density parameters in Friedmann’s equation, and Gauss’s law. These lead to the very precise values, R0=3.217E27 meters, and, MF=5.847E55kg, respectively, somewhat larger than current less accurate estimates.

A three-dimensional Moho depth model beneath the Yemeni highlands and rifted volcanic margins of the Red Sea and Gulf of Aden, Southwest Arabia

Knowing Moho discontinuity undulation is fundamental to understanding mechanisms of lithosphereasthenosphere interaction, extensional tectonism and crustal deformation in volcanic passive margins such as the study area, which is located in the southwestern corner of the Arabian Peninsula bounded by the Red Sea and the Gulf of Aden. In this work, a 3D Moho depth model of the study area is constructed for the first time by inverting gravity data from the Earth Gravitational Model(EGM2008) using the ParkerOldenburg algorithm. This model indicates the shallow zone is situated at depths of 20 km to 24 km beneath coastal plains, whereas the deep zone is located below the plateau at depths of 30 km to 35 km and its deepest part coincides mainly with the Dhamar-Rada ’a Quaternary volcanic field. The results also indicate two channels of hot magmatic materials joining both the Sana’a-Amran Quaternary volcanic field and the Late Miocene Jabal An Nar volcanic area with the Dhamar-Rada’a volcanic field. This conclusion is supported by the widespread geothermal activity(of mantle origin) distributed along these channels,isotopic data, and the upper mantle low velocity zones indicated by earlier studies.

Construction of Earth's gravitational field model from CHAMP,GRACE and GOCE data

The basic principle of spectral combination method is discussed,and the general expressions of the spectral weight and spectral combination of the united-processing of various types of gravimetric data are shown.What＇s more,based on degree error RMS of potential coefficients,the detailed expressions of spectral combination formulae and the corresponding spectral weights in the Earth＇s gravitational field model（EGM） determination using GOCE ＋ GRACE and CHAMP ＋ GRACE ＋ GOCE are derived.The fundamental situation that ulux-champ2013 s,tongji-GRACE01,go-cons-gcf-2-tim-r5 constructed respectively by CHAMP,GRACE,GOCE data and go-cons-gcf-2-dir-r5 constructed by syncretic processing of GRACE,GOCE and LAGEOS data are explained briefly,the degree error RMS,cumulative geoid height error and cumulative gravity anomaly error of these models are calculated.A syncretic model constructed from CHAMP,GRACE and GOCE data,which is expressed by champ ＋ grace ＋ goce,is obtained based on spectral combination method.Experimentation results show that the precision of CHAMP data model is the lowest in satellite-only models,so it is not needed in the determination of syncretic models.The GRACE data model can improve the GOCE data model in medium-long wavelength,so the overall precision of syncretic model can be improved.Consequently,as many types of gravimetric data as possible should be combined together in the data processing in order to strengthen the quality and reliability with widening scope and improve the precision and spatial resolution of the computational results.

Cosmic Constraints to the wCDM Model from Strong Gravitational Lensing

We study the cosmic constraint to the wCDM （cold dark matter with a constant equation of state w） model via 118 strong gravitational lensing systems which are compiled from SLA CS, BELLS, LSD and SL2S surveys, where the ratio between two angular diameter distances Dobs =DA（Zl, Zs ） / D A （ O, Zs ） is taken as a cosmic observable. To obtain this ratio, we adopt two strong tensing models： one is the singular isothermal sphere model （SIS） and the other one is the power-law density profile （PLP） model. Via the Markov chain Monte Carlo method, the posterior distribution of the cosmological model parameters space is obtained. The results show that the cosmological model parameters are not sensitive to the parameterized forms of the power-law index γ. Furthermore, the PLP model gives a relatively tighter constraint to the cosmological parameters than that of the SIS model. The predicted value of Ωm = 0.31＋0.44 -0.24 by the SIS model is compatible with that obtained by P1anck2015： Ωm = 0.313 ± 0.013. However, the value of Ωm =0.15＋0.13 -0.11 based on the PLP model is smaller and has 1.25σ tension with that obtained by Planck2015.

A comparative assessment of gravitational field modeling methods for binary asteroid landing

The tradeoff between accuracy and efficiency in gravitational field modeling for binary asteroid landing is one of the challenges in dynamical analyses.Four representative gravitational modeling methods are employed and compared in this study.These are the sphere-sphere model,ellipsoid-sphere model,inertia integral-polyhedron method,and finite element method.This study considers the differences between these four models,particularly their effects on the landing dynamics of a lander.A framework to simulate the coupled orbit-attitude motion of a lander in a binary system is first established.Numerical simulations are then performed on the natural landings on the second primary of the(66391)Moshup-Squannit system.The results show significant differences in the final landing dispersions,settling time,and sliding distance when applying the simplified models.On the basis of the modeling accuracy and computational efficiency,the finite element method should be chosen for future missions.

Balance of Datum Land Prices Among Cities Based on the City Gravitation Model and Stochastic Diffusion Equation

A balance of urban datum land prices is achieved to harmonize regional land prices and make the prices truly reflect different economic development levels and land prices among cities. The current piecewise linear interpolation balance method widely used has two drawbacks that always lead to an unsatisfactory balance among some cities. When the excess of land price in the central city to the surrounding zone reaches a certain degree, land price in the circumjacent city is not only consistent with the local land grade and land use level, but also influenced by the diffusion of land price in the central city. Thus, a new balanced scheme of datum land prices based on the city gravitation model and stochastic diffusion equation is brought forward. Finally, the new method is examined in the practice of datum land price balance in Hubei Province, China.

Rotating Lepton Model of Pions and Kaons: Mechanics at fm Distances

The present article is a continuation of a recently published paper [1] in which we have modeled the composition and structure of neutrons and other hadrons using the Rotating Lepton Model (RLM) which is a Bohr type model employing the relativistic gravitational attraction between three ultrafast rotating neutrinos as the centripetal force. The RLM accounts for special relativity and also for the De Broglie equation of quantum mechanics. In this way this force was shown to reach the value of the Strong Force while the values of the masses of the rotating relativistic neutrinos reach those of quarks. Masses computed for twelve hadrons and bosons are in very close (~2%) agreement with the experimental values. Here we use the same RLM approach to describe the composition and structure and to compute the masses of Pions and Kaons which are important zero spin mesons. Contrary to hadrons and bosons which have been found via the RLM to comprise the heaviest neutrino eigenmass m3, in the case of mesons the intermediate neutrino mass eigenstate m2 is found to play the dominant role. This can explain why the lowest masses of mesons are generally smaller than those of hadrons and bosons. Thus in the case of Pions it is found that they comprise three rotating m2 mass eigenstate neutrinos and the computed mass of 136.6 MeV/c2 is in good agreement with the experimental value of 134.977 MeV/c2. The Kaon structure is found to consist of six m2 mass eigenstate neutrinos arranged in two parallel pion-type rotating triads. The computed Kaon mass differs less that 2% from the experimental K± and K°values of 493.677 MeV/c2 and 497.648 MeV/c2 respectively. This, in conjunction with the experimentally observed decay products of the Kaons, provides strong support for the proposed K structure.

The Spherically-Symmetric Pressure Free Collapse of the White-Black Hole

The vector model for gravitational field is a modified theory of gravitational field. In this model, the gravitational field is a vector field and its source is the gravitational mass of matter. This model predicts the existence of a new universal object after the black hole disappeared. It is named the white-black hole （or white hole） in the vector model for the gravitational field. The white- black hole has many interesting properties different from that of black hole in Einstein＇s theory of gravity. This paper presents an investigation of the spherically-symmetric pressure free collapse of a white-black hole in the vector model for gravitational field from the point of view of an observer at infinity and on its surface. The obtained results have many interesting differences compared with that in the spherically-symmetric pressure free collapse of black holes. In addition, the metric of space-time of the white-black hole in modified Eddington-Finkelstein coordinates and modified Kruskal-Szekeres coordinates are found.

An economic tie network-structure analysis of urban agglomeration in the middle reaches of Changjiang River based on SNA

Due to its great strategic significance in integrating regional coordinated development and enhancing the rise of Central China, urban agglomeration in the middle reaches of Changjiang （Yangtze） River has attracted much attention from both theoretical and practical aspects. Such research into the area＇s economic network structure is beneficial for the formation of an urban- and regional-development strategy. This paper constructs an economic tie model based on a modified gravitation model. Subsequently, referring to social network analysis, the paper empirically studies the network density, network centrality, subgroups and structural holes of the middle reaches of Changjiang River＇s urban agglomeration economic network. The findings are fourfold： （1） an economic network of urban agglomeration in the middle reaches of Changjiang River has been formed, and economic ties between the cities in this network are comparatively dense; （2） the urban agglomeration in the middle reaches of Changjiang River can be divided into four significant subgroups, with each subgroup having its own obvious economic communications, while there is less economic-behavioral heterogeneity among subgroups - this is especially true for the two subgroups that exist in the Poyang Lake Ecological Economic Zone; （3） an economy pattern driven by the central cities of Wuhan, Changsha and Nanchang has emerged in the urban agglomeration of the middle reaches of Changjiang River, while these three capital cities have exerted great radiation abilities to their surrounding cities, the latter are less able to absorb resources from the former （4） the Wuhan Metropolitan Areas and the Poyang Lake Ecological Economic Zone have more structural holes than the Ring of Changsha, Zhuzhou and the Xiangtan City Clusters, meaning that cities at the periphery of these two areas are easily constrained by central cities. The Ring of Changsha, Zhuzhou and the Xiangtan City Clusters have fewer structural holes; thus, the cities in this area will not face as many constraints as those in the other two areas.