Gravitation in Theory of Space-Time Film and Galactic Soliton

The scalar field of extremal space-time film is considered as unified fundamental field. Metrical interaction between solitons-particles as gravitational interaction is considered here in approximation of a weak fundamental field. It is shown that the signature of metrics {-,+,+,+} in the model formulation provides the observable gravitational attraction to a region with bigger energy density of the fundamental field. The induced gravitational interaction in the space-time film theory is applied to stars in a galaxy. The conception of galaxy soliton of space-time film is introduced. A weak field asymptotic solution for a galaxy soliton is proposed. It is shown that the effective metrics for this solution can provide the observable velocity curves for galaxies and explains their spiral structure. Thus a solution for so-called dark matter problem in the framework of space-time film theory is proposed.

Jeans Instability, Jeans Entropy and the Entropy Origin of Gravity

An entropic origin of gravity is re-visited. Isothermal self-gravitating cloud seen as an ideal gas is analyzed. Gravitational attraction within the isothermal cloud in equilibrium is balanced by the pressure, which is of a pure entropic nature. The notion of the Jeans entropy of the cloud corresponding to the entropy of the self-gravitating cloud in mechanical and thermal equilibrium is introduced. Balance of the gravitational compression and the entropic repulsion yields the scaling relation hinting to the entropic origin of the gravitational force. The analysis of the Jeans instability enables elimination of the “holographic screen” or “holographic principle” necessary for grounding of the entropic origin of gravity.

On The Mechanism of the Formation of Atoms

The mechanism of the formation of atoms from neutrons, which decay in the process of gravitational attraction, is considered. Through the mechanism of the formation of atoms, the reason is shown why the neutrons of the nucleus do not decay, and the electrons do not fall on the nucleus. Using the deuteron as an example, it is shown what is the reason for the stability of the nucleus and why the neutron contained in the nucleus does not decay

Wave Model of Gravity

Phenomenological model of the gravitational wave the interaction of the substance of the cosmos. The formula of the gravitational interaction between the gravitating masses. The formula of gravitational attraction between the protons at very close distance between them

ELECTRIC GENERATOR POWERED BY A GYROSCOPIC SYSTEM - A THEORETICAL APPROACH

The development of our society now depends on electrical energy and the demand for electrical power increases yearly. Due to the vast amount of carbon dioxide released in the atmosphere by conventional power plants and the negative influence on the climate, new ways of producing electricity must be developed. A gyroscope consists of a spinning flywheel of mass m mounted in a suspension frame that allows the flywheel’s axle to point in any direction. In this analysis, one end of the axle is supported by a pylon situated at a distance R from the center of mass of the spinning flywheel. In order to generate electrical energy at this low speed, the same approach should be used as in wind power electrical generators. In this case, the wind and propeller are substituted by a gyroscopic system and gravitational attraction. Based on the conservation of angular momentum, the gravitational attraction can be used to create a precession strong enough to provide the energy and torque necessary to activate an electric generator similar to those in wind power generators. Instead of recovering the energy from this kinetic energy, we can use the precession rotation created by gravitational attraction to create the necessary kinetic energy.

Nonlinear Stability of Equilibrium Points in the Planar Equilateral Restricted Mass-Unequal Four-Body Problem

In this paper, we investigate the stability of equilibrium points for the planar restricted equilateral four-body problem in the case that one particle of negligible mass is moving under the Newtonian gravitational attraction of three positive masses [Formula: see text], [Formula: see text] and [Formula: see text] (called primaries). These always lie at the vertices of an equilateral triangle (Lagrangian configuration) and move with constant angular velocity in circular orbits around their center of masses. We consider the case where all the primaries have unequal masses, and investigate the nonlinear stability (in the sense of Lyapunov) of the elliptic equilibrium for the specific values of the mass [Formula: see text] and [Formula: see text] of the primary, fixed on the horizontal axis. Moreover, the [Formula: see text][Formula: see text]:[Formula: see text][Formula: see text] four-order resonant cases are determined and the stability is investigated. In this study, Markeev’s theorem and Arnold’s theorem become key ingredients.

Realize Emergent Gravity to Generic Situations

We clarify the problem in which occasions can gravitational force be regarded emergent from thermodynamics, by proposing an entropic mechanism that can extract the entropic gradient existing in spacetime, due to the variation of the Casini–Bekenstein bound in specific quasi-static processes with the heat flux $$\delta Q$$ δ Q into the whole casual wedge. We explicitly formulate the derivation of inertial force as the emergent gravitational attraction from the Entanglement First Law. We find the saturation of the bound along with the vanishing relative entropy corresponds to the variation of minimal surface. To covariant meaning, it is the Bousso bound. Besides, this understanding is connected to recent Pennington’s work on Black Hole Information Paradox, suggesting a Page-Curve function origins from removing attraction by the external heat bath. Our theory from entanglement now overcomes several criticism towards Verlinde’s original entropic force proposal, and is able to co-exist with Susskind’s Complexity Tendency. This entropic mechanism reproduces the Newton’s Second Law in Rindler space and the gravitational force (together with derivation of the Einstein equation) beyond the near-horizon region, and can be adapted into AdS/CFT and other generic situations.

Geometry of alpine overdeepenings assessed with gravimetry and 3-D modelling

<p>Interpretations of the processes leading to the formation of overdeepened valleys, where the bedrock lies well below sea level today, are contested as the overdeepenings have been filled by sediments or host lakes making observations difficult. Here, we combine gravimetric, GNSS (Global Navigation Satellite System) and borehole data within a 3D forward modelling framework (Gravi3D) to assess the 3-D subsurface geometry of such overdeepenings in the Swiss plateau, to the North of the Alps. Gravi3D has two components (PRISMA and BGPoly), which allow to obtain analytically the gravity effect of prisms and polygons (Nagy (1966) and Talwani & Ewing (1960)). PRISMA allows first to estimate the spatial extent of an overdeepening and the density contrast between the overdeepening fill and the bedrock. In contrast, BGPoly is designed to disclose the details of a complex 3-D geometry of an overdeepening fill through an approximation of its shape with polygons. Gravi3D will be open access and is designed for a larger scientific community.</p><p> <br>Here, we focus on overdeepenings beneath two valleys, the Aare valley and the Gürbe valley to the South of Bern. In this region, the occurrence of overdeepenings has already been disclosed through drilling, but the details about the geometry have not been elaborated yet. The study region is characterized by three mountain ranges oriented North-South and comprises Burdigalian Upper Marine Molasse bedrock. The Gürbe and Aare valleys in-between are c. 300 m-deep and c. 1 km-wide, where overdeepenings with a >100 m-thick Quaternary fill have already been identified by drilling. The gravity data collected along an 8 km-long profile with stations spaced between 100 and 300 m yield a Bouguer anomaly that ranges from c. -99 to -106 mGal. We relate this anomaly to the regional trend (c. 2 mGal over 8 km) and to the effect of the overdeepenings’ sedimentary fillings (2 – 4 mGal/km), disclosing a sharp anomaly pattern over the inferred tunnel valleys. The removal of the signal related to the regional trend results in a residual anomaly of c. 1 mGal for the bedrock ridge in-between the valleys (Belpberg mountain), and of -2.65 and -3.56 mGal for the Gürbe and Aare valley overdeepenings, respectively. We observe a steeper gravity gradient for the Eastern flank of both overdeepenings. The use of Nettleton method to model the residual gravity anomaly across Belpberg yields a density of 2.5 g/cm<sup>3</sup> for the Molasse bedrock. In addition, the estimation of the largest gravity response through the overdeepening fill, calculated with Prisma yields a density value of c. 2.0 – 2.2 g/cm3 for the Quaternary sediments. As a further information, Prisma predicts a maximum thickness of 140 m for the Quaternary suite beneath the Gürbe valley and at least 200 m beneath the Aare valley. This yields a minimum slope of approximately 18° for the Gürbe overdeepening.</p><p> </p><p>REFERENCES</p><p>Nagy, D.: The gravitational attraction of a right rectangular prism. Geophysics 31, 362–371, 1966.</p><p>Talwani, M., Ewing, M.: Rapid computation of gravitational attraction of three‐dimensional bodies of arbitrary shape. Geophysics 25, 203–225, 1960.</p>

A Computational Algorithm to Understand the Evolution of Size Distribution with Successive Breakage Events at Grinding

The kinetic population balance model (PBM) is widely used to predict the particle size distributions of grinding products. However, the model may not be solved if the rate of particle accelerates or decelerates in the mill hold-up, i.e., non-first-order breakage. This study presents a computational algorithm coupled with a pseudo-matrix model to simulate the product size distributions (PSDs) of successive breakage events at grinding. The algorithm’s applicability and accuracy were validated against PSDs taken from different grinding equipment. The advantages of the algorithm are as follows—(i) time can be implicitly or explicitly added to the algorithm. (ii) The parameters required to run the algorithm are quite few. (iii) The proposed algorithm can predict PSDs in the normal or abnormal breakage region. Even a short-time grinding test will be sufficient to estimate the parameters if abnormal breakage effects are reduced or eliminated. (iv) The algorithm can work with arbitrary sets of parameters that are irrelevant to the mill feed and mill type. Also, the algorithm’s framework shows that grinding is not a chaotic process; yet it may be due to the surface/gravitational attraction forces between particles and grinding media.