Primary Matter Creation in a Weyl–Dirac Cosmological Model

In the framework of an integrable Weyl–Dirac (W–D) theory a cosmological model is proposed. It describes a universe that began its expansion from a primary pre-Planckian geometric entity containing no matter. During the pre-Planckian period, from R ₀ =5.58×10 ^–36 cm to R_I=5.58×10 ^–34 cm, this embryonic universe has undergone a very rapid expansion and cosmic matter was created by geometry. At R_I the universe was already filled with matter having the Planckian density _P and being in the state of prematter (P=–), while the Weylian geometric elements were insignificant. This state is the Planckian egg that has served as the initial state of the singularity-free cosmological model ⁽¹⁾ considered in the framework of Einstein's general theory of relativity. The W–D character of the geometry and the cosmological constant are significant in the pre-Planckian period during the matter creation. In the dust-dominated period a relic of the W–D geometry causes a global dark matter effect. In between the pre-Planckian and dust period one has Einstein's framework and is negligible.     

Higgs bosons inE 6 and intermediate mass scales

Considering the importance ofE ₆ as the grand unification group in superstring theories, several breakdown patterns ofE ₆ through maximal subgroups are studied. The Higgs which break the low energy group and give masses to the fermions are determined in each case. At each scale we consider minimal Higgs and apply extended survival hypothesis to determine the limits on the mass scales. The combination of intermediate mass scales that give rise to acceptable electroweak mixing angle and unification mass is determined. Proton decay rate is found to be acceptable in all cases except one.     

Time Delay in Black Hole Gravitational Lensing as a Distance Estimator

We calculate the time delay between different relativistic images formed by black hole gravitational lensing in the strong field limit. For spherically symmetric black holes, it turns out that the time delay between the first two images is proportional to the minimum impact angle. Their ratio gives a very interesting and precise measure of the distance of the black hole. Moreover, using also the separation between the images and their luminosity ratio, it is possible to extract the mass of the black hole. The time delay for the black hole at the center of our Galaxy is just few minutes, but for supermassive black holes with M=10⁸ ÷10⁹ in the neighbourhood of the Local Group the time delay amounts to few days, thus being measurable with a good accuracy.     

The Feasibility of Testing the Inverse Square Law of Gravitation at Newtonian Strength and at Mass Separations of 1 μm

We examine the feasibility of searching for violations of the inverse square law of gravitation with Newtonian strength and at particle separations of 1 m. We discuss systematic uncertainties, such as spurious forces due to the Casimir force, and various sources of random uncertainty, including those due to patch fields and detector noise. Our analysis suggests that a cryogenic, drag-free space environment is necessary to make the experiment feasible, as thermal and vibrational noise could potentially be reduced to the required level in such an environment.     

Gravity as Archimedes’ Thrust and a Bifurcation in that Theory

Eulers interpretation of Newtons gravity (NG) as Archimedes thrust in a fluid ether is presented in some detail. Then a semi-heuristic mechanism for gravity, close to Eulers, is recalled and compared with the latter. None of these two gravitational ethers can obey classical mechanics. This is logical since the ether defines the very reference frame, in which mechanics is defined. This concept is used to build a scalar theory of gravity: NG corresponds to an incompressible ether, a compressible ether leads to gravitational waves. In the Lorentz–Poincaré version, special relativity is compatible with the ether, but, with the heterogeneous ether of gravity, it applies only locally. A correspondence between metrical effects of uniform motion and gravitation is assumed, yet in two possible versions (one is new). Dynamics is based on a (non-trivial) extension of Newtons second law. The observational status for the theory with the older version of the correspondence is summarized.     

The Mathematical Basis for Physical Laws

Laws of mechanics, quantum mechanics, electromagnetism, gravitation and relativity are derived as “related mathematical identities” based solely on the existence of a joint probability distribution for the position and velocity of a particle moving on a Riemannian manifold. This probability formalism is necessary because continuous variables are not precisely observable. These demonstrations explain why these laws must have the forms previously discovered through experiment and empirical deduction. Indeed, the very existence of electric, magnetic and gravitational fields is predicted by these purely mathematical constructions. Furthermore these constructions incorporate gravitation into special relativity theory and provide corrected definitions for coordinate time and proper time. These constructions then provide new insight into the relationship between manifold geometry and gravitation and present an alternative to Einstein’s general relativity theory.     

A Generally Covariant Field Equation for Gravitation and Electromagnetism

A generally covariant field equation is developed for gravitation and electromagnetism by considering the metric vector q in curvilinear, non-Euclidean spacetime. The field equation is

Gravitation with a modified Weber force

With a modified Weber force for gravitation we show how the values of both the advance of the perihelion of the planets and the gravitational deflection of fast particles of general relativity can be reproduced.     

On limiting field strengths in gravitation

We consider through the equivalence principle the existence of maximal and minimal field strengths in gravitation. We explore the consequences for gravitational collapse and for explaining the rotation curve of galaxies without invoking dark matter. Other interesting implications like maximal size of planetary systems are outlined.1. Note that, in our case, such results, both for electromagnetic and gravitational fields, are obtained when torsion is considered [8]: In fact, we have arrived at a minimum radius, for instance, of the electron, starting explicitly frm a modified Poisson's equation when a term containing the spin is incorporated through torsion.     

THE CHARACTERISTIC FINITE DIFFERENCE METHOD FOR THREE-DIMENSIONAL MOVING BOUNDARY VALUE PROBLEM

The software for oil-gas transport and accumulation is to describe the history of oil-gas transport and accumulation in basin evolution. It is of great value in rational evaluation of prospecting and exploiting oil-gas resources. The mathematical model can be discribed as a coupled system of nonlinear partial differential equations with moving boundary value problem. For a generic case of the three-demensional bounded region, bi this thesis, the effects of gravitation、buoyancy and capillary pressure are considered, we put forward a kind of characteristic finite difference schemes and make use thick and thin grids to form a complete set, and of calculus of vaviations, the change of variable, the theory of prior estimates and techniques, Optimal order estimates in l~2 norm are derived for the error in approximate assumption, Thus we have completely solved the well-known theoretical problem proposed by J. Douglas, Jr.