Physics in curved spacetime

Electromagnetic field theory, and the physics of continuous media (fluids, solids) in curved spacetime are discussed. Generalized Maxwell’s equations are written down and their justifaction is briefly presented. Then we turn to thermodynamics and continuous media. The concept of energy and momentum conservation is carefully expounded, and then the equations for fluid flow (continuity equation and Euler equation) are developed from the divergence of the energy tensor. The Bernoulli equation and the equation for hydrostatic equilibrium are obtained. The chapter then goes on to a general discussion of how general relativity operates and how gravitational phenomena are calculated and observed. The relation between gravity and other aspects of physics such as particle physics is discussed, along with the notion of general covariance.

Spatiotemporal Patterns in a General Networked Activator-Substrate Model

For the purpose of understanding the spatiotemporal pattern formation in the random networked system, a general activator-substrate model with network structure is introduced. Firstly, we investigate the boundedness of the non-constant steady state of the elliptic system of the continuous media system. It is found that the non-constant steady state admits their upper and lower bounds with certain conditions. Then, one investigates some properties and non-existence of the non-constant steady state with the no-flux boundary conditions. The main results show that the diffusion rate of activator should greater than the diffusion rate of substrate. Otherwise, there might be no pattern formation of the system. Afterwards, a general random networked activator-substrate model is made public. The conditions of the stability, the Hopf bifurcation, the Turing instability and a co-dimensional-two Turing-Hopf bifurcation are yield by the method of stability analysis and bifurcation theorem. Finally, we choose a suitable sub-system of the general activator-substrate model to verify the theoretical results, and full numerical simulations are well verified these results. Especially, an interesting finding is that the stability of the positive equilibrium will switch from unstable to stable one with the change of the connection probability of the nodes, this is different from the pattern formation in the continuous media systems.

Mathematical modeling of electromag-netic and gravitational phenomena by the methodology of continuous media mechanics

The book of well-known Russian scientists systematically presents a new theoretical approach to studying nature's fundamental phenomena using the hypothesis of the physical vacuum, or the ether, as some environment in which all the processes develop. In the proposed studies, the ether is represented as some one-component continuous media that satisfies generally accepted conservation laws: of matter and momentum. From the appropriate two equations, a number of consequences are obtained to which a physical interpretation is given. For the first time, 150 years after studies of Faraday and Maxwell, it is shown that these single premises mathematically give basic physical laws established experimentally: the Maxwell equations, the Lorentz force, the Gauss theorem; the laws: Coulomb, Biot - Savard, Ampere, electromagnetic induction, Ohm, Joule - Lenz, Wiedemann - Franz, universal gravitation, and etc. Details of mechanisms of many processes, that seemed previously paradoxical, have been disclosed. A method of the model substantiation adopted in the mathematical modeling methodology allows to conclude that the presented mathematical model of the ether adequately describes electromagnetic and gravitational processes. Qualitative and quantitative analysis of hundreds of known and new experimental facts allows in the methodology of physics, as science summarizing the experiments data, to confirm a conclusion about the existence of the ether (physical vacuum). The content of the book is based on the works of authors done during the last fourteen years. Many results are published for the first time. The book is intended for specialists in the field of electrodynamics, electrical engineering, gravity and kinetics, as well as for graduate students and students, interested in the fundamental principles of these scientific directions. This book is unique in terms of the comprehensive consideration of the problem and the depth of its analysis.

Physics and Mechanizm of Creation, Separation and Orbiting of the Solar System Bodies Based on Jacobi Dynamics

Our work sets forth and builds upon the fundamentals of the dynamics of natural systems in formulating the problem presented by Jacobi in his famous lecture series “Vorlesung über Dynamik”. In the dynamics of systems described by models of discrete and continuous media, the many-body problem is usually solved in some approximation, or the behavior of the medium is studied at each point of the space it occupies. Such an approach requires the system of equations of motion to be written in terms of space co-ordinates and velocities, in which case the requirements of an internal observer for a detailed description of the processes are satisfied.

Numerical Methods for Solving Dynamic Equilibrium Equations

Once the number of degrees of freedom exceeds a certain number, it would be impossible to solve the dynamic equilibrium equation manually, hence the need to switch to a numerical resolution, whose general principle is to convert a dynamic equation into a static one. We are interested, for the dynamic analysis of the structures and the continuous media, in “one-step” algorithms rather than “multi-step” one. It is mainly because the systems to be solved are of large size and that it is important to minimize the number of operations and value to be memorized to the detriment, if necessary, of precision. A “one-step” algorithm, like that of Newmark, makes it possible to calculate the solution at time tn+1, starting from the solution at time tn. In addition to the disadvantage of requiring the storage of several steps, the “multi-step” algorithms such as that of Houbolt requires a startup procedure. This chapter allows the reader to enumerate and understand different numerical method with different examples.