Nonlocal Astrophysics

Non-Local Astrophysics: Dark Matter, Dark Energy and Physical Vacuum highlights the most significant features of non-local theory, a highly effective tool for solving many physical problems in areas where classical local theory runs into difficulties. The book provides the fundamental science behind new non-local astrophysics, discussing non-local kinetic and generalized hydrodynamic equations, non-local parameters in several physical systems, dark matter, dark energy, black holes and gravitational waves. Devoted to the solution of astrophysical problems from the position of non-local physics Provides a solution for dark matter and dark energy Discusses cosmological aspects of the theory of non-local physics Includes a solution for the problem of the Hubble Universe expansion, and of the dependence of the orbital velocity from the center of gravity

Relativity theory is based on a postulate of locality, which means that the past history of the observer is not directly taken into account. This book argues that the past history should be taken into account. In this way, nonlocality—-in the sense of history dependence—-is introduced into relativity theory. The deep connection between inertia and gravitation suggests that gravity could be nonlocal, and in nonlocal gravity the fading gravitational memory of past events must then be taken into account. Along this line of thought, a classical nonlocal generalization of Einstein's theory of gravitation has recently been developed. A significant consequence of this theory is that the nonlocal aspect of gravity appears to simulate dark matter. According to nonlocal gravity theory, what astronomers attribute to dark matter should instead be due to the nonlocality of gravitation. Nonlocality dominates on the scale of galaxies and beyond. Memory fades with time; therefore, the nonlocal aspect of gravity becomes weaker as the universe expands. The implications of nonlocal gravity are explored in this book for gravitational lensing, gravitational radiation, the gravitational physics of the Solar System and the internal dynamics of nearby galaxies, as well as clusters of galaxies. This approach is extended to nonlocal Newtonian cosmology, where the attraction of gravity fades with the expansion of the universe. Thus far, scientists have only compared some of the consequences of nonlocal gravity with astronomical observations.

Relativity theory assumes locality, without accounting for the observer's past history. This work introduces nonlocality, or history dependence, into relativity theory. Inertia and gravitation are deeply tied, suggesting gravity may be nonlocal. The gravitational memory of past events must then be taken into account

Provides abstracts and full text for articles on astronomy and astrophysics.

Applied mathematics is a central connecting link between scientific observations and their theoretical interpretation. Nonlinear analysis has surely contributed major developments which nowadays shape the face of applied mathematics. At the beginning of the millennium, all sciences are expanding at increased speed. Technological, ecological, economical and medical problem solving is a central issue of every modern society. Mathematical models help to expose fundamental structures hidden in these problems and serve as unifying tools to deepen our understanding. What are the new challenges applied mathematics has to face with the increased diversity of scientific problems? In which direction should the classical tools of nonlinear analysis be developed further? How do new available technologies influence the development of the field? How can problems be solved which have been beyond reach in former times? It is the aim of this book to explore new developments in the field by way of discussion of selected topics from nonlinear analysis.

This thesis presents significant new results on the problem of understanding the origin of dark energy in cosmology. The work develops an original approach based on modifications of General Relativity at cosmological scales, introducing non-local effective terms that can in principle emerge from fundamental local theories. Both the phenomenological consequences and theoretical aspects of the proposal are developed in depth. The thesis also contains significant new material compared to that published by the author in scientific journals.

Unified Non-Local Theory of Transport Processess, 2nd Edition provides a new theory of transport processes in gases, plasmas and liquids. It is shown that the well-known Boltzmann equation, which is the basis of the classical kinetic theory, is incorrect in the definite sense. Additional terms need to be added leading to a dramatic change in transport theory. The result is a strict theory of turbulence and the possibility to calculate turbulent flows from the first principles of physics. Fully revised and expanded edition, providing applications in quantum non-local hydrodynamics, quantum solitons in solid matter, and plasmas Uses generalized Boltzmann kinetic theory as an highly effective tool for solving many physical problems beyond classical physics Addresses dark matter and energy Presents non-local physics in many related problems of hydrodynamics, gravity, black holes, nonlinear optics, and applied mathematics

This book presents new developments in non-local mathematical modeling and mathematical analysis on the behavior of solutions with novel technical tools. Theoretical backgrounds in mechanics, thermo-dynamics, game theory, and theoretical biology are examined in details. It starts off with a review and summary of the basic ideas of mathematical modeling frequently used in the sciences and engineering. The authors then employ a number of models in bio-science and material science to demonstrate applications, and provide recent advanced studies, both on deterministic non-local partial differential equations and on some of their stochastic counterparts used in engineering. Mathematical models applied in engineering, chemistry, and biology are subject to conservation laws. For instance, decrease or increase in thermodynamic quantities and non-local partial differential equations, associated with the conserved physical quantities as parameters. These present novel mathematical objects are engaged with rich mathematical structures, in accordance with the interactions between species or individuals, self-organization, pattern formation, hysteresis. These models are based on various laws of physics, such as mechanics of continuum, electro-magnetic theory, and thermodynamics. This is why many areas of mathematics, calculus of variation, dynamical systems, integrable systems, blow-up analysis, and energy methods are indispensable in understanding and analyzing these phenomena. This book aims for researchers and upper grade students in mathematics, engineering, physics, economics, and biology.