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Based on the idea that the components of a cosmological metric may be determined by the total gravitational potential of the universe, the scalar field $\phi=1/G$ in the Jordan-Brans-Dicke (JBD) theory is introduced as evolving with the…
We study the cosmological stability of a class of theories with a dynamical preferred frame. For a range of actions, we find cosmological solutions which are compatible with observations of the recent history of the Universe: a matter…
The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of `absolute space'. When applied to classical mechanics, under the guise of an…
The role of global topology in the dynamics of the Universe is poorly understood. Along with observational programmes for determining the topology of the Universe, some small theoretical steps have recently been made. Heuristic…
We present a consistent relativistic formulation of Mach principle within a geometric theory of gravitation. In this approach, neither inertia nor free fall is assumed a priori. Instead, the motion of any local system arises from its…
This paper investigates a family of dynamical systems arising from an evolutionary re-interpretation of certain optimal control and optimization problems. We focus particularly on the application in image registration of the theory of…
We study models where the gauge coupling constants, masses and the gravitational constant are functions of some conserved charge in the universe, and furthermore a cosmological constant that depends on the total charge of the universe. We…
Quantum theory expresses the observable relations between physical properties in terms of probabilities that depend on the specific context described by the "state" of a system. However, the laws of physics that emerge at the macroscopic…
Dynamics is considered as a corollary of the space-time geometry. Evolution of a particle in the space-time is described as a chain of connected equivalent geometrical objects. Space-time geometry is determined uniquely by the world…
An alternative, scalar theory of gravitation has been proposed, based on a mechanism/interpretation of gravity as being a pressure force: Archimedes' thrust. In it, the gravitational field affects the physical standards of space and time,…
A complete global analysis of spatially-flat, four-dimensional cosmologies derived from the type IIA string and M-theory effective actions is presented. A non--trivial Ramond-Ramond sector is included. The governing equations are written as…
Relational mechanics is a gauge theory of classical mechanics whose laws do not govern the motion of individual particles but the evolution of the distances between particles. Its formulation gives a satisfactory answer to Leibniz's and…
Classical cosmology exhibits a particular kind of scaling symmetry. The dynamics of the invariants of this symmetry forms a system that exhibits many of the features of open systems such as the non-conservation of mechanical energy and the…
Dynamics of the structured particles consisting of potentially interacting material points is considered in the framework of classical mechanics. Equations of interaction and motion of structured particles have been derived. The expression…
Newtonian dynamics is derived from prior information codified into an appropriate statistical model. The basic assumption is that there is an irreducible uncertainty in the location of particles so that the state of a particle is defined by…
Collapse models possibly suggest the need for a better understanding of the structure of space-time. We argue that physical space, and space-time, are emergent features of the Universe, which arise as a result of dynamical collapse of the…
Do the spacetime manifolds which feature in our best scientific theories reflect anything metaphysically weighty in the world (e.g., any fundamental substances or relations)? Should we extend our notions of space and time beyond the…
Environmental science almost invariably proposes problems of extreme complexity, typically characterized by strongly nonlinear evolution dynamics. The systems under investigation have many degrees of freedom - which makes them complicated -…
Our knowledge of the Universe remains discovery-led: in the absence of adequate physics-based theory, interpretation of new results requires a scientific methodology. Commonly, scientific progress in astrophysics is motivated by the…
We outline two subjects of relativistic mechanics: (i) the set of allowable world lines, and (ii) the origin of the relativistic law of dynamics governing point particles. We show that: (i) allowable world lines in the classical theory of…