Related papers: A dynamical system approach to higher order gravit…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…
We analyse a mechanical system in two-dimensional relative motion with friction. Although the system is simple, the peculiar interplay between two kinetic friction forces and gravity leads to the wide range of admissible solutions exceeding…
The climate system is a forced, dissipative, nonlinear, complex and heterogeneous system that is out of thermodynamic equilibrium. The system exhibits natural variability on many scales of motion, in time as well as space, and it is subject…
This note discusses dynamical systems-systems that evolve through time. We start with two contemporary examples illustrating the qualitative and the quantitative behavior of dynamical systems. These are two broad categories, usually called…
A theory of gravity in $d+1$ dimensions is dynamically generated from a theory in $d$ dimensions. As an application we show how $N$ dynamically coupled gravity theories can reduce the effective Planck mass.
Arguments are reviewed and extended in favor of presenting special relativity at least in part from a more mechanistic point of view. A number of generic mechanisms are catalogued and illustrated with the goal of making relativistic effects…
The traditional view from particle physics is that quantum gravity effects should only become detectable at extremely high energies and small length scales. Due to the significant technological challenges involved, there has been limited…
The dynamical systems of the form $\ddot\bold r=\bold F (\bold r,\dot\bold r)$ in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force…
We will review some of the theoretical progresses that have been in the study of complex systems in physics and of their applications to biology.
Two-dimensional case in the theory of dynamical systems admitting the normal shift differs crucially from multidimensional case. Features of two-dimensional case are gathered and studied in this thesis.
Modeling of urban traffic flows is required due to the complexity of their successful forecasting, as well as due to the impact of various random factors on them, and the complexity of transport systems in modern cities. Forecasting of…
In this thesis we introduce the concept of a guided dynamical system, and exploit this idea to solve various problems in functional equations and PDE's. Our main results are 1) a necessary and sufficient condition for unique-solvability of…
We propose a new dynamical system formalism for the analysis of f(R) cosmologies. The new approach eliminates the need for cumbersome inversions to close the dynamical system and allows the analysis of the phase space of f(R)-gravity models…
The dynamical friction force experienced by a body moving at relativistic speed in a gaseous medium is examined. This force, which arises due to the gravitational interaction of the body with its own gravitationally-induced wake, is…
This paper is motivated by the theory of sequential dynamical systems, developed as a basis for a mathematical theory of computer simulation. It contains a classification of finite dynamical systems on binary strings, which are obtained by…
A new way of orthogonalizing ensembles of vectors by "lifting" them to higher dimensions is introduced. This method can potentially be utilized for solving quantum decision and computing problems.
The kinetic theory of a self-gravitating system is considered in the framework of Bhatnager-Gross-Krook model. This approach offers a unique and tractable setup for studying the central, collision-dominated region of the system, as well as…
We use experiment-supported dimensional analysis to further bolster our arguments that crucial information on the emergence and/or nature of space could be extracted from the combination of the properties of gravitational and strong…