Related papers: Simple Dynamics on the Brane
A general system of particles (of one or several species) on a one dimensional lattice with boundaries is considered. Two general behaviors of such systems are investigated. The stationary behavior of the system, and the dominant way of the…
This paper presents some cosmological consequences of the five dimensional, two brane Randall-Sundrum brane scenario. The radius of the compact extra dimension is taken to be time dependent. It is shown that the cosmology consistent with…
In this paper we show, through the study of concrete examples, that, depending on the cosmic dynamics of the energy density of matter degrees of freedom living in the brane, Randall-Sundrum (RS) brane effects can be important not only at…
Physical systems obey strict symmetry principles. We expect that machine learning methods that intrinsically respect these symmetries should have higher prediction accuracy and better generalization in prediction of physical dynamics. In…
The low energy regime of 5D braneworld models with a bulk scalar field is studied. The setup is rather general and includes the Randall-Sundrum and dilatonic braneworlds models as particular cases. We discuss the cosmological evolution of…
One of the basic frameworks in science views behavioral products as a process within a dynamic system. The mechanism might be seen as a representation of many instances of centralized control in real time. Many real systems, however,…
We examine a 2DOF Hamiltonian system, which arises in study of first-order mean motion resonance in spatial circular restricted three-body problem "star-planet-asteroid", and point out some mechanisms of chaos generation. Phase variables of…
We will review some of the theoretical progresses that have been recently done in the study of slow dynamics of glassy systems: the general techniques used for studying the dynamics in the mean field approximation and the emergence of a…
This short paper presents an abstract, tunable model of genomic structural change within the cell lifecycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include…
The study of adaptive dynamics, involving many degrees of freedom on two separated timescales, one for fast changes of state variables and another for the slow adaptation of parameters controlling the former's dynamics is crucial for…
We elucidate the escape properties of stars moving in the combined gravitational field of a binary system of two interacting dwarf spheroidal galaxies. A galaxy model of three degrees of freedom is adopted for describing the dynamical…
We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed…
In spin glass models one can remove minimization of free energy by some order parameter. One can consider hierarchy of order parameters. It is possible to divide energy among these parts. We can consider relaxation process in glass system…
We study the dynamics and the phase-space structures of Coulombic and self-gravitating versions of the classical one-dimensional 3-body system with periodic boundary conditions. We demonstrate that such a 3-body system may be reduced…
A new model for biological growth is introduced that couples the geometry of an organism (or part of the organism) to the flow and deposition of material. The model has three dynamical variables (a) a Riemann metric tensor for the geometry,…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
The mathematical structure of higher-dimensional physical phase spaces of the nondiagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity by using dynamical system methods. Critical points of the Hamiltonian…
Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to…
We present the first numerical study of the full dynamics of a braneworld scenario, working within the framework of the single brane model of Randall and Sundrum (RSII). In particular, we study the process of gravitational collapse driven…
Evolution is a dynamic process. The two classical forces of evolution are mutation and selection. Assuming small mutation rates, evolution can be predicted based solely on the fitness differences between phenotypes. Predicting an…