Related papers: Simple Dynamics on the Brane

When a set of particles are moving in a potential field, two aspects are concerned: 1) the relative motion of particle in spatial domain; 2) the particle velocity variations in time domain. The difficulty on treating the systems is…

In this paper, we investigate a non-canonical scalar field model in the background dynamics of anisotropic Locally Rotationally Symmetric (LRS) Bianchi type I universe where gravity is coupled minimally to scalar field which is taken as…

We consider a system of two competing populations in two-dimensional heterogeneous environments. The populations are assumed to move horizontally and vertically with different probabilities, but are otherwise identical. We regard these…

A phase-field model that takes into account the bending energy of fluid vesicles is presented. The Canham-Helfrich model is derived in the sharp-interface limit. A dynamic equation for the phase-field has been solved numerically to find…

We analyze the morphological transition of a one-dimensional system described by a scalar field, where a flat state looses its stability. This scalar field may for example account for the position of a crystal growth front, an order…

We consider a 6D space-time which is periodic in one of the extra dimensions and compact in the other. The periodic direction is defined by two 4-brane boundaries. Both static and non-static exact solutions, in which the internal spacetime…

We present the explicit form of the four-dimensional effective supergravity action which describes low-energy physics of the Randall--Sundrum model with moduli fields in the bulk and charged chiral matter living on the branes. The…

We propose a method for developing the flows of stochastic dynamical systems, posed as Ito's stochastic differential equations, on a Riemannian manifold identified through a suitably constructed metric. The framework used for the stochastic…

We investigate a class of Cardassian scenarios of the universe evolution in notions of the qualitative theory of dynamical systems. This theory allows us to analyze all solutions for all possible initial conditions on the phase plane. In…

We present static solutions to Einstein's equations corresponding to branes at various angles intersecting in a single 3-brane. Such configurations may be useful for building models with localized gravity via the Randall-Sundrum mechanism.…

We analyze the cosmology of the Randall-Sundrum model and that of compact brane models in general in the presence of a radius stabilization mechanism. We find that the expansion of our universe is generically in agreement with the expected…

Several interesting physical systems, such as the Lovelock extension of General Relativity in higher dimensions, classical time crystals, k-essence fields, Horndeski theories, compressible fluids, and nonlinear electrodynamics, have…

We present the theory of time-dependent point transformations to find independent dynamical normal modes for 2D systems subjected to time-dependent control in the limit of small oscillations. The condition that determines if the independent…

We numerically investigate the aging dynamics of a monatomic Lennard-Jones glass, focusing on the topology of the potential energy landscape which, to this aim, has been partitioned in basins of attraction of stationary points (saddles and…

We consider the dimensional reduction of a bulk scalar field in the Randall-Sundrum model. By allowing the scalar field to be non-minimally coupled to the spacetime curvature we show that it is possible to generate spontaneous symmetry…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

Braneworld scenarios with compact extra-dimensions need the volume of the extra space to be stabilized. Goldberger and Wise have introduced a simple mechanism, based on the presence of a bulk scalar field, able to stabilize the radius of…

We explore the possibility of constructing stable, warped two--brane models which solve the hierarchy problem, with a bulk non--canonical scalar field (tachyon matter) as the source term in the action. Among our examples are two models--one…

Obtaining dynamic models of continuum soft robots is central to the analysis and control of soft robots, and researchers have devoted much attention to the challenge of proposing both data-driven and first-principle solutions. Both avenues…

We explore how to extract effective dynamics from loop quantum gravity and spinfoams truncated to a finite fixed graph, with the hope of modeling symmetry-reduced gravitational systems. We particularize our study to the 2-vertex graph with…