Related papers: Simple Dynamics on the Brane
We study the dynamics of homogeneous and isotropic Friedmann-Lema\^itre-Robertson-Walker cosmological models with positive spatial curvature within the context of mimetic gravity theory by employing dynamical system techniques. Our analysis…
In this paper we study the cosmological dynamics of Randall-Sundrum braneworld type scenarios in which the five-dimensional Weyl tensor has a non-vanishing projection onto the three-brane where matter fields are confined. Using dynamical…
We investigate the dynamics of a spherically symmetric vaccum on a Randall and Sundrum 3-brane world. Under certain natural conditions, the effective Einstein equations on the brane form a closed system for spherically symmetric dark…
The form and evolution of multi-phase biomembranes is of fundamental importance in order to understand living systems. In order to describe these membranes, we consider a mathematical model based on a Canham--Helfrich--Evans two-phase…
We report results on the construction of cosmological braneworld models in the context of the Einstein-Gauss-Bonnet gravity, which include the leading correction to the Einstein-Hilbert action suggested by superstring theory. We obtain and…
We investigate the evolutionary dynamics of an idealised model for the robust self-assembly of two-dimensional structures called polyominoes. The model includes rules that encode interactions between sets of square tiles that drive the…
We give a very short introduction to discrete and continuum models for the evolutionary and spatial dynamics of cancer through two case studies: a model for the evolutionary dynamics of cancer cells under cytotoxic therapy and a model for…
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential energy. However, in the nonlinear context, there may be other…
The original Hardenberg's model of biomass patterns in arid and semi-arid regions is revisited to extend it to more general non flat regions. It is proposed a technique to study these more generalized (non-flat) regions using both a…
In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the…
The H\'enon-Heiles system, initially introduced as a simplified model of galactic dynamics, has become a paradigmatic example in the study of nonlinear systems. Despite its simplicity, it exhibits remarkably rich dynamical behavior,…
We present a systematic numerical iteration approach to study the evolution properties of the spin-boson systems, which works well in whole coupling regime. This approach involves the evaluation of a set of coefficients for the formal…
Standandard Hamiltonian mechanics in its homogeneous formulation is applied to the study of discontinuities representing rapid changes of Hamiltonians. Different formulations of Hamiltonian mechanics are reviewed. An original representation…
A thermodynamic description of cosmological spacetimes may provide insights into the fundamentals of the cosmic evolution that remain otherwise obscure, similar to `black hole thermodynamics'. We investigate the thermodynamic properties of…
We propose a new procedure to monitor and forecast the onset of transitions in high dimensional complex systems. We describe our procedure by an application to the Tangled Nature model of evolutionary ecology. The quasi-stable…
Perhaps the simplest approach to constructing models with sub-dimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and…
We observe that the fully nonlinear evolution equations of Rosenau and Hymann, often abbreviated as $K(n,\,m)$ equations, can be reduced to Hamiltonian form only on a zero-energy hypersurface belonging to some potential function associated…
Easy steps through essential Hamiltonian dynamics are outlined, from necessary definitions of Poisson brackets and canonical transformations, to a quick proof that Hamiltonian evolution is made by canonical transformations, the quickest…
We consider the dynamics of a small trojan companion of a hypothetical giant exoplanet under the secular perturbations of additional planets. By a suitable choice of action-angle variables, the problem is amenable to the study of the slow…
We combine incentive, adaptive, and time-scale dynamics to study multipopulation dynamics on the simplex equipped with a large class of Riemmanian metrics, simultaneously generalizing and extending many dynamics commonly studied in dynamic…