Related papers: Dynamical systems approach to stellar modelling in…
We study the dynamics of a non-minimally coupled scalar field cosmology with a potential function. We use the framework of dynamical systems theory to investigate all evolutional paths admissible for all initial conditions. Additionally, we…
In this paper, we have outlined the development of an autonomous dynamical system within a general scalar-tensor gravity framework. This framework encompasses the overall structure of the non-minimally coupled scalar field functions for…
We have investigated some bouncing models in the framework of an extended gravity theory where the usual Ricci scalar in the gravitational action is replaced by a sum of the Ricci scalar and a term proportional to the trace of the energy…
We present a dynamical analysis in terms of new expansion-normalized variables for homogeneous and anisotropic Bianchi-I spacetimes in $f(R)$ gravity in the presence of anisotropic matter. With a suitable choice of the evolution parameter,…
The local statistical and geometric structure of three-dimensional turbulent flow can be described by properties of the velocity gradient tensor. A stochastic model is developed for the Lagrangian time evolution of this tensor, in which the…
Using hydrodynamic approach, it is shown that the properties of a marginally stable collisionless stellar disc resemble those of a thermodynamic system undergoing a gas--liquid phase transition. The maximum in Toomre's stability diagram,…
We analyze dynamical instability of non-static reflection axial stellar structure by taking into account generalized Euler's equation in metric $f(R)$ gravity. Such an equation is obtained by contracting Bianchi identities of usual…
We study the long-term dynamics of a planetary system composed of a star and a planet. Both bodies are considered as extended, non-spherical, rotating objects. There are no assumptions made on the relative angles between the orbital angular…
We examine the scenario of non-minimally coupled relativistic fluid and $k$-essence scalar field in a flat Friedmann-Lemaitre-Robertson-Walker universe. By adding a non-minimal coupling term in the Lagrangian level, we study the variation…
Stellar dynamics is almost unreasonably well suited for an implementation in terms of special-purpose hardware. Unlike the case of molecular dynamics, stellar dynamics deals exclusively with a long-range force, gravity, which leads to a…
The theoretical understanding of active matter, which is driven out of equilibrium by directed motion, is still fragmental and model oriented. Stochastic thermodynamics, on the other hand, is a comprehensive theoretical framework for driven…
In this paper, we study the dynamical behaviour of the Universe in the $F(R,G)$ theory of gravity, where $R$ and $G$ respectively denote the Ricci scalar and Gauss-Bonnet invariant. Our wide analysis encompasses the energy conditions,…
We introduce a general method to construct classes of dynamical systems invariant under generalizations of the Carroll and of the Galilei groups. The method consists in starting from a space-time in $D+1$ dimensions and partitioning it in…
A two-component isothermal equilibrium model is applied to reproduce basic structural properties of dynamically hot stellar systems immersed in their massive dark haloes. The origin of the fundamental plane relation for giant ellipticals is…
We present a novel approach to modified theories of gravity that consists of adding to the Einstein-Hilbert Lagrangian an f(R) term constructed a la Palatini. Using the respective dynamically equivalent scalar-tensor representation, we show…
We have developed a new formulation to obtain self-gravitating, axisymmetric configurations in permanent rotation. The formulation is based on the Lagrangian variational principle, and treats not only barotropic but also baroclinic…
We develop a thermodynamic framework for modeling innovation adoption and abandonment dynamics using statistical mechanics. Starting from a mathematical model for an adoption distribution that fits empirically obtained date, we construct a…
We perform a phase space analysis of a generalized modified gravity theory with nonminimally coupling between geometry and matter. We apply the dynamical system approach to this generalized model and find that in the cosmological context,…
There are many different formulations of relativistic elasticity. Most of them are only concerned with formal questions rather than questions regarding the PDE point of view. The aim of this thesis is to obtain various local existence…
We study the stability of 5D gravitational solutions containing an arbitrary number of scalar fields. A closed set of equations is derived which governs the background and perturbations of N scalar fields and the metric, for arbitrary bulk…