Related papers: Dani's Work on Dynamical Systems on Homogeneous Sp…
This work reflects on mechanics as an epistemological framework on the state of a physical system to regard dynamics as the distribution of mechanical properties over spacetime coordinates. The resulting distribution is taken to be the…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…
Generalized hydrodynamics (GHD) was proposed recently as a formulation of hydrodynamics for integrable systems, taking into account infinitely-many conservation laws. In this note we further develop the theory in various directions. By…
In this work we explore the dynamical system phase space of Einstein-Gauss-Bonnet theory in the cosmological minisuperspace. This approach binds the main features of the theory through a system of autonomous differential equations, in the…
Existence of random dynamical systems for a class of coalescing stochastic flows on $\mathbb{R}$ is proved. A new state space for coalescing flows is built. As particular cases coalescing flows of solutions to stochastic differential…
The theory of quantum dynamical semigroups within the mathematically rigorous framework of completely positive dynamical maps is reviewed. First, the axiomatic approach which deals with phenomenological constructions and general…
This paper establishes a general framework for describing hybrid dynamical systems which is particularly suitable for numerical simulation. In this context, the data structures used to describe the sets and functions which comprise the…
We provide a self-contained, accessible introduction to Ratner's Equidistribution Theorem in the special case of horocyclic flow on a complete hyperbolic surface of finite area. This equidistribution result was first obtained in the early…
We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1,1) and so(2,2). Energy…
A simple general theorem is used as a tool that generates nonlocal constants of motion for Lagrangian systems. We review some cases where the constants that we find are useful in the study of the systems: the homogeneous potentials of…
The dynamics of distributed sources is described by nonlinear partial differential equations. Lagrangian analytical solutions of these (and associated) equations are obtained and discussed in the context of Lagrangian modeling - from the…
Dynamical heterogeneities have been introduced in the context of the glass transition of molecular liquids and the lengthscale associated with them has been argued to be at the origin of the observed quasi-universal behaviour of glassy…
Exploration of the structure formation and dynamics of animate and inanimate matter on the nanometer scale is a highly interdisciplinary field of rapidly emerging research. It is relevant for various molecular and nanoscale systems of…
Dynamical scaling in ageing systems, notably in phase-ordering kinetics, is well-established. New evidence in favour of Galilei-invariance in phase-ordering kinetics is reviewed.
In this paper we provide a new method to study global dynamics of planar quasi--homogeneous differential systems. We first prove that all planar quasi--homogeneous polynomial differential systems can be translated into homogeneous…
The generation of magnetic field in an electrically conducting fluid generally involves the complicated nonlinear interaction of flow turbulence, rotation and field. This dynamo process is of great importance in geophysics, planetary…
It is investigated a possibility of physical interpretation of vector fields (dynamic flows) in Euclidean spaces of higher dimension. There are analyzed the methods of measurements of dynamic flows, the characteristics of dynamic flow and…
We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a…
The paper provides a review of A.M. Mathai's applications of the theory of special functions, particularly generalized hypergeometric functions, to problems in stellar physics and formation of structure in the Universe and to questions…
A multicomponent extension of our recent theory of simple fluids [ U.M.B. Marconi and S. Melchionna, Journal of Chemical Physics, 131, 014105 (2009) ] is proposed to describe miscible and immiscible liquid mixtures under inhomogeneous, non…