Related papers: An algebraic approach to systems with dynamical co…
We use the correspondence between the $f(R)$ theory and an Einstein-scalar field system to study late-time dynamics of solutions of $f(R)$ theory. We discuss how reasonable assumptions on the potential of the scalar field lead to…
In cosmological framework, Noether symmetry technique has revealed a useful tool in order to examine exact solutions. In this work, we first introduce the Jordan-frame Lagrangian and apply the conformal transformation in order to obtain the…
We search for viable f(R) theories of gravity, making use of the equivalence between such theories and scalar-tensor gravity. We find that models can be made consistent with solar system constraints either by giving the scalar a high mass…
We investigate dynamics of large scale and slow deformations of layered structures. Starting from the respective model equations for a non-conserved system, a conserved system and a binary fluid, we derive the interface equations which are…
The Hamiltonian theory of a relativistic string is considered in a specific reference frame in terms the diffeo-invariant variables. The evolution parameter and energy invariant with respect to the time-coordinate transformations are…
We first review the application of Dirac's method to the dynamics of a classical particle constrained to a circle and its subsequent quantization. Then, we extend the analysis to a particle constrained to move on an ellipse. Particularly,…
In this paper a new formulation of quantum dynamics of totally constrained systems is developed, in which physical quantities representing time are included as observables. In this formulation the hamiltonian constraints are imposed on a…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
It is shown via the principle of path independence that the (time gauge) constraint algebra derived in (Class. Quantum Grav. 5 (1988) pg. 1405) for vielbein General Relativity is a generic feature of any covariant theory formulated in a…
The aim of this contribution is to study the particle dynamics in a storage ring under the influence of noise. Some simplified stochastic beam dynamics problems are treated by solving the corresponding Fokker-Planck equations numerically.
We present a dynamical system framework for understanding Nesterov's accelerated gradient method. In contrast to earlier work, our derivation does not rely on a vanishing step size argument. We show that Nesterov acceleration arises from…
We review the geometric formulation of the second Noether's theorem in time-dependent mechanics. The commutation relations between the dynamics on the final constraint manifold and the infinitesimal generator of a symmetry are studied. We…
The purpose of this paper is to derive the dynamical equations for the period vectors of a periodic system under constant external stress. The explicit starting point is Newton's second law applied to halves of the system. Later statistics…
The main topic of this work concerns the formulation of the equations of motion and the consequent energy balance that they imply for this type of systems, In particular, the analytical development that we will carry out on the equations of…
We use a quantum mechanical charged particle as a test particle which probes the dynamics of force-related fields it is subject to. We allow for geodesic motion and relations involving gravitation appear. Gravitation affects quantum…
The aim of this paper is to present a new approach to construct constants of motion associated with scaling symmetries of dynamical systems. Scaling maps could be symmetries of the equations of motion but not of its associated Lagrangian…
Working notes on setting up approximate dynamical systems and nonlinear eigenvalue problems, here embedded within the theory of complex nonlinear dynamics. Computations parallel those of linear quantum theory except that we use functional…
The unified constrained dynamics is formulated without making use of the Dirac splitting of constraint classes. The strengthened, completely--closed, version of the unified constraint algebra generating equations is given. The fundamental…
This paper is devoted to constructing and studying exactly solvable dynamical systems in discrete time obtained from some algebraic operations on matrices, to reductions of such systems leading to classical field theory models in…
In this paper we derive the equations of motion for nonholonomic systems subject to inequality constraints, both, in continuous-time and discrete-time. The last is done by discretizing the continuous time-variational principle which defined…