Related papers: A conceptual approach to the problem of action-ang…
In this article we provide a comparison of classical dynamical x-ray diffraction theory with the dynamical theory for the wide-angle case. It is shown that it is possible for the true value of the angular variable to be introduced without…
The article is devoted to the study of non-autonomous Navier-Stokes equations. First, the authors have proved that such systems admit compact global attractors. This problem is formulated and solved in the terms of general non-autonomous…
The aim of this work is to ascertain the characterization of the existence of coexistence states for a class of cooperative systems supported by the study of an associated non--local equation through classical variational methods. Thanks to…
It is well known that the dynamics of three point vortices moving in an ideal fluid in the plane can be expressed in Hamiltonian form, where the resulting equations of motion are completely integrable in the sense of Liouville and Arnold.…
We propose in these notes a list of some old and new questions related to quasi-periodic dynamics. A main aspect of quasi-periodic dynamics is the crucial influence of arithmetics on the dynamical features, with a strong duality in general…
A comparative discussion of the normal form and action angle variable method is presented in a tutorial way. Normal forms are introduced by Lie series which avoid mixed variable canonical transformations. The main interest is focused on…
A global time-discretized scheme for the Navier-Stokes equation system in its Leray projection form is defined. It is shown that the scheme converges to a bounded global classical solution for smooth data which have polynomial decay at…
The problem of estimating the angular speed of a solid body from attitude measurements is addressed. To solve this problem, we propose an observer whose dynamics are not constrained to evolve on any specific manifold. This drastically…
A discrete action principle for general quantum automata is proposed. This action principle is particularized to Discrete Time Quantum Walks (DTQWs) and then extended into an energy and momentum preserving, manifestly covariant formulation.…
A general method to describe stochastic dynamics of Markov processes is suggested. The method aims to solve three related problems. The determination of an optimal coordinate for the description of stochastic dynamics. The reconstruction of…
We present a kinetic theory for inhomogeneous systems with weak long-range interactions. Starting from the Klimontovich equation and using a quasilinear theory, we obtain a closed kinetic equation describing the relaxation of the…
In this paper, we introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…
Using the fact that extremum of variation of generalized action can lead to the fractional dynamics in the case of systems with long-range interaction and long-term memory function, we consider two different applications of the action…
We consider the action principle to derive the classical, relativistic motion of a self-interacting particle in a 4-D Lorentzian spacetime containing a wormhole and which allows the existence of closed time-like curves. In particular, we…
We introduce an elementary method for proving the absolute continuity of the time marginals of one-dimensional processes. It is based on a comparison between the Fourier transform of such time marginals with those of the one-step Euler…
The rigid body attitude estimation problem is treated using the discrete-time Lagrange-d'Alembert principle. Three different possibilities are considered for the multi-rate relation between angular velocity measurements and direction vector…
As historically acknowledged in the Reasoning about Actions and Change community, intuitiveness of a logical domain description cannot be fully automated. Moreover, like any other logical theory, action theories may also evolve, and thus…
The work reported here originates in the discovery, four decades ago, of a previously unknown type of self-organizing interaction among oscillating systems -- so-called argumental interactions -- and of "quantized" modes of behavior in…
Averaging principle is an effective method for investigating dynamical systems with highly oscillating components. In this paper, we study three types of averaging principle for stochastic complex Ginzburg-Landau equations. Firstly, we…
Whereas in a coordinate-dependent setting the Euler-Lagrange equations establish necessary conditions for solving variational problems in which both the integrands of functionals and the resulting paths are assumed to be sufficiently…