Related papers: On the information content of the difference from …
Hamilton's principle is extended to have compatible initial conditions to the strong form. To use a number of computational and theoretical benefits for dynamical systems, the mixed variational formulation is preferred in the systems other…
In this paper we study a rate-independent system for the propagation of damage and plasticity. To construct solutions we resort to approximation in terms of viscous evolutions, where viscosity affects both damage and plasticity with the…
Quantum parallelism implies a spread of information over the space in contradistinction to the classical mechanical situation where the information is "centered" on a fixed trajectory of a classical particle. This means that a quantum state…
The recently developed method (Paper 1) enabling one to investigate the evolution of dynamical systems with an accuracy not dependent on time is developed further. The classes of dynamical systems which can be studied by that method are…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
We develop a unified geometric framework for mechanical systems that combine conservative and dissipative dynamics by formulating them on contact manifolds. Within this setting, we identify the Reeb vector field as the intrinsic generator…
The focus is on discrete defects that can be modeled by continuum mechanics, but where the discreteness of the carriers of plastic deformation plays a significant role. The formulations are restricted to small deformation kinematics and the…
A methodology for deriving dual variational principles for the classical Newtonian mechanics of mass points in the presence of applied forces, interaction forces, and constraints, all with a general dependence on particle velocities and…
As a generalization and extension of our previous paper [Escobar-Ruiz and Azuaje, J. Phys. A: Math. Theor. 57, 105202 (2024)], in this work, the notions of particular integral and particular integrability in classical mechanics are extended…
Dissipation in mechanics, optics, acoustics, and electronic circuits is nowadays recognized to be not always detrimental but can be exploited to achieve non-Hermitian topological phases or properties with functionalities for potential…
We study the connection between Lagrangian and Hamiltonian descriptions of closed/open dynamics, for a collection of particles with quadratic interaction (closed system) and a sub-collection of particles with linear damping (open system).…
Hamilton's principle of stationary action lies at the foundation of theoretical physics and is applied in many other disciplines from pure mathematics to economics. Despite its utility, Hamilton's principle has a subtle pitfall that often…
Biological, artificial, and physical systems dissipate energy to accurately transmit information. While tools of information theory have been used to characterize information-processing capabilities, how reliably this information is…
On this paper, we have proposed an approach to observe the time-centered difference scheme for dissipative mechanical systems from a Hamiltonian perspective and to introduce the idea of symplectic algorithm to dissipative systems. The…
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…
We have in earlier papers presented an extension of Mueller's dipole cascade model, which includes subleading effects from energy conservation and running coupling as well as colour suppressed effects from pomeron loops via a ``dipole…
This article develops a Hamilton--Jacobi theory for non-conservative classical field theories, with particular emphasis on dissipative systems, in the framework of co-oriented k-contact geometry. We introduce evolution k-contact k-vector…
We develop a dissipative extension of classical mechanics based on a complex, and more generally quaternionic, action principle that endows every classical system with an intrinsic environment. Decomposing the action into conservative and…
We study a dynamical system with time dependent Hamiltonian by numerical experiments so as to find a relation between thermodynamics and chaotic nature of the system. Excess information loss, defined newly based on Lyapunov analysis, is…
Dissipative Lagrangians and Hamiltonians having Coulomb, viscous and quadratic damping,together with gravitational and elastic terms are presented for a formalism that preserves the Hamiltonian as a constant of the motion. Their derivations…