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Hamiltonian Computational Chemistry: Geometrical Structures in Chemical Dynamics and Kinetics.
Entropy (Basel)
April 2024
Department of Chemistry, University of Crete, GR-700 13 Heraklion, Greece.
The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space.
View Article and Find Full Text PDFRings of light caused by gravitational waves.
Sci Rep
June 2022
Departament of Physics, Universidad de los Andes, Bogota, 111711, Colombia.
We reconsider the case of the geodesic motion of a massive and massless beam of test particles in a gravitational wave. In particular, we use a direct Lagrangian approach which simplifies the calculation. Our findings differ partly from previously performed calculations The final result can be interpreted as rings of light seen by the observer.
View Article and Find Full Text PDFChaotic advection in a recirculating flow: Effect of a fluid-flexible-solid interaction.
Chaos
April 2022
Department of Mechanical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India.
The present work is on laminar recirculating flow-induced deformation as well as motion of a neutrally buoyant flexible elliptical solid, resulting in Lagrangian chaos in a two-dimensional lid-driven cavity flow. Using a fully Eulerian and monolithic approach-based single-solver for the fluid flow and flexible-solid deformation, a chaotic advection study is presented for various aspect ratios β ( =0.5-1.
View Article and Find Full Text PDFFully kinetic simulations of strong steady-state collisional planar plasma shocks.
Phys Rev E
November 2021
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA.
We report on simulations of strong, steady-state collisional planar plasma shocks with fully kinetic ions and electrons, independently confirmed by two fully kinetic codes (an Eulerian continuum and a Lagrangian particle-in-cell). While kinetic electrons do not fundamentally change the shock structure as compared with fluid electrons, we find an appreciable rearrangement of the preheat layer, associated with nonlocal electron heat transport effects. The electron heat-flux profile qualitatively agrees between kinetic- and fluid-electron models, suggesting a certain level of "stiffness," though substantial nonlocality is observed in the kinetic heat flux.
View Article and Find Full Text PDFMori-Zwanzig projection operator formalism: Particle-based coarse-grained dynamics of open classical systems far from equilibrium.
Phys Rev E
August 2021
Weapons and Materials Research Directorate, U.S. Army DEVCOM Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005, USA.
We present a generalized Langevin equation (GLE) of motion that governs exactly the time evolution of phase-space observables in finite open systems described by classical Hamiltonians with explicitly time-dependent potentials. This formalism is based on the Mori-Zwanzig projection operator (PO) method with a time-independent Zwanzig PO within a Heisenberg (Lagrangian) picture and reduced description of Hamiltonian systems in terms of canonical relevant and irrelevant coordinates. We demonstrate that, similarly to closed systems, GLE dynamics in Hamiltonian systems in the presence of time-dependent potentials is determined by conservative, dissipative memory, and projected force fields, and that the memory functions relate to the projected force, which is a two-time process, in a way that is reminiscent of the equilibrium second fluctuation-dissipation relation.
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