Periodic orbits in biological molecules: Phase space structures and selectivity in alanine dipeptide

2007 ◽  
Vol 126 (17) ◽  
pp. 175101 ◽  
Author(s):  
Stavros C. Farantos
Keyword(s):  
Phase Space ◽  
Periodic Orbits ◽  
Biological Molecules ◽  
Space Structures ◽  
Alanine Dipeptide

scholarly journals Hamiltonian flow over saddles for exploring molecular phase space structures

2018 ◽  
Vol 376 (2115) ◽  
pp. 20170148 ◽  
Author(s):  
Stavros C. Farantos
Keyword(s):  
Phase Space ◽  
Potential Energy Surfaces ◽  
Initial Conditions ◽  
Space Structures ◽  
Hamiltonian Flow ◽  
Molecular Configuration ◽  
Geometrical Structures ◽  
Classical Dynamical System ◽  
Energy Surfaces ◽  
Alanine Dipeptide

Despite using potential energy surfaces, multivariable functions on molecular configuration space, to comprehend chemical dynamics for decades, the real happenings in molecules occur in phase space, in which the states of a classical dynamical system are completely determined by the coordinates and their conjugate momenta. Theoretical and numerical results are presented, employing alanine dipeptide as a model system, to support the view that geometrical structures in phase space dictate the dynamics of molecules, the fingerprints of which are traced by following the Hamiltonian flow above saddles. By properly selecting initial conditions in alanine dipeptide, we have found internally free rotor trajectories the existence of which can only be justified in a phase space perspective. This article is part of the theme issue ‘Modern theoretical chemistry’.

scholarly journals CHAINS OF ROTATIONAL TORI AND FILAMENTARY STRUCTURES CLOSE TO HIGH MULTIPLICITY PERIODIC ORBITS IN A 3D GALACTIC POTENTIAL

2011 ◽  
Vol 21 (08) ◽  
pp. 2331-2342 ◽  
Author(s):  
M. KATSANIKAS ◽  
P. A. PATSIS ◽  
A. D. PINOTSIS
Keyword(s):  
Phase Space ◽  
Hamiltonian System ◽  
Periodic Orbit ◽  
Periodic Orbits ◽  
Color Variation ◽  
Space Structures ◽  
Unstable Periodic Orbits ◽  
Unstable Periodic Orbit ◽  
Surface Of Section ◽  
Autonomous Hamiltonian System

This paper discusses phase space structures encountered in the neighborhood of periodic orbits with high order multiplicity in a 3D autonomous Hamiltonian system with a potential of galactic type. We consider 4D spaces of section and we use the method of color and rotation [Patsis & Zachilas, 1994] in order to visualize them. As examples, we use the case of two orbits, one 2-periodic and one 7-periodic. We investigate the structure of multiple tori around them in the 4D surface of section and in addition, we study the orbital behavior in the neighborhood of the corresponding simple unstable periodic orbits. By considering initially a few consequents in the neighborhood of the orbits in both cases we find a structure in the space of section, which is in direct correspondence with what is observed in a resonance zone of a 2D autonomous Hamiltonian system. However, in our 3D case we have instead of stability islands rotational tori, while the chaotic zone connecting the points of the unstable periodic orbit is replaced by filaments extending in 4D following a smooth color variation. For more intersections, the consequents of the orbit which started in the neighborhood of the unstable periodic orbit, diffuse in phase space and form a cloud that occupies a large volume surrounding the region containing the rotational tori. In this cloud the colors of the points are mixed. The same structures have been observed in the neighborhood of all m-periodic orbits we have examined in the system. This indicates a generic behavior.

Classical nonlinearity and quantum decay: The effect of classical phase-space structures

2001 ◽  
Vol 64 (5) ◽  
Author(s):  
Yosef Ashkenazy ◽  
Luca Bonci ◽  
Jacob Levitan ◽  
Roberto Roncaglia
Keyword(s):  
Phase Space ◽  
Space Structures ◽  
Classical Phase Space

An algorithm for computing phase space structures in chemical reaction dynamics using Voronoi tessellation

2021 ◽  
pp. 133047
Author(s):  
Yuta Mizuno ◽  
Mikoto Takigawa ◽  
Saki Miyashita ◽  
Yutaka Nagahata ◽  
Hiroshi Teramoto ◽  
...  
Keyword(s):  
Phase Space ◽  
Chemical Reaction ◽  
Voronoi Tessellation ◽  
Reaction Dynamics ◽  
Space Structures ◽  
Chemical Reaction Dynamics

Detection of Phase Space Structures of the Cat Map with Lagrangian Descriptors

2018 ◽  
Vol 23 (6) ◽  
pp. 751-766 ◽  
Author(s):  
Víctor J. García-Garrido ◽  
Francisco Balibrea-Iniesta ◽  
Stephen Wiggins ◽  
Ana M. Mancho ◽  
Carlos Lopesino
Keyword(s):  
Phase Space ◽  
Space Structures ◽  
Lagrangian Descriptors

scholarly journals Role of phase space structures in collisionless drift wave turbulence and impact on transport modeling

2017 ◽  
Vol 57 (7) ◽  
pp. 072006 ◽  
Author(s):  
Y. Kosuga ◽  
S.-I. Itoh ◽  
P.H. Diamond ◽  
K. Itoh ◽  
M. Lesur
Keyword(s):  
Phase Space ◽  
Transport Modeling ◽  
Space Structures ◽  
Wave Turbulence ◽  
Drift Wave Turbulence ◽  
Drift Wave

scholarly journals The formation of relativistic plasma structures and their potential role in the generation of cosmic ray electrons

2008 ◽  
Vol 15 (6) ◽  
pp. 831-846 ◽  
Author(s):  
M. E. Dieckmann
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Magnetic Energy ◽  
Ion Beam ◽  
Cosmic Ray ◽  
Compact Objects ◽  
Space Structures ◽  
Magnetic Field Generation ◽  
Particle In Cell ◽  
Field Generation

Abstract. Recent particle-in-cell (PIC) simulation studies have addressed particle acceleration and magnetic field generation in relativistic astrophysical flows by plasma phase space structures. We discuss the astrophysical environments such as the jets of compact objects, and we give an overview of the global PIC simulations of shocks. These reveal several types of phase space structures, which are relevant for the energy dissipation. These structures are typically coupled in shocks, but we choose to consider them here in an isolated form. Three structures are reviewed. (1) Simulations of interpenetrating or colliding plasma clouds can trigger filamentation instabilities, while simulations of thermally anisotropic plasmas observe the Weibel instability. Both transform a spatially uniform plasma into current filaments. These filament structures cause the growth of the magnetic fields. (2) The development of a modified two-stream instability is discussed. It saturates first by the formation of electron phase space holes. The relativistic electron clouds modulate the ion beam and a secondary, spatially localized electrostatic instability grows, which saturates by forming a relativistic ion phase space hole. It accelerates electrons to ultra-relativistic speeds. (3) A simulation is also revised, in which two clouds of an electron-ion plasma collide at the speed 0.9c. The inequal densities of both clouds and a magnetic field that is oblique to the collision velocity vector result in waves with a mixed electrostatic and electromagnetic polarity. The waves give rise to growing corkscrew distributions in the electrons and ions that establish an equipartition between the electron, the ion and the magnetic energy. The filament-, phase space hole- and corkscrew structures are discussed with respect to electron acceleration and magnetic field generation.

Sign in / Sign up

Export Citation Format

Share Document