Visualizing Molecular Phase Space: Nonstatistical Effects in Reaction Dynamics

A tube dynamics perspective governing stability transitions: An example based on snap-through buckling

“…Tube dynamics is a conceptual dynamical systems framework initially used to study the isomerization reactions in chemistry [12][13][14][15]29] as well as other fields, like resonance transitions in celestial mechanics [9,11,17,18,30] and capsize in ship dynamics [8]. Here we extend the application of tube dynamics to structural mechanics: the snap-through of a shallow arch, or buckled-beam.…”

“…Transitions from one side of the bottleneck can be understood in terms of sets of trajectories which are bounded by topological cylinders. The transition dynamics, which has in some contexts been known as tube dynamics [9][10][11][12][13][14][15][16][17][18][19], has been developed for studying transitions between stable states (the potential wells) in a number of disparate contexts, and here it is applied to a structural mechanics situation in which snap-through buckling [2] is the key phenomenological transition. Conditions are determined whereby the initial energy imparted to the system is characterized in terms of subsequent escape from the initial potential well.…”

Central configurations

“…(a) Tubes connecting realms, the largest pieces of phase space, as seen in the phase space of a Hamiltonian system with three degrees of freedom. For visualization, three of the phase space dimensions have been suppressed (adapted from Topper [1997]). (b) A 3-dimensional section of the 4-dimensional lobe structure from work by Lekien [2003].…”

“…Such a unification is strongly needed. Chemists have used variants of both tube dynamics (Topper [1997]; De Leon, Mehta, and Topper [1991a,b]; Ozorio de Almeida, De Leon, Mehta, and Marston [1990]) and lobe dynamics (Davis and Gray [1986]; Davis [1985]) to study molecular dynamics, but these two pictures, which have remained distinct, should come together.…”

Lagrangian descriptors of driven chemical reaction manifolds

“…Nonstatistical effects in the reactive flux [51][52][53][54][55][56], can be prominent, specifically at the onset (transient) portions of the transition processes [57,58]. Moreover, describing the complex and often nonintuitive TS structures [19] in thermally-activated [41][42][43] and fieldinduced reactions [57][58][59][60] has provided a significant hurdle to rate theory.…”