75 citations · 397 across the 23 of their papers we have counts for
9 papers · 1 filter
Transition criteria and phase space structures in a three degree of freedom system with dissipation
Jun Zhong, Shane D. Ross
Escape from a potential well through an index-1 saddle can be widely found in some important physical systems. Knowing the criteria and phase space geometry that govern escape even…
Geometry of escape and transition dynamics in the presence of dissipative and gyroscopic forces in two degree of freedom systems
Jun Zhong, Shane D. Ross
Escape from a potential well can occur in different physical systems, such as capsize of ships, resonance transitions in celestial mechanics, and dynamic snap-through of arches and…
Finite-time Lyapunov exponents in the instantaneous limit and material transport
Peter J. Nolan, Mattia Serra, Shane D. Ross
Lagrangian techniques, such as the finite-time Lyapunov exponent (FTLE) and hyperbolic Lagrangian coherent structures (LCS), have become popular tools for analyzing unsteady fluid…
Experimental validation of phase space conduits of transition between potential wells
Shane D. Ross, Amir E. BozorgMagham, Shibabrat Naik +1
A phase space boundary between transition and non-transition, similar to those observed in chemical reaction dynamics, is shown experimentally in a macroscopic system. We present a…
Trajectory-free approximation of phase space structures using the trajectory divergence rate
Gary K. Nave, Peter J. Nolan, Shane D. Ross
This paper introduces the trajectory divergence rate, a scalar field which locally gives the instantaneous attraction or repulsion of adjacent trajectories. This scalar field may b…
A Tube Dynamics Perspective Governing Stability Transitions: An Example Based on Snap-through Buckling
Jun Zhong, Lawrence N. Virgin, Shane D. Ross
The equilibrium configuration of an engineering structure, able to withstand a certain loading condition, is usually associated with a local minimum of the underlying potential ene…