# Experimental validation of phase space conduits of transition between potential wells

@article{Ross2018ExperimentalVO, title={Experimental validation of phase space conduits of transition between potential wells}, author={Shane D. Ross and Amir E. BozorgMagham and Shibabrat Naik and Lawrence N. Virgin}, journal={Physical Review E}, year={2018} }

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 validation of the phase space flux across rank one saddles connecting adjacent potential wells and confirm the underlying phase space conduits that mediate the transition. Experimental regions of transition are found to agree with the theory to within 1\%, suggesting the robustness of phase space conduits of… Expand

#### 15 Citations

Transition criteria and phase space structures in a three degree of freedom system with dissipation

- Physics, Mathematics
- Journal of Physics A: Mathematical and Theoretical
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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 events plays an… Expand

Geometry of escape and transition dynamics in the presence of dissipative and gyroscopic forces in two degree of freedom systems

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The geometry of escape across a saddle in some widely known physical systems with two degrees of freedom is summarized and the criteria of escape is established providing both a methodology and results under the conceptual framework known as tube dynamics. Expand

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- Medicine, Physics
- Physical chemistry chemical physics : PCCP
- 2020

The hierarchy of the reactive islands as indicated in the recent work by Patra and Keshavamurthy is shown to be related to the temporal features in committor probabilities and the use of the Lagrangian descriptor in the high-dimensional phase space of the system-bath model is discussed. Expand

On experimentally locating saddle-points on a potential energy surface from observed dynamics

- Computer Science
- Mechanical Systems and Signal Processing
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The experimental results suggest that this method can effectively locate the saddle equilibria in a system, and the robustness of the approach is assessed relative to the effect of noise, size of the local neighborhood, etc., in addition to providing information on the local dynamics. Expand

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- Materials Science
- 2020

This paper describes a primarily experimental study in which a nonlinear structural component (a slender, mechanically buckled panel) is subject to probing. That is, equilibrium configurations are… Expand

Finding normally hyperbolic invariant manifolds in two and three degrees of freedom with Hénon-Heiles-type potential.

- Physics, Medicine
- Physical review. E
- 2019

This article presents a method based on a Lagrangian descriptor for revealing the high-dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 saddle, including a normally hyperbolic invariant manifold and its stable and unstable manifolds. Expand

Differential Correction and Arc-Length Continuation Applied to Boundary Value Problems: Examples Based on Snap-Through of Circular Arches and Spherical Shell

- Computer Science
- 2020

The results obtained by the proposed algorithm and COCO agree well with each other, suggesting the validity and robustness of differential correction for boundary-value problems. Expand

Probing the Force Field to Identify Potential Energy

- Physics
- Journal of Applied Mechanics
- 2019

A small ball resting on a curve in a gravitational field offers a simple and compelling example of potential energy. The force required to move the ball, or to maintain it in a given position on a… Expand

Stabilizing higher-order equilibria of post-buckled beams using piezoelectric actuation

- Materials Science
- European Journal of Mechanics - A/Solids
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Abstract The higher-order static equilibria of post-buckled structures are nominally unstable. Recently it has been shown that by actuating two piezoelectric patches bonded to a post-buckled beam,… Expand

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