Metastable transitions in inertial Langevin systems: What can be different from the overdamped case?

@article{Souza2018MetastableTI,
  title={Metastable transitions in inertial Langevin systems: What can be different from the overdamped case?},
  author={Andr'e M. C. Souza and Molei Tao},
  journal={European Journal of Applied Mathematics},
  year={2018},
  volume={30},
  pages={830 - 852}
}
Metastable transitions in Langevin dynamics can exhibit rich behaviours that are markedly different from its overdamped limit. In addition to local alterations of the transition path geometry, more fundamental global changes may exist. For instance, when the dissipation is weak, heteroclinic connections that exist in the overdamped limit do not necessarily have a counterpart in the Langevin system, potentially leading to different transition rates. Furthermore, when the friction coefficient… 
Parametric resonance for enhancing the rate of metastable transition
Abstract. This work is devoted to quantifying how periodic perturbation can change the rate of metastable transition in stochastic mechanical systems with weak noises. A closed-form explicit
Accurate and Efficient Simulations of Mechanical Systems with Discontinuous Potentials
This article considers Newtonian mechanical systems with potential functions admitting jump discontinuities. The focus is on an accurate and efficient numerical approximation of their solutions,
Accurate and Efficient Simulations of Hamiltonian Mechanical Systems with Discontinuous Potentials
  • Molei Tao, Shi Jin
  • Mathematics, Computer Science
    Journal of Computational Physics
  • 2021
TLDR
This article considers Hamiltonian mechanical systems with potential functions admitting jump discontinuities, and recommends a first-order symplectic integrator for general problems, and an adaptive time-stepping version of the previous high-order method.
Metastable nonlinear vibrations: Third chaos of bistable asymmetric composite laminated square shallow shell under foundation excitation
Abstract The occurrence conditions of the metastable chaotic vibrations are firstly studied in the bistable asymmetric composite laminated square shallow shell under the foundation excitation. The

References

SHOWING 1-10 OF 58 REFERENCES
Generalisation of the Eyring–Kramers Transition Rate Formula to Irreversible Diffusion Processes
In the small noise regime, the average transition time between metastable states of a reversible diffusion process is described at the logarithmic scale by Arrhenius’ law. The Eyring–Kramers formula
A Primer on Noise-Induced Transitions in Applied Dynamical Systems
TLDR
An overview of the theory underlying the dynamics of rare events for stochastic models along with some example applications is provided.
Hyperbolic periodic orbits in nongradient systems and small-noise-induced metastable transitions
Abstract Small noise can induce rare transitions between metastable states, which can be characterized by Maximum Likelihood Paths (MLPs). Nongradient systems contrast gradient systems in that MLP
Long Term Effects of Small Random Perturbations on Dynamical Systems: Theoretical and Computational Tools
TLDR
The theoretical and computational aspects behind differential equations with multiplicative noise, Markov jump processes, and systems with fast and slow degrees of freedom are reviewed, and an algorithm that simplifies the geometric minimum action method to minimize the action in the space of arc-length parametrized curves is proposed.
The geometric minimum action method: A least action principle on the space of curves
Freidlin-Wentzell theory of large deviations for the description of the effect of small random perturbations on dynamical systems is exploited as a numerical tool. Specifically, a numerical algorithm
The Smoluchowski-Kramers Limit of Stochastic Differential Equations with Arbitrary State-Dependent Friction
We study a class of systems of stochastic differential equations describing diffusive phenomena. The Smoluchowski-Kramers approximation is used to describe their dynamics in the small mass limit. Our
Minimum Action Method for the Study of Rare Events
The least-action principle from the Wentzell-Freidlin theory of large deviations is exploited as a numerical tool for finding the optimal dynamical paths in spatially extended systems driven by a
Pathways of maximum likelihood for rare events in nonequilibrium systems: application to nucleation in the presence of shear.
TLDR
A general purpose algorithm is applied to predict the pathway of transition in a bistable stochastic reaction-diffusion equation in the presence of a shear flow, and to analyze how the shear intensity influences the mechanism and rate of the transition.
The instanton method and its numerical implementation in fluid mechanics
A precise characterization of structures occurring in turbulent fluid flows at high Reynolds numbers is one of the last open problems of classical physics. In this review we discuss recent
Self-organization in systems of self-propelled particles.
TLDR
A continuum version of the discrete model consisting of self-propelled particles that obey simple interaction rules is developed and it is demonstrated that the agreement between the discrete and the continuum model is excellent.
...
1
2
3
4
5
...