The escape problem in a classical field theory with two coupled fields

Gong, Lan; Stein, D. L.

doi:10.1088/1751-8113/43/40/405004

Cited by 3 publications

(12 citation statements)

References 74 publications

(130 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Solving for the transition rate therefore requires knowledge of the saddle state. The model developed in [15] allows for an analytical solution to the saddle state in the case of certain special potentials. To solve the nanowire stability problem, however, we need to find the transition path and lifetime in more general cases.…”

Section: Overview Of the Nanowire Stability Problemmentioning

confidence: 99%

See 1 more Smart Citation

Lifetimes of metal nanowires with broken axial symmetry

et al. 2015

Self Cite

View full text Add to dashboard Cite

We present a theoretical approach for understanding the stability of simple metal nanowires, in particular monovalent metals such as the alkalis and noble metals. Their cross sections are of order one nanometer so that small perturbations from external (usually thermal) noise can cause large geometrical deformations. The nanowire lifetime is defined as the time required for making a transition into a state with a different cross-sectional geometry. This can be a simple overall change in radius, or a change in the cross section shape, or both. We develop a stochastic field theoretical model to describe this noise-induced transition process, in which the initial and final states correspond to locally stable states on a potential surface derived by solving the Schrödinger equation for the electronic structure of the nanowire numerically. The numerical string method is implemented to determine the optimal transition path governing the lifetime. Using these results, we tabulate the lifetimes of sodium and gold nanowires for several different initial geometries.

show abstract

Section: Overview Of the Nanowire Stability Problemmentioning

confidence: 99%

“…As discussed in [15] and [16], the time evolution of the fields under noise can be described by the coupled Langevin equations˙…”

Section: The Dynamical Systemmentioning

confidence: 99%

Lifetimes of metal nanowires with broken axial symmetry

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…Computation of exit behavior requires knowledge of the transition path(s), in particular behavior near the local minimum and the saddle. In our model, both are found as solutions of two coupled nonlinear differential equations [1]. A powerful numerical technique constructed explicitly for this type of problem is the "string method" of E, Ren, and Vanden-Eijnden [19,20].…”

Section: Calculation Of the Minimum Energy Pathmentioning

confidence: 99%

“…In a previous paper [1] (hereafter GS), the authors introduced and solved a system of two coupled nonlinear stochastic partial differential equations. Such equations are useful for modelling noise-induced activation processes of spatially varying systems with multiple basins of attraction.…”

Section: Introductionmentioning

confidence: 99%

“…where sn(.|m)and dn(.|m) are the Jacobi elliptic functions with parameter m, whose periods are 4K(m) and 2K(m) respectively, with K(m) the complete elliptic integral of the first kind [17]. The parameter m ∈ [0, 1] is related to interval length L through the Neumann boundary conditions, with m → 0 + corresponding to L → L + c , where L c is the critical length, and m → 1 corresponding to L → ∞ [1,11,12]. When κ 1 = κ 2 = 1,…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Noisy classical field theories with two coupled fields: Dependence of escape rates on relative field stiffness

Gong

Stein

2011

Phys. Rev. E

Self Cite

View full text Add to dashboard Cite

Exit times for stochastic Ginzburg-Landau classical field theories with two or more coupled classical fields depend on the interval length on which the fields are defined, the potential in which the fields deterministically evolve, and the relative stiffness of the fields themselves. The latter is of particular importance in that physical applications will generally require different relative stiffnesses, but the effect of varying field stiffnesses has not heretofore been studied. In this paper, we explore the complete phase diagram of escape times as they depend on the various problem parameters. In addition to finding a transition in escape rates as the relative stiffness varies, we also observe a critical slowing down of the string method algorithm as criticality is approached.

show abstract

A Bifurcation Monte Carlo Scheme for Rare Event Simulation

Liu¹,

Goodman²

2016

Preprint

View full text Add to dashboard Cite

The bifurcation method is a way to do rare event sampling -to estimate the probability of events that are too rare to be found by direct simulation. We describe the bifurcation method and use it to estimate the transition rate of a double well potential problem. We show that the associated constrained path sampling problem can be addressed by a combination of Crooks-Chandler sampling and parallel tempering and marginalization.

show abstract

The escape problem in a classical field theory with two coupled fields

Cited by 3 publications

References 74 publications

Lifetimes of metal nanowires with broken axial symmetry

Lifetimes of metal nanowires with broken axial symmetry

Noisy classical field theories with two coupled fields: Dependence of escape rates on relative field stiffness

A Bifurcation Monte Carlo Scheme for Rare Event Simulation

Contact Info

Product

Resources

About