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Isotopic Effect in Double Proton Transfer Process of Porphycene Investigated by Enhanced QM/MM Method

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Minimum action method for the Kardar-Parisi-Zhang equation.

Hans C Fogedby¹, Weiqing Ren

¹Department of Physics and Astronomy, University of Aarhus, Ny Munkegade, 8000 Aarhus C, Denmark. fogedby@phys.au.dk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2009

Summary

This summary is machine-generated.

We used a numerical method to study the Kardar-Parisi-Zhang equation. The study reveals that interface growth transitions are driven by step nucleation and propagation, consistent with theoretical predictions.

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Area of Science:

Physics
Statistical Mechanics
Nonlinear Dynamics

Background:

The Kardar-Parisi-Zhang (KPZ) equation models the dynamics of interfaces in various physical systems.
Understanding large-scale transitions in KPZ models is crucial for predicting system behavior.
Previous analytical studies explored the weak noise limit of the 1D KPZ equation.

Purpose of the Study:

To investigate the transition pathways between different height configurations in the KPZ equation.
To apply a numerical minimum action method based on Wentzell-Freidlin theory.
To analyze the role of facets and steps in interface growth dynamics.

Main Methods:

Numerical minimum action method derived from Wentzell-Freidlin theory.
Application to the Kardar-Parisi-Zhang equation for interface height profiles.
Analysis of one-dimensional and brief discussion of two-dimensional cases.

Main Results:

In 1D, transition pathways are governed by the nucleation and propagation of facets/steps.
This mechanism corresponds to domain wall movement in the underlying noise-driven Burgers equation.
Findings align with analytical results in the asymptotic weak noise limit.

Conclusions:

The study elucidates the mechanism of large-scale transitions in the 1D KPZ equation.
Facet and step dynamics are identified as key drivers of interface reconfiguration.
The numerical approach provides insights complementary to analytical methods.