We present a new and efficient method for computing the transition pathways, free energy barriers, and transition rates in complex systems with relatively smooth energy landscapes. The method proceeds by evolving strings, i.e. smooth curves with intrinsic parametrization whose dynamics takes them to the most probable transition path between two metastable regions in the configuration space. Free energy barriers and transition rates can then be determined by standard umbrella sampling technique around the string. Applications to Lennard-Jones cluster rearrangement and thermally induced switching of a magnetic film are presented.PACS numbers: 82.20.Wt The dynamics of complex systems are often driven by rare but important events (for a review see e.g. [1]). Wellknown examples include nucleation events during phase transition, conformational changes in macromolecules, and chemical reactions. The long time scale associated with these rare events is a consequence of the disparity between the effective thermal energy and typical energy barrier of the systems. The dynamics proceeds by long waiting periods around metastable states followed by sudden jumps from one state to another.Sophisticated numerical techniques have been developed to find the transition pathways and transition rates between metastable states in complex systems for which the mechanism of transition is not known beforehand [2,3,4]. With the exception of the transition path sampling technique [3], most of these methods seem to require that the energy landscape be relatively smooth. One typical example of such techniques is the nudged elastic band (NEB) method [4]. NEB connects the initial and the final states by a chain of states. The states move in a force field which is the combination of the normal component of the potential force and the tangential component of the spring force connecting the states. The spring force helps to evenly space the states along the chain.In this paper we propose an alternative approach for computing transition pathways, free energy barriers, and transition rates. We sample the configuration space with strings, i.e. smooth curves with intrinsic parametrization such as arclength, or energy weighted arclength which connect two metastable states (or regions), A and B. The string satisfies a differential equation which by construction guarantees that it evolves to the most probable transition pathway connecting A and B. One can then perform an umbrella sampling of the equilibrium distribution of the system in the hyperplanes normal to the string and thereby determine free energy barriers and transition rates.Consider the example of a system modeled bywhere γ is the friction coefficient, ξ(t) is a white-noise with ξ j (t)ξ k (0) = 2γk B T δ jk δ(t). The metastable states are localized around the minima of the potential V (q). Assuming V (q) has at least two minima, A and B, we look for the minimal energy paths (MEPs) connecting these states. By definition, a MEP is a smooth curve ϕ ⋆ connecting A and B which satisfieswhere ...

We present a simplified and improved version of the string method, originally proposed by E et al. [Phys. Rev. B 66, 052301 (2002)] for identifying the minimum energy paths in barrier-crossing events. In this new version, the step of projecting the potential force to the direction normal to the string is eliminated and the full potential force is used in the evolution of the string. This not only simplifies the numerical procedure, but also makes the method more stable and accurate. We discuss the algorithmic details of the improved string method, analyze its stability, accuracy and efficiency, and illustrate it via numerical examples. We also show how the string method can be combined with the climbing image technique for the accurate calculation of saddle points and we present another algorithm for the accurate calculation of the unstable directions at the saddle points.

The physical processes near a moving contact line are investigated systematically using molecular dynamics and continuum mechanics. Constitutive relations for the friction force in the contact line region, the fluid-fluid interfacial force and the stresses in the fluid-solid interfacial region are studied. Verification of force balance demonstrates the importance of the normal stress difference across the contact line region. Effective boundary conditions are derived using force balance. The effective continuum model is solved numerically and the behavior of the apparent contact angle and the wall contact angle is studied. It is found that the fluid-fluid interface near the wall exhibits a universal behavior. The onset of the nonlinear response for the contact line motion is studied within the framework of Blake's molecular kinetic theory.