Static interface profiles for contact lines on an elastic membrane with the Willmore energy.

We consider a fluid interface in contact with an elastic membrane and study the static profiles of the interface and the membrane. Equilibrium conditions are derived by minimizing the total energy of the system with volume constraints. The total energy consists of surface energies and the Willmore energy; the latter penalizes the bending of the membrane.

Liquid-vapor transition on patterned solid surfaces in a shear flow.

Liquids on a solid surface patterned with microstructures can exhibit the Cassie-Baxter (Cassie) state and the wetted Wenzel state. The transitions between the two states and the effects of surface topography, surface chemistry as well as the geometry of the microstructures on the transitions have been extensively studied in earlier work. However, most of these work focused on the study of the free energy landscape and the energy barriers.

Numerical study of the effects of surface topography and chemistry on the wetting transition using the string method.

Droplets on a solid surface patterned with microstructures can exhibit the composite Cassie-Baxter (CB) state or the wetted Wenzel state. The stability of the CB state is determined by the energy barrier separating it from the wetted state. In this work, we study the CB to Wenzel transition using the string method [E et al.

Numerical study of vapor condensation on patterned hydrophobic surfaces using the string method.

Vapor condensation on solid surfaces plays a crucial role across a wide range of industrial applications. Recent advances of nanotechnology have made possible the manipulation of the condensation process through the control of surface structures. In this work, we study vapor condensation on hydrophobic surfaces patterned with microscale pillars.

Wetting transition on patterned surfaces: transition states and energy barriers.

We study the wetting transition on microstructured hydrophobic surfaces. We use the string method [J. Chem.

A climbing string method for saddle point search.

The string method originally proposed for the computation of minimum energy paths (MEPs) is modified to find saddle points around a given minimum on a potential energy landscape using the location of this minimum as only input. In the modified method the string is evolved by gradient flow in path space, with one of its end points fixed at the minimum and the other end point (the climbing image) evolving towards a saddle point according to a modified potential force in which the component of the potential force in the tangent direction of the string is reversed. The use of a string allows us to monitor the evolution of the climbing image and prevent its escape from the basin of attraction of the minimum.

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

We apply a numerical minimum action method derived from the Wentzell-Freidlin theory of large deviations to the Kardar-Parisi-Zhang equation for the height profile of a growing interface. In one dimension we find that the transition pathway between different height configurations is determined by the nucleation and subsequent propagation of facets or steps, corresponding to moving domain walls or growth modes in the underlying noise-driven Burgers equation. This transition scenario is in accordance with recent analytical studies of the one-dimensional Kardar-Parisi-Zhang equation in the asymptotic weak noise limit.

Application of the string method to the study of critical nuclei in capillary condensation.

We adopt a continuum description for liquid-vapor phase transition in the framework of mean-field theory and use the string method to numerically investigate the critical nuclei for capillary condensation in a slit pore. This numerical approach allows us to determine the critical nuclei corresponding to saddle points of the grand potential function in which the chemical potential is given in the beginning. The string method locates the minimal energy path (MEP), which is the most probable transition pathway connecting two metastable/stable states in configuration space.

Adaptive minimum action method for the study of rare events.

An adaptive minimum action method is proposed for computing the most probable transition paths between stable equilibria in metastable systems that do not necessarily have an underlying energy function, by minimizing the action functional associated with such transition paths. This new algorithm uses the moving mesh strategy to adaptively adjust the grid points over the time interval of transition. Numerical examples are presented to demonstrate the efficiency of the adaptive minimum action method.

Simplified and improved string method for computing the minimum energy paths in barrier-crossing events.

We present a simplified and improved version of the string method, originally proposed by E et al. [Phys. Rev.

Finite temperature string method for the study of rare events.

A method is presented for the study of rare events such as conformational changes arising in activated processes whose reaction coordinate is not known beforehand and for which the assumptions of transition state theory are invalid. The method samples the energy landscape adaptively and determines the isoprobability surfaces for the transition: by definition the trajectories initiated anywhere on one of these surfaces has equal probability to reach first one metastable set rather than the other. Upon weighting these surfaces by the equilibrium probability distribution, one obtains an effective transition pathway, i.

Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide.

The finite-temperature string method proposed by E, et al. [W. E, W.

Numerical simulations of self-focusing of ultrafast laser pulses.

Simulation of nonlinear propagation of intense ultrafast laser pulses is a hard problem, because of the steep spatial gradients and the temporal shocks that form during the propagation. In this study we adapt the iterative grid distribution method of Ren and Wang [J. Comput.