1. Methodology
(Introduction to the Methodology)
1.1.
Numerical Methods
SE-FIT® is a significant enhancement to the underlying Surface Evolver computation engine, providing
both increased functionality using new algorithms and enhanced usability through a graphical user
interface (GUI). In this study, the recently implemented Parameter Sweep Function (PSF) is used
extensively to probe a large parameter space that includes geometric half angle (), gravitational
component directions (, ), contact angle (), and Bond number (Bo). The PSF allows the user to define
incremental parameter changes, as well as define ‘control’ parameters that are automatically varied until a
user-defined spatial trigger is met. In effect, it enables ‘intelligent’ computation of equilibrium surfaces
for parameter values across certain ranges in a batch-like process\cite{ZIMMERLI:ORLANDO2011}.
In our study, the Bond number is the control parameter which is varied until a critically stable surface is
found. In searching for the critical value, PSF employs a bi-sectioning method to identify a critical value
for the surface with a coarse mesh. It then computes a stable equilibrium surface with a fine mesh at a
value of the parameter which is lower than the identified value. Afterwards, equilibrium surfaces are
computed for the parameter value increased properly. The increment of the parameter value is kept small
enough so that no significant disturbance to the surface is introduced.
An unstable surface is detected when it moves past user-defined x, y, or z bounding planes. SE-FIT®
iterates on the control variable using a bisection method, efficiently seeking out the critical values, and in
this study, the critical Bond number (Bocr). Though the PSF can significantly increase productivity, it is
still under development and requires script tuning to handle particularly difficult cases. Even so, scripts in
SE-FIT® have been developed to determine the convergence of the computation, to investigate the
eigenvalues of the Hessian matrix, and to perform necessary operations to identify the stability of the
surfaces. Because the scripts are open to the user, they can be modified to handle special cases where
needed. Finally, a file layer mechanism\cite{YKC:ORLANDO2011} enables the handling of exceptions,
such as hanging of the computation engine, which is not native to the underlying Surface Evolver.
Overall, the combination of SE-FIT® and accompanying scripts has effectively minimized userinteraction time while significantly increasing productivity. Computations that previously took weeks to
complete with attentive user interaction can now be completed in days or hours with user interaction
reduced to minutes.
1.2.
Numerical Observations
(Stuff that was observed, hence the title)
Original Draft Content
SE-FIT is created with an intention to substantially extend the application of the Surface Evolver and to
streamline the computational processes. For example, Parametric Sweep Function (PSF) is created for
such purposes. It enables the computation of equilibrium surfaces for parameters values across certain
ranges in a batch process\cite{ZIMMERLI:ORLANDO2011}. When studying interfacial instability, it
also enables the determination of the critical value of a relevant parameter across a certain range in an
automated way. In Surface Evolver it is possible to set up batch process but the functionality is limited
and Evolver could stall due to any error or hanging of the computation. In SE-FIT, scripts have been
developed to determine the convergence of the computation, to investigate the eigenvalues of the Hessian
matrix, and to perform necessary operations to identify the stability of the surfaces. The file layer
mechanism\cite{YKC:ORLANDO2011} enables the handling of exceptions such as the hanging of the
computation engine. As a result, the necessity of human computer interaction is reduced to a minimum.
In searching for the critical value of a parameter, PSF employs a bi-sectioning method to identify a
critical value for the surface with a coarse mesh. It then computes a stable equilibrium surface with a fine
mesh at a value of the parameter which is lower than the identified value. Afterwards, equilibrium
surfaces are computed for the parameter value increased properly. The increment of the parameter value
is kept small enough so that no significant disturbance to the surface is introduced.
With PSF, computation time for a typical data line that consists of 36 data points is reduced from weeks
to days or even hours. Furthermore, discovery could be made due to the availability of large amount of
data\cite{YKC:CEBD2011}.