the material solidification of static and dynamic multiphase systems. The
main focus is on the solidification of water droplets, which may undergo
normal or supercooled freezing. We model the different regimes of freezing
such as supercooling, nucleation, recalescence, isothermal freezing and
solid cooling accordingly to capture physical dynamics during impact and
solidification of water droplets onto solid surfaces. The numerical
simulations are validated by comparison to analytical results and
experimental observations. The present simulations demonstrate the ability
of the method to capture sharp solidification front, handle contact line
dynamics, and the simultaneous impact, merging and freezing of a drop.
Parameter studies have been conducted, which show the influence of the
Stefan number on the regularity of the shape of frozen droplets. Also, it
is shown that impacting droplets with different sizes create ice shapes
which are uniform near the impact point and become dissimilar away from it.
In addition, surface wettability determines whether droplets freeze upon
impact or bounce away.
imaging techniques. The goal of image registration is to find
geometrical correspondences between two or more images. Image
registration is commonly phrased as a variational problem that is known
to be ill-posed and thus regularization is commonly used to ensure
existence of solutions and/or introduce prior knowledge about the
application in mind. Many relevant applications, e.g., in biomedical
imaging, require that plausible transformations are diffeomorphic, i.e.,
smooth mappings with a smooth inverse.
This talk will present and compare two modeling strategies and numerical
approaches to diffeomorphic image registration. First, we will discuss
regularization approaches based on nonlinear elasticity. Second, we will
phrase image registration as an optimal control problem involving
hyperbolic PDEs which is similar to the popular framework of Large
Deformation Diffeomorphic Metric Mapping (LDDMM). Finally, we will
consider computational aspects and present numerical results for
real-life medical imaging problems.
optimization problem of identifying the state of a stochastic dynamical
system based on noisy observations of the system. Well known numerical
simulation methods include unscented Kalman filters and particle
filters. In this talk, we consider a class of efficient numerical
methods based on forward backward stochastic differential equations.
The backward SDEs for nonlinear filtering problems are similar to the
Fokker-Planck equations for SDEs. We will describe the process of
deriving such backward SDEs as well as high order numerical algorithms
to solve them, which in turn solve nonlinear filtering problems.
pathways of communication and sociocultural influence. But while language
change has long been a topic of study in sociolinguistics, traditional
linguistic research methods rely on circumstantial evidence, estimating the
direction of change from differences between older and younger speakers. In
this research, we use a data set of several million Twitter users to track
language changes in progress. First, we show that language change can be
viewed as a form of social influence: we observe complex contagion for
``netspeak'' abbreviations (e.g., lol) and phonetic spellings, but not for
older dialect markers from spoken language. Next, we test whether specific
types of social network connections are more influential than others, using
a parametric Hawkes process model. We find that tie strength plays an
important role: densely embedded social ties are significantly better
conduits of linguistic influence. Geographic locality appears to play a
more limited role: we find relatively little evidence to support the
hypothesis that individuals are more influenced by geographically local
social ties, even in the usage of geographical dialect markers.
projects that had simulation and painting involved. One is iPad-based ultra-low-cost real
time simulation of old photography process to compute effects that modern day users may
find interesting. The other is more full-blown fluid simulation for painting using
highest-end GPU. Even with massive processing power of GPU, real time high fidelity
painting simulation is hard since computation budget is limited. Basically we should deal
with large errors. It may sound odd if someone says that very low-accuracy simulation is
interesting - but this is very true. In particular, we tried to pull most pressure effect
out from about 10 Jacobi iterations that we could afford. I would like to share my
experience on improving fixed number of fixed point iterations.