We present a novel method to enrich standard rigid-body impact models
with a spatially varying coefficient of restitution map, or Bounce Map. Even
state-of-the art methods in computer graphics assume that for a single
rigid body, post- and pre-impact dynamics are related with a single global,
constant, namely the coefficient of restitution. We first demonstrate that this
assumption is highly inaccurate, even for simple objects. We then present a
technique to efficiently and automatically generate a function which maps
locations on the object’s surface along with impact normals, to a scalar
coefficient of restitution value. Furthermore, we propose a method for twobody
restitution analysis, and, based on numerical experiments, estimate a
practical model for combining one-body Bounce Map values to approximate
the two-body coefficient of restitution. We show that our method not only
improves accuracy, but also enables visually richer rigid-body simulations.
The phenomenon regarding how cancer cell moves against and invades nearby tissue is an interesting yet difficult subject to study due to its multiphysics nature. In this work, we proposed a simplified yet elegant theoretical framework in an attempt to model the system. Physical assumptions were made to amount the modeling of cell locomotion to solving a classical elastostatic problem; during the process, cancer cells can secrete enzymes such as matrix metalloproteases to degrade the material. Therefore, in general the elastostatic problem happens on nonlinear, inhomogeneous substrate, which needs to be mathematically modeled. On the other hand, we hypothesized that multiple species of proteases can be secreted by the cell and they follow diffusion processes and can therefore react with the substrate at different rates. This is a two-way coupled system with cell invasion depth (or substrate deformation) depends on the results of both mechanical and chemical processes, whose outcome can be predicted in a very efficient way under the current framework. In particular, we first applied the regular perturbation method to give an analytical solution for the nonlinear elastostatic equation given a force profile assuming weak nonlinearity. Second, we designed and implemented a numerical, finite-difference based solver to model the diffusion-reaction system that can spatially distribute different species of proteases during the chemical process. This solver is then coupled to the elastostatic problem to close the loop. Several predictions based on this framework were given, such as the parametrized studies for invasion efficiency based on mechanical force distribution and colocalized enzyme distribution.
Effects of sea states on seafloor compliance studies
Jui-Hsien Wang, Wu-Cheng Chi, R. Nigel Edwards, and Eleanor C. Willoughby
Gas hydrates affect the bulk physical properties of marine sediments, in particular, elastic parameters. Shear modulus is an important parameter for estimating the distribution of hydrates in the marine sediments. However, S-wave information is difficult to recover without proper datasets. Seafloor compliance, the transfer function between pressure induced by surface gravity waves and the associated seafloor deformation, is one of few techniques to study shear modulus in the marine sediments. The coherence between recorded time series of displacement and pressure provides a measure of the quality of the calculated transfer function, the seafloor compliance. Thus, it is important to understand how to collect high coherence datasets. Here we conducted a 10-month pilot experiment using broadband seismic sensors and differential pressure gauges. We found that data collected in shallow water depth and during rough seas gave high coherence. This study is the first time long-term datasets have been employed to investigate seafloor compliance data quality and its dependence on sea state. These results will help designing future large-scale compliance experiments to study anomalously high shear moduli associated with the presence of gas hydrate or cold vents, or alternatively anomalously low shear moduli, associated with partial melt and magma chamber.
Real-time Aerodynamic Sound Synthesis for Slender Objects
Final project for CS5643: Physically Based Animation for Computer Graphics
In this project, I explored the problem of real-time, physics-based aerodynamic sound synthesis for slender objects. It is largely inspired by the paper by Dobashi et al. [Dobashi et al. 2003]. The aerodynamic sound when we swing a slender object, such as a stick, is originated from the complex interaction between the air flow and the stick. Sufficient spatial/temporal resolution was regarded to be essential to capture the physics and thus the characteristics of the sound generated. However, the required fluid simulation is too expensive to run at audio stepping rate. To avoid such computation, I first precomputed a comprehensive database that contains relevant sound textures evaluated from high-quality grid-based fluid simulation, and then at runtime, this database is fetched and textures are blended to effectively resynthesize the aerodynamic swinging sound. Next, to increase the interactivity of the project, I interfaced the sound system with Leap Motion sensor to give real-time motion capture data. The system is proven to be quite reliable and can run at real-time even on a low-end laptop, and create realistic swinging sound.