Applied Mathematics

2007 Group

Summer Research Opportunities at UCLA

Overview

This is an opportunity to participate in an 8-10 week summer program in the Applied Mathematics group at UCLA. Students will have the opportunity to join an active research group with projects in image processing,  control theory,  fluid dynamics. and the interaction of mathematics and sociology. The successful applicant will work with faculty members from UCLA and Harvey Mudd College, postdoctoral fellows, graduate students and other undergraduates.  The project was founded by HMC mathematics professor Andrew Bernoff, who continues to be involved in all aspects of the program.   HMC mathematics professor Rachel Levy will be the on-campus faculty advisor again this summer.  Pictured above is the group from Summer 2007 (left to right):  Andrew Bernoff, Parousia Rockstroh, Stephen Rosenthal, Chris Fox, Trevor Ashley, Kenn Tevin and Rachel Levy.

Students will start around June 18th and finish mid-August. Exact dates will be worked out with the faculty advisor, Rachel Levy. Students will generally be housed in the vicinity of UCLA.

Stipends and Support

Students will receive a stipend of roughly $4,000 for the summer and roughly $1,000 to cover housing and living expenses.

Application Process

Applicants should submit to Professor Levy (levy @ hmc . edu) the following:
Applications received by March 1st will be given preference.

Projects

The projects for this summer are currently being developed.  Examples of likely projects for this year are described below.  Projects from previous years are described here:
Project Descriptions 2005-2007




Spatio-temporal Event Pattern Recognition


In this project, a team of students will model a disaster scenario and use it to generate data.  Then they will develop algorithms to unravel the data and
propose response strategies.  The response will have to include some specific strategies such as
The final scenario will include internet attacks and employ fixed sensors that wake and sleep.

LA traffic

Overhead of heavy traffic on freeway( Los Angeles, CA)
gwp101023 Glow Images Royalty Free Photograph



Hyperspectral Imaging


These pictures illustrate how it is possible to detect a plastic plant among real plants using HySpex data. Top: Image shown with "normal" colours (RGB). Middle: Using the IR information which is displayed in red (red channel chosen above chlorophyll red edge at ~700nm). Bottom: Classification image where the real plants are green, the fake plant is red and the pottery is blue. As can be seen, a plastic plant can easily be detected among real plants using a HySpex camera even though the plastic plants visually look identical to the human eye.

plants1

plants2

plants3

http://www.neo.no/products/hyperspectral.html


Mudslides, Slurry Flows and Particle Tracking


Slurry flows are models of mudslides; UCLA has on ongoing numerical, experimental and theoretical study of slurry flows.  Glass beads of a uniform size are mixed into a less dense viscous fluid. The resulting slurry is poured into a reservoir at the top of an inclined plane. A controlled amount of the slurry is allowed to flow through a gate down the incline. At low inclination angles and concentrations, the particles tend to settle out of the mixture and stick to the surface of the incline, leaving a clear fluid to flow down the slope. At intermediate angles and concentrations, a well-mixed slurry flows down the slope, producing the characteristic fingering pattern seen in visous films. At high inclination angles and particle concentrations, the beads tend to collect at the front of the film; their presence drastically changes the dynamics of the contact line, supressing fingering and producing a pronounced ridge.

Slurry

The figure above shows a typical experimental run with 1000 cstoke silicone oil with 54% concentration of glass beads.
Notice the high degree of fingering in the fluid flow.
The position of the front of the fluid can be approximated as the average of the actual fluid front.






 Rachel Levy* Andrew Bernoff * Department of Mathematics * Harvey Mudd College
Page Maintained by Rachel Levy
Last modified:  February 3rd,  2008