Pizza Lunch Meeting

Leighton Zhao, Wayzata High School, Minnesota
Simons Fellow working with Phil Allen

Normal Mode Analysis of a 7 Particle System

Stony Brook Professor Peter Koch collected data on a two-dimensional "minicrystal" of seven steel balls. The balls repel each other and are confined inside a circular steel wall because they are magnetized by a uniform applied magnetic field. Koch drove the system with a jostling in one direction and recorded the positions of the seven balls over time to create trajectories.  For my Simons summer research project, I am working with my mentor Philip Allen to analyze these trajectories based on the normal modes of the system.  I first determined a normal mode basis for the system by taking advantage of its symmetry properties and then projected the velocity vectors onto this basis.  I next fit Gaussian distribution functions onto the resulting velocity distributions and applied autocorrelation functions and discrete Fourier transforms.  My results show that the system can be modeled as a set of forced damped oscillators.

Taylor Esformes, Stony Brook University
Masters student working with Rich Migliaccio

Hyperspectral Imaging: An Overview

Hyperspectral Imaging (HSI) is a highly versatile application of imaging spectroscopy used to take very detailed, spatially resolved images of a wide variety of targets. Each pixel detected by the device contains the reflected spectrum of that section of the object imaged, allowing researchers to get a complex chemical picture of their subjects quickly. HSI devices can be mounted on aircraft, laboratory surfaces, telescopes or portable mounts, and can be used to identify the chemical makeup and often some of the physical structure of materials by their spectra. The processing of hyperspectral data requires the use of new data structures, as well as mathematical techniques for dealing with high volumes of multi-dimensional data. The challenge of correlating spectral data to specific materials and gauging the level of concentration and spectral mixing is an active and widely-impacting field of mathematical, physics and computer science research. For this presentation, several different methods of taking HSI data are discussed, as well as some of the common methods of categorizing and processing HSI data. Applications of HSI technology are listed as well.

Marty Cohen, LTC Mentor

Marty gave a brief overview and demonstration of a BEC imaging project. Currently, images made with the coherent laser beam contain extra interference fringes due to dust etc. on the glass surrounding the vacuum cell. He proposed using an engineered diffuser in combination with an acousto-optic modulator (to hopefully also eliminate speckle) to lower the spatial coherence of the laser beam used to image the BEC. After going through the diffuser, the beam would need to be coupled into a multimode fiber.