"Dr. John and the SVD"
Dr. John and the SVD: The singular value decomposition (SVD) is a powerful linear algebra algorithm that can be used to compress the information needed to represent an image. The original image is treated as a matrix in color space and is decomposed into a ranked ordering of its singular vectors. The Dr. John images (ordered from left to right and top to bottom) contain the first 5, 10, 20, 40, or 80 singular values, and the original image. The image with 80 singular values requires about 1% of the storage of the original image.
This is a picture of a long filament swimming in a viscoelastic fluid by undulating its body (the thick black line). The copper tones in the background show the amount of rotation in the fluid caused by the swimming motion at one moment in time. The thin black squiggles show the motion of marked fluid particles over several undulations. Each particle moves in a helix that is distorted depending on where it is in relation to the body.
Landscape of the energy surface in an optimization problem arising from an attempt to approximate 9 data points by a linear function in the p = 0.1 norm.
"Rotation of a Slender Fiber in Shear Flow"
The dynamics of slender filaments immersed in a fluid play a significant role in many physical and biological systems. Motivated by the wish to understand the motions of diatom chains in the ocean, we study the fundamental fluid dynamics of a flexible fiber suspended in shear flow. The picture shows different configurations of the fiber undergoing "S" turns. The initial position is displayed in black.
This is the CCS collaboration with the University of Maine.
"Interactions of Two Helical Rings"
In an effort to understand the function of the transverse flagellum in dinoflagellate motility, we have simulated a simple fluid mechanical system of waving cylindrical rings moving in a viscous fluid. We conclude that the traveling wave imposed around the ring induces both rotational and translational motion. In this picture, the two rings are approaching each other (upper frame) and rotate in the opposite directions (lower frame).
This is the CCS collaboration with the University of North Carolina.
"CCS Random Walk"
The position of each point changes randomly in an iterative process. Each point can move in any direction but the distance it moves from its previous position varies according to the distance from the point to the CCS letters. The closer to the CCS, the smaller the distance that a point moves.
The graph of a smooth function on a distorted grid.
"Percolation in 2D"
Activity of 1000x1000 2D lattice folded into torus at some time, as a consequence of vertices following the states of their neighbors more likely.
"Sound in a Room"
In a room with explosions microphones capture the traveling sound waves. The microphones are placed along the walls of the room at regular intervals. From the sound recordings an acoustic image of the room is reconstructed. The top row shows the arriving sound waves for an increasing number of microphones. The bottom row shows the image of the room generated from the data.
"Turn for the Worst"
Each circle is a realization of the spread of an epidemic, or the proportion of people infected, for a particular transmission rate. It starts with one infected person (the slender part of the shape) and spreads as time passes (the open end of the shape). The inner circle is formed by using a very low transmission rate and the outer circle is formed by using a high transmission rate. Each line on the grid from bottom to top represents a step in time.
"Salinity in the Louisiana Costal Area"
The water flow and the salinity in the Louisiana costal area were computed using the CFD tool, FVCOM2.7 (http://fvcom.smast.umassd.edu). The Mississippi river (fresh water) is shown only near the estuary.
This study is a part of the Geo-Cloud Research project (http://geo-cloud.net) in collaboration with DQSI, LLC and Dr. Georgiou (UNO).
"Impact of a Droplet"
An impact of liquid drop onto a liquid surface was computed with the moving-particle semi-implicit method (MPS). The NVIDIA Tesla GPU was used.
"Lung Parenchyma and Airway Deformation"
The deformation of lung alveoli near a reopening bronchiole was computed. This is a sliced image of the 3D alveoli-airway model. The pressure in the left half of the tube is higher than in the right, simulating that an air bubble pushes through a liquid occluding airway.
Newton's Method is iterative procedure which produces a sequence of points that move towards the places where a function is zero. By coloring and shading points according to which root, and how quickly, this procedure converges, fractal images are produced. This image is the result of randomly perturbing Newton's Method to produce a low-resolution version of such a fractal.
"Mysterious Creatures Masquerading as a Breathing Aid"
Surfactant concentration gradients generated in the surrounding occluding fluid as a semi-infinite finger of air oscillates and progresses in a model of airway reopening.
Center for Computational Science, Stanley Thomas Hall 402, New Orleans, LA 70118 email@example.com