The two systems above may seem very different (one is a granular system made up of thousands of photo-elastic disks and the other is a school of several fish), but they are similar in very interesting ways. Our lab studies soft condensed matter systems which are composed of many small parts that exhibit observable large scale properties. How do local interactions influence global properties? How do these systems transition from disordered to ordered states? How do they respond to external conditions such as strain or stress?
Collective Animal Behavior: Visual Perturbations of Laboratory Schools: (Julia)
Collective animal behavior is observed across many scales and organisms. While different species have different environmental and social pressure, many similar structures are found across the animal kingdom. Clearly, these group behaviors are a strategy nature likes to use which helps individuals work together and respond to their environment in a rather general way. These structures emerge from from interactions between individuals. A common model for collective animal behavior involves zones of repulsion, orientation, and attraction. Individual animals seek to maintain a safe distance from and align with their neighbors. While several models exists and qualitatively mimic nature, they do not capture the dynamics well. We address this issue by obtaining and analyzing precise spatiotemporal data of the response of laboratory schools of rummy nose tetra to environmental stimuli. Using high-speed video, we track individuals and investigate how emergent properties arise from individual behaviors.
The trajectories of each fish in the school provides us with a wealth of data to apply statistical mechanics. Some of the metrics we are looking at are: density, speed, volume, social force magnitudes, and rotational and translational order parameters. We also use our data to study phase transitions of schools and examine how they go from a disorganized state to a mill (shown below).
So that we do not disturb our fish, our camera captures an infrared image of the fish — which the fish cannot see. We calibrate the camera to correct for lens distortion and transform pixel coordinates into world coordinates. The water in our experimental tank is temperature controlled, pH controlled, current controlled, and shallow to create a pseudo-two-dimensional system. This provides a powerful tool to determine how individual interactions connect with the dynamics of the school.
Using a projector, we perturb groups of rummy nose tetra with dynamic light gradients (as seen in the video below). Rummy nose tetra are a social tropical species that naturally avoid areas of high light intensity and move towards darker regions. We can therefore manipulate our laboratory schools and observe their collective response. The noise image consists of two images superimposed: a moving gaussian blob (seen easily in the figure to the left), and a multi-frequency noise field. We use this to examine the performance of the school in tracking the darkness.
Below is a video of the noisy image that is projected onto the experimental tank with an image of the fish (tracked by the infrared camera) overlay in red/orange.
Day-to-day, our work largely consists of caring for populations of rummy nose tetra, maintaining and improving our apparatus, and writing and developing the computer programs that we use to stimulate experimental schools, process data, and analyze data. There are several challenges that arise from working with such a complex living system. Collecting and analyzing data can be very time consuming because we collect very large amounts of data. Throughout the rest of the summer we will continue exploring the interesting physical properties of social animal groups.
Simulations of Collective Animal Behavior: (Aawaz)
Our fish are negatively phototactic — which means they like to be where its dark. But how do fish find the darkest spot? A previous study showed that fish cannot see the gradient of their environment (getting lighter or darker) only the absolute light level. Yet, somehow, collectively the group can find the darkest spot. We continue this work and further examine the mechanisms of the school that lead to this emergent sensing.
We examine this effect using a simulation of our school of fish in a noisy environment. The rules of the simulation are simple: don’t get too close to others, move toward others if too far away, align with others that are somewhere between, and slow down the darker the background. Implementing this simulation using a GPU is not so simple.
What’s amazing is that the fish have no way of detecting the gradient (slope) of the darkness — so how do they find the darkest spot? This is an example of emergent sensing: see the video below of one of our simulations.
Granular Materials: (Alex)
Granular materials are the second most utilized substance in industry next to water. Despite this, granular materials are still not well understood and models are still lacking predictive power that would be lifesaving (earthquakes, avalanches). One promising approach is using statistical mechanics to examine these systems as an ensemble of particles. In the PuckettLab, we analyze a two dimensional granular system composed of plastic cylinders (PSM-4). But this is special plastic, when view between crossed polarizers, a fringed image is formed that is unique to the force on the particle. Below left is an image of our granular material and to the right is an image of the stress network.
Much of the work this summer has been in the vein of error elimination and apparatus automation. To mitigate parallax error a dual camera system was constructed so as to stitch together the low parallax zones of two images. The Parallax Inhibiting Camera Setup (PICS) has hence been deconstructed replaced with a single camera and mirror setup which increases the visual path length enough that the parallax angle is acceptably small. This Focal Length Extension Mechanism (FLEM) has the added benefit of decreasing computer processing time as standalone images suffice for our data collection.
To switch between particle finding and stress network images the analyzer was previously rotated in front of the camera by a stepper motor. However due to the nature of the motor the analyzer partially undershoot or its ideally polarizing location. This had the effect of randomly decreasing the fidelity of stress images with non-parallel transmission axes. A new Automated Analyzer Actuation Apparatus (AAAA) has since been constructed which linearly moves the analyzer. This contraption does have uncertainty in its polarized and unpolarized endpoints however this is made negligible with a large enough analyzer as the transmission axes will always be at the same angle between data points.
The compress-image-polarize-image-unpolarize-shear-image-polarize-image-unpolarize-shear-etc process has been successfully automated with a LabView Virtual Interface. The particle finder and stress network analysis programs are being refined.