Project | 01
Project | 01 Traffic Flow Modelling With Lego Robots

In this project, we use mathematical models to represent physics of movements of a Lego robot. A PID controller is used to control both the Lego robot and the Matlab simulation. We plan to design smarter controllers that can work for any type of path at high speeds. The eventual purpose of this project is to simulate vehicles and study the events on the road.

Project | 02
Project | 02 Autonomous Vehicle Simulation Using Duckiebots

In this project, we use duckiebots to simulate autonomous vehicles.

Project | 03
Project | 03 Raspberry Pi Robot

In this project, we design a robot based on Raspberry Pi with a camera and ultrasonic distance sensors. We plan to design the robot so that it can autonomously move on a miniature road network using image processing. We expect this robot to be able to move faster than the ones with two wheels. 

Project | 04
Project | 04 Off-Ramp Coupling Conditions Devoid of Spurious Blocking and Re-Routing

When modeling vehicular traffic flow on highway networks via macroscopic models, suitable coupling conditions at the network nodes are crucial. Frequently, the evolution of traffic flow on each network edge is described in a lane-averaged fashion using a single-class Lighthill-Whitham-Richards model. At off-ramps, split ratios (i.e., what percentage of traffic exits the highway) are prescribed that can be drawn from historical data. In this situation, classic FIFO coupling conditions yield unrealistic results, in that a clogged off-ramp yields zero flux through the node. As a remedy, non-FIFO conditions have been proposed. However, as we demonstrate here, those lead to spurious re-routing of vehicles. A new coupling model, FIFO with queue (FIFOQ), is presented which preserves the desirable properties of non-FIFO models while not leading to any spurious re-routing.

Project | 05
Project | 05 Estimating the readiness time of sourdough through mathematical modeling of Yeast Fermentation

This problem was presented to us by our industry partners at the Amber Grain Bakery in New Jersey.  The aim of this project was to mathematically model the evolution of the volume of sourdough as a function various factors such as ambient temperature and initial ingredient ratios.

Through the course of our work, we investigate the problem experimentally by growing sourdough culture using varied initial ratios at varied ambient temperatures. We then fit the data we gather to a mathematical model which tracks the amount of yeast produced over time. Additionally, we study the microbes present in a sample of culture under a microscope using imaging software. Based on our experimental observations as well as the results of our model, we conclude that the ambient temperature, rather than the initial ratio of flour to water to starter used, is the key factor affecting the time to readiness, contrary to initial expectations. 

We designed the sourdough sleeping room, shown in the picture, by hacking a wine cooler and controlling it with an high precision temperature sensor and a micro-controller. The microcontroller regularly reported the temperature to a channel on website.

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Research Statement
Research Statement is available upon request.