# TREND 2019

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**August 9, 2019**

### TREND 2019 Projects

**(l-r):**Juan Pablo Speer, Daniel Van Beveren, Kush Maheshwari (top), Laramy Head (bottom), Joy Hamlin (top), Rachel Slover (bottom), David Jin (top), Sarah Chang (bottom), Nolan Coble, Nathnael Feleke*, Thomas Coleman* (top), Chavonne Bowen* (bottom). *GRAD-MAP participants.

**Using reservoir computing to predict temperature fluctuations in turbulent Rayleigh-Bénard convection, Sarah Chang****Parallel Machine Learning Prediction of Network Dynamics, Nolan Coble and Joy Hamlin****Examining Akt in HL-60/dHL-60 cells with and without an applied electric field, Laramy Head****Laminar Chaos Observed with Arduino-Based Mackey-Glass Feedback Circuit with Variable Delay, David Jin and Juan Pablo Speer****3D Simulations of Test Particle Propagation in the Fields of Whistler Waves, Kush Maheshwari****Understanding the Behavior of Single and Two-Vortex Systems Through Mathematical Modeling, Rachel Slover****Interactions between bathtub vortices in a rotating experiment, Daniel Van Beveren**

**Winners of TREND Fair 2019**

Best overall project:

**David Jin and Juan Pablo Speer**(Yanne Chembo, Tom Murphy, and Rajarshi Roy)Best overall project runner-up:

**Nolan Coble and Joy Hamlin**Tom Antonsen, Michelle Girvan, and Ed Ott)Best presentation:

**Daniel Van Beveren**(Daniel Lathrop)Best poster:

**Kush Maheshwari**(James Drake and Marc Swisdak)Best media project:

**Nolan Coble and Joy Hamlin**Tom Antonsen, Michelle Girvan, and Ed Ott)**Using reservoir computing to predict temperature fluctuations in turbulent Rayleigh-Bénard convection**

**Using reservoir computing to predict temperature fluctuations in turbulent Rayleigh-Bénard convection***Sarah Chang, Swarthmore College*

*Sarah Chang, Swarthmore College**(Mentor: Prof. Daniel Lathrop)*

*(Mentor: Prof. Daniel Lathrop)*

Turbulent flows are ubiquitous in the fundamental processes of nature—from the Earth’s mantle to its atmosphere and oceans. Among their many complexities, turbulent flows are chaotic, which makes it computationally expensive to simulate and difficult to study analytically. Thus, prediction of turbulent systems is an ongoing challenge. Machine learning methods, specifically reservoir computing, have shown promise in predicting turbulent flows. Reservoir computing is a recurrent neural network model that uses a reservoir of randomly connected and weighted nodes to process the input data and predict the output for the next time step. As a proof-of-concept, here we test the effectiveness of reservoir computing on temperature fluctuations in turbulent Rayleigh-Bénard convection because it has a relatively simple experimental setup and relevant applications, like weather prediction. Rayleigh-Bénard convection is a buoyancy-driven flow, and when the temperature difference between the top and bottom of the container is large enough, turbulent convection results. We train the reservoir computer with our experimental data, taken from the water-filled cylindrical convection apparatus and thermistor temperature measurement system we built, in an attempt to predict turbulent temperature fluctuations. Further study will help improve machine learning tools for predicting the properties of turbulent flows and other chaotic systems.

**(Slides)**

**Media Project**

**Parallel Machine Learning Prediction of Network Dynamics**

**Parallel Machine Learning Prediction of Network Dynamics**

*Nolan Coble, SUNY Brockport*

*Nolan Coble, SUNY Brockport*

*Joy Hamlin, SUNY Stony Brook*

*Joy Hamlin, SUNY Stony Brook*

*(Mentors: Profs. Tom Antonsen, Michelle Girvan, and Ed Ott)*

*(Mentors: Profs. Tom Antonsen, Michelle Girvan, and Ed Ott)*

Reservoir computing is a machine learning technique that is especially useful for predicting the evolution of chaotic systems. Although the method performs well in predicting isolated chaotic systems, its fails to predict large interconnected systems due to computational limitations. We proposed and tested a parallel prediction scheme for network-coupled dynamical systems, whereby every node of the system receives a reservoir, and each reservoir shares output information with its neighbors. In assigning one reservoir per node, the technique remains useful regardless of the network size. The Kuramoto oscillator model serves as our test model for the parallel approach.

**(Slides)**

**Media Project**

*Laramy Head, University of North Georgia*

*Laramy Head, University of North Georgia*

*(Mentor: Prof. Wolfgang Losert)*

*(Mentor: Prof. Wolfgang Losert)*

The human immune system is led by neutrophils that account for most of the white blood cells in a human and are able to migrate freely throughout the body, through vein walls and tissues, to quickly attack pathogens. They can be differentiated (dHL-60) to behave like neutrophils, which allows them to be used as a model system for wound healing. Protein kinase B (Akt) is a known signaling protein that is a key component in motility upstream of actin dynamics. The pH domain of Akt in HL-60 cells was examined to better understand its role in cellular motility. Its appearance within the cell was confirmed and its activity in the presence of an electric field was verified. In vivo, neutrophils are attracted to electrically negative wound sites because of the disruption of the transepithelial potential difference. In vitro, this electrical signaling is simulated with electrolytic cells. This model system for immune cells could contribute to the enhancement of cell migration dynamics for wound and disease healing.

**(Slides)**

**Media Project****Laminar Chaos Observed with Arduino-Based Mackey-Glass Feedback Circuit with Variable Delay**

**Laminar Chaos Observed with Arduino-Based Mackey-Glass Feedback Circuit with Variable Delay**

*David Jin, Grinnell College*

*David Jin, Grinnell College*

*Juan Pablo Speer, University of Alabama at Brimingham*

*Juan Pablo Speer, University of Alabama at Brimingham*

*(Mentors: Profs. Yanne Chembo, Tom Murphy, and Rajarshi Roy)*

*(Mentors: Profs. Yanne Chembo, Tom Murphy, and Rajarshi Roy)*

The Mackey-Glass delayed differential equation (DDE), which was originally developed to model physiological systems, has been used to explore a wide range of periodic and chaotic dynamics. An electronic feedback circuit that simulates the behavior of the Mackey-Glass equation was built with a nonlinear device made up of two coupled JFET transistors. Uniquely, our system uses an Arduino DUE board to implement a time delay and low-pass filter into the feedback loop, resulting in the dynamical behaviors predicted by the DDE. Furthermore, by introducing a variable time delay to the system via the Arduino board, we have been able to observe a new type of chaotic behavior called Laminar Chaos. Laminar Chaos is characterized by nearly constant laminar phases that are separated by short and irregular burst-like transitions. We are the first to observe this type of chaotic behavior in an electronic system using the Mackey-Glass nonlinearity. We are exploring different ranges of parameters for the variable delay including frequency and the amplitude of modulation.

**(Slides)**

**Media Project**

**3D Simulations of Test Particle Propagation in the Fields of Whistler Waves**

**3D Simulations of Test Particle Propagation in the Fields of Whistler Waves**

*Kush Maheshwari, UC Berkeley*

*Kush Maheshwari, UC Berkeley*

*(Mentor: Prof. James Drake and Dr. Marc Swisdak)*

*(Mentor: Prof. James Drake and Dr. Marc Swisdak)*

Whistler waves are oscillations in plasma thought to help inhibit energy transport in the solar wind and in galaxy clusters. Previous particle-in-cell simulations studying the effect of whistler waves on astrophysical plasmas were restricted to 2D due to computational constraints. To study the full dimensionality of a whistler-mediated plasma, we build a test particle simulation using a Boris stepper algorithm, which preserves numerical accuracy of a particle’s energy extremely well. The particles themselves do not generate their own electromagnetic fields or influence the wave. In a one-wave simulation, after verifying that canonical momentum is conserved in the dimensionally invariant direction, we find that kinetic energy is bounded and that particle trajectories are bounded in the plane perpendicular to the guide magnetic field. Adding a second wave not in the same plane as the first wave breaks dimensional invariance in the system, allowing the particles to diffuse arbitrarily far in the plane perpendicular to the guide field.

**(Slides)**

**Media Project****Understanding the Behavior of Single and Two-Vortex Systems Through Mathematical Modeling**

**Understanding the Behavior of Single and Two-Vortex Systems Through Mathematical Modeling**

*Rachel Slover, UNC Chapel Hill*

*Rachel Slover, UNC Chapel Hill*

*(Mentor: Prof. Derek Paley)*

*(Mentor: Prof. Derek Paley)*

Vortices are swirling patterns of fluid flow that are essential in the study of aerodynamics, fluid mechanics, and the use of this study for bio-inspired robotics. Potential Flow Theory provides a helpful framework for studying these flow patterns in a simplified manner that allows for modeling in MATLAB. However, many factors affect the path and behavior of vortices, such as strength, the presence of a doublet, the number of vortices, the initial positions, and the direction of flow relative to the surroundings and to each other. This investigation aimed to apply previously derived flow equations to both a single-vortex model and a two-vortex model, for each adding a case with a doublet that we represent as a cylinder. Then, we aimed to model the flow patterns of each of these in MATLAB, plotting both the trajectory and the phase portrait. Research was slowed more than anticipated, so results for the two-vortex model and the phase portraits are anticipated for future study, as well as expanding to a system of 3 or more vortices.

**Media Project***Daniel Van Beveren, Haverford College*

*Daniel Van Beveren, Haverford College**(Mentors: Prof. Daniel Lathrop)*

*(Mentors: Prof. Daniel Lathrop)*

The bathtub vortex is a flow pattern uniquely suited for laboratory study, as the flow through a drain hole provides a radial inflow and vortex stretching in a controlled location, thus stabilizing the vortex. While these radial flow patterns provide stability, the attraction they cause between any number of such vortices makes it difficult to achieve a stable state of multiple bathtub vortices, thus limiting their utility as models for experimental study of vortex interactions. Here we test the effect of global rotation on such vortices by spinning a cylindrical container with two drain holes in the bottom, which we find allows the formation of multiple bathtub vortices in a co-rotating stable state. The orbit period of these vortices is observed to change with the global rotation rate, and apparently spontaneous switching between states with different numbers of vortices is observed, with larger numbers of vortices possible at higher global rotation rates. We thank NSF Award PHY-1756179 and EAR-1909055.

**(Slides)**

**Media Project**