# TREND 2018

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**August 10, 2018**

### TREND 2018 Projects

**(l-r):**José Ortiz Tavárez, Helena Yoest, Kyle Ritchie, Jessica Christian, Tatiana Davidson-Bajandas, Viktor Belay, Ben Ruben, Kathleen Hamilton, Ethan van Woerkom, William Fines-Kested, Shyline Santana, Daniel Belkin.

**Modeling the collective behavior of***Dictyostelium discoideum*under electrotaxis and nanotopographical guidance, Viktor Belay**Numerical and Thermodynamic Reversibility in Magnetic Reconnection, Daniel Belkin and Kyle Ritchie****Exploration of quantum, classical, and superposition optical state tomography, Jessica Christian****Reservoir Computing: Observation and Prediction of Chaos, Tatiana Davidson Bajandas****Building Dynamic Models Using Reservoir Computing, William Fines-Kested****Longitudinal RF Confinement in UMER, Kathleen Hamilton****Herding Cats: Inducing Cooperation of Uncooperative Multi-Dimensional Agents, José Ortiz Tavárez and Ben Ruben****Global Bifurcation in a Simple Pendulum with Nonlinear Damping, Shyline Santana****Zero-lag Synchronisation in a three-node Opto-electronic Oscillator Network, Ethan van Woerkom****The Effect of External Magnetic Fields on the Hall Effect of a Dusty Plasma Tornado, Helena Yoest****Possible improvements in four-wave mixing: Eskma top-hat beam shaping lens, Kwasi Fahie - JQI**

**Winners of TREND Fair 2018**

Best overall project:

**José Ortiz Tavárez and Ben Ruben**(Tom Antonsen, Michelle Girvan, and Ed Ott)Best overall project runner-up:

**Ethan van Woerkom**(Tom Murphy and Raj Roy)Best presentation:

**Shyline Santana**(Brian Beaudoin)Best poster:

**Viktor Belay**(Wolfgang Losert)Best media project:

**José Ortiz Tavárez and Ben Ruben**(Tom Antonsen, Michelle Girvan, and Ed Ott)**Modeling the collective behavior of ***Dictyostelium discoideum* under electrotaxis and nanotopographical guidance

**Modeling the collective behavior of***Dictyostelium discoideum*under electrotaxis and nanotopographical guidance*Viktor Belay, American University*

*Viktor Belay, American University**(Mentor: Prof. Wolfgang Losert)*

*(Mentor: Prof. Wolfgang Losert)*

Cellular migration is a function that is ubiquitous across a vast number of organisms. This phenomenon is observed in many biological functions such as embryogenesis, tissue regeneration, tumor metastasis, muscle contraction, and more. Cellular migration is influenced by many various factors; principally, by chemical, mechanical, and electrical cues. We utilize the model organism

*Dictyostelium discoideum*to study the effects of nanotopographical guidance and electrostatic fields on the motion of cells. We develop a coarse-grain stochastic model of the influence of nanotopography, electrostatic fields, and signaling by the messenger chemical cyclic adenosine monophosphate on the motion of*D. discoideum*cells. Model simulations show that unidirectional guidance by nanoridges allows for consistent Dicty streaming and aggregation, while bidirectional nanotopography creates a cell bifurcation in which there is little to no streaming or aggregation. Dicty cells also exhibit directed collective motion when under the influence of a unidirectional electric field. Our results implicate that the random motion of*D. discoideum*cells is overtaken when cells undergo electrotaxis or chemotaxis, and when cells migrate on nanotopography.

**(Slides)**

**Media Project**

**Numerical and Thermodynamic Reversibility in Magnetic Reconnection**

**Numerical and Thermodynamic Reversibility in Magnetic Reconnection**

*Daniel Belkin, Swarthmore College*

*Daniel Belkin, Swarthmore College*

*Kyle Ritchie, University of New Mexico*

*Kyle Ritchie, University of New Mexico*

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

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

Magnetic reconnection plays an important role in driving solar flares, coronal mass ejections, and the Northern Lights. Ubiquitous in astrophysical systems, it occurs when magnetic field lines align such that topological changes allow them to reduce their magnetic energy. This unstable configuration causes the field lines to break and reconnect, which results in an explosive release of kinetic energy. It is an open question whether magnetic reconnection is an irreversible process in some sense, and why. To investigate this question, we use particle-in-cell simulations to study the behavior of a two-dimensional collisionless reconnection configuration in reverse and observe particle trajectories near the x-line. We do not observe fully-developed or self-driving reverse reconnection. Early data suggest that the sensitivity of particle trajectories to phase differences in their Larmor orbits near the x-line contribute to the numerical irreversibility of reconnection. We show that the loss of phase information may be modeled by an effective collision operator. Finally, we suggest a model based on Zubarev’s method for non-equilibrium statistical mechanics as an appropriate means of characterizing the entropic irreversibility of magnetic reconnection.

**(Slides)**

**Media Project**

**Exploration of quantum, classical, and superposition optical state tomography**

**Exploration of quantum, classical, and superposition optical state tomography**

*Jessica Christian, University of Maryland Baltimore County*

*Jessica Christian, University of Maryland Baltimore County*

*(Mentor: Profs. Mohammad Hafezi)*

*(Mentor: Profs. Mohammad Hafezi)*

As a primary parameter of electromagnetic waves, optical polarization communicates the spatial orientation of incoming light waves and the degree to which an electromagnetic wave fits a certain profile. Polarization state can therefore conveniently be used to determine properties of light such as superposition or quantum entanglement, permitting further study of these unique phenomena. Within the field of optics, the ability to reliably create and identify optical states is foundational to experimental potential and is necessary to validate all further experiments performed: all optics laboratories must, in advance of any and all study, establish the legitimacy of their chosen state. In doing so ourselves, our lab demonstrates techniques to create a variety of optical states and to verify them by performing state tomography. We also provide a discussion of the optical states’ superposition natures and the implications therein. Among those evaluated are classical and single-photon one-qubit states, as well as two-photon entangled states of alike and opposite polarizations, representing the majority of possible states among one- and two-photon configurations.

**(Slides)**

**Media Project****Reservoir Computing: Observation and Prediction of Chaos**

**Reservoir Computing: Observation and Prediction of Chaos**

*Tatiana Davidson Bajandas, University of Chicago*

*Tatiana Davidson Bajandas, University of Chicago*

*(Mentors: Profs. Tom Murphy and Raj Roy)*

*(Mentors: Profs. Tom Murphy and Raj Roy)*

A vast number of systems can become chaotic in their dynamics in both nature and the man-made world, however until recently they remained difficult to model, characterize, and predict. The use of reservoir computing, a variation on artificial neural networks, has propelled our understanding of these systems forward with such capabilities as observation and prediction. In these tasks, input variables in the observation task and future output variables in the prediction task are projected with startling accuracy compared to the time scale of the system dynamics for an extended period of time. A tabletop experiment is compared to a reservoir computer implemented digitally on a laptop, wherein it is hoped that specific calculations will be faster than computations on a laptop. Observation and prediction tasks are conducted for the Lorenz chaotic system using a truncated sin2 nonlinearity function. Applications exist in a varied array of fields from meteorology to cell biology to economics where characterization of chaotic systems is becoming increasingly important.

**(Slides)**

**Media Project**

**Building Dynamic Models Using Reservoir Computing**

**Building Dynamic Models Using Reservoir Computing**

*William Fines-Kested, Massachusetts College of Liberal Arts*

*William Fines-Kested, Massachusetts College of Liberal Arts*

*(Mentor: Prof. Dan Lathrop)*

*(Mentor: Prof. Dan Lathrop)*

Prediction of chaotic dynamical systems has been difficult due to the sensitivity of the system to initial conditions in the system’s state. Work has been done to build predictive models using numerical methods and simulated data, but little work has been done in this field using experimental data that includes noise. Recent work done in a machine learning field called “reservoir computing” demonstrates success in predicting dynamical systems. We test this reservoir computing technique on a time series data set containing the concentration of bromide ions in a Belousov-Zhabotinsky reaction. We find that we are able to obtain both short-term predictions with minimal error, as well as long-term predictions with error that oscillates and mimics the behavior of the original data that includes noise.

**(Slides)**

**Media Project****Longitudinal RF Confinement in UMER**

**Longitudinal RF Confinement in UMER**

*Kathleen Hamilton, University of Maryland College Park*

*Kathleen Hamilton, University of Maryland College Park*

*(Mentor: Research Prof. Brian Beaudoin)*

*(Mentor: Research Prof. Brian Beaudoin)*

Conventionally, the longitudinal confinement on the University of Maryland Electron Ring (UMER) has employed barrier buckets. This method accelerates and decelerates particles at the outermost edges of the beam to maintain the rectangular longitudinal beam distribution without modifying the central region of a long 100ns bunch. While these barrier buckets have been successful for single bunch operations, multi-bunch mode can’t be sustained using this scheme for confinement. We test an induction cell and radiofrequency (RF) amplifier experiment, applying sinusoidal wave bursts at the revolution frequency to confine a single-bunch, 60ns beam in the linear slope regions of the wave. Future tests will involve higher frequencies to test multi-bunch confinement with the same system. Keeping the beams confined also entails avoiding particle loss. As in the RF cavities of other accelerators, there will be distinct regions of stability. We calculate the separatrices, which mark the boundaries of these areas and provide necessary information about beam cohesion, with a central synchronous particle. Although only single bunches have been tested so far, this work paves the way for multi-bunch confinement. This would advance the capabilities of the longitudinal confinement system, allowing UMER to increase its performance and modes of operation for different experiments.

**(Slides)**

**Media Project**

(Interactive diagram -art from www.vecteezy.com-)

*José Ortiz Tavárez, University of Puerto Rico Mayagüez*

*José Ortiz Tavárez, University of Puerto Rico Mayagüez**Ben Ruben, Rice University*

*Ben Ruben, Rice University**(Mentors: Profs. Tom Antonsen, Michelle Girvan, and Ed Ott)*

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

Systems of uncooperative or contrarian agents naturally tend toward disorder. Can a sufficiently strong leader overcome inter-agent uncooperativeness and force partial or complete cooperation within the population? Motivated by this question, we consider a multi-dimensional Kuramoto-like model consisting of repulsively coupled agents subjected to external periodic driving of constant magnitude. Using a generalization of the Ott-Antonsen method, we reduce the dynamics of the many-agent system to a low-dimensional system of differential equations. By varying the extent of the repulsive inter-agent coupling, we observe continuous and discontinuous transitions from partial coherence to full coherence ('cooperation'). Full system simulations agree well with our theoretical predictions of both time asymptotic steady states, as well as the transient time evolution toward them.

**(Slides)**

**Media Project**

**Global Bifurcation in a Simple Pendulum with Nonlinear Damping**

**Global Bifurcation in a Simple Pendulum with Nonlinear Damping***Shyline Santana, University of Puerto Rico Río Piedras*

*Shyline Santana, University of Puerto Rico Río Piedras**(Mentor: Prof. Derek Paley)*

*(Mentor: Prof. Derek Paley)*

Swimming motion of a robotic fish driven by an internal reaction wheel has been shown to be analogous to the dynamics of a Chaplygin sleigh. We study a simple pendulum with nonlinear damping from a simplified form of Chaplygin sleigh motion under a feedback control law. Under certain values of the control gains the sleigh enters a limit cycle that produces forward motion. We conduct a bifurcation analysis for possible variations of the bifurcations and dynamics that occur on the system as these control gains are varied. The basic dynamical properties are analyzed by phase portraits. For certain values of our controlled gains, a global bifurcation occurs that splits the desirable stable limit cycle into two undesirable limit cycles that results in unbounded spinning of the sleigh. Numerical simulations are carried out to optimize the forward sleigh motion or smooth swimming by obtaining our bifurcations parameters and knowing where our stable limit cycle lies.

**(Slides)**

**Media Project****Zero-lag Synchronisation in a three-node Opto-electronic Oscillator Network**

**Zero-lag Synchronisation in a three-node Opto-electronic Oscillator Network***Ethan van Woerkom, University of Edinburgh*

*Ethan van Woerkom, University of Edinburgh**(Mentors: Profs. Tom Murphy and Raj Roy)*

*(Mentors: Profs. Tom Murphy and Raj Roy)*

Isochronous synchronisation between nodes is investigated in a small network of coupled opto-electronic oscillators that includes both coupling and feedback time delays. Intermediate nodes act as either a relay, or a driver. We examine this behaviour for different values of coupling. Synchronisation under these conditions was shown to be resistant to both parameter and time delay changes. Different coupling time delays induced phase lags in node dynamics.

**(Slides)**

**Media Project**

**Blog post on synchronization in chaotic networks**

**The Effect of External Magnetic Fields on the Hall Effect of a Dusty Plasma Tornado**

**The Effect of External Magnetic Fields on the Hall Effect of a Dusty Plasma Tornado***Helena Yoest, Bucknell University*

*Helena Yoest, Bucknell University**(Mentor: Prof. Dan Lathrop)*

*(Mentor: Prof. Dan Lathrop)*

We present results from our experiment designed to characterize the way external magnetic fields influence the Hall Effect of a turbulent granular system. We agitated polystyrene particles in a vertical cylindrical annulus by applying wind against gravity, thus creating a model of a dusty plasma tornado. Because colliding particles lose or gain charge through the process of granular electrification, we can observe a resulting voltage difference between the concentric cylinders due to this agitation. We characterize the mean and RMS voltage between the cylinders due to the charge difference. The apparatus is placed inside of a vertical magnetic field of strength 0.62 T and aligned with the dipole. From here, we observe how the imposed magnetic field influences the voltage of the apparatus, and we find that there is a measurable difference as we vary the strength of the magnetic field.

**(Slides)**

**Media Project**

**Possible improvements in four-wave mixing: Eskma top-hat beam shaping lens - JQI**

**Possible improvements in four-wave mixing: Eskma top-hat beam shaping lens - JQI***Kwasi Fahie - Participation through JQI*

*Kwasi Fahie - Participation through JQI**(Mentor: Dr. Kevin Jones)*

*(Mentor: Dr. Kevin Jones)*

In our lab, we study exotic states of light by four-wave mixing (FWM) Gaussian waves in a Rb-cell. Across the length of the cell, Gaussian intensities vary in strength and size, causing distortions in the observed output. A potential improvement to these experiments is replacing the Gaussian intensity beam with a uniform-intensity beam. Optics meant for this are commercially available, and we have studied such a lens for potential use. The Eskma top-hat converter is a beam shaping lens which - when paired with a focusing lens - takes Gaussian intensity light and produces near-uniform intensity at focal length. This experiment analyses the wave profile at a working distance (WD) near focal length (500 mm) and examines phase aberrations and amplitude interference induced by the lens. Light input came from a fiber optic, coupled with an aspherical lens and resized through a series of Kepler beam expander. Using a translating stage and beam profiler, we observed changes in the top-hat profile shape for WDs above and below the focal length. We then observed phase interference with a modified Mach-Zehnder interferometer; high-contrast fringes occurred at focal length, suggesting unexpected phase shifts caused by the lens. We will consider these changes in intensity and phase before implementing the beam shaping lens in a FWM process.