# TREND 2015

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**August 9, 2015**

### TREND 2015 Projects

**Back (l-r):**Sergio Smith (JQI program), Steven Lee, Alan Preciado (JQI program), Eric Cooper, Amy Davis, Anneleise Rillinger (JQI program), Alisa Babcock, non-participant, non-participant, Remi Boros, Dylan Powers, Michael Tripepi.

**Front:**Christopher Fritz.

**Silicon-on-Insulator Optical Chips as Robust Beam Splitters | Alisa Babcock****Shocks and Singularities after Cord Reconnection | Remi Boros****Noise to Synchrony in Coupled Photon-Counting Feedback Loops | Jae Young Chang****3D Imaging the Convection and Rotation of Grains under Cyclic Compression | Eric Cooper and Dylan Powers****Stability and Bifurcation Analysis of the Planar Two-Point Vortex System | Amy Davis****Frequency Coupling in an Optoelectronic Oscillator | Christopher Fritz****Exploring the Effects of Jet Lag with the Forced Kuramoto Model | Kevin Klein-Cardeña and Steven Lee****Mechanism for Helium-3 Abundance Enhancements in Solar Flares | Nick McGrievy****Designing and Testing Laser-Driven Electron Sources | Michael Tripepi**

**Winners of TREND Fair 2015**

Best Overall Project and Presentation: Jae Young Chang

Best Overall Project and Presentation: 1st Runner-Up: Remi Boros

Best Overall Project and Presentation: 2nd Runner-Up: Anneleise Rillinger (JQI program)

*Alisa Babcock, Ithaca College*

*Alisa Babcock, Ithaca College*

*(Mentor: Prof. Mohammad Hafezi)*

*(Mentor: Prof. Mohammad Hafezi)*

Topologically robust transport of photons has been observed in silicon-on-insulator optical chips. We investigate beam splitters as a potential application for these systems. Results are presented from a simulation of adjacent areas with opposite synthetic gauge fields. We examine the robustness of the system with respect to simulated disorder and discuss the potential efficacy of a silicon-on-insulator chip as a beam splitter based on the results.

**Multimedia Project**

*Remi Boros, Brandeis University*

*Remi Boros, Brandeis University*

*(Mentor: Prof. Daniel Lathrop)*

*(Mentor: Prof. Daniel Lathrop)*

Inspired by the propagation of Kelvin waves in superfluid helium, we sought to imitate the motion of a vortex just after a vortex reconnection event. With the use of a high speed camera, we were able to analyze wave and shock propagation along an upright, stretched length of 1/4" diameter latex cord. We observed a recurring shape in the outline of our elastic band, implying self-similar motion over time. By choosing a suitable physical and temporal origin, we found that the cord’s motion could be closely collapsed onto a single contour edge, confirming the existence of hypothesized similarity solutions to our system. This solution collapse is reminiscent of the similarity solutions used to describe quantum vortex shape after a reconnection event in superfluid helium.

**Multimedia Project**

*Jae Young Chang, Cornell University*

*Jae Young Chang, Cornell University*

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

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

The phenomenon of synchrony in coupled deterministic chaotic systems is well established and understood theoretically. In reality, many of these systems incorporate physical mechanisms that are unpredictable and stochastically described. For example, the intensity fluctuations and single photon detections from a coherent state of a single mode semiconductor laser light are described by Poisson processes, and when such light is injected into an opto-electronic feedback loop, we realize a system which approaches determinism as the injected photon rate increases. By uni-directionally coupling two optoelectronic feedback loops that can have adjustable proportions of randomness and deterministic dynamics by adjusting the injected photon rates, we experimentally demonstrate a coupled system whose signals evolve from uncorrelated shot noises to deterministic synchronized chaos as the photon rates increase.

*Eric Cooper, Pomona College*

*Eric Cooper, Pomona College*

*Dylan Powers, University of Maryland College Park*

*Dylan Powers, University of Maryland College Park*

*(Mentor: Prof. Wolfgang Losert)*

*(Mentor: Prof. Wolfgang Losert)*

Real-world granular systems, such as sand at the base of ocean wind turbines, frequently undergo repeated compressions. Prior studies have found bulk granular flows which can compromise structural stability, but have left open questions at the granular scale. During the TREND program, we have constructed a fast 3D-scanning system that tracks the movement and rotation of individual grains in repeatedly compressed granular piles. We will present the conclusions drawn from the data we collected.

**Multimedia Project**

*Amy Davis, Covenant College*

*Amy Davis, Covenant College*

*(Mentor: Prof. Derek Paley)*

*(Mentor: Prof. Derek Paley)*

In order to help understand vortex systems in the ocean, we studied the planar two-point vortex system in the co-rotating frame. We found the equilibria and studied their stability. Numerical and analytical linear analysis shows that there exist two bifurcation points: one when the circulation of one vortex vanishes and the other when the circulations are equal but opposite. Around the first, the number of equilibria and their stability changes; around the second, the equilibrium locations change. These findings might prove useful to planning measurement paths around ocean vortex systems in the future.

**Multimedia Project**

*Christopher Fritz, Dickinson College*

*Christopher Fritz, Dickinson College*

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

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

Mathematical analysis of a nonlinear optoelectronic oscillator suggests that the frequencies of the electric signal will be coupled with one another. This implies that a large bandwidth system can have many thousands of dynamically coupled oscillators. Three frequencies are selected using a frequency comb filter implemented on a Field Programmable Gate Array (FPGA). Theoretical analysis of the system is presented to show how coupling can occur between frequencies. Experimental data suggesting coupling are also presented and analysed.

*Kevin Klein-Cardeña, DePaul University*

*Kevin Klein-Cardeña, DePaul University*

*Steven Lee, Brooklyn CUNY*

*Steven Lee, Brooklyn CUNY*

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

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

Cells in the region of the hypothalamus known as the suprachiamatic nucleus (SCN) are known regulated circadian rhythms in mammals. We model synchronization of SCN cells using the forced Kuramoto model, which consists of a population of phase oscillators with heterogeneous intrinsic frequencies, weak coupling, and external periodic forcing (to capture the role of the diurnal light cycle). Using this framework, we study the effects of changes in external forcing, such as those induced by jet lag, which we represent by a phase shift in the sinusoidal driving term. To connect the mathematical model with empirical data, we estimate model parameters from experimental studies of mouse SCN activity. Our modeling approach illustrates how eastward and westward travel can have different effects on the recovery of circadian rhythms and how the length of time required to adjust from jet lag may be non-monotonic in the number of time zones crossed.

*Nick McGreivy, University of Pennsylvania*

*Nick McGreivy, University of Pennsylvania*

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

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

A new mechanism for abundance enhancements of high-energy helium-3 produced by impulsive flares is explored. Observations have shown a 103-104 increase in the high-energy helium-3 abundance following impulsive solar flares. A likely mechanism is the resonant heating of helium-3 by Alfvén-cyclotron waves. The source of these waves has not been established. We propose that magnetic reconnection drives these waves. We have shown, through two-dimensional PIC simulations of magnetized plasmas, that low-beta magnetic reconnection produces strong temperature anisotropy, with a higher temperature perpendicular to the magnetic field. Simulations reveal that this temperature anisotropy drives Alfvén-cyclotron waves which resonate with helium-3 and lead to an increase in the helium-3 temperature by a factor of 3-7. These simulations establish the potential viability of this mechanism.

**Multimedia Project**

*Michael Tripepi, Hillsdale College*

*Michael Tripepi, Hillsdale College*

*(Mentor: Dr. Eric Montgomery)*** **

*(Mentor: Dr. Eric Montgomery)*

Photocathodes utilize the photoelectric effect to emit electrons in response to incident photons. This allows the photocathodes to act as a controllable electron source for other applications such as free electron lasers and ultrafast electron diffraction. A natural quantity of interest is the ratio of electrons emitted to the number of photons incident on the photocathode. This value is called the quantum efficiency (QE). Modifications have been made to the photocathode testing apparatus at the University of Maryland including the installation and testing of an Auger spectrometer and the design and installation of separate gold and antimony evaporation sources. Measurements using the newly commissioned apparatus will be shared with analysis in light of nonlinear models of electron transport including a view towards unanswered photocathode questions and new materials research.

**Multimedia Project**