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# TREND 2016

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**August 13, 2016**

### TREND 2016 Projects

**(l-r):**Savannah Gowen, Treacy Hanley, Kevin Fei, David Hathcock, Kimberly Crain, Thomas Hartke, Molly Mosher, Landry Horimbere, Benjamin Gruey.

**Modeling the Network Dynamics of Pulse-Coupled Neurons, Kimberly Crain and David Hathcock****The Amplification of Noise by Chaos in an Optoelectronic Feedback Loop, Kevin Fei****Experimental Studies of Acoustics in a Spherical Couette Flow, Savannah Gowen****Particle Swarm Optimization of Electron Rings, Ben Gruey****Determining the Chern Number of Systems Described by Hamiltonians, Treacy Hanley****The Rate of Reconnection at the Magnetopause and its Implications for Space Weather, Thomas Hartke****Development of Exploding Wire Plasma System for Studying Magnetic Reconnection, Landry Horimbere****Esotaxis Beats Chemotaxis (The Effect of Substrate Texture on Collective Migration of Dictyostelium discoideum), Molly Mosher****Improving Vertical Steering on University of Maryland Electron Ring, Claudia Richoux****Investigation of Losses in Four-Wave Mixing Squeezed Light Experiments, Ashay Patel - JQI**

**Winners of TREND Fair 2016**

Best overall project:

**Claudia Richoux**(Brian Beaudoin)Best overall project runner-up:

**Molly Mosher**(Wolfgang Losert)Best presentation: Tie between

**Kevin Fei**(Tom Murphy and Raj Roy) and**Thomas Hartke**(Jim Drake and Marc Swisdak)Best multimedia project:

**Savannah Gowen**(Dan Lathrop)*Kimberly Crain, Iowa State University*

*Kimberly Crain, Iowa State University*

*David Hathcock, Case Western Reserve University*

*David Hathcock, Case Western Reserve University*

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

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

Recently, President Obama announced ‘The Brain Initiative,’ a long range plan of scientific research into human brain function. Computer modeling of brain neural dynamics will surely play an important role in this body of work. A barrier to such modeling is the practical limit on computer resources versus the enormous number of neurons in the human brain (~10

^{11}). Our work addresses this problem by developing a method for obtaining low dimensional macroscopic descriptions for functional groups consisting of many neurons. Specifically, we formulate a mean-field approximation to investigate the macroscopic dynamics of large networks of pulse-coupled neurons and use the ansatz of Ott and Antonsen to derive a reduced system of ordinary differential equations describing the dynamics. We find that solutions of the reduced system agree with those of the full network. This dimensional reduction allows for more efficient characterization of system phase transitions and attractors. For example, depending on the network topology, we find the possibility of transitions to a synchronously spiking state through Hopf and Homoclinic bifurcations. Our results show the utility of these techniques for analyzing the effects of network topology on macroscopic behavior in neuronal networks.**Multimedia Project**

**Website on using math to model neuronal networks (static PDF)**

**The Amplification of Noise by Chaos in an Optoelectronic Feedback Loop**

**The Amplification of Noise by Chaos in an Optoelectronic Feedback Loop**

*Kevin Fei, Harvard University*

*Kevin Fei, Harvard University*

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

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

Noise, the stochastic variation of observed quantities, is a factor fundamentally unavoidable in experimental physics. While present in all dynamical systems, its effect is especially important in chaotic dynamics. Chaos characteristically amplifies small variations in initial conditions, resulting in drastically different outcomes. It has long been claimed that chaos also amplifies intrinsic noise, which presents continuous variation rather than variation at one time. That is to say the system is harder to predict when the noise is fed back into the dynamics than when the noise is only present in the measurement process. To test this, we use a time-delayed optoelectronic feedback loop with a photon detector. With our apparatus, we have the unique ability to vary the amount of intrinsic shot noise that is fed back into the system by controlling the photon rate. This allows us to experimentally demonstrate a result that has so far only been theoretically predicted and computationally verified in simple mathematical models. Our results showed quantitatively that the chaos does indeed amplify the intrinsic noise. This experiment opens the door to further investigation of the interplay between noise and chaos. The study of the impact of noise on synchronization and desynchronization of chaotic systems and entropy rates in random number generation are immediate possible applications.

**Multimedia Project**

**Interactive website on the use of noise and chaos for random number generation (Static PDF)**

**Experimental Studies of Acoustics in a Spherical Couette Flow**

**Experimental Studies of Acoustics in a Spherical Couette Flow**

*Savannah Gowen, Mount Holyoke College*

*Savannah Gowen, Mount Holyoke College**(Mentor: Prof. Dan Lathrop)*

*(Mentor: Prof. Dan Lathrop)*

The Earth, like many other astrophysical bodies, contains turbulent flows of conducting fluid which are able to sustain magnetic field. To investigate the hydromagnetic flow in the Earth’s outer core, we have created an experiment which generates flows in liquid sodium. However, measuring these flows remains a challenge because liquid sodium is opaque. One possible solution is the use of acoustic waves. Our group has previously used acoustic wave measurements in air to successfully determine flow, but measurements attempted in liquid sodium remain challenging. In the current experiments we measure acoustic modes and their Doppler shifts in both air and water in a spherical Couette device. The device is comprised of a hollow 30-cm outer sphere which contains a smaller 10-cm rotating inner sphere to drive flow in the fluid in between. We use water because it has material properties that are similar to those of sodium, but is more convenient and less hazardous. Modes are excited and measured using a speaker and microphones. Measured acoustic modes and their Doppler shifts correspond well with the predicted frequencies in air. However, water modes are more challenging. Further investigation is needed to understand acoustic measurements in the higher density media.

**Multimedia Project****Particle Swarm Optimization of Electron Rings**

**Particle Swarm Optimization of Electron Rings**

*Ben Gruey, University of California Santa Cruz*

*Ben Gruey, University of California Santa Cruz*

*(Mentor: Prof. Brian Beaudoin)*

*(Mentor: Prof. Brian Beaudoin)*

*Treacy Hanley, National University of Ireland Galway*

*Treacy Hanley, National University of Ireland Galway**(Mentor: Prof. Mohammad Hafezi)*

*(Mentor: Prof. Mohammad Hafezi)*

Physical systems can be described in terms of many different properties, one being a system’s topology. An exciting development in condensed matter physics is the classification of insulators based on topological principles. Here, I discuss topological insulators and superconductors. These systems can be characterized by a Chern number, a topological invariant which is a generalized winding number. This quantity is related to the conductance of the system. Since the bulk of an insulator is always non-conducting, it is the edge states of the topological insulator which contribute to any nonzero conductance. Since the existence of these states is based on topological principles, they should be robust to disorder and imperfections in the system. This makes topology a very useful tool in characterizing real systems. I will present both analytic and numerical methods to evaluate the Chern number. I will apply these techniques to Hamiltonians which describe both topological insulators and superconductors.

**Multimedia Project***Thomas Hartke, Princeton University*

*Thomas Hartke, Princeton University**(Mentors: Prof. Jim Drake and Dr. Marc Swisdak)*

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

Space and laboratory plasmas can quickly dissipate trapped magnetic energy when oppositely directed magnetic fields in two nearby regions of space combine, rearrange, and annihilate each other. This process, called magnetic reconnection, can divert charged particles through the Earth’s magnetopause which can potentially damage terrestrial power grids and harm satellite electronics. The rate of this reconnection process is well understood experimentally and theoretically for reconnection between regions with symmetric, oppositely-aligned magnetic fields. However, many reconnection events at the Earth’s magnetopause occur between plasmas that, in addition to having non-symmetric magnetic fields, have different temperatures and densities. These additional asymmetries produce complications such as plasma diamagnetic drift, which are known to alter the reconnection rate. This study used massively parallelized code to simulate billions of individual plasma particles during a reconnection event. By repeatedly simulating reconnection with different initial temperature, density, and magnetic field configurations, our results address how the reconnection rate varies in asymmetric configurations. This project represents a step in being able to predict more realistic reconnection events in interplanetary space between the magnetic field of the Earth and the magnetic field of the Sun.

**Multimedia Project**(interactive when viewed with Acrobat)

**Development of Exploding Wire Plasma System for Studying Magnetic Reconnection**

**Development of Exploding Wire Plasma System for Studying Magnetic Reconnection***Landry Horimbere, University of Maryland, College Park*

*Landry Horimbere, University of Maryland, College Park**(Mentor: Prof. Dan Lathrop)*

*(Mentor: Prof. Dan Lathrop)*

We are developing an exploding wire plasma system to study magnetic field reconnection at high densities with a range of magnetic helicities. Magnetic helicity is a measure of the topological interlinkage of magnetic field loops and is conserved during reconnection. Magnetic reconnection plays a central role in energy transfer between magnetic fields and in the separation and merging of plasma structures. As a mode of magnetic energy dissipation, reconnection plays an important role in magnetic confinement devices for fusion research, in space weather phenomena such as solar flares, and in the energy transfer between the solar wind and earth’s magnetosphere. Past experiments exploring the interaction of plasma arcs with various helicity configurations have, in the counter helical case, yielded high soft X-ray fluxes and evidence of residual plasma structures. Our experiment will investigate higher particle, field and energy densities, as well as the effect of turbulent phase transition, on the evolution of reconnecting plasmas. To reach this parameter space, our experimental plasma is produced using the exploding wire method combined with an externally applied quadrupole guiding field to produce a highly non-linear screw pinch collision. We have constructed the experimental chamber and are in the process of constructing and testing the pulse power and diagnostic systems. >

**Multimedia Project****Esotaxis Beats Chemotaxis (The Effect of Substrate Texture on Collective Migration of ***Dictyostelium discoideum*)

**Esotaxis Beats Chemotaxis (The Effect of Substrate Texture on Collective Migration of***Dictyostelium discoideum*)*Molly Mosher, Pomona College*

*Molly Mosher, Pomona College**(Mentor: Prof. Wolfgang Losert)*

*(Mentor: Prof. Wolfgang Losert)*

Cell migration is important in many processes such as wound healing and cancer metastasis. The physical features of the surface over which cells move can affect migration outcomes. In this context, we aim to examine the effect of various nanoscale surface textures on collective cellular migration. The well-studied amoeba

*Dictyostelium discoideum*(Dicty) is a model system due to its relative durability and ease of manipulation, and because it presents a well-defined collective cellular migration cycle known as “streaming”. When starved, Dicty cells follow each other and migrate together in streams to form clumps of cells called mounds. This migration is facilitated by cyclic AMP (cAMP) signaling that results in directional polymerization of the cytoskeletal protein actin. We imaged the streaming cycle of the Dicty migrations using a bright field microscope and were able to establish successful streaming parameters such as total number of cells and imaging settings. By analyzing the behavior of the streams using particle image velocimetry and optic flow algorithms to track cells, we can Dicty stream on different surfaces. From preliminary data it appears that the surfaces cause a distinct phenotype change when compared to the control: Initially the cells are more active. However, as time passes we see unsuccessful streaming. This may be explained by the competition between both surfaces and cAMP competing for actin monomers within the cell, as both have been shown to facilitate the polymerization of actin. The next step of the study is to look at these occurrences on a smaller scale, imaging the cells at a higher magnification using fluorescent microscopy to investigate the behavior of the actin during the cells’ migrations on surfaces.

**Multimedia Project***Claudia Richoux, Chicago University*

*Claudia Richoux, Chicago University**(Mentor: Prof. Brian Beaudoin)*

*(Mentor: Prof. Brian Beaudoin)*

>UMER, or the University of Maryland Electron Ring, is a high-intensity but low-energy particle accelerator used mainly to study beam dynamics and optics applicable in larger accelerators. Horizontal steering is excellent, within a few millimeters of the ideal trajectory, but vertical steering is severely lacking, and it is not possible to make large vertical steering improvements without new magnets. This study demonstrates through simulation that ideal vertical steering is not feasible without the addition of about 18 new vertical steering dipole magnets to the ring. As a solution, a prototype of a modified dipole that includes vertical steerers is presented.

**Multimedia Project****Website on particle accelerators (like the Large Hadron collider) (Static PDF)**

**Investigation of Losses in Four-Wave Mixing Squeezed Light Experiments**

**Investigation of Losses in Four-Wave Mixing Squeezed Light Experiments***Ashay Patel, Williams College - Participation through JQI*

*Ashay Patel, Williams College - Participation through JQI**(Mentor: Prof. Paul Lett)*

*(Mentor: Prof. Paul Lett)*

Squeezed states are non-classical states of light with noise in either their intensity or phase below the standard quantum limit of those of a coherent state. The noise properties of squeezed states can be used to improve the sensitivity of the finest interferometers like LIGO, which has the capacity to detect gravitational wave activity. Furthermore, squeezed states are testbeds to study basic questions about quantum entanglement and quantum information. Our lab produces intensity-difference squeezed, entangled twin beams through four-wave mixing in a hot rubidium vapor cell. Since any loss in this system leads to the introduction of random vacuum fluctuations that reduce the measured squeezing, our experiments are very sensitive to minor losses. This project is an investigation of losses in the four-wave mixing setup in order to eliminate them and optimize the measured squeezing. I devised an improved, easily implemented scheme to heat the rubidium vapor cell to prevent metallic rubidium plating out onto the cell windows, causing loss. Furthermore, I designed, built, and tested a low noise, balanced photodetector for use in the squeezed light experiments. The group tested potentially higher quantum efficiency photodiodes, which show promise to improve the measured squeezing in the four-wave mixing experiments.