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# TREND Fair 2004

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**August 13, 2004**

### On this page... TREND 2004 Presentations

- Random Oscillating Gate Interactions, Julie Arrighi
- Lorentz Forces and Power Dissipation in Turbulent Flows, Barbara Brawn
- Chaotic Communication with Mutually Coupled Ring Lasers, Adam Cohen
- A Markov Partitioning Method for Maps on Surfaces, Alan Diaz
- Finding Stable Pepriodic Orbits in Families of One-Dimensional Maps, Michael Hall
- Dynamic Shear Band Dependence on Particle Size, Katie Newhall
- Velocimetry in Spherical Couette Flow with Independently Rotating Boundaries, Sandra Penny
- Communications with Macky-Glass Electronic Circuits, Chris Sramek
- Dictyostelium Manipulation Using Holographic Optical Tweezers, Ryan Smith
- Electron Energization in Magnetic Reconnection, Wor Thongthai

### Random Oscillating Gate Interactions

#### Julie Arrighi, Rensselear Polytechnic Institute

Advisor: Professor Daniel Lathrop

Logic gates will oscillate in various ways when connected in loops. Theory suggests that these oscillating gates, when connected into complex networks, will oscillate with characteristics similar to many natural networks. These other systems include neural, gene expression, and chemical reaction networks. Connecting our oscillating gates into networks of long loops has yielded lengthy, intricate, periodic, and aperiodic patterns. We hope that the resulting data will help test theories regarding the many ways natural systems interact with each other and how they behave as whole networks.

### Lorentz Forces and Power Dissipation in Turbulent Flows

(Presentation)

#### Barbara Brawn, University of Maryland College Park

Advisor: Professor Daniel Lathrop

Continuing our examination of the instantaneous local power in turbulent flows from TREND 2003, we will experimentally measure the local velocity in a sodium flow. Instantaneous local power can be expressed using the local velocity of the fluid element and the local force on that same fluid element: P=**U·F**. Our goal is to determine the power by experimentally measuring **u**, while specifying **F** in a volume. To obtain these measurements, we have constructed a container in which turbulent flow is produced via the Lorentz force, **F _{L}=J×B**, where

**J**is applied current density and

**B**is magnetic field. Our experiment has evolved from creating flows in a salt-water medium, using electrodes and permanent magnets, to creating flows in liquid sodium, using electrodes and electromagnets. We expect that, with this adaptation, we will be able to utilize larger values of

**J**and

**B**, and therefore larger forces in the experiment. Our method of characterizing these flows has moved from three-dimensional particle image velocimetry (PIV) to ultrasound velocity profiling. We have already used this system to observe flows within our liquid sodium experiment. It is our hope that, with effective measurements of

**u**, we will indeed be able to improve our measurements of instantaneous local power fluctuations in turbulent flows.

### Chaotic Communication with Mutually Coupled Ring Lasers

#### Adam Cohen, Bucknell University

Advisor:Professor Rajarshi Roy

Communication techniques using mutually coupled synchronized erbium-doped fiber ring lasers (EDFRLs) are demonstrated. High bandwidth digital communication masking and recovery are powerful applications of synchronized chaotic laser systems. Three schemes were designed and implemented that successfully encoded and decoded data. Computer simulation via a short timescale model of the EDFRL system showed good agreement with experimental results. Injection ring-down, message recovery threshold, and synchronization thresholds were quantified. Synchrony between mutually coupled systems is difficult to break and therefore is a robust means of communication.

### A Markov Partitioning Method for Maps on Surfaces

#### Alan Diaz, Georgia Tech

Advisor: Professor James Yorke

Finding a Markov partition is a useful step in studying the dynamics of a given map. Typically such partitions, whose boundaries consist of the stable and unstable manifolds of a given fixed point of the map, are constructed heuristically on a case-by-case basis. We propose a method for finding Markov partitions and explore its applicability for various 2d linear maps, particularly for automorphisms on the torus and square sphere. A goal is to prove that a two-part partitition can be found for any hyperbolic map on the torus. One motivation for this work comes from mixing problems involving zero Reynolds number flow (Stokes flow). Other researchers have noted that in Stokes flow one cannot expect to get mixing from the randomization coming out of inertial effects. However, a deterministic mixing process that is chaotic can be sought. Some such processes can be reduced to the types of maps on surfaces we have studied here.

### Finding Stable Periodic Orbits in Families of One-Dimensional Maps

#### Michael Hall, University of Maryland College Park

Advisors: Assistant Professor Brian Hunt

We investigate methods of detecting proximity to stable periodic orbits within families of parameter dependent dynamical systems. As our main example we use the quadratic family, x_{n+1} - (x_{n}^{2}) - C, with -1/4 < C < 2, though our methods will be applicable to experimental systems since they do not require knowledge of the underlying maps. We follow the trajectory of a point numerically, and when it exhibits near p-periodic behavior we examine the behavior an approximate derivative of the p^{th} iterate of our map. From the behavior of this derivative, we derive methods of locating parameter regions of stable periodic behavior.

### Dynamic Shear Band Dependence on Particle Size

#### Katie Newhall, RPI

Advisor: Assistant Professor Wolfgang Losert

Shear bands are investigated in the Taylor-Couette shear cell geometry with the inner cylinder and bottom surface connected and rotating. The shear band location, quantified by the angular velocity profile in the radial direction, is different for various depths of beads. A general linear velocity profile is observed upon reversal of shear direction, due to memory effects, and is independent of the steady state profile. The study of bidisperse mixtures as compared to monodisperse mixtures indicates the length scale for the material to return to steady state depends upon particle size.

### Velocimetry in Spherical Couette Flow with Independently Rotating Boundaries

#### Sandra Penny, University of Oregon, Eugene

Advisor: Professor Daniel Lathrop

We examine a system of two concentric independently rotating spheres with a fluid-filled gap of aspect ratio beta = 2.1. This spherical Couette geometry is of particular interest because of its similarity to the outer core of the earth. Using ultrasound Doppler velocimetry we obtain velocity ratios of poloidal (radial and polar) to toroidal (azimuthal) motions. In electrically conducting liquid, this type of flow may support self-generated magnetic fields when the poloidal:toroidal ratio is close to 1.0. We measure this ratio directly with an ultrasound velocity profiler in a variety of cases with different rotation rate ratio Ω_{inner}/Ω_{outer}. This data will be used to plan sodium experiments in a similar geometry.

### Communications with Macky-Glass Electronic Circuits

#### Chris Sramek, Rice University

Advisor:Professor Rajarshi Roy

We demonstrate an encoded communication system relying on synchronized chaotic time-delay circuits. Synchronization of coupled circuits based on the Mackey-Glass system has previously been shown. By encoding a message in the chaotic signal of a drive circuit and subtracting the synchronized signal from the response system, secure communication can be realized. Successful operation of such a system is demonstrated over a simple wire channel. Synchronization error and cross-correlation of the driver/response circuit outputs are measured when the coupling signal is band-limited by a filter.

### Dictyostelium Manipulation Using Holographic Optical Tweezers

(Presentation all files must be downloaded for it to play correctly)

#### Ryan Smith, Illinois Wesleyan University

Advisor: Assistant Professor Wolfgang Losert

We demonstrate the motility of *Dictoyostelium discoideum* cells. *Distyostelium* have an affinity for cyclic-AMP (cAMP). Through the use of holographic optical tweezers (HOTs), the cells can be manipulated with fine precision. Throughout the summer, a continuous supply of various genetically modified *Dictyostelium* cultures were sustained using known biological techniques. *Dictyostelium* as well as rat brain cancer cells were observed and manipulated under the HOTs. In addition, particle tracking was performed on a culture of cells moving towards a microfluidic injector filled with cAMP. From this data, velocities of the *Dictyostelium* can be obtained. Finally, a framework has been laid for future experiments to utilize the tweezers to study PIP3 aggregation as well as response to a change in cAMP gradient.

### Electron Energization in Magnetic Reconnection

#### Wor Thongthai, University of Idaho

Advisor: Professor James Drake

Magnetic reconnection is a process where magnetic field lines break and reform to release their magnetic energy into the surrounding plasma. This process is believed to be responsible for energizing charged particles observed in explosive events such as solar flares and violent magnetic storms in the Earth's magnetosphere. Although energetic electrons detected by satellites passing through the Earth's magnetotail has supported this notion, the exact mechanism of particle energization still remains unknown. While the diffusion region near the x-line is believed to be a location where electrons can be energized, there are proposals for electron energization in other regions as well. We examine the acceleration of particles and record their trajectories and energies by advancing test-particles in electromagnetic fields output from a full-particle reconnection simulation with nonzero guide field. We find that in addition to the diffusion region there is evidence of electron acceleration in the secondary island and in the low-density cavity along the separatrix.