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# TREND Fair 2005

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**August 12, 2005**

### On this page... TREND 2005 Presentations

- Laser with Feedback in a Crisis: Transition from Dropouts to Coherence Collapse, Bethany Adams and Nathaniel Karst
- Measurement of Quantum Efficiency of Cesiated Silver Photocathodes, Anne Balter
- Power Input Measurements in Lorentz Force-Driven Turbulent Flows, Barbara Brawn
- Air Hockey Implies Chaos, Kristen Casalenuovo
- Imaging Optical Transition Radiation from 10 keV Electrons, Sean Casey
- Rotating Rayleigh-Benard Convection for High Rayleigh Numbers, Christie Chew
- Surface Flow of Sloshing Granular Matter, Kenneth Desmond
- Single-Particle Motion and Collective Plasma Dynamics in Thin Current Sheets, Robyn Dunstan
- Nonlinear Dynamics of Traveling Wave Tube Amplifiers, Lindsey Goodman
- Measurements of Droplet Pinch-Off in Liquid Sodium, Matthew Lohr
- Analyzing Fluctuations of Liposomal Membranes Induced by Laser-Directed Deformation, Jozsef Meszaros
- Exploring Hysteresis and Homogeneity of Gelatin Networks through Active and Passive Microrheology, Jacqueline Owens
- Fractal Patterns in Chaotic Mixing, Jennifer Rieser and Amir Ahmadi

### TREND 2005 Results

#### Winners

- Laser with Feedback in a Crisis: Transition from Dropouts to Coherence Collapse, Bethany Adams and Nathaniel Karst
- Surface Flow of Sloshing Granular Matter, Kenneth Desmond
- Fractal Patterns in Chaotic Mixing, Jennifer Rieser and Amir Ahmadi

#### Honorable Mention

- Power Input Measurements in Lorentz Force-Driven Turbulent Flows, Barbara Brawn

### Laser with Feedback in a Crisis: Transition from Dropouts to Coherence Collapse

#### Bethany Adams, Albright College

Nathaniel Karst, Olin College

Advisor: Professor Rajarshi Roy

By placing a mirror in front of a semiconductor laser and reflecting the beam back into the laser cavity, it is possible to create an external cavity laser system with a much higher number of lasing modes than the solitary laser can otherwise produce. The presence and interaction of these modes results in a chaotic output signal from the system. When the bias current is steadily increased, the laser output undergoes a series of transformations via an attractor-widening interior crisis from the low-frequency fluctuation (LFF) regime to fully developed coherence collapse. In order to more fully understand the complicated dynamics of this transition, we will explore the chaotic behavior of an external cavity semiconductor laser with optical feedback by increasing the injection current. We will additionally analyze the reconstructed attractors in the LFF regime through time-delay embedding of data collected and compare these phase space trajectories to those generated by numerical simulation.

### Quantum Efficiency of Cesiated Silver Photocathodes

#### Anne Balter, Oglethorpe University

Advisors: Professor Patrick O'Shea and Nathan Moody

Durable and efficient laser-driven photocathodes are imperative to the creation of high-quality electron beams for use in short-wavelength free electron lasers. In preparation for the fabrication of dispenser cathodes, the quantum efficiency and lifetime of cesiated silver was tested. Quantum efficiency (QE) is a useful figure of merit for photocathodes and is defined as the ratio of the number of photoemitted electrons to incident photons. By adding cesium to the silver surface, a reduction in the energy required to liberate electrons via photoemission from silver is observed. Experiments reveal the QE of Cs-Ag using a 405 nm continuous wave (CW) laser has a peak of approximately .09% for less than one atomic layer of cesium. The Cs-Ag cathode shows a lifetime in excess of 150 hours in a vacuum of several nano-torr (nT). The results found in this experiment have also been compared to a theory in development at the Naval Research Laboratory and a qualitative agreement is seen.

### Power Input Measurements in Lorentz Force-Driven Turbulent Flows

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

Advisor:Professor Daniel Lathrop

We experimentally measure the local power input in a turbulent flow. Instantaneous local power can be measured using the local velocity of the fluid element and the local force on that same fluid element: P = **U · F**. We determine the power by experimentally measuring **u**, while imposing a known body force **F**. The turbulent flow is produced via Lorentz forces, **F _{L} = J × B**, where

**J**is the applied current density and

**B**is an externally imposed magnetic field. Our experiment has evolved from creating flows in a saltwater medium, using electrodes and permanent magnets, to creating flows in liquid sodium, using electrodes and electromagnets. With this adaptation, we are able to utilize larger values of

**J**without extraordinary heating;therefore, larger forces are brought to bear in the experiment. Our method of characterizing these flows has moved from three-dimensional particle image velocimetry (PIV) to ultrasound velocity profiling. We have successfully used this system to observe flows within our liquid sodium experiment. With effective measurements of

**u**, we will indeed be able to improve our measurements of instantaneous local power fluctuations in turbulent flows and to examine our experiment's correspondence to the fluctuation dissipation theorem (FDT). We find that the ratio of positive-to-negative power probabilities is exponential to P, in agreement with the FDT. As

*local*power investigations lie outside the standard FDT context of global behavior, this suggests an extension of the theory to include local as well as global power fluctuations.

### Air Hockey Implies Chaos

#### Kristen Casalenuovo, Longwood University

Advisor: Professor James Yorke

Chaotic scattering is essentially the relationship between an input variable and its corresponding output variable. The chaotic scattering problem as expressed in its simplest example involves a point particle moving through a field of electric potential (i.e., the scattering region). The question is what is the relationship between the initial trajectory path and the shifting in direction caused by the interaction with the electric field? We are extending this chaotic scattering problem to macroscopic cases where the force of friction is involved. Due to the friction force, a torque will also be present in the collision, causing the rotational motions to interact as well. We have derived mechanical equations that factor in friction, elasticity, translational velocity, and angular velocity. Next, we parameterized the equations and compiled them into a Java animation program to visually examine the system while simultaneously extracting data. Our model is a two-dimensional billiards system of one spinning circular object (puck) entering into the scattering region bounded by two fixed, spinning objects (barriers). Our question is does friction cause a significant quantitative difference in the output and, if so, will previous observations that make scattering "chaotic" still hold true?

### Imaging Optical Transition Radiation from 10 keV Electrons

#### Sean Casey, Dickinson College

Advisor: Professor Patrick O'Shea, Dr. Donald Feldman, and Dr. Ralph Fiorito

When a charged particle propagating in a medium crosses the interface of another medium with a different dielectric constant, it annihilates its image charge and light is emitted. 10 keV electrons supplied by the University of Maryland Electron Ring (UMER) produced measurable light signals when fired at an A1 coated-Si OTR screen. At currents of 10-100 mA, light intensity was measured using a photomultiplier tube. Measurements of the angular distribution, polarization, and wavelength dependence of light through a quartz viewing window were made. The light intensity was on the same timescale and showed similar rise and fall times as the current pulse. The light intensity demonstrated linearity with respect to electron beam current, showed sin^{2}α dependence on polarizer angle α, and demonstrated a linear dependence on wavelength, all in accordance with theory. Additionally, the relative light intensity demonstrated a qualitative agreement with theoretical predictions of the angular distribution. We have observed optical transition radiation from 10 keV electrons.

### Rotating Rayleigh-Benard Convection for High Rayleigh Numbers

#### Christie Chew, University of Maryland College Park

Advisors: Professor Daniel Lathrop and Gregory Bewley

We will explore rotating Rayleigh-Benard convection at high Rayleigh numbers (large thermal forcing). Two large copper plates sit at either end of a vertically oriented hollow acrylic cylinder. The cylinder is filled with water in which convection occurs as the bottom plate is heated and the top plate cooled. The entire setup is mounted to rotate about the vertical axis. High Rayleigh numbers are achieved by both a large temperature difference between the plates and a large distance of separation between the plates, relative to the diameter of the cylinder. The behavior of the water in this high Rayleigh number rotating Rayleigh-Benard setup is observed using particle image velocimetry. Fluorescent polystyrene spheres are added to the water in a very small concentration which will allow measurements of the velocity field. Images will be taken by video camera to show the motion of particles at different points in time, from which the velocity can be determined. This information will provide insight into the behavior of convection with or without rotation. Rotating convection is ubiquitous in nature. For instance, the experimental setup is analogous to the earth's atmosphere, which is constantly cooled by the vastness of space on top and heated by the earth's surface on the bottom. Gaining insight into the behavior of fluid motion under such circumstances could prove valuable to understanding more about the world around us.

### Surface Flow of Sloshing Granular Matter

#### Kenneth Desmond, Rochester Institute of Technology

Advisors: Michael Newey and Assistant Professor Wolfgang Losert

We studied the fluidity of the flowing layer of grains in a tumbler through gentle sideways sloshing and how the flow of large and small particles differs. Monodisperse beads were rotated in a long partially filled drum while also being gently vibrated sinusoidal along the axial direction. As a result of the motion of the drum, the beads sloshed slightly back and forth also with sinusoidal motion. We compared the response of the sloshing for big and small particles. The response of the sloshing was a measure of the phase difference between the motion of the particles and the drum. It was determined that the phase difference is directly proportional to the frequency of vibration with a proportionality constant (η) that increased with fluidity. The proportionality constant may also be a measure of the fluidity of the grains, and η was shown to scale with the logarithm of rotation rate and the square root of the bead diameter.

### Single-Particle Motion and Collective Plasma Dynamics in Thin Current Sheets

#### Robyn Dunstan, Elizabethtown College

Advisors: Dr. Parvez Guzdar and Dr. Mikhail Sitnov

The orbits of charged particles in antiparallel and curved magnetic fields are analyzed. Adiabatic invariants and drift velocities for orbits in an antiparallel magnetic field are calculated. Chaos in a curved magnetic field is explored. The effect of a shear magnetic field component on orbits in a curved magnetic field with a small normal component is discussed. Collective plasma dynamics in current sheets with the thickness comparable to the thermal ion gyroradius are studied by means of a massively parallelized particle code. The effect of the magnetic shear on plasma dynamics is investigated.

### Nonlinear Dynamics of Traveling Wave Tube Amplifiers

#### Lindsey Goodman, Binghamton University

Advisor: Dr. John Rodgers

Traveling wave tube (TWT) amplifiers are often used in satellites to amplify RF signals. These amplifiers produce linear gain when the amplitudes of the input signals are relatively small. However, as the power of the input signal grows, gain becomes nonlinear and starts to behave in a complex fashion. The gain characteristics of each tube differ. Thus, using the 10-watt 8524H TWT amplifier, we will explore the behavior of the tube as the amplitudes and frequencies of the input RF signal are varied. Once a gain function is extracted for signals in the nonlinear regime, we will configure the tube as a time-delayed feedback oscillator. Theory has shown that the signal output will exhibit chaotic characteristics which will depend on this time-delayed feedback and the nonlinear gain characteristics of the tube. Ultimately, we hope to experimentally demonstrate the existence of this chaos and investigate the parameters leading to chaos in these systems.

### Measurements of Droplet Pinch-Off in Liquid Sodium

#### Matthew Lohr, Penn State University

Advisor: Professor Daniel Lathrop

Droplet separation in liquids results in very fine connecting capillaries which form moments before pinch-off. In previous studies of droplet pinch-off, the thinnest portion of the droplet neck was partially obscured due to the irregular shape of the liquid droplet. Instead of using an optical technique, our goal is to study this portion of the pinch-off by running an electric current vertically through the droplet neck, yielding a resistance proportional to the minimum cross-sectional area of the pinch-off. To create this electrically connected pinch-off, we slowly draw apart two sodium-wetted electrodes until the sodium bridge between the two electrodes pinches off. A similar study carried out by a research group at UC Irvine used mercury as the liquid medium. They observed minimum filament lengths of 2.7 nanometers. By using less resistive sodium as our liquid medium, we hope to reduce the RC time constant of the circuit and thus improve resolution at the point of pinch-off. This experiment could thus yield data to smaller length scales than the previous study, perhaps allowing us to observe pinch-off at the atomic level. We also intend to study the same pinch-off under the influence of a strong magnetic field.

### Analyzing Fluctuations of Liposomal Membranes Induced by Laser-Directed Deformation

#### Jozsef Meszaros, University of Maryland College Park

Advisors: Assistant Professor Wolfgang Losert and C. Poole

Giant unilamellar vesicles (GUVs), or liposomes, are an attractive model system for cellular membranes, permitting study of various important properties observable in many cells. In particular, the elastic properties of cell membranes can be studied most easily and without artifact through the use of GUVs. It is the deformable nature of many cells that allows their chemical and biological functions to be regulated. The research described herein outlines a procedure, along with pertinent results, useful for determining the elasticity and rigidity of dioleoylphosphatidylcholine giant unilamellar vesicles (DOPC-GUV). Unlike previous studies which have relied on micropipette aspiration or passive observation of GUVs, this research focuses exclusively on vesicles that are actively deformed with the aid of a holographic laser tweezer array. Fourier transforms are used to extract information about the amounts of elliptical and square character present in each GUV and how these amounts vary in time. From this information, rates of decay for various vesicles were determined to be between 3% and 13% elliptical character/sec; alternately, rates of decay for the fourth mode were found to vary between 9% and 50% "rectangular" character/sec. There was a strong dependence on the initial conditions, with vesicles that were initially more flexible displaying greater high mode fluctuations than their more rigid counterparts. With the aid of computer modeling, decay times for these modes could be related to specific elasticity constants of the cellular membrane.

### Exploring Hysteresis and Homogeneity of Gelatin Networks through Active and Passive Microrheology

#### Jacqueline Owens, University of Maryland College Park

Advisor: Assistant Professor Wolfgang Losert

Gelatin networks consist of denatured strands of collagen triple helices that have been renatured into loose strands lightly bound in regions by triple helices. We are studying gelatin networks through passive and active microrheology to determine the local strength and possible heterogeneity of the network. Silica microspheres 0.97 um in diameter are imbedded into gelatin networks and their thermal Brownian motion is measured and recorded. In active microrheology, a laser tweezer array is used to pull the 0.97 um microspheres through the network, and the resistive force of the network is measured. Characterization of motion through particle tracking, mean-squared displacements, and distribution of bead motilities are used to view multiple points in a very small sample, about 25 uL, and to determine the heterogeneity of local networks. Gelatin networks also experience a hysteretic loop by which their melting point and their gellation point are at different temperatures depending on whether the sample is being heated or cooled. In addition to determining the strength and homogeneity of gelatin networks as a function of temperature, we hope also to explore this hysteretic loop and to determine the state of the network between definite melting and definite gelation.

### Fractal Patterns in Chaotic Mixing

#### Jennifer Rieser, Georgia Institute of Technology

Amir Ali Ahmadi, University of Maryland College Park

Advisors: Professor Edwaard Ott and Professor Thomas Antonsen

We study the fractal properties of passive salar advection-diffusion in chaotic fluid flows. The spatial distribution of the passive scalar is numerically calculated as a function of time. As time increases, chaotic mixing causes the scalar density to develop variations on a finer and finer scale, therefore resulting in a fractal structure. We calculate the spectrum of the fractal dimension, D_{q}, to quantitatively characterize the observed fine scale pattern behavior. In order to compare our results to theoretical predictions for D_{q}, we compute both the distribution of finite-time Lyapunov exponents as well as the decay rate of the spatial scalar variance.