Lucas Illing's homepage

Lucas Illing, Ph.D.: Associate Professor
In 1990, after the wall came down and I could finally visit my relatives in the "West", my uncle gave me a copy of J. Gleick's book, Chaos: Making a New Science. Ever since, I have been interested in and studied the complex behavior of nonlinear dynamical systems.

2018 Summer Students

Kees Benkendorfer
Reed College Science Research Fellowship: Stabilizing fast periodic solutions through bandpass filtering
Yunjia Bao
Delord-Mockett Fund: (1) Periodic and quasiperiodic dynamics of optoelectronic oscillators with narrowband time-delayed feedback.
(2) Amplitude Death in directly coupled optoelectronic oscillators.
Noah Shofer (Cambridge, Sperling)
Reservoir computer as observer for 2D spatio-temporal chaos

2017/2018 Thesis Students

Matthew Chau
Thesis: Analyzing 3-Point Symmetric Contacts of Photoelastic Disks
A method is developed for determining the magnitude of three point-contact forces that symmetrically compress a photoelastic disk.
Giovanni Corti
Thesis: Avalanches in Granular Material
In this thesis the physics of granular avalanches are investigated. A rough inclined plane is constructed and the angles of inclination at which a layer of known uniform thickness is either stable, meta-stable or unstable are measured. The location of stability region boundaries are compared to theoretical predictions and we find a good match to the data.
Noah Shofer (Cambridge, Sperling)
Thesis: Reservoir Computing: Memory, Nonlinearity, and Spatial Observers
This thesis covers the background and implementation of reservoir computers. We show that these reservoir computers can act as observers for the Lorenz and Rössler chaotic systems, i.e. they are able to predict unobserved dynamical variables of these systems, and are able to learn the Lorenz or Rössler attractors. Furthermore, coupled map lattice dynamics were generated experimentally and in silico. We found an optimized parameter set that enabled the reservoir computer to predict the dynamics of the unobserved nodes of a 1D lattice when given the dynamics of a few nodes within the lattice.

2017 Summer Students

Yunjia Bao
Reed College Science Research Fellowship: Dynamics of dual delay oscillators with narrowband feedback
Edgar Perez (NIST, U Maryland)
A high speed all electronic programmable time delay

2016/2017 Thesis Students

Yuka Esashi (UC Boulder/JILA)
Thesis: Generation and Characterization of Nondiffracting Beams
The theory and application of nondiffracting beams beams are reviewed, and the generation of these beams using a setup involving a spatial light modulator is described. Several interesting properties of these beams, including propagation-invariance, self-healing, and angular momentum were measured and found to be in good agreement with theory.
Robby Gottesman
Thesis: Lighting the Way: Computations of Stable Forms of Optical Lift
An optical ray tracing module was developed in Mathematica to characterize the efficiency of optical wing designs. This procedure calculates the optical forces and resulting torque on a homogenous, transparent body with constant index of refraction and finds whether the body experiences stable angles of attack and lift forces.
Lara Kincheloe (SFSU)
Thesis: Maxwell's Dæmon in an Information Engine
This thesis is an exploration of the implications of associating thermodynamic entropy with information, and the ways in which chaos dynamics inform the association. The Szilárd engine is identified as a system of particular interest and its thermodynamic, informational, and chaotic properties are assessed and compared with two physical systems exhibiting similar dynamical behavior.

2016 Summer Students

Ella Banyas (UC Berkeley)
James Borders Physics Student Fellowship: Amplitude and phase dynamics of delay coupled oscillators
Kyu Yeon Cho
Summer Experience Award: Fun with bucket brigade devices
Edgar Perez
Reed College Science Research Fellowship: A flexible electronic programmable time delay
Noah Shofer
Reed College Science Research Fellowship: An electro-optic device to investigate cluster synchronization

2015/2016 Thesis Students

Ace Furman (UT Austin)
Thesis: Electromagnetically Induced Transparency: The Zeeman Method
Electromagnetically induced transparency (EIT) — a quantum phenomenon wherein a material undergoes optical and dispersive modifications under the influence of resonant electromagnetic fields — was observed in warm rubidium vapor using the Zeeman method.
Mateo Ochoa Coloma
Thesis: Origins of Chaos in Nonlinear Oscillatory Hamiltonian Systems
An exposition of chaos in perturbed, oscillatory Hamiltonian systems is provided, including the fundamentals of the Hamiltonian formalism, the construction of Hamiltonian maps, and the use of the KAM theorem and the Poincare-Birkhoff theorem to identify the origin of chaos in the vicinity of the separatrix for arbitrarily small perturbation strengths.
Colleen Werkheiser (Harvard)
Thesis: The Dynamics of a Nonlinear Time-Delayed Electronic System
We study the dynamics of a nonlinear time-delayed electronic oscillator consisting of a comparator, time delay, lowpass filter, and amplifier. Positive feedback resulted in a signal that decayed in finite time, while negative feedback resulted in slowly oscillating periodic solutions.

2013/2014 Thesis Students

Anya Demko
Thesis: Dynamic Stabilization of an Invert Pendulum
Counter to intuition, the inverted position of a pendulum with a vertically oscillating pivot point can be stable. A pendulum is constructed using a mechanical wave driver to oscillate the pendulum's pivot point. Experimentally determined regions of stability agree well with theoretically predicted boundary lines.
Rachel Pincus
Thesis: Photoacoustic spectroscopy: a method for investigating weak molecular absorption
Photoacoustic spectroscopy is ideal for the study of samples exhibiting low absorption of light. This thesis aims to explain the basic theory and construction of a photoacoustic spectrometer. To validate its construction, studies were conducted on laboratory air and nitrous oxide.
Tobias Koppel
Thesis: Demonstrating a Negative index of Refraction
A metamaterial intended to have a negative index of refraction is fabricated using aluminum plates and split ring resonators printed onto circuit boards. The angle of refraction is used to characterize the index of refraction of the material.

2013 Summer Students

Dan Guo
Chaos in hybrid dynamical systems
Lindsay Sonderhouse
Phase dynamics of two mutually coupled optoelectronic systems with unequal delays
Andrew Warren
Reed College Science Research Fellowship: Phase and amplitude dynamics of delay-coupled oscillators

2012/2013 Thesis Students

Xueping Long (UCLA)
Thesis: Implementation of a Chaotic Electromechanical Oscillator Described by a Hybrid Differential Equation
This thesis describes an electromechanical oscillator whose governing equation of motion is an exactly solvable chaotic differential equation that takes the form of a force driven harmonic oscillator with negative damping coeffcient and a discrete switch condition to control and set two different equilibrium positions. Strong agreement is found between experiment and analytic solutions.
Jon Kindem (Applied Physics at Caltech)
Thesis: Optical Precursors
Starting from Maxwell's equation, the weakly dispersive, narrow resonance approximation is used to derive expressions for the time evolution of the precursor field. Optical precursors are experimentally observed in cold rubidium gas in a magneto-optical trap and a stacking effect between multiple off-resonance precursors is achieved.
Lukas Kuczynski (Portland: Lightcraft Technology)
Thesis: Extending Piecewise-Linear Chaos to Ultra-High-Frequencies Using Time-Delayed Feedback
Extension of exactly solvable piecewise-linear chaos to the regime of ultra-high-frequencies. In doing so, the issues surrounding the decreased timescale of dynamics are mitigated through the use of time-delayed feedback and control loops in a fully electronic circuit.
Lindsay Sonderhouse (NIST; UC Boulder)
Thesis: Phase and Amplitude Instability in an Optoelectronic Oscillator with Delayed Self-Feedback
The dynamics of a single optoelectronic oscillator perturbed by time-delayed self-feedback are explored experimentally and investigated theoretically through the Kuramoto (phase only) model and the Stuart-Landau (phase and amplitude) equation. The experimentally observed behavior can be explained by the stability conditions derived using the Stuart-Landau model but is inconsistent with the predictions of the Kuramoto model.

2012 Summer Students

Xueping Long
Exactly Solvable Chaos
Cris Panda
Dynamics of coupled optoelectronic systems with unequal delays

2011/2012 Thesis Students

Gray Davidson
Thesis: The Damped Driven Pendulum: Bifurcation Analysis of Experimental Data
When a pendulum is acted on both by a velocity dependent damping force, and a periodic driving force, it can display both ordered and chaotic behaviors, for certain ranges of parameters. Chaotic dynamics and the damped driven pendulum are examined via a professionally manufactured instrument from Daedalon.
Wes Erickson (UOregon)
Thesis: Electromagnetically Induced Transparency
Electromagnetically induced transparency (EIT) is a phenomenon that dramatically modifies the optical properties of a medium by creating a transparency window at a normally highly absorbing atomic resonance, and by greatly enhancing the medium's dispersion. The electric susceptibility describing these properties is derived and an experimental setup to observe the effect is detailed, including results demonstrating EIT in Rubidium 87.
Cris Panda (Harvard)
Thesis: Phase Dynamics and Synchronization of Delay-Coupled Optoelectronic Oscillators
We study experimentally, numerically, and analytically the phase dynamics and synchronization of two nonlinear optoelectronic oscillators with weak time-delayed mutual coupling and strong time-delayed self-feedback. Three distinct phase dynamic behaviors are observed as a function of the ratio of coupling to feedback delay: in-phase locking, anti-phase locking, and multi-timescale oscillations.
Jeremy Lawrence (Portland: Celly)
Thesis: Analyzing photoelastic disks
We develop methods for determining the forces acting on a single diametrically compressed photoelastic disk by analyzing the fringe pattern the disk exhibits when viewed in a crossed circular polariscope illuminated with monochromatic light.

2011 Summer Students

Cris Panda
Chaos and Synchrony of optoelectronic delay system.

2009-2010

Lauren Shareshian, M.A. in Mathematics: Research Assistant
Nonlinear dynamics of coupled delay systems.

2010 Summer Students

Cris Panda
Chaos and Synchrony in a system of three optoelectronic delay system.
Conference Presentation: Isochronous chaos synchronization of delay-coupled optoelectronic oscillators, 12th Annual Meeting of the Northwest Section of APS, Walla Walla, WA, Oct 1-2, 2010 (poster). Bulletin of the APS, Vol. 55, Num. 6
Paper: L. Illing, C. D. Panda, and L. Shareshian, Isochronal chaos synchronization of delay-coupled optoelectronic oscillators, Phys. Rev. E, vol. 84, 016213 (2011).
Alison Saunders (SLAC National Accelerator Laboratory; UC Berkeley)
Reed College Science Research Fellowship: The dynamics of the Malkus water wheel.
Conference Presentation: The dynamics of the Malkus water wheel, 12th Annual Meeting of the Northwest Section of APS, Walla Walla, WA, Oct 1-2, 2010 (poster). Bulletin of the APS, Vol. 55, Num. 6
Papers: L. Illing, A. M. Saunders, and D. Hahs, Multi-parameter identification from scalar time series generated by a Malkus-Lorenz water wheel, Chaos, vol. 22, 013127 (2012).
L. Illing, R. F. Fordyce, A. M. Saunders, and R. Ormond, Experiments with a Malkus-Lorenz water wheel: Chaos and Synchronization, Am. J. Phys., vol. 80 (3), 192 (2012).

2009/2010 Thesis Students

Greg Hoth (Materials Science Inst. at UOregon; NIST; UC Boulder)
Thesis: The Dynamics of Delay Coupled Optoelectronic Devices
The oscillation onset for a pair of cross-coupled optoelectronic oscillators is investigated experimentally, analytically, and numerically. It is shown that these systems undergo a sharp onset of oscillations at a critical value of the coupling strength and that there is a scaling law that governs the relationship between the coupling strength and the amplitude of oscillations.
Conference Presentation: The scaling behavior of oscillations arising in delay-coupled optoelectronic devices, APS March Meeting 2010, Portland, OR, May 15-19, 2010 (talk). Bulletin of the American Physical Society, Vol. 55, Num. 2
Paper: L. Illing, G. Hoth, L. Shareshian, and C. May, Scaling behavior of oscillations arising in delay-coupled optoelectronic oscillators,
Phys. Rev. E, vol. 83, 026107 (2011).
Sam Spencer (Optics Institute at URochester)
Thesis: Active Modelocking an Open-Cavity Helium-Neon Laser
We discuss the physical mechanisms that lead to modelocking as well as the nonlinear phenomenon of injection locking and the role it plays in making modelocking an experimental reality. We experimentally demonstrate modelocking using a Helium-Neon laser tube with external cavity mirrors and an acoustooptic modulator.

2009 Summer Students

Matthew Jemielita (UOregon)
Bifurcations and modeling of a pulsed opto-electronic delay system.
Greg Hoth
Reed College Science Research Fellowship: Dynamics of cross-coupled opto-electronic delay systems.
Adarsh Pyarelal (UArizona)
Chaotic dynamics and bifurcations of the Malkus Water Wheel.

2008/2009 Other Advisees

Kevin J. Lynagh
Reed College Melon Foundation Opportunity Grant: Nanopore Sequencing

2008/2009 Thesis Students

Rachel Fordyce (Plant Biology at UC Davis)
Thesis: Chaotic Waterwheel
Experimental implementation of the chaotic Malkus waterwheel, a mechanical device whose dynamics are modeled by the famous Lorenz equations. The observed dynamical behavior in both the chaotic and periodic operating regime is analyzed qualitatively using phase space plots and spectra.
Paper: L. Illing, R. F. Fordyce, A. M. Saunders, and R. Ormond, Experiments with a Malkus-Lorenz water wheel: Chaos and Synchronization, Am. J. Phys., vol. 80 (3), 192 (2012).
Cody Myers
Thesis: Monochromatic Plane Waves in a Corrugated Tube System
Experimental and theoretical study of acoustic transmission properties of a corrugated tube. As with many periodic systems, there are band gaps for the acoustic wave propagation through the corrugated tube, i.e. large ranges of incident sound frequency over which there is virtually no sound transmission.

2008 Summer Students

Matthew Jemielita
Reed College Science Research Fellowship: Bifurcations of a pulsed opto-electronic delay system
Christopher May
Chaos synchronization of mutually coupled opto-electronic devices.
Seth Terashima
Chaos and bifurcations in the electronic "Rulkov" circuit.

2007/2008 Thesis Students

Drew Atwater (Environmental Sciences at UC Riverside)
Thesis: A Brief Study of Thermoacoustic Cooling
Experimental and theoretical study of a thermoacoustic engine, a device where sound from a speaker is used to establish and maintain a temperature difference across a stack inside a pipe.
Christopher May (Portland: Lucky Sort, Puppet Labs)
Thesis: Feedback, Synchronization, and Communication in Chaotic Time-Delay Opto-Electronic Feedback Circuits
Feeding back an amplified output signal of a nonlinear device to itself can result in self-sustained oscillations. Here, the nonlinearity is an integrated opto-electronic mach-zehnder modulator and the oscillations can be periodic or chaotic, depending on the feedback strength. Synchronized chaotic oscillations are achieved by coupling two such devices, which then are utilized for communication.
Conference Presentation: Chaos Synchronization and Communication using Optoelecronic Time-Delay Feedback Circuits, 10th Annual Meeting of the Northwest Section of APS, Portland, OR, May 16-17, 2008 (poster).
Bulletin of the American Physical Society, Vol. 53, Num. 6, C1.00006
Paper: L. Illing, G. Hoth, L. Shareshian, and C. May, Scaling behavior of oscillations arising in delay-coupled optoelectronic oscillators,
Phys. Rev. E, vol. 83, 026107 (2011).
Erin McCowen (Forestry at Colorado State University)
Thesis: Bioconvection: The Effect of Density on Wavelength
Bioconvection of Bacillus subtilis, a phenomenon where the interplay of active upward swimming of the bacteria, gravity, and fluid dynamics result in spontaneous pattern formation.