# Kurt WiesenfeldGeorgia Institute of Technology | GT · School of Physics

Kurt Wiesenfeld

PhD

## About

186

Publications

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25,433

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## Publications

Publications (186)

We report in experiment and simulation the spontaneous formation of dynamically bound pairs of shape changing smarticle robots undergoing locally repulsive collisions. Borrowing terminology from Conway's simulated Game of Life, these physical `gliders' robustly emerge from an ensemble of individually undulating three-link two-motor smarticles and c...

A variety of nonequilibrium systems display intermittent switching between semistable macroscopic behaviors. We identify a certain type of indeterminacy, with episodes of patterned behavior irregularly punctuated by transitions. It appears that the long-lived patterns are, not coincidentally, also low-fluctuation states. We describe these linked tr...

Noise and disorder are known, in certain circumstances and for certain systems, to improve the level of coherence over that of the noise-free system. Examples include cases in which disorder enhances response to periodic signals, and those where it suppresses chaotic behavior. We report a new type of disorder-enhancing mechanism, observed in a mode...

Self-organization is frequently observed in active collectives, from ant rafts to molecular motor assemblies. General principles describing self-organization away from equilibrium have been challenging to identify. We offer a unifying framework that models the behavior of complex systems as largely random, while capturing their configuration-depend...

Self-organization is frequently observed in active collectives as varied as ant rafts and molecular motor assemblies. General principles describing self-organization away from equilibrium have been challenging to identify. We offer a unifying framework that models the behavior of complex systems as largely random while capturing their configuration...

Robot locomotion is typically generated by coordinated integration of single-purpose components, like actuators, sensors, body segments, and limbs. We posit that certain future robots could self-propel using systems in which a delineation of components and their interactions is not so clear, becoming robust and flexible entities composed of functio...

Localized traveling-wave solutions to a nonlinear Schrödinger equation were recently shown to be a consequence of Fourier mode synchronization. The reduced dynamics describing mode interaction take the form of a phase model with novel ternary coupling. We analyze this model in the presence of quenched disorder and explore transitions to partial and...

A clinical study of tinnitus patients found promising results using a noninvasive therapy. We introduce a dynamical model to explore both the onset of tinnitus and the effects of coordinated reset therapy. Our model extends an existing theory of individual outer hair cell dynamics to include their mutual interaction, and considers how sustained act...

Localized traveling-wave solutions to a nonlinear Schrodinger equation were recently shown to be a consequence of Fourier mode synchronization. The reduced dynamics describing mode interaction take the form of a phase model with novel ternary coupling. We analyze this model in the presence of quenched disorder and explore transitions to partial and...

Natural and artificial self-propelled systems must manage environmental interactions during movement. In complex environments, these interactions include active collisions, in which propulsive forces create persistent contacts with heterogeneities. Due to the driven and dissipative nature of these systems, such collisions are fundamentally differen...

The damped driven nonlinear Schrödinger equation (NLSE) has been used to understand a range of physical phenomena in diverse systems. Studying this equation in the context of optical hyperparametric oscillators in anomalous-dispersion dissipative cavities, where NLSE is usually referred to as the Lugiato-Lefever equation, we are led to a reduced no...

We investigate the dynamical origin of synchronization and phase locking of hyperparametric oscillations in Kerr-nonlinear media. These oscillations occur in the presence of parametric gain and, although arising from modulational instability of random vacuum fluctuations with arbitrary phases, lead to phase-locked states in the form of pulse trains...

We introduce a new, reduced nonlinear oscillator model governing the spontaneous creation of sharp pulses in a damped, driven, cubic nonlinear Schroedinger equation. The reduced model embodies the fundamental connection between mode synchronization and spatiotemporal pulse formation. We identify attracting solutions corresponding to stable cavity s...

We introduce a new nonlinear oscillator model governing the spontaneous creation of ultrashort pulses in Kerr-nonlinear parametric oscillators. This model explains the π and π/2 steps in our phase spectrum measurements of microresonator-based frequency combs.

We propose a method for soliton formation in whispering-gallery-mode (WGM)
resonators through input phase modulation. Our numerical simulations of a
variant of the Lugiato-Lefever equation suggest that modulating the input phase
at a frequency equal to the resonator free-spectral-range and at modest
modulation depths provides a deterministic route...

We investigate the dynamical origin of phase locking of optical frequency combs in Kerr-nonlinear media using few-mode approximations of the Lugiato-Lefever equation. We find analytical expressions which reveal the essence of phase locking.

Experiments on mechanical oscillator arrays show that complete inphase synchronization can emerge in a matter of minutes, even for fairly large arrays started from random initial conditions. At the same time, one expects complete inphase synchronization to become increasingly difficult to observe as array size grows. We explore the conditions under...

Gram-positive bacteria can transport molecules necessary for their survival through holes in their cell wall. The holes in cell walls need to be large enough to let critical nutrients pass through. However, the cell wall must also function to prevent the bacteria's membrane from protruding through a large hole into the environment and lysing the ce...

We study the role of amplifier saturation in eliminating feedback noise in
self-sustained oscillators. We extend previous works that use a saturated
amplifier to quench fluctuations in the feedback magnitude, while
simultaneously tuning the oscillator to an operational point at which the
resonator nonlinearity cancels fluctuations in the feedback p...

Undulatory locomotion, a gait in which thrust is produced in the opposite direction of a traveling wave of body bending, is a common mode of propulsion used by animals in fluids, on land, and even within sand. As such, it has been an excellent system for discovery of neuromechanical principles of movement. In nearly all animals studied, the wave of...

DOI:https://doi.org/10.1103/PhysRevLett.109.209902

We study vertical jumping in a simple robot comprising an actuated
mass-spring arrangement. The actuator frequency and phase are systematically
varied to find optimal performance. Optimal jumps occur above and below (but
not at) the robot's resonant frequency $f_0$. Two distinct jumping modes
emerge: a simple jump which is optimal above $f_0$ is ac...

We develop a generic iterative map model of coupled oscillators based on simple physical processes common to many such systems. The model allows us to understand, from a unified perspective, the range of different outcomes reported for experiments by Huygens and modern realizations of his two coupled clocks.

A significant degree of heterogeneity in synaptic conductance is present in neuron to neuron connections. We study the dynamics of weakly coupled pairs of neurons with heterogeneities in synaptic conductance using Wang-Buzsaki and Hodgkin-Huxley model neurons which have Types I and II excitability, respectively. This type of heterogeneity breaks a...

This report summarizes our five year project to study coherent beam combining using an array of passively coupled fiber lasers. Our approach is a novel one, based on a dynamical description of the fundamental physical processes involved. Our primary objective was to develop a fundamental, quantitative understanding of coherent beam combining in fib...

Some 344 years ago (give or take) Chritiaan Huygens observed two pendulum clocks spontaneously synchronize; the pendulums always locked in anti-phase. He traced the interaction to the minute motion of the wooden beam which supported the two clocks. In contrast, a simple classroom demonstration using metronomes in place of pendulum clocks -- with th...

We compare a simple dynamical model of fiber laser arrays with independent experiments on two coupled lasers. The degree of agreement with experimental observations is excellent. Collectively the evidence presented supports this dynamical approach as an alternative to the traditional static eigenmode analysis of the coupled laser cavities.

Recent experiments have demonstrated synchronization of fiber laser arrays at low and moderate pump levels. It has been suggested that a key dynamical process leading to synchronized behavior is the differential phase shift induced by the gain media. We explore theoretically the role of this effect in generating inphase dynamics. We find that its p...

With modification, a recently proposed laser array model is found to agree quantitatively with fiber laser experiments. Comparisons of transient behavior, stable dynamical states, and transitions are made using both previously published and new experiments. While the original model agrees well for fibers with relatively low losses, achieving quanti...

In this chapter, we discuss a surprising discovery made in the 1980s known as stochastic resonance. It concerns a cooperative
effect seen in certain nonlinear systems in the presence of random noise. The signature of stochastic resonance is that the
coherence of the system output improves with an increase of random noise, at least over some range o...

We propose a modification of the Kuramoto model to account for the effective change in the coupling constant among the oscillators, as suggested by some experiments on Josephson junction, laser arrays, and mechanical systems, where the active elements are turned on one by one. The resulting model is analytically tractable and predicts that both fir...

We present a theory which connects two-state and excitable versions of stochastic reso-nance. The latter appears as an extreme asymmetric limit of traditional two-state rate theory. To achieve this unified view we are led to a simple generalization of excitable stochastic resonance.

A largely adopted model for the description of high-temperature superconductors such as BSCCO results in several long Josephson junctions one on the top of the other (“stacked”). The dynamics of the basic nonlinear excitation of the isolated long Josephson junction, the Josephson vortex, is modified by the coupling among the junctions, so the motio...

Noise and coupling can optimize the response of arrays of nonlinear elements to periodic signals. We analyze such array-enhanced stochastic resonance (AESR) using finite-state transition rate models. We simply derive the transition rate matrices from the underlying potential energy function of the corresponding Langevin problem. Our implementation...

A novel synchronization mechanism observed in a model of coupled fiber laser arrays is explained [1]. The arrays can operate in a highly coherent way if some elements are driven more strongly than others. The synchronized state of such an inhomogeneous array, although sub-optimal relative to a uniformly pumped array, is far more robust with respect...

Synchronization of coupled fiber lasers has been reported in recent experiments [Bruesselbach, Opt. Lett. 30, 1339 (2005); Minden, Proc. SPIE 5335, 89 (2004)]. While these results may lead to dramatic advances in laser technology, the mechanism by which these lasers synchronize is not understood. We analyze a recently proposed [Rogers, IEEE J. Quan...

We describe a mutual synchronization mechanism observed in a model of fiber laser arrays. Though suboptimal in terms of total coherent power, the weak-link-synchronized state is far more robust than the in-phase state of a uniformly pumped array, with respect to parameter mismatch among the individual elements. We find similar dynamical behavior in...

Self-organized criticality refers to a mechanism whereby complex dissipative dynamical systems naturally evolve to a self-sustaining critical point, exhibiting correlations on all length scales and time scales. A recent theory based on a real space renormalization group approach sheds light on fundamental aspects of the phenomenon.

A prime example of long-range cooperative behavior is when populations of nonlinear oscillators spontaneously synchronize. This phenomenon crops up in many places in biology and applied physics. Some twenty years ago, Yoshiki Kuramoto introduced a simple tractable model which captures key elements of the phenomenon. It also provides new answers to...

In transducing mechanical stimuli into electrical signals, at least some hair cells in vertebrate auditory and vestibular systems respond optimally to weak periodic signals at natural, nonzero noise intensities. We understand this stochastic resonance by constructing a faithful mechanical model reflecting the hair cell geometry and described by a n...

Fiber lasers have small size, high conversion rates and excellent thermal properties. On the other hand they generally produce smaller output intensity than semiconductor lasers. Recent experiments reported that a small number of fiber lasers can be synchronized simply by coupling them with an optical waveguide coupler near the output end. As a res...

Recent experiments have shown that a small number of fiber lasers can spontaneously form coherent states when suitably coupled. The observed synchrony persisted for a long time without any active control. In this paper, we develop a dynamical model for fiber laser arrays that is valid in the high gain regime. In the limiting case of a single laser...

Recent experiments (1) have shown that a small number of fiber lasers can spontaneously form coherent states when suitably coupled. The observed synchrony persisted for a long time without any active control. In this paper we develop a dynamical model for fiber laser arrays that is valid in the high gain regime. Analysis and simulations of the mode...

Josephson junction arrays provide an ideal physical realization for studying the complex dynamics of the sort found in sandpile models. They provide a means of separately investigating the dual physical effects of nonlinearity and disorder, and hold promise as an example for establishing a rigorous connection between the governing differential equa...

We use an averaging method to study the dynamics of a transmission line studded by Josephson junctions. The averaged system is used as a springboard for studying experimental strategies which rely on spatial non-uniformity to achieve en-hanced synchronization. A reduced model for the near resonant case elucidates in physical terms the key to achiev...

We describe a peculiar type of spontaneous synchronization in a transmission line studded with nonlinear oscillators. After a transient period of complicated interactions, the elements form strongly synchronized pairs with interactions between these pairs virtually nil. The creation of these “dynamical dimers” appears to stem from the coupling intr...

We study a cellular automaton derived from the phenomenon of magnetic flux creep in two-dimensional granular superconductors. We model the superconductor as an array of Josephson junctions evolving according to a set of coupled ordinary differential equations. In the limit of slowly increasing magnetic field, we reduce these equations to a simple c...

A remarkable property of nonlinear oscillators is that, when coupled to each others, they can adjust their phases and frequencies and oscillate in synchrony. Coupled oscillators are used to model various systems in science and engineering such as lasers, Josephson junction arrays, generators in power plants, cardiac pacemaker cells and many others....

Using functional magnetic resonance imaging (fMRI), we studied the neural correlates of the complexity of rhythmic finger tapping. Our experiments measured the brain activity of 13 subjects performing rhythmic tapping on a response box with multistable rhythms of 1 to 5 different interresponse intervals. From the button press response times, we con...

We explore the transition to in-phase synchronization in globally coupled oscillator arrays, and compare results for van der Pol arrays with Josephson junction arrays. Our approach yields in each case an analytically tractable iterative map; the resulting stability formulas are simple because the expansion procedure identifies natural parameter gro...

An analytic approach that has recently led to dramatic progress in the study of Josephson junction arrays was explored. The method was applied to a globally coupled array of van der Pol oscillators. The result for the stability boundary of the in-phase state was found to be simple and in agreement with numerical simulations. However, its structure...

Stochastic resonance has been studied intensively by physicists over the past decade or so. The phenomenon is seen in an extraordinarily wide variety of physical systems. More recently, researchers have asked whether stochastic resonance may be relevant to problems in sensory biology. We give a brief overview of the subject and discuss our work on...

At high frequencies, the dynamics of a Josephson array shows fundamental differences from its low-frequency behavior. We consider a simple array where the high-frequency effects are dominant, a current biased series array without any external load. Despite the absence of a load, the oscillators are dynamically coupled at high frequencies, and synch...

Using functional magnetic resonance imaging, we investigate the variation in dynamical complexity of human brain activity for different mental loads. Our experiments measured the activity of ten subjects under three experimental conditions: a rest condition, a periodic task of finger opposition, and a task of finger opposition alternated with mathe...

The 336–year–old synchronization observations of Christiaan Huygens are re–examined in modern experiments. A simple mode of synchronization is proposed.

By deriving an N-dimensional Poincare map, we explore the enhanced stability of Josephson series arrays using capacitive junctions. The analytic expression for the critical Floquet multiplier has a direct physical interpretation, affording new insight into the conditions that affect inphase stability. In particular, we generalize the well-known sta...

The 336-year-old synchronization observations of Christiaan Huygens are re-examined in modern experiments. A simple model of synchronization is proposed.

As dynamical models, cellular automata sometimes provide compelling alternatives to differential equations. In addition to rapid simulations, their stylized dynamics may elucidate the essence of the underlying physics. In this Letter, we demonstrate the efficacy with which cellular automata can model spatiotemporal nonlinear dynamics. We explicitly...

We have investigated variations in the excitability of mammalian cutaneous mechanoreceptor neurons. We focused on the phase dynamics of an action potential relative to a periodic stimulus, showing that the excitability of these sensory neurons has interesting nonstationary oscillations. Using a wavelet analysis, these oscillations were characterize...

A controlled stochastic resonance circuit applies stochastic resonance to bias a nonlinear device with a control signal having a selected amplitude, frequency, and phase to enhance or suppress the response of the device to a periodic signal embedded in noise.

This Resource Letter provides a guide to the literature on scaling laws in physics and allied fields. Journal articles and books are cited for the following topics: dimensional analysis, critical phenomena, fractals, nonlinear dynamics, and nonequilibrium physics.

We study the oscillator equations describing a particular class of nonlinear amplifier, exemplified in this work by a two-junction superconducting quantum interference device. This class of dynamic system is described by a potential energy function that can admit minima (corresponding to stable solutions of the dynamic equations), or "running state...

The problem of disordered two-dimensional arrays of underdamped
Josephson junctions is addressed. Our simulations show that when coupled
to a high-Q cavity, the array exhibits synchronized behavior, and the
power emitted can be considerably increased once enough junctions are
activated to pump the cavity. The highly resonant cavity induces
synchron...

We study the normal form equation arising for spike generation in a Morris-Lecar model of cortical pyramidal cells--and oscillations in two-junction Superconducting Quantum Interference Device (SQUID) magnetometers--when these systems are tuned close to their saddle-node bifurcation point. Just beyond the onset of the spontaneous oscillations, thes...

The complex dynamics of avalanching systems is usually studied using "toy" cellular automaton models. The connection between these and conventional physics models is poorly understood. This complicates the discussion of whether self-organized criticality is relevant to realistic physical systems. An excellent candidate to explore these issues is pr...

We study the entrainment of coupled solid-state lasers by an external injected field. We show that the total output intensity exhibits unexpected nonmonotonic behavior as a function of the injected field and find the critical amplitude marking the transition to the low-intensity branch. In addition, we also show that substantial partial entrainment...

We consider a relatively new application of mutually interacting, synchronized oscillators. The idea is to intentionally introduce variations among the elements to induce phase shifts between the oscillators. Though often unwanted, in certain instances these phase shifts are highly desirable: We discuss how to manipulate array parameters in order t...

We resolve a long standing puzzle concerning synchronization in Josephson junction series arrays. We introduce a modified averaging technique to recover a crucial piece of the collective dynamics. The predicted transition between inphase and splay states is fundamentally changed, introducing the hysteresis long known to be observed in these systems...

We study the oscillator equations describing a type of nonlinear amplifier, exemplified by a two-junction superconducting quantum interference device. Just beyond the onset of spontaneous oscillations, the system is known to show significantly enhanced sensitivity to very weak magnetic signals. The global phase-space structure allows us to apply a...

We study the detection of very weak time-periodic magnetic signals via a double-junction (dc) Superconducting Quantum Interference Device (SQUID). The device, represented by two coupled nonlinear differential equations for the quantum mechanical junction phase differences, admits long-time static or oscillatory solutions, the transition between the...

We study the detection of very weak time‐periodic magnetic signals via a double‐junction (dc) Superconducting Quantum Interference Device (SQUID). The device, represented by two coupled nonlinear differential equations for the quantum mechanical junction phase differences, admits long‐time static or oscillatory solutions, the transition between the...

We resolve a long standing puzzle concerning synchronization in Josephson junction series arrays. We introduce a modified averaging technique to recover a crucial piece of the collective dynamics. The predicted transition between inphase and splay states is fundamentally changed, introducing the hysteresis long known to be observed in these systems...

Stochastic resonance has been observed in several biological systems. However, an important issue not fully addressed is whether optimal noise levels correspond to the noise levels found under physiological conditions. We have found that mechanoelectrical transduction in hair cells is enhanced by Brownian motion of the cells' sensory organelle, the...