Oscillator models and collective motion

A description of the so called "particles with coupled oscillator dynamics" (PCOD) is presented which is used to model, analyze and synthesize collective motion. An oscillator model with spatial dynamics is presented to help describe how to design steering control laws while it is being used to study biological collectives. Lastly, both engineering and biological analysis were described.

Stabilization of planar collective motion: All-to-all communication

This paper proposes a design methodology to stabilize isolated relative equilibria in a model of all-to-all coupled identical particles moving in the plane at unit speed. Isolated relative equilibria correspond to either parallel motion of all particles with fixed relative spacing or to circular motion of all particles with fixed relative phases. The stabilizing feedbacks derive from Lyapunov functions that prove exponential stability and suggest almost global convergence properties. The results of the paper provide a low-order parametric family of stabilizable collectives that offer a set of primitives for the design of higher-level tasks at the group level. © 2007 IEEE.

Collective motion, sensor networks, and ocean sampling

This paper addresses the design of mobile sensor networks for optimal data collection. The development is strongly motivated by the application to adaptive ocean sampling for an autonomous ocean observing and prediction system. A performance metric, used to derive optimal paths for the network of mobile sensors, defines the optimal data set as one which minimizes error in a model estimate of the sampled field. Feedback control laws are presented that stably coordinate sensors on structured tracks that have been optimized over a minimal set of parameters. Optimal, closed-loop solutions are computed in a number of low-dimensional cases to illustrate the methodology. Robustness of the performance to the influence of a steady flow field on relatively slow-moving mobile sensors is also explored © 2006 IEEE.

Collective motion of self-propelled particles: Stabilizing symmetric formations on closed curves

We provide feedback control laws to stabilize formations of multiple, unit speed particles on smooth, convex, and closed curves with definite curvature. As in previous work we exploit an analogy with coupled phase oscillators to provide controls which isolate symmetric particle formations that are invariant to rigid translation of all the particles. In this work, we do not require all particles to be able to communicate; rather we assume that inter-particle communication is limited and can be modeled by a fixed, connected, and undirected graph. Because of their unique spectral properties, the Laplacian matrices of circulant graphs play a key role. The methodology is demonstrated using a superellipse, which is a type of curve that includes circles, ellipses, and rounded rectangles. These results can be used in applications involving multiple autonomous vehicles that travel at constant speed around fixed beacons. ©2006 IEEE.

Oscillator models and collective motion: Splay state stabilization of self-propelled particles

This paper presents a Lyapunov design for the stabilization of collective motion in a planar kinematic model of N particles moving at constant speed. We derive a control law that achieves asymptotic stability of the splay state formation, characterized by uniform rotation of N evenly spaced particles on a circle. In designing the control law, the particle headings are treated as a system of coupled phase oscillators. The coupling function which exponentially stabilizes the splay state of particle phases is combined with a decentralized beacon control law that stabilizes circular motion of the particles. © 2005 IEEE.

Collective motion: Bistability and trajectory tracking

This paper presents analysis and application of steering control laws for a network of self-propelled, planar particles. We explore together the two stably controlled group motions, parallel motion and circular motion, for modeling and design purposes. We show that a previously considered control law simultaneously stabilizes both parallel and circular group motion, leading to Instability and hysteresis. We also present behavior primitives that enable piecewise-linear network trajectory tracking.

Plane-strain discrete dislocation plasticity with climb-assisted glide motion of dislocations

A small-strain two-dimensional discrete dislocation plasticity (DDP) framework is developed wherein dislocation motion is caused by climb-assisted glide. The climb motion of the dislocations is assumed to be governed by a drag-type relation similar to the glide-only motion of dislocations: such a relation is valid when vacancy kinetics is either diffusion limited or sink limited. The DDP framework is employed to predict the effect of dislocation climb on the uniaxial tensile and pure bending response of single crystals. Under uniaxial tensile loading conditions, the ability of dislocations to bypass obstacles by climb results in a reduced dislocation density over a wide range of specimen sizes in the climb-assisted glide case compared to when dislocation motion is only by glide. A consequence is that, at least in a single slip situation, size effects due to dislocation starvation are reduced. By contrast, under pure bending loading conditions, the dislocation density is unaffected by dislocation climb as geometrically necessary dislocations (GNDs) dominate. However, climb enables the dislocations to arrange themselves into lower energy configurations which significantly reduces the predicted bending size effect as well as the amount of reverse plasticity observed during unloading. The results indicate that the intrinsic plasticity material length scale associated with GNDs is strongly affected by thermally activated processes and will be a function of temperature. © 2013 IOP Publishing Ltd.

Aberration correction in Spatial Light Modulator based mode multiplexers

The Spatial Light Modulator in a mode demultiplexer is used to measure the aberrations of the system in which it is installed before applying aberration correction to improve the insertion loss and modal extinction ratios. © 2013 OSA.

Detecting bipedal motion from correlated probabilistic trajectories

This paper is about detecting bipedal motion in video sequences by using point trajectories in a framework of classification. Given a number of point trajectories, we find a subset of points which are arising from feet in bipedal motion by analysing their spatio-temporal correlation in a pairwise fashion. To this end, we introduce probabilistic trajectories as our new features which associate each point over a sufficiently long time period in the presence of noise. They are extracted from directed acyclic graphs whose edges represent temporal point correspondences and are weighted with their matching probability in terms of appearance and location. The benefit of the new representation is that it practically tolerates inherent ambiguity for example due to occlusions. We then learn the correlation between the motion of two feet using the probabilistic trajectories in a decision forest classifier. The effectiveness of the algorithm is demonstrated in experiments on image sequences captured with a static camera, and extensions to deal with a moving camera are discussed. © 2013 Elsevier B.V. All rights reserved.

Aberration correction in spatial light modulator based mode multiplexers

The Spatial Light Modulator in a mode demultiplexer is used to measure the aberrations of the system in which it is installed before applying aberration correction to improve the insertion loss and modal extinction ratios. © 2013 OSA.

Aberration correction in spatial light modulator based mode multiplexers

The Spatial Light Modulator in a mode demultiplexer is used to measure the aberrations of the system in which it is installed before applying aberration correction to improve the insertion loss and modal extinction ratios. © 2013 OSA.

Aberration correction for free space optical communications using rectangular zernike modal wavefront sensing

A time multiplexed rectangular Zernike modal wavefront sensor based on a nematic phase-only liquid crystal spatial light modulator and specially designed for a high power two-electrode tapered laser diode which is a compact and novel free space optical communication source is used in an adaptive beam steering free space optical communication system, enabling the system to have 1.25 GHz modulation bandwidth, 4.6° angular coverage and the capability of sensing aberrations within the system and caused by atmosphere turbulence up to absolute value of 0.15 waves amplitude and correcting them in one correction cycle. Closed-loop aberration correction algorithm can be implemented to provide convergence for larger and time varying aberrations. Improvement of the system signal-to-noise-ratio performance is achieved by aberration correction. To our knowledge, it is first time to use rectangular orthonormal Zernike polynomials to represent balanced aberrations for high power rectangular laser beam in practice. © 2014 IEEE.

Decadal persistence of cycles in lava lake motion at Erebus volcano, Antarctica

Studies of Erebus volcano's active lava lake have shown that many of its observable properties (gas composition, surface motion and radiant heat output) exhibit cyclic behaviour with a period of ~10 min. We investigate the multi-year progression of the cycles in surface motion of the lake using an extended (but intermittent) dataset of thermal infrared images collected by the Mount Erebus Volcano Observatory between 2004 and 2011. Cycles with a period of ~5-18 min are found to be a persistent feature of the lake's behaviour and no obvious long-term change is observed despite variations in lake level and surface area. The times at which gas bubbles arrive at the lake's surface are found to be random with respect to the phase of the motion cycles, suggesting that the remarkable behaviour of the lake is governed by magma exchange rather than an intermittent flux of gases from the underlying magma reservoir. © 2014 The Authors.