Impulsive perturbations to differential equations: stable/unstable pseudo-manifolds, heteroclinic connections, and flux

State-dependent time-impulsive perturbations to a two-dimensional autonomous flow with stable and unstable manifolds are analysed by posing in terms of an integral equation which is valid in both forwards- and backwards-time. The impulses destroy the smooth invariant manifolds, necessitating new definitions for stable and unstable pseudo-manifolds. Their time-evolution is characterised by solving a Volterra integral equation of the second kind with discontinuous inhomogeniety. A criteria for heteroclinic trajectory persistence in this impulsive context is developed, as is a quantification of an instantaneous flux across broken heteroclinic manifolds. Several examples, including a kicked Duffing oscillator and an underwater explosion in the vicinity of an eddy, are used to illustrate the theory

Transport between two fluids across their mutual flow interface: the streakline approach

Mixing between two different miscible fluids with a mutual interface must be initiated by fluid transporting across this fluid interface, caused for example by applying an unsteady velocity agitation. In general, there is no necessity for this physical flow barrier between the fluids to be associated with extremal or exponential attraction as might be revealed by applying Lagrangian coherent structures, finite-time Lyapunov exponents or other methods on the fluid velocity. It is shown that streaklines are key to understanding the breaking of the interface under velocity agitations, and a theory for locating the relevant streaklines is presented. Simulations of streaklines in a cross-channel mixer and a perturbed Kirchhoff's elliptic vortex are quantitatively compared to the theoretical results. A methodology for quantifying the unsteady advective transport between the two fluids using streaklines is presented

Local stable and unstable manifolds and their control in nonautonomous finite-time flows

It is well-known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each instance in time is the focus of this article. Within a nearly autonomous setting, it is shown that these time-varying directions can be characterised through the accumulated effect of velocity shear. Connections to Oseledets spaces and projection operators in exponential dichotomies are established. Availability of data for both infinite and finite time-intervals is considered. With microfluidic flow control in mind, a methodology for manipulating these directions in any prescribed time-varying fashion by applying a local velocity shear is developed. The results are verified for both smoothly and discontinuously time-varying directions using finite-time Lyapunov exponent fields, and excellent agreement is obtained.Comment: Under consideration for publication in the Journal of Nonlinear Science

Nonautonomous control of stable and unstable manifolds in two-dimensional flows

We outline a method for controlling the location of stable and unstable manifolds in the following sense. From a known location of the stable and unstable manifolds in a steady two-dimensional flow, the primary segments of the manifolds are to be moved to a user-specified time-varying location which is near the steady location. We determine the nonautonomous perturbation to the vector field required to achieve this control, and give a theoretical bound for the error in the manifolds resulting from applying this control. The efficacy of the control strategy is illustrated via a numerical example

A biologically inspired computational vision front-end based on a self-organised pseudo-randomly tessellated artificial retina

This paper considers the construction of a biologically inspired front-end for computer vision based on an artificial retina pyramid with a self-organised pseudo-randomly tessellated receptive field tessellation. The organisation of photoreceptors and receptive fields in biological retinae locally resembles a hexagonal mosaic, whereas globally these are organised with a very densely tessellated central foveal region which seamlessly merges into an increasingly sparsely tessellated periphery. In contrast, conventional computer vision approaches use a rectilinear sampling tessellation which samples the whole field of view with uniform density. Scale-space interest points which are suitable for higher level attention and reasoning tasks are efficiently extracted by our vision front-end by performing hierarchical feature extraction on the pseudo-randomly spaced visual information. All operations were conducted on a geometrically irregular foveated representation (data structure for visual information) which is radically different to the uniform rectilinear arrays used in conventional computer vision

Finding Street Gang Members on Twitter

Most street gang members use Twitter to intimidate others, to present outrageous images and statements to the world, and to share recent illegal activities. Their tweets may thus be useful to law enforcement agencies to discover clues about recent crimes or to anticipate ones that may occur. Finding these posts, however, requires a method to discover gang member Twitter profiles. This is a challenging task since gang members represent a very small population of the 320 million Twitter users. This paper studies the problem of automatically finding gang members on Twitter. It outlines a process to curate one of the largest sets of verifiable gang member profiles that have ever been studied. A review of these profiles establishes differences in the language, images, YouTube links, and emojis gang members use compared to the rest of the Twitter population. Features from this review are used to train a series of supervised classifiers. Our classifier achieves a promising F1 score with a low false positive rate.Comment: 8 pages, 9 figures, 2 tables, Published as a full paper at 2016 IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2016

Steady free-surface flow over spatially periodic topography

Two-dimensional free-surface flow over a spatially periodic channel bed topography is examined using a steady periodically forced Korteweg-de Vries equation. The existence of new forced solitary-type waves with periodic tails is demonstrated using recently developed non-autonomous dynamical-systems theory. Bound states with two or more co-existing solitary waves are also identified. The solution space for varying amplitude of forcing is explored using a numerical method. A rich bifurcation structure is uncovered and shown to be consistent with an asymptotic theory based on small forcing amplitude..J. Binder, M.G. Blyth and S. Balasuriy

Gradient evolution for potential vorticity flows

International audienceTwo-dimensional unsteady incompressible flows in which the potential vorticity (PV) plays a key role are examined in this study, through the development of the evolution equation for the PV gradient. For the case where the PV is conserved, precise statements concerning topology-conservation are presented. While establishing some intuitively well-known results (the numbers of eddies and saddles is conserved), other less obvious consequences (PV patches cannot be generated, some types of Lagrangian and Eulerian entities are equivalent) are obtained. This approach enables an improvement on an integrability result for PV conserving flows (if there were no PV patches at time zero, the flow would be integrable). The evolution of the PV gradient is also determined for the nonconservative case, and a plausible experiment for estimating eddy diffusivity is suggested. The theory is applied to an analytical diffusive Rossby wave example