Asymptotic dynamics of attractive-repulsive swarms

We classify and predict the asymptotic dynamics of a class of swarming models. The model consists of a conservation equation in one dimension describing the movement of a population density field. The velocity is found by convolving the density with a kernel describing attractive-repulsive social interactions. The kernel's first moment and its limiting behavior at the origin determine whether the population asymptotically spreads, contracts, or reaches steady-state. For the spreading case, the dynamics approach those of the porous medium equation. The widening, compactly-supported population has edges that behave like traveling waves whose speed, density and slope we calculate. For the contracting case, the dynamics of the cumulative density approach those of Burgers' equation. We derive an analytical upper bound for the finite blow-up time after which the solution forms one or more $\delta$-functions.Comment: 23 pages, 10 figures; revised version updates the analysis in sec. 2.1 and 2.2, and contains enhanced discussion of the admissible class of social interaction force

Continuum modeling of the equilibrium and stability of animal flocks

Groups of animals often tend to arrange themselves in flocks that have characteristic spatial attributes and temporal dynamics. Using a dynamic continuum model for a flock of individuals, we find equilibria of finite spatial extent where the density goes continuously to zero at a well-defined flock edge, and we discuss conditions on the model that allow for such solutions. We also demonstrate conditions under which, as the flock size increases, the interior density in our equilibria tends to an approximately uniform value. Motivated by observations of starling flocks that are relatively thin in a direction transverse to the direction of flight, we investigate the stability of infinite, planar-sheet flock equilibria. We find that long- wavelength perturbations along the sheet are unstable for the class of models that we investigate. This has the conjectured consequence that sheet-like flocks of arbitrarily large transverse extent relative to their thickness do not occur. However, we also show that our model admits approximately sheet-like, 'pancake-shaped', three-dimensional ellipsoidal equilibria with definite aspect ratios (transverse length- scale to flock thickness) determined by anisotropic perceptual/response characteristics of the flocking individuals, and we argue that these pancake-like equilibria are stable to the previously mentioned sheet instability.Comment: 37 pages, 8 figure

A qualitative investigation into the impact of domestic abuse on women’s desistance

While criminological literature, criminal justice practice, and to a lesser extent, state policy have acknowledged a link between women’s criminalisation and gendered violence (MoJ, 2018; Österman, 2018; Prison Reform Trust, 2017; Roberts, 2015), there has been much less acknowledgement of the role of historical and contemporaneous experiences of violence in the desistance scripts of criminalised women. Combining findings from two research projects exploring gender and desistance, this article argues that (i) criminalised women’s experiences of gendered violence are such that any exploration of gender and desistance which does not acknowledge this is incomplete, (ii) coercion and control can inform women’s entry into the criminal justice system, (iii) expressions of agency and resistance in abusive interpersonal relationships can also inform women’s offending, yet (iv) women’s experiences of desistance from crime can mask the harm they face in coercive, controlling, and violent relationships. Thus, the article argues for a reframing of desistance from crime as desistance from harm both theoretically and in practice, and considers what this might entail