Contagion Shocks in One Dimension

We consider an agent-based model of emotional contagion coupled with motion in one dimension that has recently been studied in the computer science community. The model involves movement with a speed proportional to a “fear” variable that undergoes a temporal consensus averaging based on distance to other agents. We study the effect of Riemann initial data for this problem, leading to shock dynamics that are studied both within the agent-based model as well as in a continuum limit. We examine the behavior of the model under distinguished limits as the characteristic contagion interaction distance and the interaction timescale both approach zero. The limiting behavior is related to a classical model for pressureless gas dynamics with “sticky” particles. In comparison, we observe a threshold for the interaction distance vs. interaction timescale that produce qualitatively different behavior for the system - in one case particle paths do not cross and there is a natural Eulerian limit involving nonlocal interactions and in the other case particle paths can cross and one may consider only a kinetic model in the continuum limit

Smart Swarms of Bacteria-Inspired Agents with Performance Adaptable Interactions

Collective navigation and swarming have been studied in animal groups, such as fish schools, bird flocks, bacteria, and slime molds. Computer modeling has shown that collective behavior of simple agents can result from simple interactions between the agents, which include short range repulsion, intermediate range alignment, and long range attraction. Here we study collective navigation of bacteria-inspired smart agents in complex terrains, with adaptive interactions that depend on performance. More specifically, each agent adjusts its interactions with the other agents according to its local environment – by decreasing the peers' influence while navigating in a beneficial direction, and increasing it otherwise. We show that inclusion of such performance dependent adaptable interactions significantly improves the collective swarming performance, leading to highly efficient navigation, especially in complex terrains. Notably, to afford such adaptable interactions, each modeled agent requires only simple computational capabilities with short-term memory, which can easily be implemented in simple swarming robots

Two-frequency forced Faraday waves: Weakly damped modes and pattern selection

Recent experiments (Kudrolli, Pier and Gollub, 1998) on two-frequency parametrically excited surface waves exhibit an intriguing "superlattice" wave pattern near a codimension-two bifurcation point where both subharmonic and harmonic waves onset simultaneously, but with different spatial wavenumbers. The superlattice pattern is synchronous with the forcing, spatially periodic on a large hexagonal lattice, and exhibits small-scale triangular structure. Similar patterns have been shown to exist as primary solution branches of a generic 12-dimensional D_6____dot{+}T^2-equivariant bifurcation problem, and may be stable if the nonlinear coefficients of the bifurcation problem satisfy certain inequalities (Silber and Proctor, 1998). Here we use the spatial and temporal symmetries of the problem to argue that weakly damped harmonic waves may be critical to understanding the stabilization of this pattern in the Faraday system. We illustrate this mechanism by considering the equations developed by Zhang and Vinals (1997, J. Fluid Mech. 336) for small amplitude, weakly damped surface waves on a semi-infinite fluid layer. We compute the relevant nonlinear coefficients in the bifurcation equations describing the onset of patterns for excitation frequency ratios of 2/3 and 6/7. For the 2/3 case, we show that there is a fundamental difference in the pattern selection problems for subharmonic and harmonic instabilities near the codimension-two point. Also, we find that the 6/7 case is significantly different from the 2/3 case due to the presence of additional weakly damped harmonic modes. These additional harmonic modes can result in a stabilization of the superpatterns

Spatiotemporal chaos and quasipatterns in coupled reaction–diffusion systems

In coupled reaction–diffusion systems, modes with two different length scales can interact to produce a wide variety of spatiotemporal patterns. Three-wave interactions between these modes can explain the occurrence of spatially complex steady patterns and time-varying states including spatiotemporal chaos. The interactions can take the form of two short waves with different orientations interacting with one long wave, or vice verse. We investigate the role of such three-wave interactions in a coupled Brusselator system. As well as finding simple steady patterns when the waves reinforce each other, we can also find spatially complex but steady patterns, including quasipatterns. When the waves compete with each other, time varying states such as spatiotemporal chaos are also possible. The signs of the quadratic coefficients in three-wave interaction equations distinguish between these two cases. By manipulating parameters of the chemical model, the formation of these various states can be encouraged, as we confirm through extensive numerical simulation. Our arguments allow us to predict when spatiotemporal chaos might be found: standard nonlinear methods fail in this case. The arguments are quite general and apply to a wide class of pattern-forming systems, including the Faraday wave experiment

A healthier life? Managing healthcare in Ireland

SIGLEAvailable from British Library Document Supply Centre-DSC:99/36446 / BLDSC - British Library Document Supply CentreGBUnited Kingdo