The disruption of multiplanet systems through resonance with a binary orbit.

Most exoplanetary systems in binary stars are of S-type, and consist of one or more planets orbiting a primary star with a wide binary stellar companion. Planetary eccentricities and mutual inclinations can be large, perhaps forced gravitationally by the binary companion. Earlier work on single planet systems appealed to the Kozai-Lidov instability wherein a sufficiently inclined binary orbit excites large-amplitude oscillations in the planet's eccentricity and inclination. The instability, however, can be quenched by many agents that induce fast orbital precession, including mutual gravitational forces in a multiplanet system. Here we report that orbital precession, which inhibits Kozai-Lidov cycling in a multiplanet system, can become fast enough to resonate with the orbital motion of a distant binary companion. Resonant binary forcing results in dramatic outcomes ranging from the excitation of large planetary eccentricities and mutual inclinations to total disruption. Processes such as planetary migration can bring an initially non-resonant system into resonance. As it does not require special physical or initial conditions, binary resonant driving is generic and may have altered the architecture of many multiplanet systems. It can also weaken the multiplanet occurrence rate in wide binaries, and affect planet formation in close binaries.

Order-Disorder Phase Transition in Black-Hole Star Clusters.

The centers of most galaxies contain massive black holes surrounded by dense star clusters. The structure of these clusters determines the rate and properties of observable transient events, such as flares from tidally disrupted stars and gravitational-wave signals from stars spiraling into the black hole. Most estimates of these rates enforce spherical symmetry on the cluster. Here we show that, in the course of generic evolutionary processes, a star cluster surrounding a black hole can undergo a robust phase transition from a spherical thermal equilibrium to a lopsided equilibrium, in which most stars are on high-eccentricity orbits with aligned orientations. The rate of transient events is expected to be much higher in the ordered phase. Better models of cluster formation and evolution are needed to determine whether clusters should be found in the ordered or disordered phase.

A framework for reconstructing transmission networks in infectious diseases.

In this paper, we propose a general framework for the reconstruction of the underlying cross-regional transmission network contributing to the spread of an infectious disease. We employ an autoregressive model that allows to decompose the mean number of infections into three components that describe: intra-locality infections, inter-locality infections, and infections from other sources such as travelers arriving to a country from abroad. This model is commonly used in the identification of spatiotemporal patterns in seasonal infectious diseases and thus in forecasting infection counts. However, our contribution lies in identifying the inter-locality term as a time-evolving network, and rather than using the model for forecasting, we focus on the network properties without any assumption on seasonality or recurrence of the disease. The topology of the network is then studied to get insight into the disease dynamics. Building on this, and particularly on the centrality of the nodes of the identified network, a strategy for intervention and disease control is devised.

Shepherding in a Self-gravitating Disk of Trans-Neptunian Objects.

A relatively massive and moderately eccentric disk of trans-Neptunian objects (TNOs) can effectively counteract apse precession induced by the outer planets, and in the process shepherd highly eccentric members of its population into nearly stationary configurations that are antialigned with the disk itself. We were sufficiently intrigued by this remarkable feature to embark on an extensive exploration of the full spatial dynamics sustained by the combined action of giant planets and a massive trans-Neptunian debris disk. In the process, we identified ranges of disk mass, eccentricity, and precession rate that allow apse-clustered populations that faithfully reproduce key orbital properties of the much-discussed TNO population. The shepherding disk hypothesis is, to be sure, complementary to any potential ninth member of the solar system pantheon, and could obviate the need for it altogether. We discuss its essential ingredients in the context of solar system formation and evolution, and argue for their naturalness in view of the growing body of observational and theoretical knowledge about self-gravitating disks around massive bodies, extra-solar debris disks included.

Unexpected stray attractors in confined leader-follower dynamics driven by cone-of-vision interactions.

Experiments with groups of fish inside a circular tank have provided valuable insights into the nature of leadership in social groups. Sophisticated mathematical models were constructed with a view to recovering observed schooling and leadership behavior in such experiments. Here, and with the help of variations on a promising class of such models, we explore a dual set of social concerns, namely the likelihood of permanent evasion from a cohesive group by a controlled individual in confinement. Our minimal model reduces to a leader-follower configuration, with cone-of-vision driven interactions inside a circular domain. We show that the resulting dynamical system sustains a rich supply of non-aligned, straying "follower" states, the dynamics on which displays (chaotic) intermittency between boundary following behavior and infrequent long flights. We map these states in configuration space and explore transitions between them. We demonstrate robustness of observed behavior by considering model variations, as well as alternate leader control trajectory. While it is too early to draw the implications of leader-follower dynamics to collective behavior, we do confirm that a model stray fish relates to a self-organized school bouncing back and forth along the diameter very much like a follower responds to a point leader in our model. We further draw the implications of our results to the study of dynamical systems with discontinuities, robotics, and the study of human behavior in the face of normative control and confinement.

Steady and transient states in low-energy swarms: Stability and first-passage times.

We investigate a class of agent-based models of self-propelled particles (SPP) that interact according to a Morse potential in the presence of friction, a class which was able to reproduce many of the intriguing patterns of collective motion observed in nature. Specifically, we compare two closely related SPP models in the literature that differ by their prescription of particle drag and self-propulsion. Writing both models in terms of nondimensional parameters allows us to show that the dynamics in the highly viscous regime is independent of the precise forms of drag and propulsion. In contrast to what is indicated in the literature both models yield the same low-energy self-organized states: the coherent flock and the rigid rotation states which are highly ordered in both the coordinate and the velocity spaces and a velocity-disordered droplet state where particles are confined to rings which pass through the lattice points of the underlying Lagrange configuration. In contrast to the first two states which are stable, the third state is found to be a long-lived transient. In the regime studied, relaxing to one of the ordered steady states is inevitable, but how and when the transition occurs and what is the probability of ending in one state rather than the other are functions of the model parameters. Two types of transitions are characterized and first passage times are computed. Eventually, the evolution of the order parameter is explored in the framework of a Langevin-type equation, and the possible metastability of the random droplet state is discussed.

Self-organization in two-dimensional swarms.

We undertake a systematic numerical exploration of self-organized states in a deterministic model of interacting self-propelled particles in two dimensions. In the process, we identify various types of collective motion, namely, disordered swarms, rings, and droplets. We construct a "phase diagram," which summarizes our results as it delineates phase transitions (all discontinuous) between disordered swarms and vortical flocks on one hand and bound vortical flocks and expanding formations on the other. One of the transition lines is found to have a close analogy with the temperature-driven gas-liquid transition, in finite clusters with the same interparticle potential. Furthermore, we report on a type of flocking which takes place in the presence of a uniform external driver. Altogether, our results set a rather firm stage for experimental refinement and/or falsification of this class of models.