Order, chaos, and dimensionality transition in a system of swarmalators.

Similarly to sperm, where individuals self-organize in space while also striving for coherence in their tail swinging, several natural and engineered systems exhibit the emergence of swarming and synchronization. The arising and interplay of these phenomena have been captured by collectives of hypothetical particles named swarmalators, each possessing a position and a phase whose dynamics are affected reciprocally and also by the space-phase states of their neighbors. In this work, we introduce a solvable model of swarmalators able to move in two-dimensional spaces.

Travel distance, frequency of return, and the spread of disease.

Human mobility is a key driver of infectious disease spread. Recent literature has uncovered a clear pattern underlying the complexity of human mobility in cities: [Formula: see text], the product of distance traveled r and frequency of return f per user to a given location, is invariant across space. This paper asks whether the invariant [Formula: see text] also serves as a driver for epidemic spread, so that the risk associated with human movement can be modeled by a unifying variable [Formula: see text].

Modeling the Interplay Between Seasonal Flu Outcomes and Individual Vaccination Decisions.

Seasonal influenza presents an ongoing challenge to public health. The rapid evolution of the flu virus necessitates annual vaccination campaigns, but the decision to get vaccinated or not in a given year is largely voluntary, at least in the USA, and many people decide against it. In some early attempts to model these yearly flu vaccine decisions, it was often assumed that individuals behave rationally, and do so with perfect information-assumptions that allowed the techniques of classical economics and game theory to be applied.

Quantifying the sensing power of vehicle fleets.

Sensors can measure air quality, traffic congestion, and other aspects of urban environments. The fine-grained diagnostic information they provide could help urban managers to monitor a city's health. Recently, a "drive-by" paradigm has been proposed in which sensors are deployed on third-party vehicles, enabling wide coverage at low cost.

Ring states in swarmalator systems.

Synchronization is a universal phenomenon, occurring in systems as disparate as Japanese tree frogs and Josephson junctions. Typically, the elements of synchronizing systems adjust the phases of their oscillations, but not their positions in space. The reverse scenario is found in swarming systems, such as schools of fish or flocks of birds; now the elements adjust their positions in space, but without (noticeably) changing their internal states.

Oscillators that sync and swarm.

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through space. A complementary form of self-organization occurs among swarming insects, flocking birds, or schooling fish; now the individuals move through space, but without conspicuously altering their internal states.

Correlated disorder in the Kuramoto model: Effects on phase coherence, finite-size scaling, and dynamic fluctuations.

We consider a mean-field model of coupled phase oscillators with quenched disorder in the natural frequencies and coupling strengths. A fraction p of oscillators are positively coupled, attracting all others, while the remaining fraction 1-p are negatively coupled, repelling all others. The frequencies and couplings are deterministically chosen in a manner which correlates them, thereby correlating the two types of disorder in the model.

Transient dynamics of pulse-coupled oscillators with nonlinear charging curves.

We consider the transient behavior of globally coupled systems of identical pulse-coupled oscillators. Synchrony develops through an aggregation phenomenon, with clusters of synchronized oscillators forming and growing larger in time. Previous work derived expressions for these time dependent clusters, when each oscillator obeyed a linear charging curve.

Phase coherence induced by correlated disorder.

We consider a mean-field model of coupled phase oscillators with quenched disorder in the coupling strengths and natural frequencies. When these two kinds of disorder are uncorrelated (and when the positive and negative couplings are equal in number and strength), it is known that phase coherence cannot occur and synchronization is absent. Here we explore the effects of correlating the disorder.

Synchronization as Aggregation: Cluster Kinetics of Pulse-Coupled Oscillators.

We consider models of identical pulse-coupled oscillators with global interactions. Previous work showed that under certain conditions such systems always end up in sync, but did not quantify how small clusters of synchronized oscillators progressively coalesce into larger ones. Using tools from the study of aggregation phenomena, we obtain exact results for the time-dependent distribution of cluster sizes as the system evolves from disorder to synchrony.