Related papers: On the Dynamical Hierarchy in Gathering Protocols …
New model equations are derived for dynamics of self-aggregation of finite-size particles. Differences from standard Debye-Huckel and Keller-Segel models are: the mobility of particles depends on the configuration of their neighbors and…
Understanding human mobility is essential for applications ranging from urban planning to public health. Traditional mobility models such as flow networks and colocation matrices capture only pairwise interactions between discrete…
Identifying and comparing topological features, particularly cycles, across different topological objects remains a fundamental challenge in persistent homology and topological data analysis. This work introduces a novel framework for…
Motivated by applications to a wide range of assemble-to-order systems, operations scheduling, healthcare systems and collaborative economy applications, we introduce a stochastic matching model on hypergraphs, extending the model in [15]…
Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of…
Collective motion in actively propelled particle systems is triggered on the very local scale by nucleation of coherently moving units consisting of just a handful of particles. These units grow and merge over time, ending up in a…
We study a family of weighted random walks on complete graphs. These `democratic walks' turn out to be explicitly solvable, and we find the hierarchy window for which the characteristic time scale saturates the so-called fast scrambling…
Open dynamical systems are mathematical models of machines that take input, change their internal state, and produce output. For example, one may model anything from neurons to robots in this way. Several open dynamical systems can be…
We consider translation invariant measures on families of nearest-neighbor semi-infinite walks on the integer lattice. We assume that once walks meet, they coalesce. In $2d$, we classify the collective behavior of these walks under mild…
We investigate a generalization of topological order from closed systems to open systems, for which the steady states take the place of ground states. We construct typical lattice models with steady-state topological order, and characterize…
This paper considers a group of mobile autonomous agents moving in Euclidean space with point mass dynamics. We introduce a set of coordination control laws that enable the group to generate the desired stable flocking motion. The control…
We show that a scaling approach successfully characterizes clustering and intermittency in space and time, in systems of noninteracting particles driven by fluctuating surfaces. We study both the steady state and the approach to it, for…
We study the entanglement dynamics of accelerated atoms using the theory of open quantum systems. We consider two atoms travelling along different hyperbolic trajectories with different proper times. We use the generalized master equation…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
We introduce a minimal model of multilevel selection on structured populations, considering the interplay between game theory and population dynamics. Through a bottleneck process, finite groups are formed with cooperators and defectors…
This paper presents a new approach to behavioral-social dynamics of human crowds. First order models are derived based on mass conservation at the macroscopic scale, while methods of the kinetic theory are used to model the decisional…
We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and…
Graph-limit theory focuses on the convergence of sequences of graphs when the number of nodes becomes arbitrarily large. This framework defines a continuous version of graphs allowing for the study of dynamical systems on very large graphs,…
Granular simulations are used to probe the particle scale dynamics at short, intermediate, and long time scales for gravity driven, dense granular flows down an inclined plane. On approach to the angle of repose, where motion ceases, the…
Networks and graphs provide a simple but effective model to a vast set of systems which building blocks interact throughout pairwise interactions. Unfortunately, such models fail to describe all those systems which building blocks interact…