Related papers: Discrete two-countour system with one-directional …
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…
We formulate a novel technique for the detection of functional clusters in discrete event data. The advantage of this algorithm is that no prior knowledge of the number of functional groups is needed, as our procedure progressively combines…
An ecosystem is a nonlinear dynamical system, its orbits giving rise to the observed complexity in the system. The diverse components of the ecosystem interact in discrete time to give rise to emergent features that determine the trajectory…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
We study the mechanism of formation of synchronized clusters in coupled maps on networks with various connection architectures. The nodes in a cluster are self- synchronized or driven-synchronized, based on the coupling strength and…
In the history of mechanics, there have been two points of view for studying mechanical systems: Newtonian and Cartesian. According the Descartes point of view, the motion of mechanical systems is described by the first-order differential…
We study a two-particle circular billiard containing two finite-size circular particles that collide elastically with the billiard boundary and with each other. Such a two-particle circular billiard provides a clean example of an…
An important problem in the theory of finite dynamical systems is to link the structure of a system with its dynamics. This paper contains such a link for a family of nonlinear systems over the field with two elements. For systems that can…
Dynamical behavior of the clusters during relaxation is studied in two-dimensional Potts model using cluster algorithm. Average cluster size and cluster formation velocity are calculated on two different lattice sizes for different number…
Starting from a dataset with input/output time series generated by multiple deterministic linear dynamical systems, this paper tackles the problem of automatically clustering these time series. We propose an extension to the so-called…
Recurrence is a fundamental characteristic of dynamical systems with complicated behavior. Understanding the inner structure of recurrence is challenging, especially if the system has many degrees of freedom and is subject to noise. We…
Globular clusters are stellar dynamical systems which evolve on stellar evolutionary and both internal and external dynamical timescales. Quantitative comparison of cluster properties with realistic evolutionary dynamical models is becoming…
In this study, we investigate the clustering of 5000 droplets, each originating from one of five distinct droplet classes, each representing a unique geometry. The shape coordinates of the droplets are mapped to a 2D latent space through a…
We consider a piecewise linear two-dimensional dynamical system that couples a linear equation with the so-called stop operator. Global dynamics and bifurcations of this system are studied depending on two parameters. The system is…
A coupled map model for cloud dynamics is proposed, which consists of the successive operations of the physical processes; buoyancy, diffusion, viscosity, adiabatic expansion, fall of a droplet by gravity, descent flow dragged by the…
We report computer simulation results on the cluster formation of dipolar colloidal particles driven by a rotating external field in a quasi-two-dimensional setup. We focus on the interplay between permanent dipolar and hydrodynamic…
Molecular dynamics simulations are used to study the local dynamics of counterion-charged polymer association at charge densities above and below the counterion condensation threshold. Surprisingly, the counterions form weakly-interacting…
The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher…
We discuss a simple model of particles hopping in one dimension with attractive interactions. Taking a hydrodynamic limit in which the interaction strength increases with the system size, we observe the formation of multiple clusters of…
We apply a one-dimensional discrete dynamical system originally considered by Arnol'd reminiscent of mathematical billiards to the study of two-move riders, a type of fairy chess piece. In this model, particles travel through a bounded…