Related papers: Dynamical clusters of infinite particle dynamics
A finite dynamical system with $n$ components is a function $f:X\to X$ where $X=X_1\times\dots\times X_n$ is a product of $n$ finite intervals of integers. The structure of such a system $f$ is represented by a signed digraph $G$, called…
We study finite particle systems on the one-dimensional integer lattice, where each particle performs a continuous-time nearest-neighbour random walk, with jump rates intrinsic to each particle, subject to an exclusion interaction which…
A biclique of a graph $G$ is an induced complete bipartite subgraph of $G$ such that neither part is empty. A star is a biclique of $G$ such that one part has exactly one vertex. The star graph of $G$ is the intersection graph of the…
We study some percolation problems on the complete graph over $\mathbf N$. In particular, we give sharp sufficient conditions for the existence of (finite or infinite) cliques and paths in a random subgraph. No specific assumption on the…
We investigate dynamics and interactions of particles levitated and trapped by the thermophoretic force in a vacuum cell. Our analysis is based on footage taken by orthogonal cameras that are able to capture the three dimensional…
We study arc graphs and curve graphs for surfaces of infinite topological type. First, we define an arc graph relative to a finite number of (isolated) punctures and prove that it is a connected, uniformly hyperbolic graph of infinite…
This paper studies clustering algorithms for dynamically evolving graphs $\{G_t\}$, in which new edges (and potential new vertices) are added into a graph, and the underlying cluster structure of the graph can gradually change. The paper…
The total graph of $G$, $\mathcal T(G)$ is the graph whose set of vertices is the union of the sets of vertices and edges of $G$, where two vertices are adjacent if and only if they stand for either incident or adjacent elements in $G$. Let…
Interacting particle systems play a key role in science and engineering. Access to the governing particle interaction law is fundamental for a complete understanding of such systems. However, the inherent system complexity keeps the…
We study a driven system in which interaction between particles causes their directional, coupled movement. In that model system, two particles move alternatingly in time on two coupled chains. Without interaction, both particles diffuse…
Statistical models on infinite graphs may exhibit inhomogeneous thermodynamic behaviour at macroscopic scales. This phenomenon is of geometrical origin and may be properly described in terms of spectral partitions into subgraphs with well…
In this paper we consider a class of interacting particle systems on dynamic random networks, in which the joint dynamics of vertices and edges acts as one-way feedback, i.e., edges appear and disappear over time depending on the state of…
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong…
We study the stability in finite times of the trajectories of interacting particles. Our aim is to show that in average and uniformly in the number of particles, two trajectories whose initial positions in phase space are close, remain…
We investigate both experimentally and theoretically the traffic of particles flowing in microfluidic obstacle networks. We show that the traffic dynamics is a non-linear process: the particle current does not scale with the particle…
We consider a gas of point particles moving on the one-dimensional line with a hard-core inter-particle interaction that prevents particle crossings --- this is usually referred to as single-file motion. The individual particle dynamics can…
Suspensions of hard core spherical particles of diameter $D$ with inter-core connectivity range $\delta$ can be described in terms of random geometric graphs, where nodes represent the sphere centers and edges are assigned to any two…
In this paper a general theorem of constructing infinite particle systems of jump types with long range interactions is presented. It can be applied to the system that each particle undergoes an $\alpha$-stable process and interaction…
This paper constructs a new interacting particle system on a two--dimensional lattice with geometric jumps near a boundary which partially reflects the particles. The projection to each horizontal level is Markov, and on every level the…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…