Related papers: Scale Free Cluster Distributions from Conserving M…
We investigate a class of stochastic fragmentation processes involving stable and unstable fragments. We solve analytically for the fragment length density and find that a generic algebraic divergence characterizes its small-size tail.…
Cohesive powders form agglomerates that can be very porous. Hence they are also very fragile. Consider a process of complete fragmentation on a characteristic length scale $\ell$, where the fragments are subsequently allowed to settle under…
Activity or spin patterns on random scale-free network are studied by mean field analysis and computer simulations. These activity patterns evolve in time according to local majority-rule dynamics which is implemented using (i) parallel or…
Coalescence-fragmentation problems are of great interest across the physical, biological, and recently social sciences. They are typically studied from the perspective of the rate equations, at the heart of such models are the rules used…
Globally conserved interface-controlled coarsening of fractal clusters exhibits dynamic scale invariance and normal scaling. This is demonstrated by a numerical solution of the Ginzburg-Landau equation with a global conservation law. The…
Based on the competition between members of a hierarchy of length scales in complex multi-scale systems, it is shown how clustering of active quantities into concentrated sets, like bubbles in a Swiss cheese, is a generic property that…
We study the dynamics and structure of clusters in the inhomogeneous clustered regime of a freely cooling granular gas of point particles in one dimension. The coefficient of restitution is modeled as $r_0<1$ or 1 depending on whether the…
A coupled-phase oscillator model where each oscillator has an angular velocity that varies due to the interaction with other oscillators is studied. This model is proposed to deepen the understanding of the relationship between the…
We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to…
We study the percolation properties of the growing clusters model. In this model, a number of seeds placed on random locations on a lattice are allowed to grow with a constant velocity to form clusters. When two or more clusters eventually…
This work proposes stochastic partial differential equations (SPDEs) as a practical tool to replicate clustering effects of more detailed particle-based dynamics. Inspired by membrane-mediated receptor dynamics on cell surfaces, we…
Aggregation processes with an arbitrary number of conserved quantities are investigated. On the mean-field level, an exact solution for the size distribution is obtained. The asymptotic form of this solution exhibits nontrivial ``double''…
We propose a model of network growth that generalizes the deactivation model previously suggested for complex networks. Several topological features of this generalized model, such as the degree distribution and clustering coefficient, have…
Clusters are the dense inner regions of a wide-spread hierarchy of young stellar structures. They often reveal a continuation of this hierarchy inside of them, to smaller scales, when they are young, but orbital mixing eventually erases…
Several dynamical scenarios have been proposed that can lead to prompt mass segregation on the crossing time scale of a young cluster. They generally rely on cool and/or clumpy initial conditions, and are most relevant to small systems. As…
We use statistical mechanics to study model-based Bayesian data clustering. In this approach, each partition of the data into clusters is regarded as a microscopic system state, the negative data log-likelihood gives the energy of each…
Clustering is a widely used unsupervised learning method for finding structure in the data. However, the resulting clusters are typically presented without any guarantees on their robustness; slightly changing the used data sample or…
The remarkable cohesion and coordination observed in moving animal groups and their collective responsiveness to threats are thought to be mediated by scale-free correlations, where changes in the behavior of one animal influence others in…
Clustering analysis identifies samples as groups based on either their mutual closeness or homogeneity. In order to detect clusters in arbitrary shapes, a novel and generic solution based on boundary erosion is proposed. The clusters are…
We consider the fragmentation process with mass loss and discuss self-similar properties of the arising structure both in time and space, focusing on dimensional analysis. This exhibits a spectrum of mass exponents $\theta$, whose exact…