Related papers: Towards finite-dimensional gelation
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
The two-dimensional Ising model with fixed magnetization is studied using Monte Carlo techniques. At the coexistence line, the macroscopic, extensive droplet of minority spins becomes thermally unstable by breaking up into microscopic…
Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. We demonstrate how the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical…
A cluster mean-field method is introduced and the applications to the Ising and Heisenberg models are demonstrated. We divide the lattice sites into clusters whose size and shape are selected so that the equivalence of all sites in a…
We present some recent theory and simulation results addressing the phenomena of colloidal gelation at both high and low volume fractions, in the presence of short-range attractive interactions. We discuss the ability of mode-coupling…
The dynamical arrest of attractive colloidal particles into out-of-equilibrium structures, known as gelation, is central to biophysics, materials science, nanotechnology, and food and cosmetic applications, but a complete understanding is…
An exactly solvable model for the rewiring dynamics of weighted, directed networks is introduced. Simulations indicate that the model exhibits two types of condensation: (i) a phase in which, for each node, a finite fraction of its total…
We present simulation results for the contact process on regular, cubic networks that are composed of a one-dimensional lattice and a set of long edges with unbounded length. Networks with different sets of long edges are considered, that…
We first study crossing statistics in random connection models (RCM) built on marked Poisson point processes on $\mathbb R^d$. Under general assumptions, we show exponential tail bounds for the number of crossings of a box contained in the…
We apply a variant of the explosive percolation procedure to large real-world networks, and show with finite-size scaling that the university class, ordinary or explosive, of the resulting percolation transition depends on the structural…
We propose a simple mean-field theory for the structure of ring polymer melts. By combining the notion of topological volume fraction and a classical van der Waals theory of fluids, we take into account many body effects of topological…
A thermodynamically consistent visco-elastodynamical model at finite strains is derived that also allows for inelasticity (like plasticity or creep), thermal coupling, and poroelasticity with diffusion. The theory is developed in the…
We study the Gierer-Meinhardt model of reaction-diffusion on a site-disordered square lattice. Let $p$ be the site occupation probability of the square lattice. For $p$ greater than a critical value $p_c$, the steady state consists of…
We present molecular dynamics (MD) simulations results for dense fluids of ultrasoft, fully-penetrable particles. These are a binary mixture and a polydisperse system of particles interacting via the generalized exponential model, which is…
We analyze critical phenomena on networks generated as the union of hidden variables models (networks with any desired degree sequence) with arbitrary graphs. The resulting networks are general small-worlds similar to those a` la Watts and…
We model the evolution of tokens within a deep stack of Transformer layers as a continuous-time flow on the unit sphere, governed by a mean-field interacting particle system, building on the framework introduced in (Geshkovski et al.,…
When moist air meets a cold surface, it creates a breath figure characterized by numerous small droplets. The central question is how the vapor flux is distributed between the growth of previously condensed drops and the nucleation of new…
Gels in soft-matter systems are an important nonergodic state of matter. We study a colloid-polymer mixture which is quenched by increasing the polymer concentration, from a fluid to a gel. Using confocal microscopy, we study both the…
The abundances of light clusters within a formalism that considers in-medium effects are calculated using several relativistic mean-field models, with both density-dependent and density-independent couplings. Clusters are introduced as new…
We develop a full theoretical approach to clustering in complex networks. A key concept is introduced, the edge multiplicity, that measures the number of triangles passing through an edge. This quantity extends the clustering coefficient in…