Related papers: Catalytic Coagulation
We propose a kinetic model for the self-aggregation by amyloid proteins. By extending several well-known models for protein aggregation, the time evolution of aggregate concentrations containing $r$ proteins, denoted $c_r(t)$, can be…
We study hydrodynamic limits of the cluster coagulation model; a coagulation model introduced by Norris [$\textit{Comm. Math. Phys.}$, 209(2):407-435 (2000)]. In this process, pairs of particles $x,y$ in a measure space $E$, merge to form a…
In irreversible aggregation processes droplets or polymers of microscopic size successively coalesce until a large cluster of macroscopic scale forms. This gelation transition is widely believed to be self-averaging, meaning that the order…
The cohesive collective motion (flocking, swarming) of autonomous agents is ubiquitously observed and exploited in both natural and man-made settings, thus, minimal models for its description are essential. In a model with continuous space…
Collective and directed motility or swarming is an emergent phenomenon displayed by many self-organized assemblies of active biological matter such as clusters of embryonic cells during tissue development, cancerous cells during tumor…
We consider one-dimensional systems of self-gravitating sticky particles with random initial data and describe the process of aggregation in terms of the largest cluster size L_n at any fixed time prior to the critical time. The asymptotic…
We introduce a cluster growth process that provides a clear connection between equilibrium statistical mechanics and an explosive percolation model similar to the one recently proposed by Achlioptas et al. [Science 323, 1453 (2009)]. We…
Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks…
Similarly-charged polyelectrolytes are known to attract each other and aggregate into bundles when the charge density of the polymers exceeds a critical value that depends on the valency of the counterions. The dynamics of aggregation of…
The Takayasu aggregation model is a paradigmatic model of aggregation with mass injection, known to exhibit a power law distribution of mass over a range which grows in time. Working in one dimension we find that the mass profile in…
We present an end-to-end description of the formation process of globular clusters (GCs) which combines a treatment for their formation and dynamical evolution within galaxy haloes with a state-of-the-art semi-analytic simulation of galaxy…
The clustering amplitude of galaxies depends on their intrinsic luminosity. We compare the properties of publicly available galaxy formation models with clustering measurements from the two-degree field galaxy redshift survey. The model…
Statistical aspects of the dynamics of chaotic scattering in the classical model of $\alpha$-cluster nuclei are studied. It is found that the dynamics governed by hyperbolic instabilities which results in an exponential decay of the…
Mixing describes the process by which solutes evolve from an initial heterogeneous state to uniformity under the stirring action of a fluid flow. Fluid stretching forms thin scalar lamellae which coalesce due to molecular diffusion. Owing…
Crystal growth and crystal coalescence processes in supercooled systems strongly depend on the concentration of crystallization centers. We perform atomistic dynamics simulations of the crystallization process in the ultrathin metallic film…
A biological system consists of a variety of polymers that are synthesized from monomers, by catalysis that exists only for some long polymers. It is important to elucidate the emergence and sustenance of such autocatalytic polymerization.…
An explanatory model for the emergence of evolvable units must display emerging structures that (1) preserve themselves in time (2) self-reproduce and (3) tolerate a certain amount of variation when reproducing. To tackle this challenge,…
A two species reaction-diffusion model, in which particles diffuse on a one-dimensional lattice and annihilate when meeting each other, has been investigated. Mean field equations for general choice of reaction rates have been solved…
Motivated by a recent experiment [Chikkatur, et al. Science, 296, 2193 (2002)] on the merging of atomic condensates, we investigate how two independent condensates with random initial phases can develop a unique relative phase when we move…
We present a new approach to understanding star-to-star helium abundance variations within globular clusters. We begin with detailed radiation hydrodynamics simulations of cluster formation within giant molecular clouds, and investigate the…