Related papers: Stochastic Evolution of Coagulation-Fragmentation …
The native conformation of structured proteins is stabilized by a complex network of interactions. We analyzed the elementary patterns that constitute such network and ranked them according to their importance in shaping protein sequence…
Crystallization is one of the most important physicochemical processes which has relevance in material science, biology, and the environment. Decades of experimental and theoretical efforts have been made to understand this fundamental…
In a companion paper, we put forth a thermodynamic model for complex formation via a chemical reaction involving multiple macromolecular species, which may subsequently undergo liquid-liquid phase separation and a further transition into a…
Turing patterns can be observed in reaction-diffusion systems where chemical species have different diffusion constants. In recent years, several studies investigated the effects of noise on Turing patterns and showed that the parameter…
Cells in multicellular organisms adhere to the extracellular matrix through two-dimensional clusters spanning a size range from very few to thousands of adhesion bonds. For many common receptor-ligand systems, the ligands are tethered to a…
Recent theories predict that when a supercooled liquid approaches the glass transition, particle clusters with a special "amorphous order" nucleate within the liquid, which lead to static correlations dictating the dramatic slowdown of…
People organize in groups and contagions spread across them. A simple stochastic process, yet complex to model due to dynamical correlations within and between groups. Moreover, groups can evolve if agents join or leave in response to…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
We define a spatially-dependent fragmentation process, which involves rectangles breaking up into progressively smaller pieces at rates that depend on their shape. Long, thin rectangles are more likely to break quickly, and are also more…
In this paper, we consider a continuous fragmentation--coagulation model in which the reacting particles can be transported in physical space through either advection or diffusion. We prove new results on the generation of $C_0$-semigroups…
The fraction of stars forming in compact, gravitationally bound clusters (the `cluster formation efficiency' or CFE) is an important quantity for deriving the spatial clustering of stellar feedback and for tracing star formation using…
Conceiving a molecule as composed of smaller molecular fragments, or subunits, is one of the pillars of the chemical and physical sciences, and leads to productive methods in quantum chemistry. Using a fragmentation scheme, efficient…
We analyze systems of clusters and interacting upon colliding---a collision between two clusters may lead to merging or fragmentation---and we also investigate the influence of additional spontaneous fragmentation events. We consider both…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
The recent advancements in mathematical modeling of biochemical systems have generated increased interest in sensitivity analysis methodologies. There are two primary approaches for analyzing these mathematical models: the stochastic…
We use two high resolution CDM simulations to show that (i) when clusters of galaxies form the infall pattern of matter is not random but shows clear features which are correlated in time; (ii) in addition, the infall patterns are…
We study infinite systems of particles which undergo coalescence and fragmentation, in a manner determined solely by their masses. A pair of particles having masses $x$ and $y$ coalesces at a given rate $K(x,y)$. A particle of mass $x$…
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…
Clustering is a widely used unsupervised learning technique involving an intensive discrete optimization problem. Associative Memory models or AMs are differentiable neural networks defining a recursive dynamical system, which have been…
Accurate many-body treatments of condensed-phase systems are challenging because correlated solvers such as full configuration interaction (FCI) and the density matrix renormalization group (DMRG) scale exponentially with system size.…