Related papers: Continuous-time multifarious systems -- Part II: n…
We investigate the self-assembly (crystallisation) of particles with hard cores and isotropic, square-well interactions, using a Monte Carlo scheme to simulate overdamped Langevin dynamics. We measure correlation and response functions…
In living cells, proteins self-assemble into large functional structures based on specific interactions between molecularly complex patches. Due to this complexity, protein self-assembly results from a competition between a large number of…
We use computer simulations to study a model, first proposed by Wales [1], for the reversible and monodisperse self-assembly of simple icosahedral virus capsid structures. The success and efficiency of assembly as a function of…
We develop and analyze a highly efficient, second-order time-marching scheme for infinite-dimensional nonlinear geophysical fluid models, designed to accurately approximate invariant measures-that is, the stationary statistical properties…
A well-balanced second-order finite volume scheme is proposed and analyzed for a 2 X 2 system of non-linear partial differential equations which describes the dynamics of growing sandpiles created by a vertical source on a flat, bounded…
Self-assembly is a phenomenon observed in nature at all scales where autonomous entities build complex structures, without external influences nor centralised master plan. Modelling such entities and programming correct interactions among…
In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…
Continuous-time Markov chains are used to model stochastic systems where transitions can occur at irregular times, e.g., birth-death processes, chemical reaction networks, population dynamics, and gene regulatory networks. We develop a…
Biological diversity has evolved despite the essentially infinite complexity of protein sequence space. We present a hierarchical approach to the efficient searching of this space and quantify the evolutionary potential of our approach with…
Noise-induced transitions between metastable fixed points in systems evolving on multiple time scales are analyzed in situations where the time scale separation gives rise to a slow manifold with bifurcation. This analysis is performed…
Three-dimensional shell-like structures can be obtained spontaneously at the microscale from the self-folding of 2D templates of rigid panels. At least for simple structures, the motion of each panel is consistent with a Brownian process…
We propose a model to study symmetric binary fluids, based in the mesoscopic molecular simulation technique known as multiparticle collision, where space and state variables are continuous while time is discrete. We include a repulsion rule…
Biological systems, unlike physical or chemical systems, are characterized by the very inhomogeneous distribution of their components. The immune system, in particular, is notable for self-organizing its structure. Classically, the dynamics…
Self-assembly is the autonomous organization of components into patterns or structures: an essential ingredient of biology and a desired route to complex organization. At equilibrium, the structure is encoded through specific interactions,…
In this work we present a reduction result for discrete time systems with two time scales. In order to be valid, previous results in the field require some strong hypotheses that are difficult to check in practical applications. Roughly…
We present an improvement of the Gillespie Exact Stochastic Simulation Algorithm, which leverages a bitwise representation of variables to perform independent simulations in parallel. We show that the subsequent gain in computational yield…
We present a simple discrete model for the non-linear spatial interaction of different kinds of ``subpopulations'' composed of identical moving entities like particles, bacteria, individuals, etc. The model allows to mimic a variety of…
In a Hilbert setting we study the convergence properties of a second order in time dynamical system combining viscous and Hessian-driven damping with time scaling in relation with the minimization of a nonsmooth and convex function. The…
Spontaneous self-assembly in molecular systems is a fundamental route to both biological and engineered soft matter. Simple micellisation, emulsion formation, and polymer mixing principles are well understood. However, the principles behind…
We model sectoral production by serially nesting (cascading) binary compounding processes. The sequence of processes is discovered in a self-similar hierarchical structure stylized in macroscopic input-output transactions. The feedback…