Related papers: Mesoscopic modeling of stochastic reaction-diffusi…
Rheological responses are the most relevant features to describe soft matter. So far, such constitutive relations are still not well understood in terms of small scale properties, although this knowledge would help the design of synthetic…
The reaction-diffusion master equation (RDME) is a model that allows for efficient on-lattice simulation of spatially resolved stochastic chemical kinetics. Compared to off-lattice hard-sphere simulations with Brownian Dynamics (BD) or…
A variety of simulation methodologies have been used for modeling reaction-diffusion dynamics -- including approaches based on Differential Equations (DE), the Stochastic Simulation Algorithm (SSA), Brownian Dynamics (BD), Green's Function…
From a mathematical model that describes a complex chemical kinetic system of $N$ species and $M$ elementrary reactions in a rapidly stirred vessel of size $V$ as a Markov process, we show that a macroscopic chemical thermodynamics emerges…
Diffusion is a fundamental phenomenon that occurs ubiquitously in nature and remains the subject of continuous research interest. Understanding diffusion is a key to understanding leaving systems. In this Chapter, I discuss diffusion of…
Chemical reactions are a prominent feature of molecular communication (MC) systems, with no direct parallels in wireless communications. While chemical reactions may be used inside the transmitter nodes, receiver nodes or the communication…
Reaction diffusion systems describe the behaviour of dynamic, interacting, particulate systems. Quantum stochastic processes generalise Brownian motion and Poisson processes, having operator valued It\^{o} calculus machinery. Here it is…
The dynamics of steps on crystal surfaces is considered. In general, the meandering of the steps obeys a subdiffusive behaviour. The characteristic asymptotic time laws depend on the microscopic mechanism for detachment and attachment of…
Finding reduced models of spatially-distributed chemical reaction networks requires an estimation of which effective dynamics are relevant. We propose a machine learning approach to this coarse graining problem, where a maximum entropy…
We recently proposed a dynamical mesoscopic model for DNA, which is based, like statistical ones, on site-dependent finite stacking and pairing enthalpies. In the present article, we first describe how the parameters of this model are…
Reaction rate equations are ordinary differential equations that are frequently used to describe deterministic chemical kinetics at the macroscopic scale. At the microscopic scale, the chemical kinetics is stochastic and can be captured by…
We consider stochastic thermodynamics as a theory of statistical inference for experimentally observed fluctuating time-series. To that end, we introduce a general framework for quantifying the knowledge about the dynamical state of the…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…
We analyze a class of chemical reaction networks under mass-action kinetics and involving multiple time-scales, whose deterministic and stochastic models display qualitative differences. The networks are inspired by gene-regulatory…
Mesoscopic density functional theory for inhomogeneous mixtures of sperical particles is developed in terms of mesoscopic volume fractions by a systematic coarse-graining procedure starting form microscopic theory. Approximate expressions…
Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant…
Due to the intrinsic complexity and nonlinearity of chemical reactions, direct applications of traditional machine learning algorithms may face with many difficulties. In this study, through two concrete examples with biological background,…
Experience collected in mesoscopic dynamic modeling of externally driven systems indicates absence of potentials that could play role of equilibrium or nonequilibrium thermodynamic potentials yet their thermo-dynamics-like modeling is often…
Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as…
We derive a mesoscopic modeling and simulation technique that is very close to the technique known as dissipative particle dynamics. The model is derived from molecular dynamics by means of a systematic coarse-graining procedure. Thus the…