Related papers: Stochastic Analysis of Dimerization Systems
We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike…
The crystallization proceeds by the advance of the crystal faces into the disordered phase at the expense of the supersaturation which is not sustained in our model. Using a conservation constraint for the transformation ratio and a kinetic…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
Data-driven control strategies for dynamical systems with unknown parameters are popular in theory and applications. An essential problem is to prevent stochastic linear systems becoming destabilized, due to the uncertainty of the…
Stochastic differential equations (SDEs) offer powerful and accessible mathematical models for capturing both deterministic and probabilistic aspects of dynamic behavior across a wide range of physical, financial, and social systems.…
Stochastic modeling of transcription is a classic yet long-standing problem in theoretical biophysics. The lack of unified results and a computationally efficient approach for a general, fine-grained transcription model has confined…
A deterministic-stochastic coupling scheme is developed for simulating rarefied gas flows, where the key process is the alternative solving of the macroscopic synthetic equations [Su et al., J. Comput. Phys., 407 (2020) 109245] and the…
In this paper, we study a parabolic reaction diffusion system with constraints that model biofilm growth. Within a unified framework encompassing multiple numerical schemes, we derive the first general convergence rates for approximating…
Computing reaction rates in biomolecular systems is a common goal of molecular dynamics simulations. The reactions considered often involve conformational changes in the molecule, either changes in the structure of a protein or the relative…
A novel multiscale numerical method is developed to accelerate direct simulation Monte Carlo (DSMC) simulations for polyatomic gases with internal energy. This approach applies the general synthetic iterative scheme to stochastic…
Surfaces serve as highly efficient catalysts for a vast variety of chemical reactions. Typically, such surface reactions involve billions of molecules which diffuse and react over macroscopic areas. Therefore, stochastic fluctuations are…
A combination of first principle molecular dynamics (MD) simulations with a rate equation model (MD-RE approach) is presented to study the trapping and the scattering of rare gas atoms from metal surfaces. The temporal evolution of the atom…
Unlike gas-phase reactions, chemical reactions taking place on interstellar dust grain surfaces cannot always be modeled by rate equations. Due to the small grain sizes and low flux,these reactions may exhibit large fluctuations and thus…
Moment dynamics in stochastic chemical kinetics often involve an infinite chain of coupled equations, where lower-order moments depend on higher-order ones, making them analytically intractable. Moment bounding via semidefinite programming…
Applying the method of moments to the chemical master equation (CME) appearing in stochastic chemical kinetics often leads to the so-called closure problem. Recently, several authors showed that this problem can be partially overcome using…
An important goal of self-assembly is to achieve a preprogrammed structure with high fidelity. Here, we control the valence of DNA-functionalized emulsions to make linear and branched model polymers, or `colloidomers'. The distribution of…
We study the phase transition in a system composed of dimers interacting with each other via a nearest-neighbor (NN) exchange $J$ and competing interactions taken from a truncated dipolar coupling. Each dimer occupies a link between two…
To study the dynamics of chemical processes, we often adopt rate equations to observe the change in chemical concentrations. However, when the number of the molecules is small, the fluctuations cannot be neglected. We often study the…
Moment systems arise in a wide range of contexts and applications, e.g. in network modeling of complex systems. Since moment systems consist of a high or even infinite number of coupled equations, an indispensable step in obtaining a…
To understand the performance of popular density-functional theory (DFT) exchange-correlation (xc) functionals in simulations of liquid water, water monomers and dimers were extracted from a PBE simulation of liquid water and examined with…