相关论文: Diffusion-limited Reactions in Nanoscale Electroni…
Optical biosensors are often used to measure kinetic rate constants associated with chemical reactions. Such instruments operate in the \textit{surface-volume} configuration, in which ligand molecules are convected through a fluid-filled…
Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or…
In this article we propose and investigate a hierarchy of mathematical models based on partial differential equations (PDE) and ordinary differential equations (ODE) for the simulation of the biophysical phenomena occurring in the…
This work presents a physics-conditioned latent diffusion model tailored for dynamical downscaling of atmospheric data, with a focus on reconstructing high-resolution 2-m temperature fields. Building upon a pre-existing diffusion…
The dynamics of pulse solutions in a bistable reaction-diffusion system are studied analytically by reducing partial differential equations (PDEs) to finite-dimensional ordinary differential equations (ODEs). For the reduction, we apply the…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…
This paper deals with the large-time analysis of a PDE system modelling contact with adhesion, in the case when thermal effects are taken into account. The phenomenon of adhesive contact is described in terms of phase transitions for a…
This paper reports a mass transfer model of a reactant flowing in a large aspect ratio microfluidic chip made of a channel with electrodes on the side walls. A semi-analytical solution to the two-dimensional Fickian diffusion of a reactant…
This study reveals that Equilibrium Constant Differential Equations (ECDE) for nanoconfined reactions derived recently in the frameworks of statistical mechanics are useful in modeling stochastic chemical kinetics. It is assumed and…
We use a frequency-dependent electro-optic technique to measure the hole mobility in small molecule organic semiconductors, such as 6,13 bis(triisopropylsilylethynyl)-pentacene. Measurements are made on semiconductor films in bottom gate,…
We consider a quasilinear degenerate diffusion-reaction system that describes biofilm formation. The model exhibits two non-linear effects: a power law degeneracy as one of the dependent variables vanishes and a super diffusion singularity…
Nonlocally related partial differential equation (PDE) systems are useful in the analysis of a given PDE system. It is known that each local conservation law of a given PDE system systematically yields a nonlocally related system. In this…
Despite tremendous potential of highly sensitive electronic detection of bio-molecules by nanoscale biosensors for genomics and proteomic applications, many aspects of experimentally observed sensor response (S) are unexplained within…
We present theoretical models for the time-dependent voltage of an electrochemical cell in response to a current step, including effects of diffuse charge (or "space charge") near the electrodes on Faradaic reaction kinetics. The full model…
In this paper we consider a system of two coupled nonlinear diffusion--reaction partial differential equations (PDEs) which model the growth of biofilm and consumption of the nutrient. At the scale of interest the biofilm density is subject…
Equilibrium Constant Differential Equations (ECDE) are derived for several nanoconfined elemental bimolecular reactions in the frameworks of statistical mechanics and the ideal gas model. The ECDEs complement the well-known…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
We consider a finite element approximation for a system consisting of the evolution of a closed planar curve by forced curve shortening flow coupled to a reaction-diffusion equation on the evolving curve. The scheme for the curve evolution…
Biological systems are non-linear, include unobserved variables and the physical principles that govern their dynamics are partly unknown. This makes the characterization of their behavior very challenging. Notably, their activity occurs on…