Quasi–steady–state Approximation for Reaction–diffusion Equations
نویسندگان
چکیده
In this paper, we present a rigorous proof of the quasi– steady–state approximation (QSSA) used in chemistry, in two different settings: the first one corresponds to reaction–diffusion equations, while the second one is devoted to ODEs, with a particular attention to the effect of temperature.
منابع مشابه
Numerical Solution of Caputo-Fabrizio Time Fractional Distributed Order Reaction-diffusion Equation via Quasi Wavelet based Numerical Method
In this paper, we derive a novel numerical method to find out the numerical solution of fractional partial differential equations (PDEs) involving Caputo-Fabrizio (C-F) fractional derivatives. We first find out the approximation formula of C-F derivative of function tk. We approximate the C-F derivative in time with the help of the Legendre spectral method and approximation formula o...
متن کاملEnzyme Kinetics Far From the Standard Quasi-Steady-State and Equilibrium Approximations
Analytic approximations of the time-evolution of the single enzyme-substrate reaction are valid for all but a small region of parameter spsce in the positive initial enzyme-initial substrate concentration plane. We find velocity equations for the substrate decomposition and product formation with the aid of the total quasi-steady-state approximation and an aggregation technique for cases where ...
متن کاملApplication of quasi-steady-state methods to nonlinear models of intracellular transport by molecular motors
Molecular motors such as kinesin and dynein are responsible for transporting material along microtubule networks in cells. In many contexts, motor dynamics can be modelled by a system of reaction-advection-diffusion partial differential equations (PDE). Recently, quasi-steady-state (QSS) methods have been applied to models with linear reactions to approximate the behaviour of the full PDE syste...
متن کاملCommunication: limitations of the stochastic quasi-steady-state approximation in open biochemical reaction networks.
It is commonly believed that, whenever timescale separation holds, the predictions of reduced chemical master equations obtained using the stochastic quasi-steady-state approximation are in very good agreement with the predictions of the full master equations. We use the linear noise approximation to obtain a simple formula for the relative error between the predictions of the two master equati...
متن کاملAdaptive Finite Volume Element Method for Convection-diffusion-reaction Problems in 3-d∗
We present an adaptive numerical technique for solving steady-state diffusion and convection-diffusion-reaction equations in 3-D using finite volume approximations. Computational results of various model simulations of fluid flow and transport of passive chemicals in non-homogeneous aquifers are presented and discussed.
متن کامل