Unbiased tau-leap methods for stochastic simulation of chemically reacting systems

Zhouyi Xu1, Xiaodong Cai

  • 1Department of Electrical and Computer Engineering, University of Miami, Coral Gables, FL 33124, USA.

Related Concept Videos

Reaction Mechanisms: The Steady-State Approximation01:26

Reaction Mechanisms: The Steady-State Approximation

The steady-state approximation, also referred to as the quasi-steady-state approximation to differentiate it from a true steady state, is a widely used method for simplifying calculations in complex reaction mechanisms. This approach is particularly useful when dealing with multi-step reactions that involve reverse reactions or several steps, which can significantly increase mathematical complexity and make the reactions nearly unsolvable analytically.The steady-state approximation operates on...
Fast Reactions01:27

Fast Reactions

Fast reactions occurring in times shorter than the time needed to mix reactants pose a unique challenge for investigation. In a liquid-phase continuous-flow system, reactants A and B are swiftly pushed into the mixing chamber, where mixing occurs within 1 ms. The reaction mixture then flows through an observation tube, and one measures light absorption to determine species concentrations at various points of the tube. This method is most appropriate when relatively large volumes of reactants...
Predicting Reaction Outcomes02:24

Predicting Reaction Outcomes

Kinetics describes the rate and path by which a reaction occurs. In contrast, thermodynamics deals with state functions and describes the properties, behavior, and components of a system. It is not concerned with the path taken by the process and cannot address the rate at which a reaction occurs. Although it does provide information about what can happen during a reaction process, it does not describe the detailed steps of what appears on an atomic or a molecular level. On the other hand,...
Reaction Mechanisms: Rate-limiting Step Approximation01:29

Reaction Mechanisms: Rate-limiting Step Approximation

The rate-determining step, or RDS, in a chemical reaction is the slowest step that determines the overall reaction rate. It is identified by using the observed rate law and typically involves approximation methods like the RDS approximation or the steady-state approximation.In the RDS approximation, also known as the rate-limiting-step or equilibrium approximation, the reaction mechanism consists of one or more reversible reactions near equilibrium, followed by a slower RDS, and then one or...
Chemical Equilibria: Systematic Approach to Equilibrium Calculations01:21

Chemical Equilibria: Systematic Approach to Equilibrium Calculations

Equilibrium calculations for systems involving multiple equilibria are often complex. For example, to calculate the solubility of a sparingly soluble salt in an aqueous solution in the presence of a common ion, one must consider all the equilibria in this solution. Calculations for these systems can be complicated and tedious, so a systematic approach with a series of steps is often helpful. The process is detailed below.
The first step is to identify all the chemical reactions involved, The...
Transition State Theory01:25

Transition State Theory

Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...