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Related Concept Videos

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...
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...
Temperature Dependence on Reaction Rate02:55

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The Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This premise is the basis for a theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates.
The collision theory is based on the postulates that (i) the reaction rate is proportional to the rate of reactant collisions, (ii) the reacting species collide in an orientation allowing contact between...
Consecutive Reactions01:22

Consecutive Reactions

Consecutive reactions involve a sequence where the product of a preceding reaction becomes the reactant for the subsequent one. In a simple scheme, A transforms into B, which further reacts to form C, with rate constants k1 and k2, respectively. This concept is evident in the radioactive decay series. Assuming an initial state with only A present, the conservation of matter leads to three coupled differential equations, determining the concentrations of A, B, and C over time.The rate of change...
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...
Reaction Mechanisms: Rate-limiting Step Approximation01:29

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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...

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Updated: Jun 18, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Time-delay-induced instabilities in reaction-diffusion systems.

Shrabani Sen1, Pushpita Ghosh, Syed Shahed Riaz

  • 1Indian Association for the Cultivation of Science, Jadavpur, Kolkata, India.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

Introducing time delay into reaction-diffusion systems can create spatiotemporal instabilities. This delay can lead to pattern formation and spiral dynamics in systems with unequal diffusivities.

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Area of Science:

  • Chemical kinetics
  • Mathematical biology
  • Nonlinear dynamics

Background:

  • Reaction-diffusion systems are fundamental models in various scientific fields.
  • Time delays are often present in biological and chemical processes but are not always included in models.
  • Understanding the impact of delays is crucial for accurate system prediction.

Purpose of the Study:

  • To investigate the effects of time delay in the kinetic terms of reaction-diffusion systems.
  • To explore how delays influence spatiotemporal dynamics and pattern formation.
  • To analyze the emergence of Turing and Turing-Hopf instabilities due to time delays.

Main Methods:

  • Theoretical analysis of reaction-diffusion models with time delays.
  • Numerical simulations to explore parameter spaces.
  • Investigation of two distinct prototypical reaction-diffusion systems.

Main Results:

  • Short time delays, exceeding a critical threshold, can induce spatiotemporal instabilities.
  • Unequal diffusivities combined with appropriate parameter space and delay can trigger Turing instability, leading to stationary patterns.
  • Turing-Hopf transitions, resulting in spiral pattern formation, were observed.

Conclusions:

  • Time delays are a significant factor in the stability and dynamics of reaction-diffusion systems.
  • Delays can qualitatively alter system behavior, leading to complex patterns like spirals.
  • The findings provide insights into pattern formation mechanisms in systems with delayed kinetics.