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Related Concept Videos

The Thermodynamics of Mixing01:28

The Thermodynamics of Mixing

Mixing is a fascinating phenomenon in thermodynamics, particularly when considering the Gibbs energy of a mixture at constant temperature and pressure. This energy, denoted as G, tends to decrease during spontaneous mixing processes, offering insights into the composition changes that occur.Imagine two ideal gases, initially separated in different containers, with amounts nA and nB, respectively, both at a temperature T and pressure p. The chemical potentials of these gases have their 'pure'...
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
Stability01:28

Stability

The time response of a linear time-invariant (LTI) system can be divided into transient and steady-state responses. The transient response represents the system's initial reaction to a change in input and diminishes to zero over time. In contrast, the steady-state response is the behavior that persists after the transient effects have faded.
The stability of an LTI system is determined by the roots of its characteristic equation, known as poles. A system is stable if it produces a bounded...
Microtubule Instability02:17

Microtubule Instability

Microtubules are hollow cylindrical filaments having a diameter of approximately 25 nm and a length that varies from 200 nm to 25 μm. GTP-bound tubulin subunits form αβ-heterodimers for microtubule assembly. These core building blocks interact longitudinally, polymerizing into protofilaments. The protofilaments then interact with one another through lateral bonding forces to form stable cylindrical microtubules. These cylindrical filaments are dynamic as they undergo repeated assembly and...
The Integrated Rate Law: The Dependence of Concentration on Time02:39

The Integrated Rate Law: The Dependence of Concentration on Time

While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
Entropy02:39

Entropy

Salt particles that have dissolved in water never spontaneously come back together in solution to reform solid particles. Moreover, a gas that has expanded in a vacuum remains dispersed and never spontaneously reassembles. The unidirectional nature of these phenomena is the result of a thermodynamic state function called entropy (S). Entropy is the measure of the extent to which the energy is dispersed throughout a system, or in other words, it is proportional to the degree of disorder of a...

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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

Instability statistics and mixing rates.

Roberto Artuso1, Cesar Manchein

  • 1Dipartimento di Fisica e Matematica, Center for Nonlinear and Complex Systems, Università degli Studi dell'Insubria, Via Valleggio 11, 22100 Como, Italy. roberto.artuso@uninsubria.it

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

Studying large deviation properties of finite time largest Lyapunov exponents offers a powerful method for estimating time correlations and Poincaré recurrences in weakly chaotic dynamical systems.

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Last Updated: Jun 18, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
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Analyzing Mixing Inhomogeneity in a Microfluidic Device by Microscale Schlieren Technique
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Area of Science:

  • Dynamical Systems Theory
  • Statistical Mechanics
  • Chaos Theory

Background:

  • Dynamical systems with weak chaotic properties present challenges in analyzing time correlations and recurrences.
  • Traditional methods may struggle to provide quantitative estimates in these delicate systems.

Purpose of the Study:

  • To introduce a novel technique for analyzing dynamical systems with weak chaotic properties.
  • To provide quantitative estimates for the decay rates of time correlations and Poincaré recurrences.

Main Methods:

  • Analysis of probability distributions of finite time largest Lyapunov exponents.
  • Application of large deviation theory to these distributions.

Main Results:

  • The proposed method yields powerful quantitative estimates.
  • Polynomial decay rates for time correlations and Poincaré recurrences can be accurately determined.
  • The technique is particularly effective for systems with weak chaotic properties.

Conclusions:

  • Investigating large deviation properties of finite time largest Lyapunov exponents is a highly effective approach.
  • This method advances the quantitative understanding of dynamical systems, especially those with subtle chaotic behavior.