Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Correlation of Experimental Data01:23

Correlation of Experimental Data

448
Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity,...
448
Dimensional Analysis02:19

Dimensional Analysis

22.3K
The concept of dimension is important because every mathematical equation linking physical quantities must be dimensionally consistent, implying that mathematical equations must meet the following two rules. The first rule is that, in an equation, the expressions on each side of the equal sign must have the same dimensions. This is fairly intuitive since we can only add or subtract quantities of the same type (dimension). The second rule states that, in an equation, the arguments of any of the...
22.3K
Dimensional Analysis01:23

Dimensional Analysis

1.9K
Dimensional analysis is a powerful tool that is used in physics and engineering to understand and predict the behavior of physical systems. The basic idea behind dimensional analysis is to express physical quantities in terms of fundamental dimensions such as the mass, length, and time. Derived dimensions like the velocity, acceleration, and force are derived from the combinations of these fundamental dimensions.
Dimensional analysis allows us to analyze and compare physical quantities on a...
1.9K
Dimensional Analysis03:40

Dimensional Analysis

58.4K
Dimensional analysis, also known as the factor label method, is a versatile approach for mathematical operations. The main principle behind this approach is: the units of quantities must be subjected to the same mathematical operations as their associated numbers. This method can be applied to computations ranging from simple unit conversions to more complex and multi-step calculations involving several different quantities and their units.
Conversion Factors and Dimensional Analysis
The unit...
58.4K
Dimensional Analysis01:27

Dimensional Analysis

584
Dimensional analysis is a valuable technique in fluid mechanics for simplifying complex problems by reducing them into dimensionless groups. These groups capture the essential relationships between the variables involved, allowing researchers and engineers to analyze fluid flow without dealing with each variable individually. This approach reduces the number of independent variables, allowing for easier analysis and better understanding of physical phenomena.
In fluid mechanics, dimensional...
584
Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

707
Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...
707

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Delayed epidemic peak caused by infection and recovery rate fluctuations.

Chaos (Woodbury, N.Y.)·2021
Same author

Interrupting vaccination policies can greatly spread SARS-CoV-2 and enhance mortality from COVID-19 disease: The AstraZeneca case for France and Italy.

Chaos (Woodbury, N.Y.)·2021
Same author

Modeling the second wave of COVID-19 infections in France and Italy via a stochastic SEIR model.

Chaos (Woodbury, N.Y.)·2020
Same author

Permutations uniquely identify states and unknown external forces in non-autonomous dynamical systems.

Chaos (Woodbury, N.Y.)·2020
Same author

Asymptotic estimates of SARS-CoV-2 infection counts and their sensitivity to stochastic perturbation.

Chaos (Woodbury, N.Y.)·2020
Same author

On reversals in 2D turbulent Rayleigh-Bénard convection: Insights from embedding theory and comparison with proper orthogonal decomposition analysis.

Chaos (Woodbury, N.Y.)·2019

Related Experiment Video

Updated: Dec 31, 2025

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

9.9K

Correlation dimension and phase space contraction via extreme value theory.

Davide Faranda1, Sandro Vaienti2

  • 1LSCE-IPSL, CEA Saclay l'Orme des Merisiers, CNRS UMR 8212 CEA-CNRS-UVSQ, Université Paris-Saclay, 91191 Gif-sur-Yvette, France.

Chaos (Woodbury, N.Y.)
|January 8, 2020
PubMed
Summary

Extreme value theory provides new methods for estimating chaotic dynamical systems' correlation dimension and phase space contraction. The Dynamical Extremal Index offers robust, straightforward calculations from time series data.

More Related Videos

Analysis of SEC-SAXS data via EFA deconvolution and Scatter
10:59

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Published on: January 28, 2021

9.7K
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

438

Related Experiment Videos

Last Updated: Dec 31, 2025

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture
09:04

Lens-free Video Microscopy for the Dynamic and Quantitative Analysis of Adherent Cell Culture

Published on: February 23, 2018

9.9K
Analysis of SEC-SAXS data via EFA deconvolution and Scatter
10:59

Analysis of SEC-SAXS data via EFA deconvolution and Scatter

Published on: January 28, 2021

9.7K
Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis
06:44

Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

Published on: September 23, 2025

438

Area of Science:

  • Dynamical systems theory
  • Chaos theory
  • Statistical modeling

Background:

  • Estimating correlation dimension and phase space contraction is crucial for characterizing chaotic systems.
  • Traditional methods can be complex and sensitive to data length.

Purpose of the Study:

  • To introduce a novel approach using extreme value theory for estimating key dynamical system properties.
  • To develop the concept of the Dynamical Extremal Index.

Main Methods:

  • Utilizing the maxima of observables from chaotic system trajectories.
  • Applying classical extreme value laws to fit observed data.
  • Calculating the correlation dimension from the scale parameter and phase space contraction from the extremal index.

Main Results:

  • The inverse of the scale parameter directly estimates the correlation dimension.
  • The extremal index quantifies phase space contraction, relating to Lyapunov exponents and metric entropy.
  • The Dynamical Extremal Index provides robust estimates even with short time series.

Conclusions:

  • Extreme value theory offers a powerful and accessible tool for analyzing chaotic dynamical systems.
  • The Dynamical Extremal Index is a valuable indicator for characterizing system dynamics and contraction rates.