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

Noncompartmental Analysis: Mean Residence Time01:05

Noncompartmental Analysis: Mean Residence Time

297
According to statistical moment theory, mean residence time (MRT) is an important measure in pharmacokinetics. MRT can be defined as the expected mean of a probability density function distribution. It provides valuable insights into drug disposition in the body.
After the administration of a drug through intravenous bolus injection, the drug molecules are distributed throughout the body and remain there for varying periods. The MRT represents the average time these drug molecules stay in the...
297
Regression Toward the Mean01:52

Regression Toward the Mean

6.5K
Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
6.5K
Average Velocity01:12

Average Velocity

20.2K
To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position of the object during its motion, but also how fast it is moving. The speed at which an object is moving is given by the rate at which the position changes with time. For each position xi, we assign a particular time ti. If the details of the motion at each instant are not important, the rate is usually expressed as the average velocity. This...
20.2K
Weighted Mean00:57

Weighted Mean

5.5K
While taking the arithmetic, geometric, or harmonic mean of a sample data set, equal importance is assigned to all the data points. However, all the values may not always be equally important in some data sets. An intrinsic bias might make it more important to give more weightage to specific values over others.
For example, consider the number of goals scored in the matches of a tournament. While computing the average number of goals scored in the tournament, it may be more important to...
5.5K
Mean free path and Mean free time01:22

Mean free path and Mean free time

4.1K
Consider the gas molecules in a cylinder. They move in a random motion as they collide with each other and change speed and direction. The average of all the path lengths between collisions is known as the "mean free path."
4.1K
Arithmetic Mean01:08

Arithmetic Mean

15.5K
The arithmetic mean is the most commonly used measure of the central tendency of a data set. It is defined as the sum of all the elements constituting the data set, divided by the total number of elements. It is sometimes loosely referred to as the “average.”
When all the values in a data set are not unique, the sum in the numerator can be calculated by multiplying each distinct value by its frequency.
Sometimes, the arithmetic mean of a sample can be affected by a few data points...
15.5K

You might also read

Related Articles

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

Sort by
Same author

Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application.

Proceedings. Mathematical, physical, and engineering sciences·2016
See all related articles

Related Experiment Video

Updated: Sep 25, 2025

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons
07:59

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Published on: June 9, 2023

1.5K

Relationship between the methods of bounding time averages.

Sergei Chernyshenko1

  • 1Department of Aeronautics, Imperial College London, London SW7 2AZ, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|April 25, 2022
PubMed
Summary

This study connects two methods for bounding turbulent energy dissipation, showing they yield the same results. It proposes new approaches using non-quadratic functionals for advanced fluid dynamics analysis.

Keywords:
Navier–Stokes equationauxiliary function methodbackground flow methodbounddynamical systemtime average

More Related Videos

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
12:03

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

8.6K
Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
05:04

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Published on: September 21, 2017

6.1K

Related Experiment Videos

Last Updated: Sep 25, 2025

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons
07:59

Author Spotlight: Alignment of Synchronized Time-Series Data Using the Characterizing Loss of Cell Cycle Synchrony Model for Cross-Experiment Comparisons

Published on: June 9, 2023

1.5K
A Method for Tracking the Time Evolution of Steady-State Evoked Potentials
12:03

A Method for Tracking the Time Evolution of Steady-State Evoked Potentials

Published on: May 25, 2019

8.6K
Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task
05:04

Bouncing Ball with a Uniformly Varying Velocity in a Metronome Synchronization Task

Published on: September 21, 2017

6.1K

Area of Science:

  • Fluid dynamics
  • Turbulence theory
  • Mathematical physics

Background:

  • Bounding time-averaged characteristics of dynamical systems, like energy dissipation in turbulent flows, is a significant challenge.
  • The incompressible Navier-Stokes equations govern fluid motion, and understanding dissipation bounds is crucial for predicting system behavior.

Purpose of the Study:

  • To investigate the relationship between the direct method and the auxiliary functional method for bounding turbulent energy dissipation.
  • To explore extensions of existing methods using non-quadratic auxiliary functionals for improved bounds.
  • To analyze the plane Couette flow as a case study for these bounding techniques.

Main Methods:

  • Comparison of the direct method (Seis, 2015) and the auxiliary functional method (Chernyshenko et al., 2014).
  • Equivalence established between the background flow method (Doering & Constantin) and auxiliary functional methods with quadratic functionals.
  • Analysis of plane Couette flow to illustrate theoretical findings.

Main Results:

  • The direct method and auxiliary functional method are shown to be related and produce identical bounds.
  • The background flow method is a specific case of the auxiliary functional method using quadratic functionals.
  • Three novel strategies are proposed for advancing bounding techniques using non-quadratic auxiliary functionals.

Conclusions:

  • The study unifies existing methods for bounding turbulent energy dissipation and highlights their interrelation.
  • New avenues using non-quadratic auxiliary functionals are identified, promising more accurate bounds.
  • The proposed methods offer a path to leverage accumulated experience with background flow methods for future research.