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

Dimensional Analysis03:40

Dimensional Analysis

57.5K
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...
57.5K
Dimensional Analysis02:19

Dimensional Analysis

19.8K
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...
19.8K
Dimensional Analysis01:23

Dimensional Analysis

1.6K
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...
1.6K
Dimensional Analysis01:27

Dimensional Analysis

464
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...
464
Problem Solving: Dimensional Analysis01:08

Problem Solving: Dimensional Analysis

5.3K
Every mathematical equation that connects separate distinct physical quantities must be dimensionally consistent, which implies it must abide by two rules. For this reason, the concept of dimension is crucial. The first rule is that an equation's expressions on either side of an equality must have the exact same dimension, i.e., quantities of the same dimension can be added or removed. The second rule stipulates that all popular mathematical functions, such as exponential, logarithmic, and...
5.3K
Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

553
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...
553

You might also read

Related Articles

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

Sort by
Same author

LMI-Based Delayed Output Feedback Controller Design for a Class of Fractional-Order Neutral-Type Delay Systems Using Guaranteed Cost Control Approach.

Entropy (Basel, Switzerland)·2023
Same author

Numerical Design of a Thread-Optimized Gripping System for Lap Joint Testing in a Split Hopkinson Apparatus.

Sensors (Basel, Switzerland)·2023
Same author

Improved Parameter Identification for Lithium-Ion Batteries Based on Complex-Order Beetle Swarm Optimization Algorithm.

Micromachines·2023
Same author

Modified SIQR model for the COVID-19 outbreak in several countries.

Mathematical methods in the applied sciences·2022
Same author

Fractional-Order Sensing and Control: Embedding the Nonlinear Dynamics of Robot Manipulators into the Multidimensional Scaling Method.

Sensors (Basel, Switzerland)·2021
Same author

Advances in the computational analysis of SARS-COV2 genome.

Nonlinear dynamics·2021

Related Experiment Video

Updated: Nov 3, 2025

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

3.8K

Dynamical Analysis of the Dow Jones Index Using Dimensionality Reduction and Visualization.

António M Lopes1, Jóse A Tenreiro Machado2

  • 1LAETA/INEGI, Faculty of Engineering, University of Porto, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal.

Entropy (Basel, Switzerland)
|June 2, 2021
PubMed
Summary

Analyzing complex systems (CS) data, like the Dow Jones Industrial Average (DJIA) index, requires advanced methods. Dimensionality reduction and visualization effectively reveal complex patterns in time-series data.

Keywords:
clusteringcomplex systemsdata visualizationdimensionality reductiontime-series

More Related Videos

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.4K
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

9.4K

Related Experiment Videos

Last Updated: Nov 3, 2025

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy
06:37

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy

Published on: June 15, 2022

3.8K
Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.4K
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

9.4K

Area of Science:

  • Complex Systems Analysis
  • Data Science
  • Computational Finance

Background:

  • Time-series data from complex systems (CS) exhibit chaoticity, fractality, and memory effects, complicating analysis.
  • Multidimensional data analysis is crucial for understanding complex system dynamics.

Purpose of the Study:

  • To explore the dynamics of multidimensional data generated by a complex system.
  • To apply dimensionality reduction and information visualization techniques to analyze the Dow Jones Industrial Average (DJIA) time-series.

Main Methods:

  • Normalized and segmented the DJIA time-series into time window vectors.
  • Utilized various distance metrics to compare these vectors, treating them as objects representing dynamical behavior.
  • Applied dimensionality reduction and information visualization algorithms to the distance-based comparisons.

Main Results:

  • Generated meaningful representations of the DJIA dataset based on object similarities and dissimilarities.
  • Visualized non-locality and temporal evolution through point trajectories and cluster formation.
  • Revealed the complex nature of the DJIA through emergent patterns in the generated data portraits.

Conclusions:

  • Dimensionality reduction and visualization are key modeling options for processing complex data.
  • These computational techniques offer effective insights into the dynamics of complex systems with current resources.