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Related Concept Videos

Curvilinear Motion: Polar Coordinates01:27

Curvilinear Motion: Polar Coordinates

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In polar coordinates, the motion of a particle follows a curvilinear path. The radial coordinate symbolized as 'r,' extends outward from a fixed origin to the particle, while the angular coordinate, 'θ,' measured in radians, represents the counterclockwise angle between a fixed reference line and the radial line connecting the origin to the particle.
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position...
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Polar and Cylindrical Coordinates01:22

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The Cartesian coordinate system is a very convenient tool to use when describing the displacements and velocities of objects and the forces acting on them. However, it becomes cumbersome when we need to describe the rotation of objects. So, when describing rotation, the polar coordinate system is generally used.
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Potential Due to a Polarized Object01:29

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A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
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pV-Diagrams01:18

pV-Diagrams

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The pV diagram, which is a graph of pressure versus volume of the gas under study, is helpful in describing certain aspects of the substance. When the substance behaves like an ideal gas, the ideal gas equation describes the relationship between its pressure and volume. On a pV diagram, it is common to plot an isotherm, which is a curve showing p as a function of V with the number of molecules and the temperature fixed. Then, for an ideal gas, the product of the pressure of the gas and its...
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Phase Diagrams02:39

Phase Diagrams

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A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). Regions or areas labeled solid, liquid, and gas represent single phases, while lines or curves represent...
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Moments of Inertia for an Area about Inclined Axes01:18

Moments of Inertia for an Area about Inclined Axes

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In physics and engineering, understanding the moments of inertia for a given area with asymmetrical mass distribution is critical for proper design and analysis. When considering an arbitrary coordinate system, the moments of inertia can be obtained by integrating the moment of inertia for an infinitesimal area element.
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Related Experiment Video

Updated: Jul 13, 2025

Author Spotlight: Non-Invasive Imaging of Complex Bio-Structures Using Polarization-Sensitive Two-Photon Microscopy
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Interactive polar diagrams for model comparison.

Aleksandar Anžel1, Dominik Heider1, Georges Hattab2

  • 1Department of Mathematics & Computer Science, University of Marburg, Hans-Meerwein-Straße 6, Marburg, D-35032, Hesse, Germany.

Computer Methods and Programs in Biomedicine
|October 13, 2023
PubMed
Summary
This summary is machine-generated.

Evaluating complex models is challenging with traditional methods. A new library, polar-diagrams, uses interactive Taylor and Mutual Information Diagrams for easier performance assessment and comparison across diverse scientific fields.

Keywords:
AiBioinformaticsClimateClimate-model-visualizationComparisonCorrelationData-visualizationEntropyEvaluationInformation-visualizationMachine-learningMedical-dataMl-model-evaluationModel-comparisonMutual-informationMutual-information-diagramPredictive-analysisTaylor-diagramVariation-of-informationVisualization

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Area of Science:

  • Computational Science
  • Data Science
  • Scientific Modeling

Background:

  • Conventional methods for evaluating complex models across diverse fields like biology, climatology, and machine learning are often inadequate when using multiple evaluation metrics simultaneously.
  • Traditional tabular presentations of multi-model evaluation scores hinder the determination of model similarities and performance rankings.

Purpose of the Study:

  • To introduce a novel approach for assessing and comparing the performance of complex models.
  • To provide an accessible tool for visualizing model performance and relationships.

Main Methods:

  • The study combines statistics, information theory, and data visualization techniques.
  • Juxtaposed Taylor and Mutual Information Diagrams are employed to track and summarize model performance.
  • The approach allows for the visualization of linear and nonlinear relationships between models.

Main Results:

  • The developed library, polar-diagrams, offers the first publicly available interactive implementations of Taylor Diagrams and Mutual Information Diagrams.
  • These diagrams are extended to display temporality, multimodality, multivariate datasets, and scalar model properties like uncertainty.
  • The library supports both continuous and categorical data attributes.

Conclusions:

  • The polar-diagrams library provides a user-friendly solution for rapidly assessing the performance of complex models.
  • It is applicable across various domains including machine learning, climate science, and biomedical research.