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Related Concept Videos

Collisions in Multiple Dimensions: Introduction01:05

Collisions in Multiple Dimensions: Introduction

It is far more common for collisions to occur in two dimensions; that is, the initial velocity vectors are neither parallel nor antiparallel to each other. Let's see what complications arise from this. The first idea is that momentum is a vector. Like all vectors, it can be expressed as a sum of perpendicular components (usually, though not always, an x-component and a y-component, and a z-component if necessary). Thus, when the statement of conservation of momentum is written for a problem,...
Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
Multiple Bar Graph01:07

Multiple Bar Graph

As the name suggests, a multiple bar graph is the same as a bar graph but has multiple bars to depict relationships between different data values. One can include as many parameters as possible. However, each parameter must have the same unit of measurement.
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Sequence Networks of Rotating Machines01:24

Sequence Networks of Rotating Machines

A Y-connected synchronous generator, grounded through a neutral impedance, is designed to produce balanced internal phase voltages with only positive-sequence components. The generator's sequence networks include a source voltage that is exclusively in the positive-sequence network. The sequence components of line-to-ground voltages at the generator terminals illustrate this configuration.
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Protein Networks02:26

Protein Networks

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Protein Networks02:26

Protein Networks

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Related Experiment Video

Updated: Jul 18, 2026

Modeling the Functional Network for Spatial Navigation in the Human Brain
05:55

Modeling the Functional Network for Spatial Navigation in the Human Brain

Published on: October 13, 2023

[Parallel structures in multidimensional networks].

V V Smolianinov

    Biofizika
    |December 21, 2006
    PubMed
    Summary

    This study reveals how space dimension limits multidimensional regular networks using a parallel representation method. An infinite dimensional network is equivalent to an infinite tree, with implications for network topology.

    Area of Science:

    • Graph theory
    • Network topology
    • Geometric analysis

    Context:

    • Investigating the constraints imposed by spatial dimensions on the structure of regular networks.
    • Utilizing the parallel representation method to analyze multidimensional network properties.

    Purpose:

    • To establish an analytical relationship between a regular network's dimension, vertex connectivity, and elementary contour perimeter.
    • To explore the equivalence between infinite dimensional networks and infinite trees.
    • To discuss the embedding of closed regular polytops within networks.

    Summary:

    • The parallel representation method is employed to determine the restrictions space dimension places on multidimensional regular networks.
    • An analytical relation is derived connecting network dimension, vertex connectivity, and the perimeter of elementary contours.

    Related Experiment Videos

    Last Updated: Jul 18, 2026

    Modeling the Functional Network for Spatial Navigation in the Human Brain
    05:55

    Modeling the Functional Network for Spatial Navigation in the Human Brain

    Published on: October 13, 2023

  • It is demonstrated that an infinite dimensional network is topologically equivalent to an infinite tree.

    • Impact:

    • Provides fundamental insights into the geometric and topological properties of regular networks.
    • Establishes a theoretical framework for understanding network limitations based on dimensionality.
    • Offers potential applications in areas such as network design, computer science, and materials science.