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Related Concept Videos

Equilibrium Conditions for a Particle01:23

Equilibrium Conditions for a Particle

When an object is in equilibrium, it is either at rest or moving with a constant velocity. There are two types of equilibrium: static and dynamic. Static equilibrium occurs when an object is at rest, while dynamic equilibrium occurs when an object is moving with a constant velocity. In both cases, there must be a balance of forces acting on the object.
To understand the concept of equilibrium, let us first consider the forces acting on an object. When different forces act on an object, they can...
Stability of Equilibrium Configuration01:23

Stability of Equilibrium Configuration

Understanding the stability of equilibrium configurations is a fundamental part of mechanical engineering. In any system, there are three distinct types of equilibrium: stable, neutral, and unstable.
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
Stability of Equilibrium Configuration: Problem Solving01:13

Stability of Equilibrium Configuration: Problem Solving

The stability of equilibrium configurations is an important concept in physics, engineering, and other related fields. In simple terms, it refers to the tendency of an object or system to return to its equilibrium position after being disturbed. The stability of an equilibrium configuration can be analyzed by considering the potential energy function of the system and examining its behavior near the equilibrium point.
Problem-solving in the context of the stability of equilibrium configuration...
First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...
Pole and System Stability01:24

Pole and System Stability

The transfer function is a fundamental concept representing the ratio of two polynomials. The numerator and denominator encapsulate the system's dynamics. The zeros and poles of this transfer function are critical in determining the system's behavior and stability.
Simple poles are unique roots of the denominator polynomial. Each simple pole corresponds to a distinct solution to the system's characteristic equation, typically resulting in exponential decay terms in the system's response.
First Law: Particles in One-dimensional Equilibrium01:10

First Law: Particles in One-dimensional Equilibrium

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...

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Related Experiment Video

Updated: Jul 4, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions

Published on: February 22, 2018

Instability in a network coevolving with a particle system.

Sang-Woo Kim1, Jae Dong Noh

  • 1Department of Physics, University of Seoul, Seoul 130-743, Korea.

Physical Review Letters
|June 4, 2008
PubMed
Summary
This summary is machine-generated.

Particle-driven network rewiring creates hubs and dynamic phase transitions. Below a critical density, networks become star-shaped; above it, they show fat-tailed distributions and scaling behavior.

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Area of Science:

  • Complex systems
  • Network science
  • Statistical physics

Background:

  • Understanding how dynamic processes influence network structure is crucial.
  • Particle systems interacting with networks can lead to emergent behaviors.

Purpose of the Study:

  • To investigate the coupled dynamics of particle diffusion and network rewiring.
  • To identify phase transitions and emergent network structures driven by particle flux.

Main Methods:

  • Simulating particle diffusion on a network where edges rewire based on particle flux.
  • Developing analytic and scaling theories to explain observed phenomena.

Main Results:

  • The coupled dynamics induce an instability leading to hub formation.
  • A dynamic phase transition occurs at a critical particle density (rho c).
  • Low density: star-shaped networks with linear degree growth. High density: fat-tailed degree distributions and dynamic scaling.

Conclusions:

  • Particle flux can drive significant network evolution and structural changes.
  • The study reveals a mechanism for hub formation and dynamic phase transitions in evolving networks.