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Related Concept Videos

Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
Plane Potential Flows01:23

Plane Potential Flows

Plane potential flows simplify fluid motion by assuming the fluid to be irrotational and incompressible. These characteristics allow these flows to be described by a velocity potential function, ϕ, representing the flow speed in a given direction, and a stream function, ψ, that visualizes the flow path, both governed by Laplace's equation. These parameters help in estimating flow patterns, velocity distributions, and pressure fields around various hydraulic structures.
Uniform Flow
Uniform flow...
Systems of Linear Equations in Two Variables01:25

Systems of Linear Equations in Two Variables

Solving a system of linear equations is a fundamental concept in algebra. A system of equations consists of two or more linear equations involving the same set of variables. One of the most efficient algebraic methods for solving such systems is the substitution method. This technique involves expressing one variable in terms of the other from one equation and substituting it into the second equation. This method is particularly useful when one of the equations is easily rearranged.Consider the...
One-Degree-of-Freedom System01:24

One-Degree-of-Freedom System

In mechanical engineering, one-degree-of-freedom systems form the basis of a wide range of electrical and mechanical components. Using these models, engineers can predict the behavior of various parts in a larger system, which gives them insight into how different forces interact with each other.
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First Order Systems01:21

First Order Systems

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Related Experiment Video

Updated: May 28, 2026

A Simple Flight Mill for the Study of Tethered Flight in Insects
07:42

A Simple Flight Mill for the Study of Tethered Flight in Insects

Published on: December 10, 2015

Flights in a pseudo-chaotic system.

J H Lowenstein1, F Vivaldi

  • 1Department of Physics, New York University, 2 Washington Place, New York, New York 10003, USA.

Chaos (Woodbury, N.Y.)
|October 7, 2011
PubMed
Summary
This summary is machine-generated.

We discovered a new transport mechanism in a specific mathematical system, leading to long, linear movements. This process, driven by the destruction of

Related Experiment Videos

Last Updated: May 28, 2026

A Simple Flight Mill for the Study of Tethered Flight in Insects
07:42

A Simple Flight Mill for the Study of Tethered Flight in Insects

Published on: December 10, 2015

Area of Science:

  • Dynamical systems
  • Mathematical physics
  • Chaos theory

Background:

  • Studying transport phenomena in dynamical systems is crucial for understanding complex behaviors.
  • Piecewise rotations of the torus provide a model system for exploring transport properties.
  • Systems with rotation numbers near simple fractions often exhibit complex phase space structures.

Purpose of the Study:

  • To investigate transport in a one-parameter family of piecewise rotations of the torus.
  • To analyze the system's behavior as the rotation number approaches 1/4.
  • To identify novel mechanisms responsible for long-range transport in this zero-entropy system.

Main Methods:

  • Analysis of a one-parameter family of piecewise torus rotations.
  • Examination of phase space structure near rotation number 1/4.
  • Identification and characterization of accelerator-mode island destruction.
  • Statistical analysis of flight length distributions.

Main Results:

  • The system exhibits a divided phase space with island chains and a pseudo-chaotic region.
  • A novel transport mechanism, adiabatic destruction of accelerator-mode islands, is identified.
  • This mechanism leads to long flights of linear motion for a significant portion of initial conditions.
  • The probability distribution of flight lengths is linked to geometric properties of island partitions.
  • Flights of order O(1) in phase space are established, with evidence of scattering between opposite-direction flights.

Conclusions:

  • Adiabatic destruction of accelerator-mode islands is a key mechanism for long-range transport.
  • The geometric properties of phase space structures dictate transport dynamics.
  • The system demonstrates complex transport behaviors despite being zero-entropy.