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Related Concept Videos

Toroids01:27

Toroids

A toroid is a closely wound donut-shaped coil constructed using a single conducting wire. In general, it is assumed that a toriod consists of multiple circular loops perpendicular to its axis.
When connected to a supply, the magnetic field generated in the toroid has field lines circular and concentric to its axis. Conventionally, the direction of this magnetic field is expressed using the right-hand rule. If the fingers of the right hand curl in the current direction, the thumb points in the...
Schwarzschild Radius and Event Horizon01:21

Schwarzschild Radius and Event Horizon

No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely high gravitational fields.
The minimum speed required to launch a projectile from the surface of an object to which it is gravitationally bound so that it eventually escapes the object’s gravitational field is called the escape velocity. The escape velocity is independent of the mass of the object. Merging the idea of escape velocity with the...
Gauss's Law: Planar Symmetry01:27

Gauss's Law: Planar Symmetry

A planar symmetry of charge density is obtained when charges are uniformly spread over a large flat surface. In planar symmetry, all points in a plane parallel to the plane of charge are identical with respect to the charges. Suppose the plane of the charge distribution is the xy-plane, and the electric field at a space point P with coordinates (x, y, z) is to be determined. Since the charge density is the same at all (x, y) - coordinates in the z = 0 plane, by symmetry, the electric field at P...
Gauss's Law: Cylindrical Symmetry01:20

Gauss's Law: Cylindrical Symmetry

A charge distribution has cylindrical symmetry if the charge density depends only upon the distance from the axis of the cylinder and does not vary along the axis or with the direction about the axis. In other words, if a system varies if it is rotated around the axis or shifted along the axis, it does not have cylindrical symmetry. In real systems, we do not have infinite cylinders; however, if the cylindrical object is considerably longer than the radius from it that we are interested in,...
Hyperbolas01:30

Hyperbolas

A hyperbola is a conic section produced when a double-napped cone is intersected by a plane at an angle steeper than the slope of the cone, such that it cuts through both nappes. This intersection yields two separate, mirror-image curves known as branches, which open away from each other along the transverse axis. The nearest points on each branch to the hyperbola’s center are termed vertices, and the distance from the center to a vertex is denoted by a. Perpendicular to the transverse axis is...
Gravitation Between Spherically Symmetric Masses01:14

Gravitation Between Spherically Symmetric Masses

The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, assuming that the center of mass is concentrated at the respective centers of the bodies.

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Related Experiment Video

Updated: May 13, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

Chimera states on a flat torus.

Mark J Panaggio1, Daniel M Abrams

  • 1Department of Engineering Sciences and Applied Mathematics, Northwestern University, Evanston, Illinois 60208, USA. markpanaggio2014@u.northwestern.edu

Physical Review Letters
|March 19, 2013
PubMed
Summary
This summary is machine-generated.

Chimera states, where ordered and disordered regions coexist, were theoretically predicted and experimentally observed. This study identifies conditions for 2D chimeras and a new asymmetric state, crucial for understanding their dynamics.

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Last Updated: May 13, 2026

Generation and Coherent Control of Pulsed Quantum Frequency Combs
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06:42

Magnetically Induced Rotating Rayleigh-Taylor Instability

Published on: March 3, 2017

Area of Science:

  • Complex Systems
  • Nonlinear Dynamics
  • Theoretical Physics

Background:

  • Chimera states are complex spatiotemporal patterns characterized by coexisting regions of coherent and incoherent behavior.
  • First observed in numerical simulations, these states have recently been experimentally realized, generating significant scientific interest.
  • Understanding the conditions for their existence and stability is crucial for advancing nonlinear dynamics and complex systems research.

Purpose of the Study:

  • To derive the theoretical conditions for the existence of two-dimensional (2D) 'spot' and 'stripe' chimera states in periodic systems.
  • To discover and characterize novel chimera states, specifically an asymmetric chimera state.
  • To determine the dynamic stability of various chimera states through numerical verification.

Main Methods:

  • Asymptotic methods were employed to analytically derive the conditions for 2D chimera state formation.
  • Numerical simulations were utilized to verify theoretical predictions and assess the stability of identified chimera states.
  • The study focused on analyzing chimera states within a periodic spatial framework.

Main Results:

  • The study successfully derived the conditions under which 2D 'spot' and 'stripe' chimera states can exist in periodic spaces.
  • A previously undiscovered asymmetric chimera state was identified, significantly impacting the observability of other chimera states.
  • Numerical methods confirmed theoretical predictions and identified dynamically stable chimera configurations.

Conclusions:

  • The theoretical framework established provides critical insights into the formation and existence of 2D chimera states.
  • The newly discovered asymmetric chimera state is essential for a comprehensive understanding of chimera dynamics in experiments and simulations.
  • This research advances the understanding of complex spatiotemporal patterns and their stability in nonlinear systems.