Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Stability of structures

Stability of structures

In mechanical engineering, the stability of systems under various forces is critical for designing durable and efficient structures. One fundamental way to explore these concepts is by analyzing systems like two rods connected at a pivot point, O, with a torsional spring of spring constant k at the pivot point. This system is similar in appearance to a scissor jack used to change tires on a car. In this case, the arms of the linkage (equivalent to the rods in this system) are entirely vertical,...

Induced Electric Dipoles

Induced Electric Dipoles

A permanent electric dipole orients itself along an external electric field. This rotation can be quantified by defining the potential energy because the external torque does work in rotating it. Then, the potential energy is minimum at the parallel configuration and maximum at the antiparallel configuration. While the former is a stable equilibrium, the latter is an unstable equilibrium.
Since the absolute value of potential energy holds no physical meaning, its zero value can be chosen as per...

Multimachine Stability

Multimachine Stability

Multimachine stability analysis is crucial for understanding the dynamics and stability of power systems with multiple synchronous machines. The objective is to solve the swing equations for a network of M machines connected to an N-bus power system.
In analyzing the system, the nodal equations represent the relationship between bus voltages, machine voltages, and machine currents. The nodal equation is given by:

Pole and System Stability

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.

Mechanisms of Heat Transfer II

Mechanisms of Heat Transfer II

In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the buoyancy of warm air and water, transfer hot air from the tropics toward the poles and cold air from the poles toward the tropics. The Earth’s rotation interacts with those flows, causing the observed eastward flow of air in the temperate zones. Convection dominates heat transfer by air, and the amount of available space for the airflow...

Steady, Laminar Flow Between Parallel Plates

Steady, Laminar Flow Between Parallel Plates

Understanding steady, laminar flow between parallel plates is essential for analyzing and designing flow in narrow rectangular channels, commonly found in various water conveyance and drainage systems. The Navier-Stokes equations govern fluid motion and are generally challenging to solve due to their nonlinearity. However, simplifications are possible in certain cases, like the steady laminar flow between parallel plates. For this scenario, we assume steady, incompressible, laminar flow.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Multi-ring necklace vortex solitons in Kerr nonlinear media with azimuthally modulated Bessel potentials.

Journal of the Optical Society of America. A, Optics, image science, and vision·2026

Same author

Parametrically driven pure-quartic solitons.

Optics letters·2026

Same author

Stable high-order solitons in spiral potentials.

Optics letters·2026

Same author

Toroidal confinement and beyond: Vorticity-defined morphologies of dipolar ^{164}Dy quantum droplets.

Physical review. E·2026

Same author

Flat-top solitons and anomalous interactions in media with even-order dispersions and competing nonlinearities.

Optics letters·2026

Same author

Gap solitons of the Wannier and Bloch types in spin-orbit-coupled Bose-Einstein condensates with a moiré lattice.

Physical review. E·2026

Search research articles

Related Experiment Video

Updated: May 25, 2026

High-resolution Thermal Micro-imaging Using Europium Chelate Luminescent Coatings

High-resolution Thermal Micro-imaging Using Europium Chelate Luminescent Coatings

Published on: April 16, 2017

Multistable dissipative structures pinned to dual hot spots.

Cheng Hou Tsang¹, Boris A Malomed, Kwok Wing Chow

¹Department of Mechanical Engineering, University of Hong Kong, Pokfulam Road, Hong Kong.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 7, 2012

Summary

This study explores localized patterns in nonlinear dissipative systems with two hot spots (HSs). It reveals that the sign of cubic nonlinearity dictates pattern stability, with self-defocusing leading to multistability and self-focusing favoring fundamental modes.

More Related Videos

Patterned Photostimulation with Digital Micromirror Devices to Investigate Dendritic Integration Across Branch Points

Patterned Photostimulation with Digital Micromirror Devices to Investigate Dendritic Integration Across Branch Points

Published on: March 2, 2011

Related Experiment Videos

Last Updated: May 25, 2026

High-resolution Thermal Micro-imaging Using Europium Chelate Luminescent Coatings

High-resolution Thermal Micro-imaging Using Europium Chelate Luminescent Coatings

Published on: April 16, 2017

Patterned Photostimulation with Digital Micromirror Devices to Investigate Dendritic Integration Across Branch Points

Patterned Photostimulation with Digital Micromirror Devices to Investigate Dendritic Integration Across Branch Points

Published on: March 2, 2011

Area of Science:

Nonlinear Dynamics
Optical Physics
Bose-Einstein Condensates

Background:

Localized patterns in nonlinear dissipative media are crucial for understanding phenomena in optics and condensed matter physics.
Previous work identified solutions for single hot spot (HS) systems.
This study extends the analysis to systems with two interacting HSs.

Purpose of the Study:

To investigate the formation and stability of one-dimensional localized patterns in a nonlinear dissipative medium with two HSs.
To analyze the role of cubic nonlinearity (self-focusing vs. self-defocusing) in pattern formation.
To explore multistability and the emergence of complex patterns.

Main Methods:

Analytical and numerical solutions were employed to find coexisting two- and multipeak modes.
Simulations of perturbed evolution were used to assess mode stability.
The influence of the sign of cubic nonlinearity and local potentials was examined.

Main Results:

In self-focusing media, only fundamental symmetric and antisymmetric modes with two peaks are stable; higher-order modes evolve into fundamental ones.
Self-defocusing nonlinearity leads to multistability, with up to eight coexisting stable patterns (symmetric and antisymmetric).
Systems with only cubic loss exhibit behavior analogous to self-focusing/defocusing depending on HS potential, with stable fundamental modes coexisting with breathers.

Conclusions:

The sign of cubic nonlinearity is a critical factor determining the stability and diversity of localized patterns in two-hot-spot systems.
The system exhibits rich phenomena, including multistability and the formation of complex, coexisting patterns.
These findings have implications for designing and controlling localized states in optical and quantum systems.