Related Experiment Video
Updated: Jan 19, 2026
02:31
Phase Transitions and Effect of Intermolecular Forces
22.6K
Phase transition to synchronization in generalized Kuramoto model with low-pass filter
Wei Zou1, Meng Zhan2, Jürgen Kurths3,4,5
1School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China.
Physical Review. E
|September 11, 2019
Summary
Researchers found that adding a low-pass filter to the Kuramoto model leads to generic first-order explosive synchronization. This discovery offers new insights into phase transitions in coupled networks.
Area of Science:
- Nonlinear Dynamics
- Complex Systems
- Network Science
Background:
- The classic Kuramoto model typically exhibits second-order continuous synchronization.
- Coupling in dynamical networks often occurs indirectly through common environments.
Purpose of the Study:
- To investigate the synchronization dynamics of a generalized Kuramoto model with a low-pass filter (LPF) in the coupling.
- To explore the emergence of different synchronization orders in networks with indirect coupling.
Main Methods:
- Theoretical analysis of the generalized Kuramoto model with LPF.
- Rigorous mathematical treatment to establish analytical results.
- Extensive numerical simulations to validate theoretical findings.
Main Results:
- A first-order explosive synchronization is identified as a generic phenomenon in the generalized Kuramoto model with LPF.
- The LPF introduces a novel mechanism for indirect coupling, influencing synchronization behavior.
- Synchronization transitions can exhibit abrupt, first-order characteristics.
Conclusions:
- The incorporation of a low-pass filter provides a new pathway for achieving first-order explosive synchronization.
- This study deepens the understanding of first-order phase transitions in coupled dynamical networks.
- The findings offer insights into synchronization mechanisms in systems with common external environments.
Related Concept Videos
02:31Phase Transitions
22.6K
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to...
22.6K
02:33Phase Transitions: Sublimation and Deposition
19.7K
Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and standard pressure, a piece of dry ice (solid CO2) sublimes, appearing to gradually disappear without ever forming any liquid. Snow and ice sublimate at temperatures below the melting point of water, a slow process that may be accelerated by winds and the reduced atmospheric pressures at high altitudes. When solid iodine is warmed, the solid sublimes...
19.7K
02:39Phase Transitions: Melting and Freezing
14.6K
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
14.6K
02:39Phase Transitions: Vaporization and Condensation
20.7K
The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules...
20.7K
01:21Three-Phase Short Circuit—Unloaded Synchronous Machine
678
Conducting a three-phase short circuit test on an unloaded synchronous machine helps understand its impact on the system. The AC fault current's oscillogram, with the DC offset removed, reveals that the waveform amplitude decreases from an initially high value to a steady-state level for one phase of the machine.
This behavior occurs due to the magnetic flux produced by the short-circuit armature currents. Initially, these currents follow high-reluctance paths but eventually shift to...
This behavior occurs due to the magnetic flux produced by the short-circuit armature currents. Initially, these currents follow high-reluctance paths but eventually shift to...
678
09:02AC Synchronous Machine Synchronization
22.2K
Source: Ali Bazzi, Department of Electrical Engineering, University of Connecticut, Storrs, CT.
Three-phase wound-rotor synchronous generators are the main source of electrical power worldwide. They require a prime mover and an exciter in order to generate power. The prime mover can be a turbine spun by fluid (gas or liquid), thus the sources of the fluid can be water running off a dam through a long nozzle, steam from water evaporated using burned coal, etc. Most power plants including coal,...
Three-phase wound-rotor synchronous generators are the main source of electrical power worldwide. They require a prime mover and an exciter in order to generate power. The prime mover can be a turbine spun by fluid (gas or liquid), thus the sources of the fluid can be water running off a dam through a long nozzle, steam from water evaporated using burned coal, etc. Most power plants including coal,...
22.2K