Related Experiment Video
Updated: Aug 4, 2026
10:56
Confocal Imaging of Confined Quiescent and Flowing Colloid-polymer Mixtures
Published on: May 21, 2014
Stability of vacuum in coupled directed percolation processes
1School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea.
Summary
Spontaneous particle annihilation is key for stable absorbing phases in multi-species directed percolation (DP) models. Coupled branching annihilation random walks (BAW) can become unstable, unlike coupled contact processes.
Area of Science:
- Statistical Physics
- Complex Systems
- Phase Transitions
Background:
- Absorbing phase transitions are critical phenomena studied in various complex systems.
- Directed percolation (DP) serves as a fundamental model for these transitions.
- Understanding multi-species interactions is crucial for realistic system modeling.
Purpose of the Study:
- To investigate absorbing phase transitions in one-dimensional coupled directed percolation (DP) models with N-species particles.
- To analyze the role of interspecies coupling and annihilation processes on system stability.
- To characterize critical behavior and scaling exponents in different coupled systems.
Main Methods:
- Simulations of coupled directed percolation (DP) processes with N-species particles.
- Analysis of coupled contact processes and coupled branching annihilation random walks (BAW).
- Investigation of spontaneous annihilation (A-->0) and binary diffusion annihilation (A+A-->0) mechanisms.
- Inclusion of interspecies hard-core (HC) interactions in specific models.
Main Results:
- Spontaneous annihilation (A-->0) is essential for stabilizing the absorbing phase (vacuum).
- Coupled contact processes exhibit DP-type transitions for all N, irrespective of coupling strength.
- Coupled BAW models with N>=3 become unstable with increasing coupling due to branching.
- N=2 BAW shows DP transitions, but HC interactions destabilize the vacuum in strong coupling.
- Critical exponents near the zero branching point are mean-field (beta = nu(radial) = 1/2, nu(axial) = 1).
Conclusions:
- The stability of the absorbing phase in multi-species DP systems depends critically on the annihilation mechanism.
- Coupled BAW models present richer phase behavior than coupled contact processes, especially for N>=3.
- Hard-core interactions can significantly alter the phase diagram, leading to persistent activity.
Related Concept Videos
01:10First 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...
01:18First 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...
Newton's first law tells us about the...
01:19Cyclic Processes And Isolated Systems
A thermodynamic system with zero heat exchange and work is an isolated system. For these systems, the internal energy remains constant.
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each path...
In the case of a non-isolated system, the change in the internal energy is zero only if the process is cyclic. A thermodynamic process is considered cyclic if the system undergoes a series of changes and returns to its initial state.
Consider a cyclic process that returns to its initial state, undergoing a four-step process. The heat transfer along each path...
01:10Entropy Change in Reversible Processes
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
01:23Stability 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...
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...
01:13Stability 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...
Problem-solving in the context of the stability of equilibrium configuration...