Theory of pinned fronts

Area of Science:

• Theoretical Physics
• Nonlinear Dynamics
• Mathematical Biology

Background:

• Phase transitions and front propagation are fundamental phenomena across sciences.
• External fields can significantly influence the dynamics of interfaces between phases.
• Distinguishing between different transition mechanisms (e.g., bistable vs. continuous) is critical for accurate modeling.

Purpose of the Study:

• To analyze the properties of fronts between two phases in smoothly inhomogeneous external fields.
• To investigate two generic scenarios: bistable invasion and continuous (transcritical bifurcation) transitions.
• To identify reliable indicators for discriminating between these two scenarios, particularly in response to external noise.

Main Methods:

• Analytical solutions for front shape and dynamics.
• Investigation of competitive fronts under external noise.
• Analysis of fluctuation statistics as a discriminating feature.

Main Results:

• Static properties and some dynamic features cannot differentiate between bistable and continuous transitions.
• Fluctuation statistics serve as a reliable indicator: Gaussian for bifurcation, double-peaked for bistable systems.
• External fields control invasion rates in bistable scenarios.

Conclusions:

• Fluctuation statistics provide a robust method to distinguish between different phase front dynamics.
• The findings have implications for understanding complex systems, including species and community dynamics with resource gradients.
• This work offers a framework for analyzing phase transitions in systems influenced by external fields and noise.