Extended stable equilibrium invaded by an unstable state

Area of Science:

• Nonlinear dynamics
• Pattern formation
• Soft condensed matter physics

Background:

• Coexistence of multiple states is fundamental to phenomena like domain walls and shock waves.
• Wave propagation typically assumes stable states invading unstable ones, as seen in combustion or disease spread.
• Understanding the dynamics of state invasion is crucial for various macroscopic systems.

Purpose of the Study:

• To investigate the phenomenon of an unstable state invading a locally stable state in pattern-forming systems.
• To identify the underlying mechanisms and necessary conditions for this counter-intuitive invasion.
• To experimentally validate the theoretical predictions using a specific physical system.

Main Methods:

• Development of a one-dimensional model to analyze the dynamics of state invasion.
• Theoretical analysis focusing on the role of energy differences between states.
• Experimental observation using a photo-isomerization of a dye-dopant nematic liquid crystal system.

Main Results:

• Demonstrated that unstable states can generically invade locally stable states in pattern-forming systems.
• Identified the lower energy of the unstable state as the driving force for invasion.
• Confirmed this phenomenon occurs in systems exhibiting first-order spatial instability.

Conclusions:

• The study reveals a novel mechanism where lower-energy unstable states can dominate higher-energy stable states.
• This finding challenges conventional understanding of wave propagation and stability in macroscopic systems.
• Experimental observation in liquid crystals provides concrete evidence for this unusual invasion phenomenon.