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Updated: Jul 7, 2026

Orientational Transition in a Liquid Crystal Triggered by the Thermodynamic Growth of Interfacial Wetting Sheets
Published on: May 15, 2017
Type of dynamic phase transition in bistable equations
Gregory Berkolaiko1, Michael Grinfeld
1Department of Mathematics, Texas A&M University, College Station, TX 77843, USA. Gregory.Berkolaiko@math.tamu.edu
Researchers derived a simple criterion to find tricritical points (TCPs) in bistable differential equations. This localized criterion, especially in the adiabatic limit, simplifies identifying and locating TCPs in mathematical physics models.
Area of Science:
- Mathematical Physics
- Nonlinear Dynamics
- Dynamical Systems
Background:
- Bistable systems are crucial in various scientific fields.
- Periodically perturbed ordinary differential equations model complex phenomena.
- Tricritical points (TCPs) represent unique phase transitions.
Purpose of the Study:
- To derive an asymptotic criterion for the existence of tricritical points (TCPs).
- To investigate the nature of this criterion in the adiabatic limit.
- To provide a method for calculating TCP locations in parameter space.
Main Methods:
- Analysis of bistable, periodically perturbed ordinary differential equations.
- Derivation of an asymptotic criterion.
- Examination of the adiabatic limit of the equations.
Main Results:
- A simple, local asymptotic criterion for TCP existence was derived.
- The criterion is particularly straightforward in the adiabatic limit.
- The method allows for the calculation of TCP positions within the parameter space.
Conclusions:
- The study presents a significant simplification for identifying TCPs in relevant differential equations.
- The derived criterion offers practical applications in mathematical physics and related areas.
- The findings facilitate a deeper understanding of phase transitions in complex systems.
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