Summary
The STIV framework is used to derive a phase field model for front propagation in elastic media, providing a statistical mechanics derivation and implementation of non-conservative phase field models.
Highlights
- The STIV framework is applied to a one-dimensional mass-spring-chain system with double-well interactions.
- A Gaussian approximation is used for the density of states, with internal variables corresponding to mean mass positions and standard deviations.
- The resulting kinetic equations for the internal variables are a gradient flow with respect to the non-equilibrium free energy.
- The STIV model is compared to Langevin simulations and shown to accurately capture stress-induced nucleation of transition fronts.
- Two numerical methods are introduced to evaluate the STIV model for any interaction potential.
- The STIV model is applied to study phase transformations in coiled-coil proteins under external loading.
Key Insights
- The STIV framework provides a statistical mechanics derivation of phase field models, eliminating the need for phenomenological justifications.
- The resulting phase field model has a non-local free energy functional that deviates from the traditional Landau-Ginzburg form.
- The STIV model accurately captures stress-induced nucleation of transition fronts without the need for additional physics.
- The numerical methods introduced allow for the evaluation of the STIV model for any interaction potential, enabling the study of complex systems.
- The STIV model provides a quantitative estimate of the external force and total entropy production, making it a valuable tool for studying non-equilibrium systems.
- The application of the STIV model to coiled-coil proteins demonstrates its ability to capture phase transformations in complex biological systems.
- The STIV framework has the potential to be applied to a wide range of systems, providing a new perspective on non-equilibrium thermodynamics.
Mindmap
Citation
Leadbetter, T., Purohit, P. K., & Reina, C. (2024). A statistical mechanics derivation and implementation of non-conservative phase field models for front propagation in elastic media (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.17972