Deriving phase field crystal theory from dynamical density functional theory: consequences of the approximations

AJ Archer, DJ Ratliff, AM Rucklidge, P Subramanian - Physical Review E, 2019 - APS
Phase field crystal (PFC) theory is extensively used for modeling the phase behavior,
structure, thermodynamics, and other related properties of solids. PFC theory can be derived …

Reappraisal of Whitham's 1967 theory for wave–meanflow interaction in shallow water

TJ Bridges, DJ Ratliff - Wave Motion, 2022 - Elsevier
The modulation equations for Stokes waves in shallow water coupled to wave-generated
meanflow, derived in Whitham (1967), based on an averaged Lagrangian are re-visited …

A proof of validity for multiphase Whitham modulation theory

TJ Bridges, A Kostianko… - Proceedings of the …, 2020 - royalsocietypublishing.org
It is proved that approximations which are obtained as solutions of the multiphase Whitham
modulation equations stay close to solutions of the original equation on a natural time scale …

Krein signature and Whitham modulation theory: the sign of characteristics and the “sign characteristic”

TJ Bridges, DJ Ratliff - Studies in Applied Mathematics, 2019 - Wiley Online Library
In classical Whitham modulation theory, the transition of the dispersionless Whitham
equations from hyperbolic to elliptic is associated with a pair of nonzero purely imaginary …

Nonlinear theory for coalescing characteristics in multiphase Whitham modulation theory

TJ Bridges, DJ Ratliff - Journal of Nonlinear Science, 2021 - Springer
The multiphase Whitham modulation equations with N phases have 2 N characteristics
which may be of hyperbolic or elliptic type. In this paper, a nonlinear theory is developed for …

[KSIĄŻKA][B] Conservation laws, modulation and the emergence of universal forms

DJ Ratliff - 2014 - search.proquest.com
Phase modulation has been a tool used for many years to describe system behaviour about
periodic wavetrain solutions. The method has been shown to lead to well known partial …

The modulation of multiple phases leading to the modified Korteweg–de Vries equation

DJ Ratliff - Chaos: An Interdisciplinary Journal of Nonlinear …, 2018 - pubs.aip.org
This paper seeks to derive the modified Korteweg–de Vries (mKdV) equation using a novel
approach from systems generated from abstract Lagrangians possessing a two-parameter …