A unified field theory of topological defects and non-linear local excitations

Skogvoll, Vidar; Rønning, Jonas; Salvalaglio, Marco; Angheluta, Luiza

doi:10.1038/s41524-023-01077-6

Cited by 9 publications

(4 citation statements)

References 63 publications

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“…The effective GE characteristic lengths at dislocations vary with the model parameters similarly to the phase correlation length. This closely resembles variations observed for the size of defect cores in smooth theories for ordered systems [85]. Importantly, the variation in the quenching depth can be interpreted as a dependence on temperature, which may constitute the input for other theories and establishes a direct link between GE and the PFC/SH framework for order-disorder phase transition.…”

Section: Discussionsupporting

confidence: 72%

“…Ultimately, we find a proportionality constant l/W ∼ ω/W ∈ (0.4, 0.6). In models like SH or PFC, the extension of the defect core scales similarly with the correlation length [85]. Therefore, the effective characteristic length-which we recall encodes microscopic effects into (continuum) elasticity-is found to scale de facto with the core size, consistently with continuum descriptions of the elastic field of dislocations in GE theories [22,23,25].…”

Section: Discussion Of the Resultssupporting

confidence: 59%

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Gradient elasticity in Swift–Hohenberg and phase-field crystal models

Benoit-Maréchal,

Salvalaglio

2024

Modelling Simul. Mater. Sci. Eng.

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The Swift-Hohenberg (SH) and Phase-Field Crystal (PFC) models are minimal yet powerful approaches for studying phenomena such as pattern formation, collective order, and defects via smooth order parameters. They are based on a free-energy functional that inherently includes elasticity effects. This study addresses how gradient elasticity (GE), a theory that accounts for elasticity effects at microscopic scales by introducing additional characteristic lengths, is incorporated into SH and PFC models. After presenting the fundamentals of these theories and models, we first calculate the characteristic lengths for various lattice symmetries in an approximated setting. We then discuss numerical simulations of stress fields at dislocations and comparisons with analytic solutions within first and second strain-gradient elasticity. Effective GE characteristic lengths for the elastic fields induced by dislocations are found to depend on the free-energy parameters in the same manner as the phase correlation length, thus unveiling how they change with the quenching depth. The findings presented in this study enable a thorough discussion and analysis of small-scale elasticity effects in pattern formation and crystalline systems using SH and PFC models and, importantly, complete the elasticity analysis therein. Additionally, we provide a microscopic foundation for GE in the context of order-disorder phase transitions.

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Section: Discussionsupporting

confidence: 72%

Section: Discussion Of the Resultssupporting

confidence: 59%

Gradient elasticity in Swift–Hohenberg and phase-field crystal models

Benoit-Maréchal,

Salvalaglio

2024

Modelling Simul. Mater. Sci. Eng.

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“…Further extensions of the formalism presented in this work can include taking into account the roles of backflow [71], fluctuations [73], or curved geometry [74]. Another interesting extension of the method we propose would be to study the motion of dislocations [54] by using a field theoretical treatment of elasticity [75], or more sophisticated descriptions [76,77]. While some of these developments may be technically challenging, they should not entail any additional conceptual difficulty.…”

Section: Discussionmentioning

confidence: 99%

Dynamical theory of topological defects II: universal aspects of defect motion

Romano,

Mahault,

Golestanian

2024

J. Stat. Mech.

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We study the dynamics of topological defects in continuum theories governed by a free energy minimization principle, building on our recently developed framework (Romano et al 2023 J. Stat. Mech. 083211). We show how the equation of motion of point defects, domain walls, disclination lines and any other singularity can be understood with one unifying mathematical framework. For disclination lines, this also allows us to study the interplay between the internal line tension and the interaction with other lines. This interplay is non-trivial, allowing defect loops to expand, instead of contracting, due to external interaction. We also use this framework to obtain an analytical description of two long-lasting problems in point defect motion, namely the scale dependence of the defect mobility and the role of elastic anisotropy in the motion of defects in liquid crystals. For the former, we show that the effective defect mobility is strongly problem-dependent, but it can be computed with high accuracy for a pair of annihilating defects. For the latter, we show that at the first order in perturbation theory, anisotropy causes a non-radial force, making the trajectory of annihilating defects deviate from a straight line. At higher orders, it also induces a correction in the mobility, which becomes non-isotropic for the + 1 / 2 defect. We argue that, due to its generality, our method can help to shed light on the motion of singularities in many different systems, including driven and active non-equilibrium theories.

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“…In particular, in the realm of many field theories, the study of topological defects -small structures like vortices in fluids -is essential for understanding phenomena such as phase transitions, turbulence and pattern formation. Due to the shared mathematical structures of these topological defects, recent research has shown that a common computational framework can be used to study them across different physical systems, ranging from Bose-Einstein condensates to nematic liquid crystals and crystalline solids (Skogvoll et al, 2023). However, a unified computational framework that brings all these systems together is lacking.…”

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confidence: 99%

ComFiT: a Python library for computational field theory with topological defects

Skogvoll,

Rønning

2024

JOSS

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A unified field theory of topological defects and non-linear local excitations

Cited by 9 publications

References 63 publications

Gradient elasticity in Swift–Hohenberg and phase-field crystal models

Gradient elasticity in Swift–Hohenberg and phase-field crystal models

Dynamical theory of topological defects II: universal aspects of defect motion

ComFiT: a Python library for computational field theory with topological defects

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