Long-Ranged Order and Flow Alignment in Sheared<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:math>‐atic Liquid Crystals

Giomi, Luca; Toner, John; Sarkar, Niladri

doi:10.1103/physrevlett.129.067801

Cited by 8 publications

(9 citation statements)

References 33 publications

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“…Two-dimensional p -atic liquid crystals are traditionally described in terms of the orientation field

, with

the local orientation of the p -fold mesogens. A more general approach, proposed in Giomi et al, 2022a ; Giomi et al, 2022b and especially suited for hydrodynamics, revolves instead around the rank- p tensor order parameter,

with

and

, constructed upon averaging the p th tensorial power of the local orientation

. That is

…”

Section: Resultsmentioning

confidence: 99%

“…The order parameter tensor

, the mass density

, and the momentum density

, with

the local velocity field, comprise the set of hydrodynamic variables describing the dynamics of a generic p -atic fluid, which in turn is governed by the following set of partial differential equations ( Giomi et al, 2022a ; Giomi et al, 2022b ):

…”

Section: Resultsmentioning

confidence: 99%

“…energy dissipating) stresses originating from the reversible and irreversible couplings between p -atic order and flow. The generic expression of

was derived in Giomi et al, 2022b and is reported in Methods.…”

Section: Resultsmentioning

confidence: 99%

“…In conclusion, we have introduced a continuum model of collectively migrating layers of epithelial cells, built upon a recent generalization of the hydrodynamic theory of p -atic liquid crystals ( Giomi et al, 2022a ; Giomi et al, 2022b ). This approach allows one to account for arbitrary discrete rotational symmetries, thereby going beyond existing hydrodynamic theories of epithelia ( Ranft et al, 2010 ; Popović et al, 2017 ; Pérez-González et al, 2019 ; Ishihara et al, 2017 ; Czajkowski et al, 2018 ; Hernandez and Marchetti, 2021 ; Grossman and Joanny, 2022 ), where the algebraic structure of the hydrodynamic variables renders impossible to account for liquid crystal order other than isotropic (i.e.…”

Section: Resultsmentioning

confidence: 99%

“…nematic order), while leaving the small-scale hexatic order unresolved. To overcome this limitation, here we exploit recent advances toward extending the classic hydrodynamic theory of hexatic liquid crystals ( Zippelius, 1980 ; Zippelius et al, 1980 ) to account for arbitrary p -fold rotational symmetry order ( Giomi et al, 2022a ; Giomi et al, 2022b ), with

and

being the most relevant cases (but possibly not the only) in the context of epithelial dynamics. We demonstrate that multiscale order is inherent to active liquid crystals with coupled order parameters, because of the indissoluble connection between shape and forces characterizing this class of non-equilibrium systems.…”

Section: Introductionmentioning

confidence: 99%

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Hydrodynamics and multiscale order in confluent epithelia

Armengol-Collado,

Carenza,

Giomi

2024

eLife

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We formulate a hydrodynamic theory of confluent epithelia: i.e. monolayers of epithelial cells adhering to each other without gaps. Taking advantage of recent progresses toward establishing a general hydrodynamic theory of p-atic liquid crystals, we demonstrate that collectively migrating epithelia feature both nematic (i.e. p = 2) and hexatic (i.e. p = 6) order, with the former being dominant at large and the latter at small length scales. Such a remarkable multiscale liquid crystal order leaves a distinct signature in the system's structure factor, which exhibits two different power law scaling regimes, reflecting both the hexagonal geometry of small cells clusters, as well as the uniaxial structure of the global cellular flow. We support these analytical predictions with two different cell-resolved models of epithelia - i.e. the self-propelled Voronoi model and the multiphase field model - and highlight how momentum dissipation and noise influence the range of fluctuations at small length scales, thereby affecting the degree of cooperativity between cells. Our construction provides a theoretical framework to conceptualize the recent observation of multiscale order in layers of Madin-Darby canine kidney cells and pave the way for further theoretical developments.

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“…Two-dimensional p -atic liquid crystals are traditionally described in terms of the orientation field

, with

with

and

, constructed upon averaging the p th tensorial power of the local orientation

. That is

…”

Section: Resultsmentioning

confidence: 99%

“…The order parameter tensor

, the mass density

, and the momentum density

, with

…”

Section: Resultsmentioning

confidence: 99%

“…energy dissipating) stresses originating from the reversible and irreversible couplings between p -atic order and flow. The generic expression of

was derived in Giomi et al, 2022b and is reported in Methods.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

and

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Hydrodynamics and multiscale order in confluent epithelia

Armengol-Collado,

Carenza,

Giomi

2024

eLife

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Epithelia are multiscale active liquid crystals

Armengol-Collado,

Carenza,

Eckert

et al. 2023

Nat. Phys.

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Enhancing (quasi-)long-range order in a two-dimensional driven crystal

Maire,

Plati

2024

The Journal of Chemical Physics

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It has been recently shown that 2D systems can exhibit crystalline phases with long-range translational order showcasing a striking violation of the Hohenberg–Mermin–Wagner (HMW) theorem, which is valid at equilibrium. This is made possible by athermal driving mechanisms that inject energy into the system without exciting long wavelength modes of the density field, thereby inducing hyperuniformity. However, as thermal fluctuations are superimposed on the non-equilibrium driving, long-range translational order is inevitably lost. Here, we discuss the possibility of exploiting non-equilibrium effects to suppress arbitrarily large density fluctuations even when a global thermal bath is coupled to the system. We introduce a model of a harmonic crystal driven both by a global thermal bath and by a momentum conserving noise, where the typical observables related to density fluctuations and long-range translational order can be analytically derived and put in relation. This model allows us to rationalize the violation of the HMW theorem observed in previous studies through the prediction of large-wavelength phonons, which thermalize at a vanishing effective temperature when the global bath is switched off. The conceptual framework introduced through this theory is then applied to numerical simulations of a hard-disk solid in contact with a thermal bath and driven out-of-equilibrium by active collisions. Our numerical analysis demonstrates how varying driving and dissipative parameters can lead to an arbitrary enhancement of the quasi-long-range order in the system regardless of the applied global noise amplitude. Finally, we outline a possible experimental procedure to apply our results to a realistic granular system.

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Long-Ranged Order and Flow Alignment in Shearedp‐atic Liquid Crystals

Cited by 8 publications

References 33 publications

Hydrodynamics and multiscale order in confluent epithelia

Hydrodynamics and multiscale order in confluent epithelia

Epithelia are multiscale active liquid crystals

Enhancing (quasi-)long-range order in a two-dimensional driven crystal

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