Hydrodynamics and correlation functions in ordered systems: Nematic liquid crystals

Forster, Dieter

doi:10.1016/0003-4916(74)90314-5

Cited by 76 publications

(38 citation statements)

References 36 publications

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Order By: Relevance

“…(3) in this frame. For long wavelength fluctuations of the order tensor and thus for low k values, the Fourier components of the order tensor are related to those of the director field [36],…”

Section: A Order Tensor Fluctuationsmentioning

confidence: 99%

Elastic properties of the nematic phase in hard ellipsoids of short aspect ratio

Heymans

Schilling

2017

Phys. Rev. E

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We present a Monte Carlo simulation study of suspensions of hard ellipsoids of revolution. Based on the spatial fluctuations of the orientational order, we have computed the Frank elastic constants for prolate and oblate ellipsoids and compared them to the affine transformation model. The affine transformation model predicts the right order of magnitude of the twist and bend constant but not of the splay constant. In addition, we report the observation of a stable nematic phase at an aspect ratio as low as 2.5.

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Section: A Order Tensor Fluctuationsmentioning

confidence: 99%

Elastic properties of the nematic phase in hard ellipsoids of short aspect ratio

Heymans

Schilling

2017

Phys. Rev. E

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“…For our largest simulations, r s /ξ 0.003, and so a widely-given argument would say that the strings should obey the Nambu-Goto equations of motion [20,21], as the local string curvature should also be of order ξ. In the Nambu-Goto description, conservation of energy is equivalent to conservation of rest-frame string length, with corrections which decrease exponentially with ξ/r s , due to perturbative classical radiation of massive gauge and Higgs modes [22].…”

Section: Introductionmentioning

confidence: 99%

Scaling from gauge and scalar radiation in Abelian-Higgs string networks

et al. 2017

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We investigate cosmic string networks in the Abelian Higgs model using data from a campaign of large-scale numerical simulations on lattices of up to 4096 3 grid points. We observe scaling or selfsimilarity of the networks over a wide range of scales, and estimate the asymptotic values of the mean string separation in horizon length unitsξ and of the mean square string velocityv 2 in the continuum and large time limits. The scaling occurs because the strings lose energy into classical radiation of the scalar and gauge fields of the Abelian Higgs model. We quantify the energy loss with a dimensionless radiative efficiency parameter, and show that it does not vary significantly with lattice spacing or string separation. This implies that the radiative energy loss underlying the scaling behaviour is not a lattice artefact, and justifies the extrapolation of measured network properties to large times for computations of cosmological perturbations. We also show that the core growth method, which increases the defect core width with time to extend the dynamic range of simulations, does not introduce significant systematic error. We compareξ andv 2 to values measured in simulations using the Nambu-Goto approximation, finding that the latter underestimate the mean string separation by about 25%, and overestimatev 2 by about 10%. The scaling of the string separation implies that string loops decay by the emission of massive radiation within a Hubble time in field theory simulations, in contrast to the Nambu-Goto scenario which neglects this energy loss mechanism. String loops surviving for only one Hubble time emit much less gravitational radiation than in the Nambu-Goto scenario, and are consequently subject to much weaker gravitational wave constraints on their tension.

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“…But these conditions do not guarantee divv = 0 for all times. To get this ν 5 = ν 4 + ν 1 , ν 1 + ν 2 = ν 3 , and even λ = 0 have been proposed [20], in which case eq. (21) reduces to ∆p = 0.…”

Section: Incompressible Uniaxial Nematicsmentioning

confidence: 99%

Incompressibility conditions in liquid crystals

Pleiner

Brand

2002

Continuum Mechanics and Thermodynamics

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We discuss the implications of the incompressibility approximation on the number of relevant transport parameters, like viscosities, flow alignment coefficients, and rotational viscosities in uniaxial and biaxial nematic liquid crystals. A comparison between the hydrodynamic and the Leslie-Ericksen approach is given. Agreement is found, if in the latter description a redefinition of the pressure is assumed. For systems with positional order, like smectic and columnar liquid crystals and crystals, we show that, generally, incompressibility does not imply that the displacement field is source-free.

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Hydrodynamics and correlation functions in ordered systems: Nematic liquid crystals

Cited by 76 publications

References 36 publications

Elastic properties of the nematic phase in hard ellipsoids of short aspect ratio

Elastic properties of the nematic phase in hard ellipsoids of short aspect ratio

Scaling from gauge and scalar radiation in Abelian-Higgs string networks

Incompressibility conditions in liquid crystals

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