• Corpus ID: 239049759

Q-tensor gradient flow with quasi-entropy and discretizations preserving physical constraints

@article{Wang2021QtensorGF,
  title={Q-tensor gradient flow with quasi-entropy and discretizations preserving physical constraints},
  author={Yanli Wang and Jie Xu},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.11053}
}
We propose and analyze numerical schemes for the gradient flow of Q-tensor with the quasientropy. The quasi-entropy is a strictly convex, rotationally invariant elementary function, giving a singular potential constraining the eigenvalues of Q within the physical range (−1/3, 2/3). Compared with the potential derived from the Bingham distribution, the quasi-entropy has the same asymptotic behavior and underlying physics. Meanwhile, it is very easy to evaluate because of its simple expression… 

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References

SHOWING 1-10 OF 53 REFERENCES
Quasi-entropy by log-determinant covariance matrix and application to liquid crystals
  • Jie Xu
  • Computer Science
    Physica D: Nonlinear Phenomena
  • 2022
Maximum bound principles for a class of semilinear parabolic equations and exponential time differencing schemes
TLDR
It is demonstrated that the abstract framework and analysis techniques developed here offer an effective and unified approach to study the maximum bound principle of the abstract evolution equation that cover a wide variety of well-known models and their numerical discretization schemes.
On maximum-principle-satisfying high order schemes for scalar conservation laws
Unconditionally positivity preserving and energy dissipative schemes for Poisson-Nernst-Planck equations
TLDR
It is proved that the schemes are mass conservative, uniquely solvable and keep positivity unconditionally, and the first-order scheme is proven to be unconditionally energy dissipative.
Nonoscillatory High Order Accurate Self-similar Maximum Principle Satisfying Shock Capturing Schemes I
This is the rst paper in a series in which we construct and analyze a class of nonoscillatory high order accurate self-similar local maximum principle satisfying ( in scalar conservation law ) shock
Nematic Liquid Crystals: From Maier-Saupe to a Continuum Theory
We define a continuum energy functional that effectively interpolates between the mean-field Maier-Saupe energy and the continuum Landau-de Gennes energy functional and can describe both spatially
A new Lagrange multiplier approach for constructing structure preserving schemes, I. Positivity preserving
  • Q. Cheng, Jie Shen
  • Mathematics, Computer Science
    Computer Methods in Applied Mechanics and Engineering
  • 2022
On a Molecular Based Q-Tensor Model for Liquid Crystals with Density Variations
TLDR
The new Q-tensor model is the pivot and an appropriate trade-off between the classical models in three scales, including generalized Landau-de Gennes models, generalized McMillan models, and the Chen-Lubensky model.
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