• 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
  • Physics, Mathematics
  • 2020
A quasi-entropy is constructed for tensors averaged by a density function on $SO(3)$ using the log-determinant of a covariance matrix. It serves as a substitution of the entropy for tensors derived
Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential
TLDR
The unique solvability and the positivity-preserving property for the second order scheme are proved using similar ideas, in which the singular nature of the logarithmic term plays an essential role.
A novel linear second order unconditionally energy stable scheme for a hydrodynamic Q-tensor model of liquid crystals
Abstract The hydrodynamic Q -tensor model has been used for studying flows of liquid crystals and liquid crystal polymers. It can be derived from a variational approach together with the generalized
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
TLDR
It is shown that the same limiter can preserve the maximum principle for DG or finite volume schemes solving two-dimensional incompressible Euler equations in the vorticity stream-function formulation, or any passive convection equation with an incompressibles velocity field.
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
TLDR
A new Lagrange multiplier approach to construct positivity preserving schemes for parabolic type equations and is not restricted to any particular spatial discretization and can be combined with various time discretized schemes.
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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