117 research outputs found
Global Solution to the Three-Dimensional Incompressible Flow of Liquid Crystals
The equations for the three-dimensional incompressible flow of liquid
crystals are considered in a smooth bounded domain. The existence and
uniqueness of the global strong solution with small initial data are
established. It is also proved that when the strong solution exists, all the
global weak solutions constructed in [16] must be equal to the unique strong
solution
Landau-De Gennes theory of nematic liquid\ud crystals: the Oseen-Frank limit and beyond
We study global minimizers of a continuum Landau-De Gennes energy functional for nematic liquid crystals, in three-dimensional domains, subject to uniaxial boundary conditions. We analyze the physically relevant limit of small elastic constant and show that global minimizers converge strongly, in W 1,2 , to a global minimizer predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. Moreover, the convergence is uniform in the interior of the domain, away from the singularities of the limiting Oseen-Frank global minimizer. We obtain results on the rate of convergence of the eigenvalues and the regularity of the eigenvectors of the Landau-De Gennes global minimizer.\ud
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We also study the interplay between biaxiality and uniaxiality in Landau-De Gennes global energy minimizers and obtain estimates for various related quantities such as the biaxiality parameter and the size of admissible strongly biaxial regions
Blow up criterion for compressible nematic liquid crystal flows in dimension three
In this paper, we consider the short time strong solution to a simplified
hydrodynamic flow modeling the compressible, nematic liquid crystal materials
in dimension three. We establish a criterion for possible breakdown of such
solutions at finite time in terms of the temporal integral of both the maximum
norm of the deformation tensor of velocity gradient and the square of maximum
norm of gradient of liquid crystal director field.Comment: 22 page
Hydrodynamics of domain growth in nematic liquid crystals
We study the growth of aligned domains in nematic liquid crystals. Results
are obtained solving the Beris-Edwards equations of motion using the lattice
Boltzmann approach. Spatial anisotropy in the domain growth is shown to be a
consequence of the flow induced by the changing order parameter field
(backflow). The generalization of the results to the growth of a cylindrical
domain, which involves the dynamics of a defect ring, is discussed.Comment: 12 revtex-style pages, including 12 figures; small changes before
publicatio
Well-Posedness of Nematic Liquid Crystal Flow in
In this paper, we establish the local well-posedness for the Cauchy problem
of the simplified version of hydrodynamic flow of nematic liquid crystals
(\ref{LLF}) in for any initial data having small
-norm of . Here is the space of uniformly locally -integrable functions. For any
initial data with small , we show that there exists a unique, global solution
to (\ref{LLF}) which is smooth for and has monotone deceasing
-energy for .Comment: 29 page
Weak-strong uniqueness property for the full Navier-Stokes-Fourier system
The Navier-Stokes-Fourier system describing the motion of a compressible,
viscous, and heat conducting fluid is known to possess global-in-time weak
solutions for any initial data of finite energy. We show that a weak solution
coincides with the strong solution, emanating from the same initial data, as
long as the latter exists. In particular, strong solutions are unique within
the class of weak solutions
A comparison of Finite Elements for Nonlinear Beams: The absolute nodal coordinate and geometrically exact formulations
Two of the most popular finite element formulations for solving nonlinear beams are the absolute nodal coordinate and the geometrically exact approaches. Both can be applied to problems with very large deformations and strains, but they differ substantially at the continuous and the discrete levels. In addition, implementation and run-time computational costs also vary significantly. In the current work, we summarize the main features of the two formulations, highlighting their differences and similarities, and perform numerical benchmarks to assess their accuracy and robustness. The article concludes with recommendations for the choice of one formulation over the other
Liquid crystals and their defects
These lecture notes discuss classical models of liquid crystals, and the
different ways in which defects are described according to the different
models.Comment: CIME lecture course, Cetraro, 201
A Review of Fiber-Reinforced Injection Molding: Flow Kinematics and Particle Orientation
The existing flow and particle orientation models applicable to fiber- reinforced injection molding are reviewed. After a brief description of injection molding, previous studies on the flow kinematics and fiber reinforcement are presented. Basics of Hele-Shaw flows are described Including the commonly used viscosity models and foun tain flow effects. Some of the existing models for particle orientation are analyzed with particular emphasis on the amsotropic description of the material system. Concentration regions for short fiber suspensions are defined and relevant constitutive equations are dis cussed. A few example solutions are also given which describe the three-dimensional ori entation field for the filling of a sudden expansion cavity, depicting skin-core orientation structure.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline
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