相关论文: Order Reconstruction for Nematics on Squares with …

While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less in known about critical points of the corresponding energy. Saddle…

The Landau theory of phase transitions has been productively applied to phase transitions that involve rotational symmetry breaking, such as the transition from an isotropic fluid to a nematic liquid crystal. It even can be applied to the…

In this paper, we propose a unified algorithmic framework for solving many known variants of \mds. Our algorithm is a simple iterative scheme with guaranteed convergence, and is \emph{modular}; by changing the internals of a single…

In this article, we study minimization of the Landau-de Gennes energy for liquid crystal elastomer.The total energy, is of the sum of the Lagrangian elastic stored energy function of the elastomer and the Eulerian Landau-de Gennes energy of…

We consider implementations of high-order finite difference Weighted Essentially Non-Oscillatory (WENO) schemes for the Euler equations in cylindrical and spherical coordinate systems with radial dependence only. The main concern of this…

We prove the existence and uniqueness of stationary spherically symmetric positive solutions for the Schr\"{o}dinger-Newton model in any space dimension $d$. Our result is based on an analysis of the corresponding system of second order…

We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based…

We propose an approach to a multiscale problem in the theory of thermotropic uniaxial nematics based on the method of statistical field theory. This approach enables us to relate the coefficients $A$, $B$, $C$, $L_1$ and $L_2$ of the…

A new adaptive weighted essentially non-oscillatory WENO-$\theta$ scheme in the context of finite difference is proposed. Depending on the smoothness of the large stencil used in the reconstruction of the numerical flux, a parameter…

High-order reconstruction schemes for the solution of hyperbolic conservation laws in orthogonal curvilinear coordinates are revised in the finite volume approach. The formulation employs a piecewise polynomial approximation to the…

A Landau-de Gennes model that integrates the nematic quadrupolar tensor order parameter and complex smectic-A order parameters is used to simulate the two-dimensional growth of an initially homogeneous smectic-A spherulite in an isotropic…

We study nematic configurations within three-dimensional (3D) cuboids, with planar degenerate boundary conditions on the cuboid faces, in the Landau-de Gennes framework. There are two geometry-dependent variables: the edge length of the…

In this paper, a simple and efficient third-order weighted essentially non-oscillatory (WENO) reconstruction is developed for three-dimensional flows, in which the idea of two-dimensional WENO-AO scheme on unstructured meshes…

We study planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, within the Oseen-Frank and Landau-de Gennes theories for nematic liquid crystals. We analyse the defect-free state in the Oseen-Frank…

We propose a family of gradient reconstruction schemes based on the solution of over-determined systems by orthogonal or oblique projections. In the case of orthogonal projections, we retrieve familiar weighted least-squares gradients, but…

We discuss the renormalon-based approach to power corrections in non-singlet deep inelastic scattering structure functions and compare it with the general operator product expansion. The renormalon technique and its variations relate the…

Boundary integral equations and Nystrom discretization provide a powerful tool for the solution of Laplace and Helmholtz boundary value problems. However, often a weakly-singular kernel arises, in which case specialized quadratures that…

This paper considers robust solutions to a class of nonlinear least squares problems using min-max optimization approach. We give an explicit formula for the value function of the inner maximization problem and show the existence of global…

We explore universal critical behavior in models with two competing order parameters, and an O(N)+O(M) symmetry for dimensions $d \leq 3$. In d=3, there is always exactly one stable Renormalization Group fixed point, corresponding to…

We study the $O(2)$ model with $\mathbb{Z}_4$-symmetric perturbations within the framework of nonperturbative renormalization group (RG) for spatial dimensionality $d=2$ and $d=3$. In a unified framework we resolve the relatively complex…