Transition pathways between defect patterns in confined nematic liquid crystals

Han, Yucen; Hu, Yucheng; Zhang, Pingwen; Zhang, Lei

doi:10.1016/j.jcp.2019.06.028

Cited by 35 publications

(35 citation statements)

References 37 publications

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“…In fact, we conjecture that there are only N stable states on a N -polygon with N sides for odd N , and only N/2 stable states for a N -polygon with N even, in the → 0 limit, and for large c. These stable states are featured by a pair of stable interior 1/2-nematic point defects in the polygon interior, aligned either parallel to a polygon edge (N odd) or along a polygon diagonal (N even). As N → ∞ and → 0, we recover the solution landscape on a circle with tangent boundary conditions for the Q-profiles: infinitely many stable states with an interior nematic defect pair along one of the circle diagonals [42] for c > 0 and these states cannot be obtained for c = 0. The M-profiles are less affected in the regime of c > 0 and small , they retain the interior central magnetic vortex with some distortion.…”

Section: Discussionmentioning

confidence: 99%

Tailored nematic and magnetization profiles on two-dimensional polygons

et al. 2021

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We study dilute suspensions of magnetic nanoparticles in a nematic host, on two-dimensional (2D) polygons. These systems are described by a nematic order parameter and a spontaneous magnetization, in the absence of any external fields. We study the stable states in terms of stable critical points of an appropriately defined free energy, with a nemato-magnetic coupling energy. We numerically study the interplay between the shape of the regular polygon, the size of the polygon and the strength of the nemato-magnetic coupling for the multistability of this prototype system. Our notable results include (i) the co-existence of stable states with domain walls and stable interior and boundary defects, (ii) the suppression of multistability for positive nemato-magnetic coupling, and (iii) the enhancement of multistability for negative nemato-magnetic coupling.

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Section: Discussionmentioning

confidence: 99%

Tailored nematic and magnetization profiles on two-dimensional polygons

et al. 2021

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“…The Zernike polynomials Z nlm are orthogonal in the three-dimensional unit sphere, which can simplify the computation in (4.5). Similarly, for the 2D disk and cylindrical domain (Hu et al 2016, Han et al 2019, the authors choose 2D Zernike polynomials Z nl as the basis functions.…”

Section: Energy-minimization-based Approachmentioning

confidence: 99%

“…To improve the accuracy of both the MEP and the transition state without using too many nodes, Han et al (2019) proposed a multiscale scheme of the string method by applying a global coarse string and a local fine string. The global coarse string is used to obtain the whole MEP by connecting two minima, and then the local fine string is utilized to compute the local MEP by choosing two nodes with the highest energies on the global coarse string as the two ends for the case of a single energy barrier.…”

Section: Transition Pathwaysmentioning

confidence: 99%

“…To accelerate the convergence and further improve the efficiency of the dimer-type methods, Zhang et al (2016a) developed an optimization-based shrinking dimer (OSD) method by establishing a minimax optimization for the saddle searching problem and finding the unstable direction in an optimization framework. All these methods can be applied to the LC models for identifying the transition states accurately (Han et al 2019).…”

Section: Saddle Pointsmentioning

confidence: 99%

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Modelling and computation of liquid crystals

Wang¹,

Zhang

2021

Acta Numerica

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Liquid crystals are a type of soft matter that is intermediate between crystalline solids and isotropic fluids. The study of liquid crystals has made tremendous progress over the past four decades, which is of great importance for fundamental scientific research and has widespread applications in industry. In this paper we review the mathematical models and their connections to liquid crystals, and survey the developments of numerical methods for finding rich configurations of liquid crystals.

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“…Because of the nature of its unstability, computing transition state on the potential energy surface has been a challenging problem. Meanwhile, many practical problems require the knowledge of transition states, such as calculating transition rates in chemical reactions [2], predicting critical nucleus and transition pathway in phase transformation [9,10,34,35,37], etc.…”

mentioning

confidence: 99%

Global optimization-based dimer method for finding saddle points

Yu¹,

Zhang²

2021

Discrete &Amp; Continuous Dynamical Systems - B

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Searching saddle points on the potential energy surface is a challenging problem in the rare event. When there exist multiple saddle points, sampling different initial guesses are needed in local search methods in order to find distinct saddle points. In this paper, we present a novel global optimization-based dimer method (GOD) to efficiently search saddle points by coupling ant colony optimization (ACO) algorithm with optimization-based shrinking dimer (OSD) method. In particular, we apply OSD method as a local search algorithm for saddle points and construct a pheromone function in ACO to update the global population. By applying a two-dimensional example and a benchmark problem of seven-atom island on the (111) surface of an FCC crystal, we demonstrate that GOD shows a significant improvement in computational efficiency compared with OSD method. Our algorithm is the first try to apply the global optimization technique in searching saddle points and it offers a new framework to open up possibilities of adopting other global optimization methods.

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Transition pathways between defect patterns in confined nematic liquid crystals

Cited by 35 publications

References 37 publications

Tailored nematic and magnetization profiles on two-dimensional polygons

Tailored nematic and magnetization profiles on two-dimensional polygons

Modelling and computation of liquid crystals

Global optimization-based dimer method for finding saddle points

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