1. |
Junichi Fukuda, Holger Stark, Makoto Yoneya, Hiroshi Yokoyama, Configuration of nematic liquid crystals around particles under external fields, *3rd International Symposium on Slow Dynamics in Complex Systems
Slow Dynamics in Complex Systems
3rd International Symposium on Slow Dynamics in Complex Systems*, 10.1063/1.1764096, 146-147, 2004.04, We present the results of our numerical attempts to simulate the configuration of a nematic liquid crystal around a spherical particle. We focus on the effect of an external field, such as a magnetic field or a flow field, on the director configuration and the topological defects accompanied by the particles. The use of adaptive mesh refinement together with a tensor order parameter for the description of the orientational order makes it feasible to tract the dynamics of a nematic liquid crystal without any special treatment of the topological defects.. |

2. |
H. Yoshida, M. Takahashi, T. Ohkawa, Junichi Fukuda, Hirotsugu Kikuchi, M. Ozaki, Three-dimensional crystal orientation of blue phase liquid crystals on surfaces, *Liquid Crystals XXII 2018
Liquid Crystals XXII*, 10.1117/12.2323159, 2018.01, Liquid crystalline cholesteric blue phases (BPs) are of high interest for tunable electro-optic applications owing to their fast response times and quasi-polarization-independent phase modulation capabilities. Various approaches have recently been proposed to control the crystal orientation of BPs on substrates, but their basic orientation properties on standard, unidirectionally orienting substrates had not been investigated in detail. Here, detailed studies have been made on the Kossel diagrams of BPs on unidirectionally orienting substrates to understand the three-dimensional crystal orientation of BPs. We find that BPs show strong thermal hysteresis and that the structure of the preceding phase determines the orientation of BPs. Specifically, the BP II-I transition is accompanied by a rotation of the crystal such that the crystal direction defined by certain low-value Miller indices transform into different directions, and within the allowed rotations, different azimuthal configurations are obtained in the same cell depending on the thermal process. Our findings demonstrate that, for the alignment control of BPs, the thermal process is as important as the properties of the alignment layer.. |

3. |
Junichi Fukuda, Andriy Nych, Uliana Ognysta, Žumer Slobodan, Igor Muševič, Liquid-crystalline half-Skyrmion lattice spotted by Kossel diagrams, *Scientific reports*, 10.1038/s41598-018-35514-0, 8, 1, 2018.12, Skyrmions are swirl-like topological entities that have been shown to emerge in various condensed matter systems. Their identification has been carried out in different ways including scattering techniques and real-space observations. Here we show that Kossel diagrams can identify the formation of a hexagonal lattice of half-Skyrmions in a thin film of a chiral liquid crystal, in which case Kossel lines appear as hexagonally arranged circular arcs. Our experimental observations on a hexagonal lattice of half-Skyrmions and other defect structures resembling that of a bulk cholesteric blue phase are perfectly accounted for by numerical calculations and a theoretical argument attributing strong reflections yielding Kossel lines to guided mode resonances in the thin liquid crystal film. Our study demonstrates that a liquid crystal is a model system allowing the investigation of topological entities by various optical means, and also that Kossel techniques are applicable to the investigation of thin systems with non-trivial photonic band structures including topologically protected optical surface states.. |

4. |
Shigeyuki Komura, Junichi Fukuda, Scattering function of the disordered phase of block copolymers under shear flow, *Physics Letters, Section A: General, Atomic and Solid State Physics*, 10.1016/0375-9601(95)00728-L, 208, 1-2, 108-112, 1995.11, The scattering function of the disordered phase of a block copolymer (BCP) melt under a steady shear flow is investigated by the cell dynamical system (CDS) approach. Agreement with previous theoretical calculations indicates the applicability of the CDS approach to the disordered phase as well as the ordered phase.. |

5. |
Akira Onuki, Junichi Fukuda, Electric Field Effects and Form Birefringence in Diblock Copolymers, *Macromolecules*, 10.1021/ma00130a011, 28, 26, 8788-8795, 1995.12, We investigate effects of the electric field on diblock copolymers by assuming an induced dipolar interaction among the composition fluctuations. First, we show that, when an electric field is applied perpendicularly to lamellae, undulations start to grow if their in-plane wavenumbers are smaller than an electric wavenumber q_{e} proportional to the field. Subsequently, the undulations grow into larger spatial structures, eventually leading to a final square-lattice pattern. Second, we calculate the Maxwell stress tensor due to the electric field to predict a finite shear modulus in a lamellar state oriented by the electric field. Third, we examine form birefringence in disordered and ordered phases. In particular, the lamellar and hexagonal phases are shown to become birefringent on spatial scales longer than the spacing of lamellae or cylinders, even if the constituent monomers are optically isotropic. This gives rise to enhancement of depolarized light scattering from lamellar microstructures, which has indeed been observed recently. Most predictions in this paper are applicable to many situations other than those in the electric field.. |

6. |
Shigeyuki Komura, Junichi Fukuda, Glenn C. Paquette, Interface dynamics in a block copolymer melt and the effect of noise, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.53.R5588, 53, 6, 1996.01, The role of fluctuations in the disorder-lamellar transition in a block copolymer melt is investigated using a cell dynamical system simulation by measuring the propagation velocity of the interface between ordered and disordered regions. Our results strongly suggest that near the transition temperature, in the absence of noise, the velocity increases with quench depth as [Formula Presented] [[Formula Presented] is the reduced temperature measured from the transition temperature [Formula Presented]], while in the presence of noise, the velocity increases as [Formula Presented]. These results lead us to conclude that the addition of noise causes the disorder-lamellar transition to change from second order to first order. This conclusion is consistent with the prediction of Brazovskii Sov. Phys. JETP 41 85 1975.. |

7. |
Junichi Fukuda, Effect of hydrodynamic flow on kinetics of nematic-isotropic transition in liquid crystals, *European Physical Journal B*, 10.1007/s100510050168, 1, 2, 173-177, 1998, We investigate kinetics of nematic-isotropic transition by solving the hydrodynamic equations for the nematic 3 × 3 tensor order parameter Q_{αβ} and the fluid velocity in two space dimension (x-y plane). Numerical results indicate that nematic directors tend to align parallel to the x-y plane when hydrodynamic flow is incorporated. Late stage growth exponents, φ_{c} for the correlation length and φ_{def} for the number of topological defects, are not significantly altered by hydrodynamic flow. However, in contrast to the case without flow, the relation φdef = -2φ_{c} holds well, which may indicate the validity of dynamical scaling for the case with hydrodynamic flow.. |

8. |
Junichi Fukuda, Phase separation kinetics of nematic polymers Coupling between compositional order and orientational order, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.58.R6939, 58, 6, R6939-R6942, 1998.01, We numerically investigate phase separation kinetics of liquid crystalline polymers in a nematic state using time-dependent Ginzburg-Landau equations for the compositional and the orientational order parameters [Formula Presented] and [Formula Presented] The kinetics is significantly influenced by (i) the presence of the off-diagonal kinetic coefficient [Formula Presented] (ii) the coupling between [Formula Presented] and [Formula Presented] in the free energy, and (iii) the dependence of the kinetic coefficients on the orientational order.. |

9. |
Junichi Fukuda, Phase separation kinetics of liquid crystalline polymers Effect of orientational order, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.59.3275, 59, 3, 3275-3288, 1999.01, Phase separation kinetics of main-chain liquid crystalline polymers (LCP’s) is investigated by numerically solving time-dependent Ginzburg-Landau equations for the compositional order parameter φ and the orientational order parameter [Formula Presented] The kinetic coefficients are evaluated by using the biased reptation model with a microscopic model of wormlike chains. In numerical simulations we find the formation of a percolated network structure rich in LCP’s that resembles that observed in experiments. In our kinetic equations the coupling between compositional order and orientational order appears in (i) the presence of the off-diagonal kinetic coefficient [Formula Presented] and (ii) the dependence of the kinetic coefficients on [Formula Presented] (LCP’s tend to diffuse parallel to the nematic orientation). We show by a linear analysis of the growing modes that the presence of [Formula Presented] suppresses the growth of the compositional order in the early stage. We also show that the tendency of LCP’s to diffuse parallel to the nematic orientation is responsible for the breakage of the network structure.. |

10. |
Junichi Fukuda, Free energy of semiflexible polymers and structure of interfaces, *European Physical Journal B*, 10.1007/s100510050650, 7, 4, 573-583, 1999.02, The free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter φ and the orientational order parameter of second-rank tensor S_{ij} on the basis of a microscopic model of wormlike chains with variable segment lengths. We use a density functional theory and a gradient expansion to evaluate the entropie part of the free energy, which is given in a power series of Q_{ij} = S_{ij}/φ. The interaction term of the free energy is derived with a random phase approximation. For the rigid rod limit, the nematic-isotropic transition point is given by Nwφ = 4.05141, N and w being the degree of polymerization and the anisotropic interaction parameter, respectively, and the degree of ordering at the transition point is 0.33448. We also find that the contour length of polymer chains becomes larger in a nematic phase than in an isotropic phase. Interface profiles are obtained numerically for some typical cases. In the neighborhood of isotropic-isotropic interfaces, polymer chains tend to align parallel to the interface on the polymer-rich side and perpendicular on the poor side. When an isotropic region and a nematic region coexist, orientational order parallel to the interface is preferred in the nematic region.. |

11. |
Junichi Fukuda, Phase separation kinetics of main-chain liquid crystalline polymers, *Molecular Crystals and Liquid Crystals*, 10.1080/10587250108024033, 366, 901-908, 2001.01, We investigate phase separation kinetics of main-chain liquid crystalline polymers (LCP's) by numerical calculations based on a continuum description. We introduce two order parameters, the density and the orientational order of LCP's and construct a set of time-dependent Ginzburg-Landau equations to describe the dynamics of these two order parameters. We show that the morphology of the phase-separated system is crucially influenced by the coupling between the density and the orientational order which appears in the kinetics as well as in the free energy.. |

12. |
Junichi Fukuda, Hiroshi Yokoyama, Frank elasticity revisited Contribution of rotational entropy, *Molecular Crystals and Liquid Crystals*, 10.1080/10587250108023957, 366, 151-156, 2001.01, In previous molecular theories of nematic liquid crystals, rotational entropy, or the entropy loss due to molecular alignment, has been believed to make no contribution to Frank elasticity. We show that this is not true, using a field-theoretical method developed in polymer physics. We also give an exact expression of the contribution of rotational entropy to Frank elasticity for rod-like liquid crystals in terms of the orientational tensor order parameter.. |

13. |
Junichi Fukuda, H. Yokoyama, Director configuration and dynamics of a nematic liquid crystal around a two-dimensional spherical particle Numerical analysis using adaptive grids, *European Physical Journal E*, 10.1007/s101890170121, 4, 3, 389-396, 2001.03, We study numerically the director and orientational order parameter configurations in a nematic liquid crystal around a two-dimensional spherical particle on the basis of the tensor order parameter formalism. To properly account for the large length scale difference between the particle and the accompanying orientational defect, we devise an adaptive grid scheme in which the lattice spacing is automatically and locally adjusted in response to the spatial gradient of the orientational order parameter. This adaptive grid scheme is useful in studying dynamical as well as static orientational structures. We present a simulation result which shows how a hedgehog defect of topological charge -1 becomes unstable in two dimensions, and splits into a defect pair of topological charge -1/2, located symmetrically around the particle.. |

14. |
Junichi Fukuda, Hiroshi Yokoyama, Calculation of the free energy of polymeric systems in terms of compositional and orientational order parameters, *Journal of Chemical Physics*, 10.1063/1.1395561, 115, 10, 4930-4937, 2001.09, The density functional formalism by Tang and Freed was extended to the calculation of the free energy of polymeric systems in terms of the compositional and the orientational order parameters φ and Q_{ij}. As a demonstration, the formalism was applied to the case of flexible Gaussian chains and the "exact" expression for the free energy up to the second order in the gradients were obtained.. |

15. |
Junichi Fukuda, Bohdan I. Lev, Hiroshi Yokoyama, Interaction of foreign macroparticles in a cholesteric liquid crystal, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.65.031710, 65, 3, 2002.01, We calculate the interaction energy between spherical macroparticles immersed in a cholesteric liquid crystal due to the elastic deformation of the director field. We assume weak anchoring on the surface of the macroparticles and obtain the expression of the interaction energy that is valid for particle radius and interparticle distance sufficiently smaller than the cholesteric pitch. The resultant form of the interaction energy is more complex than that in a nematic liquid crystal. One of the characteristics is its dependence on the particle position as well as the interparticle distance, which arises from the intrinsic structure of a cholesteric liquid crystal, i.e., the absence of translational symmetry due to helical periodicity and local nematic ordering whose orientation depends on the position.. |

16. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Defect structure of a nematic liquid crystal around a spherical particle Adaptive mesh refinement approach, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.65.041709, 65, 4, 2002.01, We investigate numerically the structure of topological defects close to a spherical particle immersed in a uniformly aligned nematic liquid crystal. To this end we have implemented an adaptive mesh refinement scheme in an axi-symmetric three-dimensional system, which makes it feasible to take into account properly the large length scale difference between the particle and the topological defects. The adaptive mesh refinement scheme proves to be quite efficient and useful in the investigation of not only the macroscopic properties such as the defect position but also the fine structure of defects. It can be shown that a hyperbolic hedgehog that accompanies a particle with strong homeotropic anchoring takes the structure of a ring.. |

17. |
Junichi Fukuda, Hiroshi Yokoyama, Free Energy of Rigid Rods Contribution of Rotational Entropy to Frank Elasticity, *Journal of the Physical Society of Japan*, 10.1143/JPSJ.71.1463, 71, 6, 1463-1470, 2002.06, We apply the density functional formalism developed by the present authors [J. Fukuda and H. Yokoyama: J. Chem. Phys. 115 (2001) 4930] for the calculation of the free energy of rigid rods as a functional of the compositional scalar order parameter φ and the orientational order parameter of second-rank tensor Q_{ij} We model rigid rods as semiflexible wormlike chains with infinite bending elasticity and the exact expression for the entropic part of the free energy up to the second order in the gradients can be obtained. Discussion is devoted to the contribution of rotational entropy to Frank elasticity. Although none of the previous molecular theories for the Frank elasticity of liquid crystals has taken rotational entropy into account, our results indicate that rotational entropy can give a non-negligible contribution to Frank elasticity.. |

18. |
Junichi Fukuda, Hiroshi Yokoyama, Stability of a hyperbolic disclination ring in a nematic liquid crystal, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.66.012703, 66, 1, 2002.07, The stability of a hyperbolic disclination ring in a nematic liquid crystal is considered by extending the argument for a radial disclination ring due to Mori and Nakanishi. The ring configuration is indeed stable in the presence of the saddle-splay elasticity (characterized by [formula presented] The ring radius is estimated to be [formula presented] with [formula presented] being the core radius when [formula presented] where K is the Frank elastic constant in the one-constant approximation.. |

19. |
Junichi Fukuda, Bohdan I. Lev, Keiko M. Aoki, Hiroshi Yokoyama, Interaction of particles in a deformed nematic liquid crystal, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.66.051711, 66, 5, 2002.11, We investigate how the interaction of particles mediated by an elastic deformation of a nematic liquid crystal is influenced by the initial deformation of the director field. To this end, we calculate the interaction energy between particles in a nematic cell with hybrid boundary conditions, homeotropic on the surface of one confining plate and planar on the other. We find an analytic form of the interaction energy in the case of weak anchoring on the surface of the particle. This interaction energy sensitively depends on the position of the two particles as well as the interparticle distance and can be nonmonotonic with a minimum in its landscape. This nontrivial energy landscape might lead to a chainlike superstructure of particles.. |

20. |
Junichi Fukuda, Bohdan I. Lev, Hiroshi Yokoyama, Effect of confining walls on the interaction between particles in a nematic liquid crystal, *Journal of Physics Condensed Matter*, 10.1088/0953-8984/15/23/301, 15, 23, 3841-3854, 2003.06, We investigate theoretically how the confining walls of a nematic cell affect the interaction of particles mediated by the elastic deformation of a nematic liquid crystal. We consider the case where strong homeotropic or planar anchoring is imposed on the flat parallel walls so that the director on the wall surfaces is fixed and uniform alignment is achieved in the bulk. This set-up is more realistic experimentally than any other previous theoretical studies concerning the elastic-deformation-mediated interactions that assume an infinite medium. When the anchoring on the particle surfaces is weak, an exact expression of the interaction between two particles can be obtained. The two-body interaction can be regarded as the interaction between one particle and an infinite array of 'mirror images' of the other particle. We also obtain the 'self-energy' of one particle, the interaction of a particle with confining walls, which is interpreted along the same way as the interaction of one particle with its mirror images. We show that the walls play a different role in homeotropic and planar cells, which is attributed to the difference in the symmetry of the cells. We also present the landscapes of the interaction energy when one particle is fixed and demonstrate that the interaction is sensitively dependent on the fixed particle as well as the interparticle distance.. |

21. |
Makoto Yada, Junichi Fukuda, Jun Yamamoto, Hiroshi Yokoyama, Hexagonal defect array formed under steady shear flow in water-in-cholesteric liquid crystal emulsions, *Rheologica Acta*, 10.1007/s00397-003-0314-y, 42, 6, 578-584, 2003.11, The relation between the liquid crystalline textures and the steady shear viscosity has been investigated in cholesteric emulsions, composed of water, surfactants, and cholesteric liquid crystals. Both at the substrate surface and at the surfactant-coated droplet surface, a homeotropic anchoring is enforced to the adjacent liquid crystal. Under a steady shear flow with the shear rate below 100 s^{-1}, we observed that point defects spontaneously appear, and tend to adopt a regular hexagonal arrangement in the low shear-rate range of 1-20 s^{-1}. In viscosity measurements, the shear-thinning behavior was found, showing a clear correspondence to the texture change. We estimated the height of point defects in the hexagonal array from the viscosity increase in the shear-thinning, assuming that the shear-thinning behavior is caused by the reduction of the effective gap between cone and plate, owing to the presence of the hexagonal array anchored on the plate. The relation between the estimated height and the measured lateral size of point defects agreed with that of the quadrilateral array, which is formed after termination of the shear. This agreement informs that the shape of a point defect is preserved in both defect arrays, independently of shearing conditions.. |

22. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Nematic liquid crystal around a spherical particle Investigation of the defect structure and its stability using adaptive mesh refinement, *European Physical Journal E*, 10.1140/epje/e2004-00043-2, 13, 1, 87-98, 2004.01, We investigate the orientation profile and the structure of topological defects of a nematic liquid crystal around a spherical particle using an adaptive mesh refinement scheme developed by us previously. The previous work [J. Fukuda et al., Phys. Rev. E 65, 041709 (2002)] was devoted to the investigation of the fine structure of a hyperbolic hedgehog defect that the particle accompanies and in this paper we present the equilibrium profile of the Saturn ring configuration. The radius of the Saturn ring r _{d} in units of the particle radius R _{0} increases weakly with the increase of ξ , the ratio of the nematic coherence length to R _{0}. Next we discuss the energetic stability of a hedgehog and a Saturn ring. The use of adaptive mesh refinement scheme together with a tensor orientational order parameter Q_{αβ} allows us to calculate the elastic energy of a nematic liquid crystal without any assumption of the structure and the energy of the defect core as in the previous similar studies. The reduced free energy of a nematic liquid crystal, F̄ = F/L_{1} R_{0} , with L _{1} being the elastic constant, is almost independent of ξ in the hedgehog configuration, while it shows a logarithmic dependence in the Saturn ring configuration. This result clearly indicates that the energetic stability of a hedgehog to a Saturn ring for a large particle is definitely attributed to the large defect energy of the Saturn ring with a large radius.. |

23. |
Junichi Fukuda, Holger Stark, Makoto Yoneya, Hiroshi Yokoyama, Interaction between two spherical particles in a nematic liquid crystal, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.69.041706, 69, 4, 2004.01, We numerically investigate the interaction between two spherical particles in a nematic liquid crystal mediated by elastic distortions in the orientational order. We pay attention to the cases where two particles with equal radii [Formula presented] impose rigid normal anchoring on their surfaces and carry a pointlike topological defect referred to as a hyperbolic hedgehog. To describe the geometry of our system, we use bispherical coordinates, which prove useful in the implementation of boundary conditions at the particle surfaces and at infinity. We adopt the Landau–de Gennes continuum theory in terms of a second-rank tensor order parameter [Formula presented] for the description of the orientational order of a nematic liquid crystal. We also utilize an adaptive mesh refinement scheme that has proven to be an efficient way of dealing with topological defects whose core size is much smaller than the particle size. When the two “dipoles” composed of a particle and a hyperbolic hedgehog, are in parallel directions, the two-particle interaction potential is attractive for large interparticle distances [Formula presented] and proportional to [Formula presented] as expected from the form of the dipole-dipole interaction, until the well-defined potential minimum at [Formula presented] is reached. For the antiparallel configuration with no hedgehogs between the two particles, the interaction potential is repulsive and behaves as [Formula presented] for [Formula presented], which is stronger than the dipole-dipole repulsion [Formula presented] expected theoretically as an asymptotic behavior for large [Formula presented].. |

24. |
Junichi Fukuda, Holger Stark, Hiroshi Yokoyama, Wetting of a spherical particle by a nematic liquid crystal, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.69.021714, 69, 2 1, 2004.02, The phenomena of wetting of a spherical particle by a nematic liquid crystal was studied. The investigation is based on Landau-de Gennes free energy formulated in terms of second-rank nematic order parameter. It was observed that the prewetting line ends at a critical point. It was found that the splay deformations around the particle significantly influence nematic wetting of curved surfaces.. |

25. |
Junichi Fukuda, Holger Stark, Makoto Yoneya, Hiroshi Yokoyama, Interaction between two spherical particles in a nematic liquid crystal, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 69, 4 1, 2004.04, The interaction between two spherical particles in a nematic liquid crystal was investigated. The Landau-de Gennes continuum theory was adopted in terms of a second-rank tensor order parameter for the description of the orientational order of a nematic liquid crystal. An adaptive mesh refinement method was used that proves to be an efficient way of dealing with topological defects, whose core size is much smaller than the particle size. It is observed that when the dipoles composed of a particle and a hyperbolic hedgehog defect align in parallel directions, the interaction potential is attractive for large particle separations.. |

26. |
Holger Stark, Junichi Fukuda, Hiroshi Yokoyama, Nematic wetting layers in liquid crystal colloids, *Journal of Physics Condensed Matter*, 10.1088/0953-8984/16/19/004, 16, 19, 2004.05, We first review the method of treating nematic wetting of planar surfaces following the approach introduced by Sheng. We present a phase diagram, which in the present form we have not found in the original literature. Then we consider spherical geometries of arbitrary radii, such as colloidal particles, and introduce an appropriate method for handling wetting in curved geometries. We find that a prewetting transition for high curvatures or small particle radii no longer occurs.. |

27. |
Junichi Fukuda, Holger Stark, Makoto Yoneya, Hiroshi Yokoyama, Dynamics of a nematic liquid crystal around a spherical particle, *Journal of Physics Condensed Matter*, 10.1088/0953-8984/16/19/008, 16, 19, 2004.05, We present the results of our numerical calculations that focus on the dynamics of a nematic liquid crystal around a spherical particle imposing strong homeotropic anchoring at the surface. The first part of this article is devoted to the discussion of the effect of an external magnetic or electric field on the director configuration of a nematic liquid crystal. With the aid of an adaptive mesh refinement scheme, together with the tensor description of the orientational order, for the first time in numerical calculations we successfully reproduce the transition from a hyperbolic hedgehog defect to a Saturn ring defect, which was observed in a recent experiment. We also find that the trajectories of the defect core sensitively depend on the field strength. In the second part we investigate how a hydrodynamic flow influences the orientational order of a nematic liquid crystal around a particle carrying a hyperbolic hedgehog defect. We observe that for an intermediate Ericksen number, which characterizes the ratio of the viscous force to the elastic force of a nematic liquid crystal, the liquid crystal is strongly convected by the flow, which results in a considerable elastic distortion.. |

28. |
Holger Stark, Junichi Fukuda, Hiroshi Yokoyama, Capillary condensation in liquid-crystal colloids, *Physical Review Letters*, 10.1103/PhysRevLett.92.205502, 92, 20, 2004.05, The capillary condensation between two spherical particles dispersed in the isotropic phase of a nematic liquid crystal was investigated. The interaction energies due to the formation of capillary bridges that reproduce experimental observations were calculated within the Landau-de Gennes theory. The fluctuations in the particle cluster were described by an effective two-state system, close to the critical point of the transition line separating the no-bridge from the bridge configuration. It was found that for the small particles, the transition line vanishes and the shape of interaction potential depends on particle size.. |

29. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Holger Stark, Numerical investigation of liquid crystal colloids using a continuum description, *Colloids and Surfaces B: Biointerfaces*, 10.1016/j.colsurfb.2004.02.019, 38, 3-4 SPEC. ISS., 143-147, 2004.11, We investigate numerically the configuration of a nematic liquid crystal around two spherical particles. For the description of the orientational order of a nematic liquid crystal, we adopt a Landau-de Gennes continuum theory in terms of a second-rank tensor order parameter Qij together with the use of bispherical coordinates to describe the geometry of the system with two spherical particles. Above but close to the nematic-isotropic transition point, we observe capillary condensation of a nematic liquid crystal between the two particles under appropriate conditions. Below the transition point where liquid crystals possess nematic order, a point-like defect called a hyperbolic hedgehog appears close to a particle when strong normal anchoring is imposed. With the aid of an adaptive mesh refinement scheme to achieve sufficient numerical resolution to describe topological defects, we present our numerical results showing how the orientation profile of a nematic liquid crystal is distorted when the distance between two particles is small enough.. |

30. |
Junichi Fukuda, Keiko M. Aoki, Bohdan I. Lev, Hiroshi Yokoyama, Interaction between spherical particles in a deformed liquid crystal, *Molecular Crystals and Liquid Crystals*, 10.1080/15421400490437132, 413, 2004.12, We study how the initial deformation of a nematic liquid crystal affects the interaction between particles mediated by the elastic deformation of a nematic liquid crystal. We calculate the interaction energy between particles in a hybrid nematic cell, homeotropic on the surface of one confining plate and tangential (director can rotate freely) on the other. We find an analytic form of the interaction energy in the case of weak anchoring on the surface of the particle. This interaction energy can be non-monotonic and have a minimum in its landscape, which makes a clear contrast to that in a uniform nematic liquid crystal.. |

31. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Director configuration of a nematic liquid crystal around a spherical particle Numerical analysis using adaptive mesh refinement, *Molecular Crystals and Liquid Crystals*, 10.1080/15421400490437141, 413, 2004.12, We investigate numerically the orientational configuration of a nematic liquid crystal around a spherical particle. The use of adaptive mesh refinement scheme proves quite useful to overcome the numerical difficulty arising from large scale difference between a particle and a topological defect. Our scheme reproduces successfully the hedgehog and the Saturn ring configurations that have been observed experimentally. To demonstrate that dynamical behaviors can also be investigated using our scheme, we present a simulation result which exhibits a transition from a hedgehog to a Saturn ring under the application of an external field.. |

32. |
Junichi Fukuda, Hiroshi Yokoyama, Separation-independent attractive force between like particles mediated by nematic-liquid-crystal distortions, *Physical Review Letters*, 10.1103/PhysRevLett.94.148301, 94, 14, 2005.04, We investigate numerically with the aid of the Landau-de Gennes continuum theory the interaction between two spherical particles carrying the same topological charges +1 mediated by the elastic distortion of a nematic liquid crystal. We consider the case where an escaped nontopological ring disclination is situated between the particles; the director is continuous everywhere and no counterdefects are present. We find that the interaction is attractive and its potential energy depends linearly on the interparticle distance D. This behavior yields the D-independent interaction force, which was observed experimentally by Poulin, Cabuil, and Weitz [Phys. Rev. Lett. 79, 4862 (1997)] in the presence of narrow strings of birefringent regions ("bubble-gum" configuration) between the particles.. |

33. |
Junichi Fukuda, Holger Stark, Hiroshi Yokoyama, Friction drag of a spherical particle in a liquid crystal above the isotropic-nematic transition, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.72.021701, 72, 2, 2005.08, We study the friction drag of a spherical particle in the isotropic phase of a nematic liquid crystal close to the isotropic-nematic transition point. To describe the orientational order in the liquid crystal, the second-rank tensor order parameter Qαβ is employed. We solve the hydrodynamic equations for Qαβ and the fluid velocity υ in order to determine the friction drag. In our discussion of the friction drag, we concentrate on four parameters: the temperature, the surface order parameter, the particle radius, and the Ericksen number Er (characterizing the ratio of the viscous force to the elastic force). The temperature dependence of the friction drag agrees well with experiments that show an increasing friction drag when the isotropic-nematic phase transition is approached from above. Furthermore the friction drag increases with the surface order parameter due to the more pronounced surface nematic layer, and for larger particles it is less affected by this layer. Finally, we observe that in the range of Er we study, the friction drag is almost independent of Er although flow-induced order occurs for sufficiently large Er and surface order parameter.. |

34. |
Junichi Fukuda, Hiroshi Yokoyama, Makoto Yoneya, Holger Stark, Interaction between particles in a nematic liquid crystal Numerical study using the Landau-de Gennes continuum theory, *Molecular Crystals and Liquid Crystals*, 10.1080/15421400590956045, 435, 2005.12, We study numerically the interaction between particles in a nematic liquid crystal mediated by its elastic distortions with the aid of the Landau-de Gennes continuum theory. We consider the cases where two particles impose rigid normal anchoring on their surfaces and are accompanied by a hyperbolic hedgehog defect. As a function of the distance between the centers of the particles D, we evaluate the force f acting on the particles by integrating the stress tensor. The result is well described by a power law f α D^{-x}. When the "dipoles", composed of a particle and a hyperbolic hedgehog, are in parallel directions, the interaction is attractive and the exponent is x ≃ 4, consistent with the experimental observations together with the theoretical expectation of the dipole-dipole interaction. For antiparallel dipoles, repulsive interaction is observed and x ≃ 3.6, slightly stronger than the dipole-dipole interaction.. |

35. |
Makoto Yoneya, Junichi Fukuda, Hiroshi Yokoyama, Holger Stark, Effect of a hydrodynamic flow on the orientation profiles of a nematic liquid crystal around a spherical particle, *Molecular Crystals and Liquid Crystals*, 10.1080/15421400590956009, 435, 2005.12, We study the effect of a hydrodynamic flow on the orientational configuration of a nematic liquid crystal around a spherical particle imposing rigid normal anchoring. We discuss the cases of large Ericksen numbers (characterizing the ratio of viscous force to the elastic force), where strong elastic deformation by the flow is expected. We assume the Stokes flow profile and deal with a simplified dynamic equation of the orientational order parameter of a second-rank tensor Q_{αβ}. We consider the cases where a particle accompanying a hyperbolic hedgehog or a Saturn ring is subjected to a flow along the axis of rotational symmetry. In both cases the orientation profiles exhibit considerable deformation by a flow.. |

36. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Numerical treatment of the dynamics of a conserved order parameter in the presence of walls, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.73.066706, 73, 6, 2006.06, We discuss how the diffusive dynamics of a conserved order parameter should be numerically treated when impenetrable wall surfaces are present and interact with the degrees of freedom characterized by the order parameter. We derive the discretization scheme for the dynamics, paying particular attention to the conservation of the order parameter in the strict numerical sense. The discretized chemical potential, or the functional derivative of the free energy, contains a surface contribution inversely proportional to the grid spacing Δz, which was proposed heuristically in a recent paper of Henderson and Clarke [Macromol. Theory Simul. 14, 435 (2005)]. Although apparently that surface contribution diverges in the continuum limit Δz→0, we can show, by an analytic argument and numerical calculations, that this divergence does not yield any anomalies, and that our discretization scheme is well defined in this limit. We also discuss the correspondence of our treatment to the model proposed by Puri and Binder [Phys. Rev. A 46, R4487 (1992)] extensively used for the present problem.. |

37. |
Junichi Fukuda, H. Yokoyama, Stability of the director profile of a nematic liquid crystal around a spherical particle under an external field, *European Physical Journal E*, 10.1140/epje/i2006-10072-6, 21, 4, 341-347, 2006.12, We study numerically the effect of an external magnetic or electric field on the director profiles of a nematic liquid crystal around a spherical particle. We pay particular attention to the stability of a hyperbolic hedgehog defect accompanying the particle, which transforms into a Saturn-ring defect encircling the particle under a sufficiently strong external field. We focus on the particle size dependence of the two important threshold field strengths: the "thermodynamic-transition" field strength H _{1} at which the hedgehog and the Saturn-ring configurations have the equal free energy, and the critical field strength H _{2} at which the hedgehog loses its (meta)stability. Our numerical results demonstrate that while H _{1} is non-monotonically dependent on the particle radius R _{0}, H _{2} monotonically increases with R _{0} and the dependence of H _{2} is weak for large R _{0}. The non-monotonic dependence of H _{1} on R _{0} can be explained by comparing the energies of the two configurations and assuming the dependence of those energies on a rescaled field. A crude argument of the energetics of a hyperbolic hedgehog defect under an external field shows that for an asymptotically large R _{0} the critical field strength is independent of R _{0}, which agrees with our numerical finding.. |

38. |
Jin Seog Gwag, Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, In-plane bistable nematic liquid crystal devices based on nanoimprinted surface relief, *Applied Physics Letters*, 10.1063/1.2769946, 91, 7, 2007, The authors present a bistable nematic device, using a fourfold symmetrical bidirection nanometer-scale surface grating fabricated by the nanoimprinting lithography. The bistability is achieved by a composite action between two orthogonal surface undulations, which tend to stabilize the nematic director along either of the two diagonal axes. The switching between the bistable states is easily driven by orthogonal in-plane electric fields. A recent model of groove-induced surface anchoring due to Fukuda [Phys. Rev. Lett. 98, 187803 (2007)] accounts for the azimuthal bistability in the present system.. |

39. |
Jin Seog Gwag, Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Azimuthal nematic bistability at nanoimprinted surface groove, *14th International Display Workshops, IDW '07
IDW '07 - Proceedings of the 14th International Display Workshops*, 2, 405-408, 2007, Azimuthal nematic bistability was induced by a composition action between two azimuthally orthogonal anchoring energies which were led by the combination of a nanoimprinted groove and a mechanical rubbing. The azimuthal easy directions can be controlled by the modulation of groove pitch and rubbing conditions. Fukuda's model is used to express surface anchoring of nematic liquid crystal in surface groove.. |

40. |
Junichi Fukuda, Hiroshi Yokoyama, Effect of an external field on the director profile of a nematic liquid crystal around a spherical particle, *Molecular Crystals and Liquid Crystals*, 10.1080/15421400701675366, 475, 1, 165-172, 2007.01, In our previous study we have demonstrated that an adaptive mesh refinement scheme can be effectively used to investigate the orientation profiles of a nematic liquid crystal around a spherical particle when the characteristic size of the defect core is much smaller than the particle radius. We have also shown that the dynamics of a nematic liquid crystal can be properly treated to reproduce the experimentally observed structural transition from the hedgehog to the Saturn ring configuration induced by an external field. As a preliminary study for the quantitative investigation of this transition, we study in this article how the choice of the criterion for mesh refinement/unrefinement influences the stability of the hedgehog under an external field in our numerical system. The severer is the criterion for mesh refinement to produce a larger number of fine grids, the weaker field can induce the transition. Nevertheless, the dependence of the critical field strength on the criterion for mesh refinement is weak and the criterion can be systematically controlled. Therefore our numerical scheme is shown to be safely applied to the quantitative study on the stability of the hedgehog configuration under an external field.. |

41. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Surface-groove-induced azimuthal anchoring of a nematic liquid crystal Berreman's model reexamined, *Physical Review Letters*, 10.1103/PhysRevLett.98.187803, 98, 18, 2007.05, To account for azimuthal surface anchoring of a nematic liquid crystal, Berreman proposed a simple model attributing the surface anchoring to the elastic distortion of the liquid crystal induced by the grooves of a surface. He showed that the surface anchoring energy is proportional to sin2, with being the angle between the director at infinity and the direction of the surface grooves. We argue that his assumption of negligibly small azimuthal distortion of the nematic is not valid. Proper treatment of the azimuthal distortion reveals that the Berreman's model should yield a surface anchoring energy proportional to sin4. This implies that surface grooves alone cannot contribute to the surface anchoring coefficient in the usual Rapini-Papoular sense.. |

42. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Erratum Surface-groove-induced azimuthal anchoring of a nematic liquid crystal: Berreman's model reexamined (Physical Review Letters (2007) 98 (187803)), *Physical Review Letters*, 10.1103/PhysRevLett.99.139902, 99, 13, 2007.09. |

43. |
Junichi Fukuda, Configuration of a chiral smectic-C film with a circular inclusion, *European Physical Journal E*, 10.1140/epje/i2007-10216-2, 24, 1, 91-98, 2007.09, It was shown experimentally (P.V. Dolganov et al., Europhys. Lett. 76, 250 (2006)) and by numerical calculations (C. Bohley, R. Stannarius, Eur. Phys. J. E 23, 25 (2007)) that the c -director profile of a two-dimensional chiral smectic-C (SmC) film around a circular inclusion adopts dipolar rather than quadrupolar configuration observed in achiral SmC films. We give an analytical argument on how spontaneous bend inherent in chiral SmC liquid crystals influences the configuration of a SmC liquid crystal film around a circular inclusion imposing tangential anchoring. We find how the angle α between two surface defects seen from the center of the inclusion depends on the radius of the inclusion R and the strength of the spontaneous bend q . We show, however, that the contribution of the spontaneous bend to the free energy suffers from mathematical ambiguity; it depends on the mathematical treatment of the outer boundary even when it is at infinity. This might indicate that the shape as well as the treatment of the outer boundary of the film can significantly influence the equilibrium configuration of the c -director and the position of the surface defects.. |

44. |
Junichi Fukuda, Jin Seog Gwag, Makoto Yoneya, Hiroshi Yokoyama, Theory of anchoring on a two-dimensionally grooved surface, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.77.011702, 77, 1, 2008.01, We investigate analytically the anchoring of a nematic liquid crystal on a two-dimensionally grooved surface of arbitrary shape, induced by the elastic distortions of a liquid crystal adjacent to the surface. Our theoretical framework applied to a surface with square grooves reveals that such a surface can exhibit bistable anchoring, while a direct extension of a well-known theory of Berreman [Phys. Rev. Lett. 28, 1683 (1972)] results in no azimuthal anchoring in the so-called one-constant case (K1 = K2 = K3, with K1, K2, and K3 being the splay, twist, and bend elastic constants, respectively). We show under the assumption of K1 = K2 =K that the direction of the bistable easy axes and the anchoring strength crucially depend on the ratios K3 /K and K24 /K, where K24 is the saddle-splay surface elastic constant. To demonstrate the applicability of our theory to general cases and to elucidate the effect of surface shape and the elastic constants on the properties of surface anchoring, we also consider several specific cases of interest; one-dimensional grooves of arbitrary shape, rhombic grooves, and surfaces possessing 2N -fold symmetry, including hexagonal grooves, and show the following: (i) The rescaled anchoring energy f (I) /f (π/2) of one-dimensional grooves, with I being the angle between the director n and the groove direction, is independent of the groove shape. (ii) Whether two diagonal axes of rhombic grooves can become easy axes depends sensitively on K3 /K, K24 /K and the angle α between the grooves. The angle α yielding the maximum anchoring strength for given groove pitch and amplitude depends again on K3 /K and K24 /K; in some cases α=0 (one-dimensional grooves), and in other cases α 0, gives the maximum anchoring strength. Square grooves (α=π/2) do not necessarily exhibit the largest anchoring strength. (iii) A surface possessing 2N -fold symmetry can yield N -stable azimuthal anchoring. However, when K1 = K2 = K3 and N>3, azimuthal anchoring is totally absent irrespective of the value of K24. The direction of the easy axes depends on K3 /K, K24 /K, and whether N is even or odd.. |

45. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Anchoring of a nematic liquid crystal induced by surface grooves A numerical study, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.77.030701, 77, 3, 2008.03, To examine the anchoring energy of a surface with one-dimensional grooves of sinusoidal shape, we carry out numerical calculation of the Frank elastic energy of a nematic cell composed of such a grooved surface and a flat surface. We evaluate the anchoring energy of the grooved surface by carefully eliminating the contribution from a uniform twist deformation in the bulk. When qA 0.2, with q and A being the wave number and the amplitude of the surface groove, we find that the azimuthal-angle dependence of the calculated anchoring energy agrees perfectly with our previous analytical result under the assumption of qA 1. Even when qA 0.6 or 1, we observe an unexpectedly good agreement between the calculated and the analytical anchoring energies, indicating the wide applicability of the analytical anchoring energy in spite of the assumption of qA 1 in its derivation.. |

46. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Simulation study of cholesteric blue phases under an electric field, *16th International Display Workshops, IDW '09
IDW '09 - Proceedings of the 16th International Display Workshops*, 2, 627-630, 2009, We carry out a numerical study to investigate how a cholesteric blue phase responds to an electric field. Our study is based on a Landau-de Gennes continuum theory that describes the orientational order of a liquid crystal in terms of a second-rank tensor. Our numerical scheme allows the change in the size and shape of the unit cell in the course of relaxation to obtain an equilibrium profile of the orientational order. We find a distortion of the unit cell of blue phases under a weak field, which reproduces qualitatively the previous experimental findings. We also observe a rearrangement of disclination lines when a strong field is applied.. |

47. |
Hiroshi Yokoyama, Niitsuma Jun-ichi, Jin Seog Gwag, Junichi Fukuda, Makoto Yoneya, Nanostructured orientational surface patterns for functional LC alignment, *16th International Display Workshops, IDW '09
IDW '09 - Proceedings of the 16th International Display Workshops*, 3, 1647-1650, 2009, Orientational microscopic patterning of the alignment surface of liquid crystals has attracted rapidly increasing attention through the last decade as a novel approach to functionalization of otherwise inert liquid-crystal cell surfaces. Here, I will briefly review the underlying principle of the patterned alignment and also the development of fabrication processes. Recent results of photo-alignment and nanoimprint lithography technologies as applied to large-area processing are presented.. |

48. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Consistent numerical evaluation of the anchoring energy of a grooved surface, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.79.011705, 79, 1, 2009.01, We evaluate the azimuthal anchoring energy of a grooved surface by calculating numerically the Frank elastic energy of a nematic cell composed of the grooved surface and a flat one with rigid azimuthal anchoring, where the director is fixed along the φ direction. We pay attention to the surface anchoring induced by elastic distortions of the director due to its contact with a nonflat surface, which impose local planar degenerate anchoring. Surface anchoring of this kind was analyzed analytically for shallow grooves by Berreman [Phys. Rev. Lett. 28, 1683 (1972)] and critically reexamined by the present authors. We consider two types of surface. one is a surface with one-dimensional sinusoidal parallel grooves, and the other is a surface with two-dimensional square patterns whose surface height is given by a sum of two sinusoidal functions with orthogonal wave vectors. The total energy is the sum of the anchoring energy and the twist energy in the bulk. For the calculation of the twist energy to be eliminated and the evaluation of the azimuthal-angle dependence of the anchoring energy, the "average" azimuthal angle at the bottom, φ (0), must be determined. We adopt two methods to determine φ (0). One is a simple extrapolation of the twist deformation in the bulk. The other relates φ (0) to the variation of the total Frank elastic energy with respect to φ. Our calculations indicate that both methods give essentially the same results, which indicates the consistency of those two methods. We also show that, for a surface with square patterns, the agreement between theory and numerical calculations is quite good even when the maximum of the surface slope is around 0.4, which theory assumes is much smaller than unity. When the surface slope is of order unity, the deviation of numerical results from theory crucially depends on the the surface elastic constant K24.. |

49. |
Junichi Fukuda, Liquid crystal colloids A novel composite material based on Liquid crystals, *Journal of the Physical Society of Japan*, 10.1143/JPSJ.78.041003, 78, 4, 2009.04, Liquid crystal colloids are composite materials made up of colloidal particles and liquid crystalline host fluids. After introducing various specific properties of liquid crystal collloids that are absent in conventional colloidal systems, we review our studies, based mainly on computer simulations using Landau-de Gennes theory, to elicudate those properties of liquid crystal colloids. We first present our attempts to investigate the orientational profiles and defect structures of a nematic liquid crystal around one colloidal particle. We successfully reproduce two configurations observed experimentally when strong homeotropic anchoring is imposed at the particle surface; one is a configuration with a hedgehog defect, and in the other, the particle is encircled by a ring defect referred to as a Saturn ring. Next we focus on the interaction between particles mediated by the elastic distortions of the host nematic liquid crystal. We calculate the interaction between particles carrying a hedgehog, and that between particles connected by a birefringent region called a bubble-gum. The properties of those interactions obtained numerically have been recently verified experimentally in a quantitative manner. We also review some of the important and attractive features of liquid crystal colloids not mentioned in the main part of the present paper.. |

50. |
Junichi Fukuda, Slobodan Zumer, Confinement effect on the interaction between colloidal particles in a nematic liquid crystal An analytical study, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.79.041703, 79, 4, 2009.04, Motivated by a recent experimental study on the interaction between colloidal particles in a confined nematic liquid crystal, we discuss in an analytical manner how the interaction potential U between spherical colloidal particles in a confined nematic cell behaves as a function of the interparticle distance r. We show that the short-range potential follows a power law U (r) ∼ r-5 as expected from the quadrupolar nature of the interaction, while the long-range potential is dominated by an exponential function U (r) ∼ d/r exp (-2πr/d), where d is the cell thickness. These two regimes are interchanged at r/d 0.8. This behavior of U (r) is in a good semiquantitative agreement with the experimental finding.. |

51. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Simulation of cholesteric blue phases using a Landau-de Gennes theory Effect of an applied electric field, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.80.031706, 80, 3, 2009.09, We investigate numerically static and dynamic properties of cholesteric blue phases. Our study is based on a Landau-de Gennes theory describing the orientational order of a liquid crystal in terms of a second-rank tensor. To find the shape and size of the unit cell conforming to the minimum of the free energy, we let the geometrical parameters characterizing the unit cell relax in the course of the time evolution via a simple relaxational equation. We investigate the effect of an electric field on the structure of cholesteric blue phases. We study how the deformation of the unit cell in response to the electric field E depends on the strength and direction of the electric field and the original structure of cholesteric blue phases. Our results qualitatively agree with the experimental findings. Although in a weak field, the strain tensor is proportional to E2 as previously argued, for a moderate field the distortion is no longer proportional to E2 and can be even nonmonotonic with respect to E2. Furthermore, we investigate the kinetic processes of the deformation, rearrangement, and extinction of disclination lines under a strong electric field. We show that the kinetics of disclination lines is highly complicated and sensitively depends on the initial structure of blue phases, the direction of the electric field, and the sign of dielectric anisotropy Ia. In most cases, a strong field aligns the liquid crystals in a uniform (positive Ia) or helical (negative Ia) manner without disclination lines. However, for negative Ia and the direction of the electric field parallel to the body diagonal of the unit cell, disclination lines do not disappear and form a two-dimensional hexagonal lattice.. |

52. |
Junichi Fukuda, Žumer Slobodan, Novel defect structures in a strongly confined liquid-Crystalline blue phase, *Physical Review Letters*, 10.1103/PhysRevLett.104.017801, 104, 1, 2010.01, In our numerical study based on a phenomenological description of strongly confined liquid crystalline blue phase I (BP I), we find several novel structures characterized by specific configurations of topological disclination lines. The thickness of the system is of the order of the dimension of the unit cell of the bulk BP I, and the confining surfaces adopts homeotropic anchoring. The structures include an array of double-helix disclination lines accompanied by an orthorhombic lattice of double-twist cylinders, and two parallel arrays of winding disclination lines almost perpendicular to each other.. |

53. |
Junichi Fukuda, Makoto Yoneya, Hiroshi Yokoyama, Critical reexamination of Berreman's theory on surface anchoring, *Molecular Crystals and Liquid Crystals*, 10.1080/15421400903397058, 516, 12-25, 2010.01, We critically reexamine well-known Berreman's theory [Phys. Rev. Lett. 28, 1683 (1972)] on the anchoring of a nematic liquid crystal due to its elastic distortions induced by a sinusoidally grooved surface. We put emphasis on the effect of azimuthal distortions of the director n and the contribution of saddle-splay surface elasticity characterized by K24. We give a correct calculation of the anchoring energy and show that Berreman's theory gives a correct result only when K1=K2 and K24=0, where K1 and K2 are the splay and twist elastic constants, respectively. We also present our preliminary numerical attempts to evaluate the anchoring energy of a surface with square patterns and compare the anchoring energy calculated numerically with an analytical one obtained by a direct extension of our theoretical argument on one-dimensional parallel grooves.. |

54. |
Takahiro Kishita, Kenji Takahashi, Masatoshi Ichikawa, Junichi Fukuda, Yasuyuki Kimura, Arrangement dependence of interparticle force in nematic colloids, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.81.010701, 81, 1, 2010.01, We have experimentally and theoretically studied the interparticle force between two colloidal particles with different sizes accompanied by hyperbolic hedgehog defects in a nematic liquid crystal. The force f was directly measured using dual-beam optical tweezers and calculated theoretically from the equilibrium tensor field around the particles. The dependence of f on the center-to-center distance between particles of different sizes R is different from that for particles with the same size. The magnitude of f depends on the relative arrangement of the particles: f is larger when a defect between the particles belongs to the larger particle. From the theoretical calculation, the difference in f between the two arrangements, δf, monotonically increases with increasing size difference. The difference δf was experimentally and theoretically found to be proportional to R-4.6 at large R. The obtained exponent is comparable to the exponent of -5 predicted by electrostatic analogy.. |

55. |
Junichi Fukuda, Continuous transformation of a -1/2 wedge disclination line to a +1/2 one, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.81.040701, 81, 4, 2010.04, It is known that, in the order-parameter space S2 / Z2 (a typical example being a uniaxial nematic liquid crystal in three dimensions), a -1/2 wedge disclination line and a +1/2 one are topologically equivalent and can thus be transformed continuously into each other. Here we report the realization of this transformation in a simulation of a cholesteric blue phase under an electric field.. |

56. |
Junichi Fukuda, Žumer S., Cholesteric blue phases Effect of strong confinement, *Liquid Crystals*, 10.1080/02678292.2010.481909, 37, 6-7, 875-882, 2010.06, After an overview of cholesteric blue phases, we review our recent numerical studies on possible defect structures when blue phase I (BP I) is confined in a thin cell composed of two parallel surfaces imposing homeotropic anchoring. The cell thickness is of the order of the unit cell dimension of the bulk cubic BP I. We find several structures of disclination lines which, to our knowledge, have never been discussed in the field of liquid crystals as equilibrium structures. Those structures include a parallel array of double helix disclination lines, and two parallel arrays of undulating disclination lines almost (but not exactly) perpendicular to each other. A first-order transition between those two structures is possible, and the similarity between them is discussed.. |

57. |
Junichi Fukuda, Stabilization of a blue phase by a guest component An approach based on a Landau-de Gennes theory, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.82.061702, 82, 6, 2010.12, We discuss, with the aid of numerical calculations based on a Landau-de Gennes theory, the stabilization of a blue phase in chiral liquid crystals by introducing a guest component. Our argument is based on a common speculation that cores of disclination lines with higher free-energy density are replaced by the guest component. We assume that the guest component forms sharp interfaces with the liquid crystal (strong segregation). We show that, by a suitable choice of materials with small interfacial tension, a guest component of volume fraction less than 10% drastically increases the temperature range of thermodynamic stability of a blue phase, in agreement with experiments.. |

58. |
Junichi Fukuda, Žumer Slobodan, Quasi-two-dimensional Skyrmion lattices in a chiral nematic liquid crystal, *Nature Communications*, 10.1038/ncomms1250, 2, 1, 2011, Skyrmions are particle-like topological entities in a continuous field that have an important role in various condensed matter systems, including two-dimensional electron gases exhibiting the quantum Hall effect, chiral ferromagnets and Boseĝ€"Einstein condensates. Here we show theoretically, with the aid of numerical methods, that a highly chiral nematic liquid crystal can accommodate a quasi-two-dimensional Skyrmion lattice as a thermodynamically stable state, when it is confined to a thin film between two parallel surfaces imposing normal alignment. A chiral nematic liquid crystal film can thus serve as a model Skyrmion system, allowing direct investigation of their structural properties by a variety of optical techniques at room temperatures that are less demanding than Skyrmion systems discussed previously.. |

59. |
Mohammad Reza Mozaffari, Mehrtash Babadi, Junichi Fukuda, Mohammad Reza Ejtehadi, Interaction of spherical colloidal particles in nematic media with degenerate planar anchoring, *Soft Matter*, 10.1039/c0sm00761g, 7, 3, 1107-1113, 2011.02, The interaction between two spherical colloidal particles with degenerate planar anchoring in a nematic media is studied by numerically minimizing the bulk Landau-de Gennes and surface energy using a finite element method. We find that the energy achieves its global minimum when the particles are in close contact and forming an angle = 28°± 2 with respect to the bulk nematic director, in agreement with the experiments. Although the quadrupolar structure of the director field is preserved in the majority of configurations, we show that for smaller orientation angles and at smaller inter-particle separations, the axial symmetry of the topological defect-pairs is continuously broken, resulting in the emergence of an attractive interaction.. |

60. |
Junichi Fukuda, Žumer Slobodan, Ring defects in a strongly confined chiral liquid crystal, *Physical Review Letters*, 10.1103/PhysRevLett.106.097801, 106, 9, 2011.03, We find numerically that a regular array of isolated ring defects can exist as a stable state in a highly chiral liquid crystal confined in a thin cell imposing fixed planar anchoring at the parallel confining surfaces. This peculiar defect structure can be stable when the cell thickness d is around 3/4 of the helical pitch p. A cell of thickness 3p/4 with parallel surface anchoring is incompatible with helical alignment that favors d=mp/2 (with m being an integer). Formation of ring defects can thus be regarded as a result of frustrations between the helical alignment with a specific pitch and the confining surfaces that prevent it.. |

61. |
Junichi Fukuda, Report on the 9th Soft Matter Forum Conference of the Japanese Liquid Crystal Society, *Liquid Crystals Today*, 10.1080/1358314X.2011.563979, 20, 2, 68-70, 2011.04. |

62. |
Takahiro Kishita, Noboru Kondo, Kenji Takahashi, Masatoshi Ichikawa, Junichi Fukuda, Yasuyuki Kimura, Interparticle force in nematic colloids Comparison between experiment and theory, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.84.021704, 84, 2, 2011.08, We have studied the interparticle force between two colloidal particles in a nematic liquid crystal experimentally and theoretically. The force F was directly measured using dual-beam optical tweezers and was numerically calculated from the equilibrium tensor field around the particles. The dependence of F on the center-to-center distance R between the particles was studied not only for equal-sized particles but also for different-sized ones in various kinds of configurations and arrangements. The magnitude of F between different-sized particles in the dipole configuration depends on their relative arrangement. Both experimental and theoretical force curves are found to be in good agreement with each other. At large R, they also make agreement with those predicted by an electrostatic analogy of nematic field.. |

63. |
Junichi Fukuda, Žumer Slobodan, Structural forces in liquid crystalline blue phases, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.84.040701, 84, 4, 2011.10, We show numerically that the interaction potential or force mediated by a liquid crystalline blue phase (BP) between two parallel plates exhibits oscillatory behavior with variation of the interplate distance, when the parallel plates impose strong normal anchoring. Its periodicity is approximately half of the unit-cell dimension of the bulk BP. The interaction arises from the deformation of the confined BP structure around the midplane of the system. The oscillatory interaction can be regarded as a clear manifestation of the BP ordering, because the cholesteric helical alignment adopted by a chiral liquid crystal cannot yield an oscillatory interaction.. |

64. |
Žumer Slobodan, Miha Ravnik, Junichi Fukuda, Confined blue phases Trapping of colloidal particles in disclination superstructures, *Liquid Crystals XV
Liquid Crystals XV*, 10.1117/12.893160, 8114, 2011.10, In confined blue phases numerous quasi 2D disclination networks ranging from rings to double helices can be stable. We have recently demonstrated how such networks act as arrays of trapping sites that can lead to easy assembling of colloidal particles in complex 2D lattice structures. In this short overview we summarize main results of our Landau - de Gennes modeling combined with topology that was proven to be useful in bulk blue phase colloids. Effects of confinement, particle anchoring, and particle sizes that can range from micron to nanometre scale are presented. Quasi 2D colloidal crystals that can be easily manipulated by external stimuli via affecting liquid crystal and/or colloidal particles are expected to have possible photonic applications.. |

65. |
Miha Ravnik, Junichi Fukuda, Julia M. Yeomans, Žumer Slobodan, Confining blue phase colloids to thin layers, *Soft Matter*, 10.1039/c1sm05707c, 7, 21, 10144-10150, 2011.11, Colloidal assembly in strongly confined cholesteric structures is demonstrated using phenomenological modelling. Particle trapping sites and trapping potentials, which are intrinsically imposed by the strongly anisotropic orientational profile of the confined blue phases, are calculated. Locations of the trapping sites and profiles of the trapping potentials are shown to depend importantly on the particle size, and the array of trapping sites can even change symmetry. Trapping sites provide robust binding of various colloidal structures with binding energy of ∼100kT for ∼100 nm particles. Maximising the filling of the trapping sites by particles proves to lower the full free energy of the system, offering means for thermodynamic stabilisation of confined blue phases. Finally, we present formation of disclination cages, formed as a three-dimensional closed network of defect lines surrounding sufficiently large particles with strong homeotropic anchoring.. |

66. |
Junichi Fukuda, Stabilization of blue phases by the variation of elastic constants, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.85.020701, 85, 2, 2012.02, We study theoretically the effect of the variation of the elastic constants on the stability of cholesteric blue phases (BPs). We demonstrate that the stability of BPs is greatly enhanced when the bend elastic constant K _{33} is smaller, in agreement with recent experimental findings. Larger splay (K _{11}) and twist (K _{22}) elastic constants also stabilize BPs. Our argument sheds light on the subtle effect of the variation of the elastic constants on the stability of BPs, and could guide the synthesis of liquid crystals with a wider temperature range of stable BPs.. |

67. |
Junichi Fukuda, Erratum Stabilization of blue phases by the variation of elastic constants (Physical Review E - Statistical, Nonlinear, and Soft Matter Physics (2012) 85 (020701)), *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.85.029903, 85, 2, 2012.02. |

68. |
Takuya Ohzono, Junichi Fukuda, Zigzag line defects and manipulation of colloids in a nematic liquid crystal in microwrinkle grooves, *Nature Communications*, 10.1038/ncomms1709, 3, 2012.03, Spatially confined liquid crystals exhibit non-uniform alignment, often accompanied by self-organised topological defects of non-trivial shape in response to imposed boundary conditions and geometry. Here we show that a nematic liquid crystal, when confined in a sinusoidal microwrinkle groove, exhibits a new periodic arrangement of twist deformations and a zigzag line defect. This periodic ordering results from the inherent liquid crystal elastic anisotropy and the antagonistic boundary conditions at the flat liquid crystal-air and the curved liquid crystal-groove interfaces. The periodic structure can be tuned by controlling the groove geometry and the molecular chirality, which demonstrates the importance of boundary conditions and introduced asymmetry for the engineering of topological defects. Moreover, the kinks in the zigzag defects can trap small particles, which may afford a new method for manipulation of colloids. Our system, which uses easily fabricated microwrinkle grooves, provides a new microfabrication method based on the arrangement of controllable defects.. |

69. |
Junichi Fukuda, Žumer Slobodan, Simulation of a cholesteric blue phase in a thin cell Exotic defect structures and their response to an electric field, *Emerging Liquid Crystal Technologies VII
Emerging Liquid Crystal Technologies VII*, 10.1117/12.912825, 8279, 2012.03, We present our numerical attempts to simulate the structures of a cholesteric blue phase (BP) confined in a thin cell. Our simulations are based on a Landau-de Gennes theory describing the orientational order of the liquid crystal by a second-rank symmetric tensor. When the cell thickness is small enough, of the order of the lattice constant of the bulk BP a, various exotic defect structures that do not resemble those of bulk BPs are shown to be stable. They include a hexagonal lattice of Skyrmion excitations, and arrays of disclination lines in a double-helix form. We also show the dynamics of disclination lines in a thicker cell (∼ 2.6 a) under an applied electric field. The cell before the application of an electric field accommodates disclination lines of the form similar to that of bulk BP. The electric field alters their form in a non-trivial way depending on the field strength.. |

70. |
Takuya Ohzono, Yoshiko Takenaka, Junichi Fukuda, Focal conics in a smectic-A liquid crystal in microwrinkle grooves, *Soft Matter*, 10.1039/c2sm25416f, 8, 24, 6438-6444, 2012.06, Focal conic domains (FCDs) in smectic-A (SmA) liquid crystals (LCs) are a broad class of curvature defects in a layered system. Here, we report a regular array of FCDs in octylcyanobiphenyl in a SmA phase confined within sinusoidal microgrooves of microwrinkles with a specific periodicity. A semi-hybrid alignment is imposed by the air-LC interface (homeotropic) and the LC-curved-microwrinkle interface (unidirectional planar). The FCDs are periodically packed along the groove direction when the wrinkle wavelength is larger than a critical value of approximately 4 μm. The periodicity of the FCDs monotonically increases with increasing the wrinkle wavelength. From our optical observation, we propose an internal layer structure of the FCDs composed of a set of Dupin cyclides with the eccentricity of the basic ellipse being approximately 0.75.. |

71. |
Žumer Slobodan, Junichi Fukuda, Miha Ravnik, Confined colloidal blue phases with potential for photonics, *Molecular Crystals and Liquid Crystals*, 10.1080/15421406.2012.687143, 561, 107-114, 2012.08, We have recently demonstrated various quasi-2D disclination networks in blue phases confined to thin layers, ranging from rings, skyrmions, to double helices, which can provide arrays of trapping sites for an easy assembling of colloidal particles in complex 2D lattice structures. In this brief review, we summarize main findings of our phenomenological modeling combined with topology. Effects of confinement, particle sizes and anchoring are discussed. Quasi-2D colloidal crystals can be easily manipulated by external stimuli via affecting liquid crystal or colloidal particles and offer means for novel applications in photonics.. |

72. |
Takuya Ohzono, Junichi Fukuda, Kosuke Suzuki, Tomohiko Yamaguchi, ±1/2 wedge disclinations stabilized by a sinusoidal boundary in a thin hybrid nematic liquid-crystal film, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.86.030701, 86, 3, 2012.09, As an interesting example of how geometry affects the formation of defects, we study the defect structures of a hybrid nematic liquid-crystal film in a wedge-shaped cell made up of sinusoidal microwrinkles and an elastomer sheet. When the cell thickness is larger than a threshold value h _{c}, +1/2 and -1/2 disclinations are simultaneously stabilized along concave grooves and convex crests, respectively. A simple theoretical analysis gives a good estimate of h _{c}. The disclinations also show alternating optical rotations resulting from the curved boundary and liquid-crystal elastic anisotropy.. |

73. |
Junichi Fukuda, Stability of cholesteric blue phases in the presence of a guest component, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.86.041704, 86, 4, 2012.10, We investigate theoretically, with the aid of numerical calculations based on a Landau-de Gennes theory, how two cubic cholesteric blue phases of a chiral liquid crystal, BP I and BP II, are stabilized when a guest component, such as a polymer network, is introduced and replace energetically costly defect regions. We show that the temperature range of stable BP I is significantly widened by the guest component, while the stability of BP II is only modestly enhanced.. |

74. |
Takuya Ohzono, Junichi Fukuda, Transition of frustrated nematic order and fluctuation of topological defects in microwrinkle grooves, *Soft Matter*, 10.1039/c2sm26701b, 8, 45, 11552-11556, 2012.12, We show that a nematic liquid crystal confined in sinusoidal microwrinkle grooves imposing antagonistic boundary conditions exhibits noteworthy structural transitions of nematic order and associated line defects under the variation of temperature (T). The defects also show unusual temperature-dependent fluctuations whose amplitude squared depends nonlinearly on T. The temperature dependence of the elastic constants of the liquid crystal and their ratio is responsible for these transitions and fluctuations. A variety of transformable defect structures with characteristic fluctuations will open up new possibilities for organizing and manipulating colloids and a liquid crystal confined in microwrinkle grooves could be a tangible one-dimensional model system to study the nature of fluctuations.. |

75. |
Junichi Fukuda, Theory and simulation of cholesteric blue phases Effect of the elastic constants on the stability of blue phases and the response of a blue phase cell to an electric field, *Liquid Crystals XVI
Liquid Crystals XVI*, 10.1117/12.929315, 8475, 2012.12, We present our recent theoretical and numerical studies concerning the properties of cholesteric blue phases (BPs). One is on the effect of the variation of the Frank elastic constants on the stability of BPs. Our study is based on a classical and well-known theory of Meiboom et al. that gave a rough estimate of the temperature range of stable BPs in the case of equal elastic constants. We extend it to take into account the difference of the elastic constants. We show that the stability of BPs is greatly enhanced when the bend elastic constant K_{33} is smaller, which agrees well with recent experiments. We also show that larger splay (K_{11}) and twist (K _{22}) elastic constants are also favorable for the stability of BPs. The other subject of the present paper is the response of BPs in a parallel cell to an applied electric field. We carry out numerical calculations for the investigation the dynamics of orientational order and associated disclination lines. Our calculations are based on a Landau-de Gennes theory describing the orientational order of the liquid crystal by a second-rank tensor. Our preliminary calculations demonstrate that a non-uniform electric field induced by comb-like electrodes gives rise to non-trivial dynamics of disclination lines.. |

76. |
Junichi Fukuda, Žumer Slobodan, Field-induced dynamics and structures in a cholesteric-blue-phase cell, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.87.042506, 87, 4, 2013.04, We investigate numerically the relaxational dynamics of the orientational order of a cholesteric blue phase (BP) in a planar cell enforcing normal alignment in response to the application and cessation of an external electric field. We focus on the cases where blue phase I (BP I) is stable in the bulk. We show how the reorganization processes of the network of disclinations depend on the field strength and the history of the application of the field. We also demonstrate that the relaxation processes following the cessation of the field are particularly complex and depend sensitively on the profile of the orientational order before the cessation of the field.. |

77. |
Richard James, Junichi Fukuda, Effect of anchoring energy and elastic anisotropy on spherical inclusions in a nematic liquid crystal, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.88.010501, 88, 1, 2013.07, This paper explores how pairs of spherical particles with homeotropic (normal) surface anchoring cluster when immersed in nematic liquid crystal. By means of the Landau-de Gennes continuum theory we calculate how the equilibrium separation of a particle pair depends on the anchoring energy at the particle surface and the elastic anisotropy of the liquid crystal. We find that, for modest to strong anchoring strengths, the particle separation depends linearly on the elastic anisotropy and the inverse of the anchoring strength. Thus, the anchoring strength can be estimated by measuring the particle-pair separation.. |

78. |
Yasuhiro Ogawa, Junichi Fukuda, Hiroyuki Yoshida, Masanori Ozaki, Finite-difference time-domain analysis of cholesteric blue phase II using the Landau-de Gennes tensor order parameter model, *Optics Letters*, 10.1364/OL.38.003380, 38, 17, 3380-3383, 2013.09, We numerically calculated the photonic band structure of a cholesteric blue phase II (BPII) liquid crystal using two models, the tensor order parameter model and the double-twist cylinder (DTC) model. The tensor order parameter model was derived numerically from the Landau-de Gennes theory, whereas the DTC model simply assumed a three-dimensional stack of ordered cylinders. The two models yielded similar photonic band structures; however, the polarization dependence of the transmission spectrum through the (100) direction in BPII was different. The results from the tensor order parameter model gave a better qualitative agreement with experiments on the transmission spectrum. This demonstrates the importance of a precise orientation model in the analysis of the optical properties of cholesteric blue phases.. |

79. |
O. M. Tovkach, Junichi Fukuda, B. I. Lev, Peculiarity of the interaction of small particles in smectic liquid crystals, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.88.052502, 88, 5, 2013.11, We investigate the peculiarity of the interaction between particles immersed into a smectic liquid crystal with a layered structure. Such a structure of a liquid crystal imposes restrictions on possible deformations of the layer displacement field. Previous studies neglect this fact and give improper results for the interaction potential within one molecular layer. The present paper shows that such restrictions yield an interaction potential substantially different from those of previous studies. Oscillatory behavior, which was not present in the potentials of previous studies, might give rise to superstructures of immersed particles with finite interparticle distance.. |

80. |
Junichi Fukuda, Simulation of the switching dynamics of a cholesteric blue phase cell by an inhomogeneous in-plane field, *Japanese Journal of Applied Physics, Part 1: Regular Papers & Short Notes*, 10.7567/JJAP.53.010301, 53, 1, 2014.01, By numerical calculations based on a continuum theory, we investigate the dynamics of a cholesteric blue phase liquid crystal cell with comb-like electrodes generating an inhomogeneous in-plane electric field. We demonstrate that the cholesteric blue phase respond to the electric field depending sensitively on the local field strength; disclination lines inherent in cholesteric blue phases disappear under a strong field. We also show that the typical response time is much smaller than milliseconds (those of nematic cells) as shown experimentally.. |

81. |
B. I. Lev, Junichi Fukuda, O. M. Tovkach, S. B. Chernyshuk, Interaction of small spherical particles in confined cholesteric liquid crystals, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.89.012509, 89, 1, 2014.01, The theory of the elastic interaction of spherical colloidal particles immersed into a confined cholesteric liquid crystal is proposed. The case of weak anchoring on the particle surfaces is considered. We derive a general expression for the energy of the interaction between small spherical particles (with diameter much smaller than the cholesteric pitch) suspended in a cholesteric confined by two parallel planes. The resulting form of the interaction energy has a more complex spatial pattern and energy versus distance dependence than that in nematic colloids. The absence of translational symmetry related to helical periodicity and local nematic ordering in cholesteric liquid crystals manifest themselves in the complex nature of the interaction maps.. |

82. |
Yasuhiro Ogawa, Junichi Fukuda, Hiroyuki Yoshida, Masanori Ozaki, Photonic band structure and transmission analysis of cholesteric blue phase 2 Electrostriction in the [100] direction, *Optics Express*, 10.1364/OE.22.003766, 22, 4, 3766-3772, 2014.02, The photonic band structure and transmission properties of a cholesteric blue phase 2 liquid crystal, which is elongated in the [100] direction by electrostriction, are analyzed by finite-difference time-domain method. The simple cubic lattice deforms into a tetragonal lattice under the influence of an electric field, resulting in a change of the photonic band structure. Moreover, we show that the circular polarization dependence of the transmittance spectrum changes in an electric field, a behavior that has yet to be observed in experiment.. |

83. |
Richard James, Junichi Fukuda, Twist transition of nematic hyperbolic hedgehogs, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.89.042501, 89, 4, 2014.04, Stability of an idealized hyperbolic hedgehog in a nematic liquid crystal against a twist transition is investigated by extending the methodology of Rüdinger and Stark [Liq. Cryst. 26, 753 (1999)LICRE60267-829210.1080/ 026782999204840], where the hedgehog is confined between two concentric spheres. In the ideal hyperbolic-hedgehog the molecular orientation is assumed to rotate proportionally with respect to the inclination angle, θ (and in the opposite sense). However, when splay, k11, and bend, k33, moduli differ this proportionality is lost and the liquid crystal deforms relative to the ideal with bend and splay. Although slight, these deformations are shown to significantly shift the transition if k11/k33 is small. By increasing the degree of confinement the twist transition can be inhibited, a characteristic both hyperbolic and radial hedgehogs have in common. The twist transition of a hyperbolic defect that accompanies a particle is found to be well predicted by the earlier stability analysis of a thick shell.. |

84. |
Takuya Ohzono, Takahiro Yamamoto, Junichi Fukuda, A liquid crystalline chirality balance for vapours, *Nature Communications*, 10.1038/ncomms4735, 5, 2014.04, Chiral discrimination of vapours plays an important role in olfactory perception of biological systems and its realization by artificial sensors has been an intriguing challenge. Here, we report a simple method that tangibly visualizes the chirality of a diverse variety of molecules dissolved from vapours with high sensitivity, by making use of a structural change in a periodic microstructure of a nematic liquid crystal confined in open microchannels. This microstructure is accompanied by a topological line defect of a zigzag form with equal lengths of 'zig' and 'zag.' We find that a tiny amount of vapour of chiral molecules injected onto the liquid crystal induces the imbalance of 'zig' and 'zag' depending on its enantiomeric excess within a few seconds. Our liquid-crystal-based 'chirality balance' offers a simple, quick and versatile chirality-sensing/-screening method for gas-phase analysis (for example, for odours, environmental chemicals or drugs).. |

85. |
Junichi Fukuda, Žumer Slobodan, Exotic defect structures and their optical properties in a strongly confined chiral liquid crystal, *Molecular Crystals and Liquid Crystals*, 10.1080/15421406.2014.917474, 594, 1, 70-77, 2014.05, We numerically investigate structural and optical properties of a highly chiral liquid crystal when it is confined in a thin planar cell imposing strong homeotropic anchoring. Various stable exotic defect structures different from those of bulk cholesteric blue phases are found depending on temperature and cell thickness. We also study how a planar cell with these defect structures reflect and transmit incident light, paying particular attention to a structure with double-helix disclination lines and one similar to bulk BP II.. |

86. |
Miha Ravnik, Junichi Fukuda, Templated blue phases, *Soft Matter*, 10.1039/c5sm01878a, 11, 43, 8417-8425, 2015, Cholesteric blue phases of a chiral liquid crystal are interesting examples of self-organised three-dimensional nanostructures formed by soft matter. Recently it was demonstrated that a polymer matrix introduced by photopolymerization inside a bulk blue phase not only stabilises the host blue phase significantly, but also serves as a template for blue phase ordering. We show with numerical modelling that the transfer of the orientational order of the blue phase to the surfaces of the polymer matrix, together with the resulting surface anchoring, can account for the templating behaviour of the polymer matrix inducing the blue phase ordering of an achiral nematic liquid crystal. Furthermore, tailoring the anchoring conditions of the polymer matrix surfaces can bring about orientational ordering different from those of bulk blue phases, including an intertwined complex of the polymer matrix and topological line defects of orientational order. Optical Kerr response of templated blue phases is explored, finding large Kerr constants in the range of K = 2-10 × 10^{-9} m V^{-2} and notable dependence on the surface anchoring strength. More generally, the presented numerical approach is aimed to clarify the role and actions of templating polymer matrices in complex chiral nematic fluids, and further to help design novel template-based materials from chiral liquid crystals.. |

87. |
H. Yoshida, K. Asakura, Junichi Fukuda, M. Ozaki, Three-dimensional positioning and control of colloidal objects utilizing engineered liquid crystalline defect networks, *Nature Communications*, 10.1038/ncomms8180, 6, 2015.05, Topological defects in liquid crystals not only affect the optical and rheological properties of the host, but can also act as scaffolds in which to trap nano or micro-sized colloidal objects. The creation of complex defect shapes, however, often involves confining the liquid crystals in curved geometries or adds complex-shaped colloidal objects, which are unsuitable for device applications. Using topologically patterned substrates, here we demonstrate the controlled generation of three-dimensional defect lines with non-trivial shapes and even chirality, in a flat slab of nematic liquid crystal. By using the defect lines as templates and the electric response of the liquid crystals, colloidal superstructures are constructed, which can be reversibly reconfigured at a voltage as low as 1.3 V. Three-dimensional engineering of the defect shapes in liquid crystals is potentially useful in the fabrication of self-healing composites and in stabilizing artificial frustrated phases.. |

88. |
Junichi Fukuda, Yasushi Okumura, Hirotsugu Kikuchi, Calculation of confocal microscope images of cholesteric blue phases, *Emerging Liquid Crystal Technologies XI
Emerging Liquid Crystal Technologies XI*, 10.1117/12.2209210, 9769, 2016, Real-space images of bulk cholesteric blue phases (BPs) have been successfully obtained by confocal microscopy observations using structural color without doping fluorescent dye. However, theoretical interpretation of these images (for example, the understanding of the relation between intensity distribution and the ordering of BPs) remains challenging because typical lattice spacing of BPs is of the order of the wavelength of visible light, and therefore geometrical optics is entirely useless. In this work, we present a numerical approach to calculate the confocal images of BPs by solving the Maxwell equations. Calculated confocal images are consistent with experimental observations in terms of in-plane symmetry.. |

89. |
Hiroyuki Yoshida, Konkanok Anucha, Yasuhiro Ogawa, Yuto Kawata, Masanori Ozaki, Junichi Fukuda, Hirotsugu Kikuchi, Bragg reflection band width and optical rotatory dispersion of cubic blue-phase liquid crystals, *Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, 10.1103/PhysRevE.94.042703, 94, 4, 2016.10, The Bragg reflection band width and optical rotatory dispersion of liquid crystalline cholesteric blue phases (BPs) I and II are compared by numerical simulations. Attention is paid to the wavelength regions for which the reflection bands with lowest photon energies appear, i.e., the [110] direction for BP I and the [100] direction for BP II. Finite difference time domain and 4×4 matrix calculations performed on the theoretical director tensor distribution of BPs with the same material parameters show that BP II, which has simple cubic symmetry, has a wider photonic band gap than BP I, which has body centered cubic symmetry, possibly due to the fact that the density of the double-twist cylinders in BP II are twice that in BP I. The theoretical results on the Bragg reflection band width are supported by reflectance measurements performed on BPs I and II for light incident along the [110] and [100] directions, respectively.. |

90. |
Takuya Ohzono, Kaoru Katoh, Junichi Fukuda, Fluorescence microscopy reveals molecular localisation at line defects in nematic liquid crystals, *Scientific Reports*, 10.1038/srep36477, 6, 2016.11, Topological defects easily form in liquid crystals (LCs) as a result of frustrations in spatially dependent anisotropic molecular ordering, and have been regarded as promising tools for facilitating manipulation of relatively large non-LC materials such as colloids. However, it remains unclear whether low-molecular-weight (LMW) impurities that do not aggregate or self-assemble in bulk LCs because of the dominance of entropy can localise at LC defects. Here, by fluorescence microscopy, we directly show the localisation of LMW molecules at the topological line defects of a nematic LC. It is theoretically explained that excess free energy density of nematic ordering at the defect core allows LMW solutes to accumulate at a non-negligible level overcoming the entropy leading to their uniform distributions. Our results demonstrate the usefulness of LC defects as a bottom-up field that enables micromanipulation of LMW molecules and realisation of transformable three-dimensional micro-architectures composed of versatile small functional molecules.. |

91. |
Andriy Nych, Junichi Fukuda, Uliana Ognysta, Žumer Slobodan, Igor Musevic, Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film, *Nature Physics*, 10.1038/nphys4245, 2017. |

92. |
Junichi Fukuda, Do small molecules assemble at topological defects of a liquid crystal?, *2017 Emerging Liquid Crystal Technologies XII Conference, ELCT 2017
Emerging Liquid Crystal Technologies XII 2017*, 10.1117/12.2256541, 10125, 2017, It is well known that topological defects of a liquid crystal can trap colloidal particles and polymers. However, it remains unclear whether low-molecular-weight (LMW) non-LC molecules can aggregate at topological defects, because entropy towards uniform distributions becomes more dominant for smaller molecules. We show by a simple theoretical argument that topological defects indeed give rise to non-uniform distributions of such LMW guest molecules. The relaxation of the high free energy density of topological defects by the presence of LMW guest molecules is strong enough to overcome the contribution of entropy. We briefly discuss the relevance of our theoretical arguments to experiments.. |

93. |
N. Kameta, T. Matsuzawa, K. Yaoi, Junichi Fukuda, M. Masuda, Glycolipid-based nanostructures with thermal-phase transition behavior functioning as solubilizers and refolding accelerators for protein aggregates, *Soft Matter*, 10.1039/c7sm00310b, 13, 17, 3084-3090, 2017.01, The self-assembly of synthetic glycolipids produced nanostructures such as vesicles and nanotubes consisting of bilayer membranes, which underwent a gel-to-liquid crystalline thermal phase transition. Vesicles formed at temperatures above the thermal phase transition temperatures (T_{g-l}) could solubilize aggregates of denatured proteins by trapping them in the fluid bilayer membranes. Cooling to temperatures below T_{g-l} caused a morphological transformation into nanotubes that accompanied the thermal phase transition from the fluid to the solid state. This phenomenon allowed the trapped proteins to be quickly released into the bulk solution and simultaneously facilitated the refolding of the proteins. The refolding efficiency strongly depended on the electrostatic attraction between the bilayer membranes of the nanostructures and the proteins. Because of the long shape (>400 nm) of the nanotubes, simple membrane filtration through a pore size of 200 nm led to complete separation and recovery of the refolded proteins (3-9 nm sizes).. |

94. |
Takuya Ohzono, Kaoru Katoh, Chenguang Wang, Aiko Fukazawa, Shigehiro Yamaguchi, Junichi Fukuda, Uncovering different states of topological defects in schlieren textures of a nematic liquid crystal, *Scientific Reports*, 10.1038/s41598-017-16967-1, 7, 1, 2017.12, Topological defects are ubiquitously found in physical systems and therefore have been an important research subject of not only condensed matter physics but also cosmology. However, their fine structures remain elusive because of the microscopic scales involved. In the case of a liquid crystal, optical microscopy, although routinely used for the identification of liquid crystal phases and associated defects, does not have resolution high enough to distinguish fine structures of topological defects. Here we show that polarised and fluorescence microscopy, with the aid of numerical calculations on the orientational order and resulting image distortions, can uncover the structural states of topological defects with strength m = ±1 in a thin cell of a nematic liquid crystal. Particularly, defects with m = +1 exhibit four different states arising from chiral symmetry breaking and up-down symmetry breaking. Our results demonstrate that optical microscopy is still a powerful tool to identify fine states of liquid crystalline defects.. |

95. |
Andriy Nych, Junichi Fukuda, Uliana Ognysta, Slobodan Zumer, Igor Muševic, Spontaneous formation and dynamics of half-skyrmions in a chiral liquid-crystal film, *Nature Physics*, 10.1038/nphys4245, 13, 12, 1215-1220, 2017.12, Skyrmions are coreless vortex-like excitations emerging in diverse condensed-matter systems, and real-time observation of their dynamics is still challenging. Here we report the first direct optical observation of the spontaneous formation of half-skyrmions. In a thin film of a chiral liquid crystal, depending on experimental conditions including film thickness, they form a hexagonal lattice whose lattice constant is a few hundred nanometres, or appear as isolated entities with topological defects compensating their charge. These half-skyrmions exhibit intriguing dynamical behaviour driven by thermal fluctuations. Numerical calculations of real-space images successfully corroborate the experimental observations despite the challenge because of the characteristic scale of the structures close to the optical resolution limit. A thin film of a chiral liquid crystal thus offers an intriguing platform that facilitates a direct investigation of the dynamics of topological excitations such as half-skyrmions and their manipulation with optical techniques.. |

96. |
Junichi Fukuda, Slobodan Umer, Reflection spectra and near-field images of a liquid crystalline half-Skyrmion lattice, *Optics Express*, 10.1364/OE.26.001174, 26, 2, 1174-1184, 2018.01, We investigate numerically the optical properties of a hexagonal half-Skyrmion lattice exhibited by a highly chiral liquid crystal confined between two parallel plates. Our study focuses on the near and far-field reflection for normally incident light with di erent polarizations. We show that, when the wavelength of the incident light is longer than a threshold value, the reflectivity is almost insensitive to the polarization of the incident light, although the intensity profiles of the reflected light, in particular in the near-field regime, depend significantly on the polarization. The former property is attributable to the quasi two-dimensional nature of the half-Skyrmion lattice, that is, an almost uniform orientational order along the direction normal to the confining plates. Our results for the intensity of reflected light generated by evanescent as well as propagating contributions suggest that direct evidence of the formation and structure of half-Skyrmions could be provided by near-field optics with resolutions higher than that of conventional optical microscopy.. |

97. |
Junichi Fukuda, Yasushi Okumura, Hirotsugu Kikuchi, Numerical calculation of Kossel diagrams of cholesteric blue phases, *2018 Emerging Liquid Crystal Technologies XIII
Emerging Liquid Crystal Technologies XIII*, 10.1117/12.2286290, 10555, 2018.01, Kossel diagrams visualize the directions of strong Bragg reflections from a specimen with periodic ordering. They have played a pivotal role in the determination of the symmetry of cholesteric blue phases, and in the investigation of their structural changes under an electric field. In this work, we present direct numerical calculations of the Kossel diagrams of cholesteric blue phases by solving the Maxwell equations for the transmission and reflection of light incident upon a finite-thickness blue phase cell. Calculated Kossel diagrams are in good agreement with what is expected as a result of Bragg reflections, although some differences are present.. |

98. |
Kenji Tagashira, Kazuaki Z. Takahashi, Junichi Fukuda, Takeshi Aoyagi, Development of coarse-grained liquid-crystal polymer model with efficient electrostatic interaction Toward molecular dynamics simulations of electroactive materials, *Materials*, 10.3390/ma11010083, 11, 1, 2018.01, Liquid-crystal polymers (LCPs) are well known materials for functional sensor and actuators, because of their high-responsiveness to an electric field. Owing to their complex physical nature, however, the prediction of the functions of LCPs is a challenge. To attack this problem from a molecular point of view, a simulation study is a promising approach. In this work, for future applications of molecular dynamics simulations to problems involving an electric field, we develop an LCP model which consists of coarse-grained mesogenic molecules and smeared charges. For the smearing function of the electrostatic force, the Gauss error function is introduced. This smearing is optimized to attain a reasonable accuracy for phase transition phenomena of liquid crystal while numerical instabilities arising from the singularity of the Coulomb potential are circumvented. For swelling systems, our LCP model exhibits the characteristics of both liquid crystals and unentangled polymer chains; orientational order of the mesogenic units and Rouse-like relaxation dynamics. Our coarse-grained LCP model successfully incorporates electric charges and dipoles and is therefore applicable to problems concerning an electric field.. |

99. |
Misaki Takahashi, Takuma Ohkawa, Hiroyuki Yoshida, Junichi Fukuda, Hirotsugu Kikuchi, Masanori Ozaki, Orientation of liquid crystalline blue phases on unidirectionally orienting surfaces, *Journal Physics D: Applied Physics*, 10.1088/1361-6463/aaaa4b, 51, 10, 2018.02, Liquid crystalline cholesteric blue phases (BPs) continue to attract interest due to their fast response times and quasi-polarization-independent phase modulation capabilities. Various approaches have recently been proposed to control the crystal orientation of BPs on substrates; however, their basic orientation properties on standard, unidirectionally orienting alignment layers have not been investigated in detail. Through analysis of the azimuthal orientation of Kossel diagrams, we study the 3D crystal orientation of a BP material - with a phase sequence of cholesteric, BP I, and BP II - on unidirectionally orienting surfaces prepared using two methods: rubbing and photoalignment. BP II grown from the isotropic phase is sensitive to surface conditions, with different crystal planes orienting on the two substrates. On the other hand, strong thermal hysteresis is observed in BPs grown through a different liquid crystal phase, implying that the preceding structure determines the orientation. More specifically, the BP II-I transition is accompanied by a rotation of the crystal such that the crystal direction defined by certain low-value Miller indices transform into different directions, and within the allowed rotations, different azimuthal configurations are obtained in the same cell depending on the thermal process. Our findings demonstrate that, for the alignment control of BPs, the thermal process is as important as the properties of the alignment layer.. |