Rheology of cholesteric blue phases

Cholesteric blue phases are a spectacular example of disclination line networks. Here we numerically investigate their response to an imposed Poiseuille flow. We show that shear forces bend and twist and can unzip the disclination lines. Under gentle forcing the network opposes the flow and the apparent viscosity is large. With increased forcing we find strong shear thinning corresponding to the disruption of the network. As the viscosity starts to drop, the imposed flow sets the network into motion. Disclinations break up and re-form with their neighbors along the flow.     

A possible similarity between lyotropic cubic phases and cholesteric blue phases

Summary The common features in structures and properties of lyotropic cubic phases (LCP) and cholesteric blue phases (BP) are discussed. In both systems the cubic phases have nontrivial structures governed by frustrations. The frustration is connected with the double-twist in BPs and with the layer curvatures in LCPs. The structure of BP can be quantitatively described using the minimization of the Landau free energy with tensor order parameter. The order parameter of LCP is unknown till now; however, some minimization procedure can also be used for the solution of the phase problem. It is noted that in both systems the stable amorphous phases are observed (the fog phase or BPIII in BPs andL ₃ phase in lyotropic crystals). The importance of the observation of ?forbidden? reflections for the unequivocal identification of the space groups is emphasized. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Optical selection rules and structures of cholesteric blue phases

By deriving optical selection rules for cholesteric blue phases and considering the nature of the phase transitions between them, a structural assignment for the three experimentally observed phases of Johnson et al. is obtained. All three are argued to be bcc. A method of testing this structure assignment directly by polarized light scattering studies is also presented.     

Flexoelectric blue phases

We describe the occurrence and properties of liquid crystal phases showing two dimensional splay and bend distortions which are stabilized by flexoelectric interactions. These phases are characterized by regions of locally double splayed order separated by topological defects and are thus analogous to the blue phases of cholesteric liquid crystals. We present a mean-field analysis based upon the Landau-de Gennes Q-tensor theory and construct a phase diagram for flexoelectric structures using analytic and numerical results. We stress the similarities and discrepancies between the cholesteric and flexoelectric cases.     

Structure of blue phase III of cholesteric liquid crystals

We report large scale simulations of the blue phases of cholesteric liquid crystals. Our results suggest a structure for blue phase III, the blue fog, which has been the subject of a long debate in liquid crystal physics. We propose that blue phase III is an amorphous network of disclination lines, which is thermodynamically and kinetically stabilized over crystalline blue phases at intermediate chiralities. This amorphous network becomes ordered under an applied electric field, as seen in experiments.     

胆甾相和蓝相液晶的透射和反射特性

针对蓝相液晶显示器中的暗态漏光特性, 采用时域有限差分方法模拟计算了胆甾相液晶的平面态和焦锥态以及蓝相II态液晶的透射和反射特性, 得到了它们在正交和平行偏振片之间的漏光, 并提出了计算等效旋光能力的公式以比较它们的旋光能力. 通过对比焦锥态和蓝相液晶的旋光能力和漏光特性发现, 采用焦锥态替代蓝相液晶而得到良好的暗态特性是一种可行的方法. 通过研究它们的布拉格反射特性, 得知蓝相液晶的布拉格反射与平面态相似, 但反射强度小, 焦锥态无明显的布拉格反射特性.     

Structural investigations on smectic blue phases

Smectic blue phases ( BP(Sm)) are thermotropic liquid crystalline phases which exhibit both three-dimensional orientational order, such as classical blue phases, and smectic positional order. BP(Sm) appear as the three-dimensional counterpart of twist grain boundary phases. X-ray scattering and optical polarizing microscopy provide information on the hexagonal and cubic symmetries of these new phases.     

Confined cubic blue phases under shear

We study the behaviour of confined cubic blue phases under shear flow via lattice Boltzmann simulations. We focus on the two experimentally observed phases, blue phase I and blue phase II. The disclination network of blue phase II continuously breaks and reforms under shear, leading to an oscillatory stress response in time. The oscillations are only regular for very thin samples. For thicker samples, the shear leads to a 'stick-slip' motion of part of the network along the vorticity direction. Blue phase I responds very differently: its defect network undergoes seemingly chaotic rearrangements under shear, irrespective of system size.     

Optical activity measurements in the smectic blue phases

Optical activity measurements have been performed on the smectic blue phases ( BP _Sm), which are a new kind of chiral liquid crystal. BP _Sm exhibit both three-dimensional orientational order, like the classical blue phases, and smectic positional order. Thus, they can be viewed as the three-dimensional counterpart of the twist grain boundary phases. A comparison with the optical activity of the classical blue phases is carried out, and an estimation of the BP _Sm lattice parameter is reported for the first time. Received 25 May 2001     

Induced twisted-grain-boundary phases in the binary mixtures of a cholesteric and a nematic compound

Thermodynamical, optical-texture and dielectric studies have been performed to study the phase diagram of the binary system of 5-cholesten-3β-ol-octanoate and 4-n-nonyloxybenzoic acid. It is observed that low concentrations of 5-cholesten-3β-ol-octanoate (2–30?mol?%) in 4-n-nonyloxybenzoic acid induce a mean-field phase diagram derived by Renn within the framework of the chiral Chen–Lubenski model. Various optical textures of the twisted-grain-boundary (TGB) phases under different conditions of molecular anchoring have been observed. Weak transitions related to the TGB phases have been detected by temperature dependent dielectric spectroscopy.     

相对论教学中的若干问题

介绍了关于相对论的几个重要而有趣的问题,例如爱因斯坦如何创建狭义相对论,牛顿的水桶实验,双生子佯谬等.     

Real space calculation of a defectless director structure for the cholesteric blue phase

The defectless O⁸ structure for the cholesteric blue phase is modeled by a cubic close packing of right circular cylinders. The director configuration describes a curling mode within each cylinder. A variational calculation for the size of the unit cell is carried out and compared with experimental results. It is argued that Frank elastic terms which do not usually appear in a Landau free-energy formulation can have a significant effect on the size of the unit cell.     

有趣的费米问题

恩里科·费米(ENRICO FERMI,1901～1954),1926年成为意大利罗马大学理论物理学教授,1938年获诺贝尔物理学奖,1942年创造了第一次原子核的链式反应,带领科学进入原子时代.很少有物理学家能像他一样在理论物理和实验物理两个方面都取得如此突出的成就.     

Nonlinear quantum mechanics: Results and open questions

About 15 years ago, we (Heinz-Dietrich Doebner and I) proposed a special type of nonlinear modification of the usual Schrödinger time-evolution equation in quantum mechanics. Our equation was motivated by certain unitary representations of the group of diffeomorphisms of physical space, in the framework of either nonrelativistic local current algebra or quantum Borel kinematics. Subsequently, we developed this and related approaches to nonlinearity in quantum mechanics considerably further, to incorporate theories of measurement, groups of nonlinear gauge transformations, symmetry and invariance properties, unification of a large family of nonlinear perturbations, and possible physical contexts for quantum nonlinearity. Some of our results and highlights of some open questions are summarized.     

Exact results and open questions in first principle functional RG

Some aspects of the functional RG (FRG) approach to pinned elastic manifolds (of internal dimension d) at finite temperature T > 0 are reviewed and reexamined in this much expanded version of Le Doussal (2006) [67]. The particle limit d = 0 provides a test for the theory: there the FRG is equivalent to the decaying Burgers equation, with viscosity ν ∼ T-both being formally irrelevant. An outstanding question in FRG, i.e. how temperature regularizes the otherwise singular flow of T = 0 FRG, maps to the viscous layer regularization of inertial range Burgers turbulence (i.e. to the construction of the inviscid limit). Analogy between Kolmogorov scaling and FRG cumulant scaling is discussed. First, multi-loop FRG corrections are examined and the direct loop expansion at T > 0 is shown to fail already in d = 0, a hierarchy of ERG equations being then required (introduced in Balents and Le Doussal (2005) [36]). Next we prove that the FRG function R(u) and higher cumulants defined from the field theory can be obtained for any d from moments of a renormalized potential defined in an sliding harmonic well. This allows to measure the fixed point function R(u) in numerics and experiments. In d = 0 the beta function (of the inviscid limit) is obtained from first principles to four loop. For Sinai model (uncorrelated Burgers initial velocities) the ERG hierarchy can be solved and the exact function R(u) is obtained. Connections to exact solutions for the statistics of shocks in Burgers and to ballistic aggregation are detailed. A relation is established between the size distribution of shocks and the one for droplets. A droplet solution to the ERG functional hierarchy is found for any d, and the form of R(u) in the thermal boundary layer is related to droplet probabilities. These being known for the d = 0 Sinai model the function R(u) is obtained there at any T. Consistency of the ?=4-d expansion in one and two loop FRG is studied from first principles, and connected to shock and droplet relations which could be tested in numerics.