Non-linear rheology of lamellar liquid crystals

We measure the non-linear relation between the shear stress and shear rate in the lyotropic lamellar phase of C₁₂E₅ /water system. The measured shear thinning exponent changes with the surfactant concentration. A simple rheology theory of a lamellar or smectic phase is proposed with a prediction ∼ σ^3/2 , where is the shear rate and σ is the shear stress. We consider that the shear flow passed through the defect structure causes the main dissipation. As the defect line density varies with the shear rate, the shear thinning arises. The defect density is estimated by the dynamic balance between the production and annihilation processes. The defect production is caused by the shear-induced layer undulation instability. The annihilation occurs through the shear-induced defect collision process. Further flow visualization experiment shows that the defect texture correlates strongly with the shear thinning exponent.     

The two-dimensional Peierls-Nabarro model for interfacial misfit dislocation networks of cubic lattice

A model is developed to investigate the two-dimensional interfacial misfit dislocation networks that follows the original Peierls-Nabarro idea. Structure and energies of heterophase interfaces are considered for the cubic lattice. To examine the energy contribution of misfit dislocations, where interactions between two dislocation arrays are concerned, a generalized stacking fault energy is proposed. Combined with first-principles calculations, we apply this model to a practical metal-ceramic example: the Ag/MgO(100) interface. An important correction to the adhesive energy is proposed in addition to its dislocation structure being confirmed.     

Nash Bosonization in Path Integral for Quantum Riemannian Geometry

We propose an effective quantum theory for Einstein Gravitation theory by making use of the Nash Theorem of Riemann Metrics parametrized by immersions. We show the usefulness of this phenomenological (low energy) path integral bosonization scheme through the evaluation for the Classical Newton potential by means of a Wilson loop path integral evaluation.     

Cosmological dynamics in tomographic probability representation

The probability representation for quantum states of the universe in which the states are described by a fair probability distribution instead of wave function (or density matrix) is developed to consider cosmological dynamics. The evolution of the universe state is described by standard positive transition probability (tomographic transition probability) instead of the complex transition probability amplitude (Feynman path integral) of the standard approach. The latter one is expressed in terms of the tomographic transition probability. Examples of minisuperspaces in the framework of the suggested approach are presented. Possibility of observational applications of the universe tomographs are discussed.     

甲醛和过氧化氢分子振动光谱的路径积分刘维尔动力学模拟

本文采用路径积分刘维尔动力学计算偶极矩时间导数的关联函数来得到红外光谱,通过与真实振动频率相比,发现路径积分刘维尔动力学可以比较忠实地描述振动动力学过程中的核量子效应,能够准确刻画系统温度变化和同位素取代效应引起的振动光谱变化.     

Elastic theory of icosahedral quasicrystals - application to straight dislocations

In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We have calculated approximate solutions for the elastic fields induced by two-, three- and fivefold straight screw- and edge-dislocations in infinite icosahedral quasicrystals by means of a generalized perturbation method. Starting from the solution for elastic isotropy in phonon and phason spaces, corrections of higher order reflect the two-, three- and fivefold symmetry of the elastic fields surrounding screw dislocations. The fields of special edge dislocations display characteristic symmetries also, which can be seen from the contributions of all orders. Received 21 February 2001 and Received in final form 27 June 2001     

Defects in smectic C* liquid crystals

We consider the structure and properties of various topological defects that can occur in smectic C* liquid crystals. The polarization field associated with disclinations, the effect of incommensuration on the structure of dispirations, some interesting situations in the interaction between dispiration and disclination and between dispirations themselves have been discussed in detail. The properties of cholesteric type disclinations and a possible model for the core structure of a wedge disclination have also been dealt with. The author felicitates Prof. D S Kothari on his eightieth birthday and dedicates this paper to him on this occasion.     

Whole diffraction pattern-fitting of polycrystalline fcc materials based on microstructure

A method is proposed for modelling the complete diffraction pattern of fcc polycrystalline materials. The algorithm permits a simultaneous refinement of several parameters related to microstructure and lattice defects responsible for line broadening effects. Linear (dislocations) and planar (stacking faults) defects are considered in detail, together with the effect of size and shape of coherent scattering domains (crystallites). Experimentally observed profiles are modelled by Voigt functions, whose parameters are connected with those describing the dislocation field (dislocation density, outer cut-off radius, average contrast factor), twin and deformation fault probabilities, and domain size, also considering the effect of a symmetrical instrumental profile. Domain shape is assumed spherical, with a lognormal distribution of diameters; however, the approach can be generalised to different shapes and size distributions. The proposed algorithm can be extended to other crystalline structures, and can be used within the Rietveld method or as a Whole Powder Pattern Fitting (WPPF), as in the present work. Received 16 May 2000     

Primordial black hole formation by stabilized embedded strings in the early universe

Primordial black hole formation by cosmic string collapses is reconsidered in the case where the winding number of the string is larger than unity. The line energy density of a multiple winding string becomes greater than that of a single winding string so that the probability of black hole formation by string collapse during loop oscillation would be strongly enhanced. Moreover, this probability could be affected by changes in gravity theory due to large extra dimensions based on the brane universe model. In addition, a wider class of strings which are stable compared to conventional cosmic strings can contribute to such a scenario. Although the production of the multiple winding defect is suppressed and its number density should be small, the enhancement of black hole formation by the increased energy density may provide a large number of evaporating black holes in the present universe which gives more stringent constraints on the string model compared to the ordinary string scenario.     

Path integral formulation for quantized fermion and boson fluids

An isomorphism between fully quantized fermion and boson fluids and classical polymer mixtures is used as a point of departure to initiate an analytic treatment of quantum fluids.     

基于积分LOS的多无人艇协同路径跟踪

该文针对欠驱动无人艇的编队跟踪控制问题,考虑模型参数不确定和外界风浪流干扰的影响,设计了基于LOS的算法。首先,为了使三艘无人艇保持协同,设计了协同一致性控制算法,并且所有的跟随者之间的通信网络是无向的,保证每艘无人艇之间都能互相通信。其次,基于LOS算法,设计了偏航控制器和艏摇控制器,使得无人艇可以在洋流干扰下实现路径跟踪。针对控制器中的未知参数,设计了基于自适应算法的观测器,对未知参数进行估计。仿真结果验证了所提出的控制方法的有效性。     

A causal quantum theory in phase space

The causal theory for the coherent state representation of quantum mechanics is derived. The general conditions for the classical limit are given and it is shown that phase space classical mechanics can be obtained as a limit even for stationary states, in contrast to the de Broglie-Bohm quantum theory of motion.     

Incompatibility of gauge invariance and nonrelativistic locality in path integral formulation

It is shown that a modification of the usual gauge transformations is essential to the path integral formulation of nonrelativistic quantum mechanics as a consequence of defining the locality condition as follows: The contribution from each path comes entirely from the points on the path. Arguments are based on the similarity between Wiener and Feynman functional (path) integrals.     

An alternative formulation of Hall effect and quantum phases in noncommutative space

A recent method of constructing quantum mechanics in noncommutative coordinates, alternative to implying noncommutativity by means of star product is discussed. Within this approach we study Hall effect as well as quantum phases in noncommutative coordinates. The θ-deformed phases which we obtain are velocity independent.     

A Rigorous Path Integral Construction in any Dimension

A rigorous path integral construction for a wide class of Weyl evolution operators is based on a pseudo-differential -calculus on flat phase spaces of finite and infinite dimensions.     

Peaks in the CMBR power spectrum. I. Mathematical analysis of the associated real space features

The purpose of our study is to understand the mathematical origin in real space of modulated and damped sinusoidal peaks observed in cosmic microwave background radiation anisotropies. We use the theory of the Fourier transform to connect localized features of the two-point correlation function in real space to oscillations in the power spectrum. We also illustrate analytically and by means of Monte Carlo simulations the angular correlation function for distributions of filled disks with fixed or variable radii capable of generating oscillations in the power spectrum. While the power spectrum shows repeated information in the form of multiple peaks and oscillations, the angular correlation function offers a more compact presentation that condenses all the information of the multiple peaks into a localized real space feature. We have seen that oscillations in the power spectrum arise when there is a discontinuity in a given derivative of the angular correlation function at a given angular distance. These kinds of discontinuities do not need to be abrupt in an infinitesimal range of angular distances but may also be smooth, and can be generated by simply distributing excesses of antenna temperature in filled disks of fixed or variable radii on the sky, provided that there is a non-null minimum radius and/or the maximum radius is constrained.     

Elastic theory of defects in toroidal crystals

We report a comprehensive analysis of the ground-state properties of axisymmetric toroidal crystals based on the elastic theory of defects on curved substrates. The ground state is analyzed as a function of the aspect ratio of the torus, which provides a non-local measure of the underlying Gaussian curvature, and the ratio of the defect core energy to the Young modulus. Several structural features are discussed, including a spectacular example of curvature-driven amorphization in the limit of the aspect ratio approaching one. The outcome of the elastic theory is then compared with the results of a numerical study of a system of point-like particles constrained on the surface of a torus and interacting via a short-range potential. Electronic supplementary material  Supplementary material in the form of a pdf file available from the journal web page at and are accessible for authorised users.