Reduction theory for symmetry breaking with applications to nematic systems

We formulate Euler–Poincaré and Lagrange–Poincaré equations for systems with broken symmetry. We specialize the general theory to present explicit equations of motion for nematic systems, ranging from single nematic molecules to biaxial liquid crystals. The geometric construction applies to order parameter spaces consisting of either unsigned unit vectors (directors) or symmetric matrices (alignment tensors). On the Hamiltonian side, we provide the corresponding Poisson brackets in both Lie–Poisson and Hamilton–Poincaré formulations. The explicit form of the helicity invariant for uniaxial nematics is also presented, together with a whole class of invariant quantities (Casimirs) for two-dimensional incompressible flows.     

Gauge Fields in General Parametrical Approach and Their Finslerian Reduction

The covariance principle of general relativity is extended to internal space. Associated gauge fields and tensors are systematically described, whereupon the variational principle is set up for all gauge fields by applying a Palatini-type method, thereby giving rise to an attractive self-contained theory in which the Einstein equations are intrinsically synthesized with the generalized Yang-Mills equations. General gauge-covariant physical field equations are formulated, showing that currents, external + internal spin tensors, and energy-momentum tensors can be introduced unambiguously under these general conditions and that the associated conservation laws can be derived. The electromagnetic field finds its gauge-geometric origin as the gauge field related to internal densities. To be operative with the tensor indices of external and internal types, this general theory must be bimetric. The assumptions that the gauge-covariant derivatives of metric tensors should vanish simplify the theory to the level of a Finslerian gauge approach.     

Bloch-Redfield-Wangsness theory engine implementation using symbolic processing software

We describe a general method for the automated symbolic processing of Bloch-Redfield-Wangsness relaxation theory equations for liquid-phase spin dynamics in the algebraically challenging case of rotationally modulated interactions. The processing typically takes no more than a few seconds (on a contemporary single-processor workstation) and yields relaxation rate expressions that are completely general with respect to the spectral density functions, relative orientations, and magnitudes of the interaction tensors, with all cross-correlations accounted for. The algorithm easily deals with fully rhombic interaction tensors, and is able, with little if any modification, to treat a large variety of the relaxation mechanisms encountered in NMR, EPR, and spin dynamics in general.     

Nonlinear fluctuating hydrodynamics and sequence of time scales of relaxation in supercooled liquids

Nonlinear fluctuating hydrodynamic (NFH) models for relaxation in the supercooled liquid are considered. Recent results on self consistent mode coupling theory for the slow relaxation of density fluctuations are analyzed to explain the glassy dynamics. The relaxation mechanisms for different types of models with and without wave vector dependences are discussed. For the schematic models where all wave vector dependences are dropped a sequence of time scales enters the relaxation process. For the non-ergodicity parameter very close to the ideal transition point is scaled by an exponent equal to 1/2. This is demonstrated here through an analysis of the mode-coupling equations for the wave vector dependent models that follow from equations of NFH.     

Spin gap and Luttinger liquid description of the NMR relaxation in carbon nanotubes

Recent NMR experiments by Singer et al. [Singer, Phys. Rev. Lett. 95, 236403 (2005).] showed a deviation from Fermi-liquid behavior in carbon nanotubes with an energy gap evident at low temperatures. Here, a comprehensive theory for the magnetic field and temperature dependent NMR 13C spin-lattice relaxation is given in the framework of the Tomonaga-Luttinger liquid. The low temperature properties are governed by a gapped relaxation due to a spin gap ( approximately 30 K), which crosses over smoothly to the Luttinger liquid behavior with increasing temperature.     

Dynamics of a polymer chain confined in a membrane

We present a Brownian dynamics theory with full hydrodynamics (Stokesian dynamics) for a Gaussian polymer chain embedded in a liquid membrane which is surrounded by bulk solvent and walls. The mobility tensors are derived in Fourier space for the two geometries, namely, a free membrane embedded in a bulk fluid, and a membrane sandwiched by the two walls. Within the preaveraging approximation, a new expression for the diffusion coefficient of the polymer is obtained for the free-membrane geometry. We also carry out a Rouse normal mode analysis to obtain the relaxation time and the dynamical structure factor. For large polymer size, both quantities show Zimm-like behavior in the free-membrane case, whereas they are Rouse-like for the sandwiched membrane geometry. We use the scaling argument to discuss the effect of excluded-volume interactions on the polymer relaxation time.     

Linear and angular coherence momenta in the classical second-order coherence theory of vector electromagnetic fields

A new concept of vector and tensor densities is introduced into the general coherence theory of vector electromagnetic fields that is based on energy and energy-flow coherence tensors. Related coherence conservation laws are presented in the form of continuity equations that provide new insights into the propagation of second-order correlation tensors associated with stationary random classical electromagnetic fields.     

Transient grating experiments on supercooled molecular liquids II: microscopic derivation of the phenomenological equations

The constitutive equations including the energy conservation aspect, for the long-wavelength dynamics of a liquid comprised of identical, axially symmetric, rigid molecules are microscopically derived. These equations are extended to the case where the dynamics is generated by the interactions of two coherent lasers (the pumps) with the liquid. This interaction corresponds to a weak energy absorption and also to the coupling of the pumps with fluctuations in the mass density, the molecular orientation density and the temperature of the liquid. The microscopic equations generalise those phenomenologically derived in Pick et al. [1] where the role of the temperature fluctuations was ignored. Constraints on the relaxation functions related to the temperature fluctuations and to their coupling with density are derived.     

Impurity-induced phase transition in the interacting Bose gas: 1. Analytical results

We derive selfconsistency equations for the density relaxation and the longitudinal dynamical conductivity of the interacting Bose gas at temperature zero moving in a random potential. The equations describe a disorder-induced transition from a superfluid phase to an insulating phase, where the density is non-ergodic. The interaction of the bosons is treated in random phase approximation and the coupling to the impurities is calculated within generalized selfconsistent current relaxation theory. Scaling laws are discussed and explicit results are presented for the repulsive Bosgas with neutral impurities and for the charged Bose gas with charged impurities.     

射频场照射下多自旋体系弛豫的理论计算

根据Liouville-von Neumann方程，对射频场照射下多自旋体系的弛豫进行了理论描述，并用WBR理论推导出了体系的弛豫方程组，给出了各类弛豫速率的理论计算公式.在此基础上，编制了弛豫方程组数值解的计算程序，分别用此程序和Bloch方程计算了双自旋体系在不同情况下的稳态解，并对计算结果进行了简要的分析和讨论. 关键词： 核磁共振 弛豫 射频场 多自旋体系     

Equations of the electromagnetic field in the chronometric-radial invariant formulation of the general theory of relativity

Chronometric-radial invariant (CRI) vectors of the electromagnetic field are introduced in the CRI formulation of the general theory of relativity proposed by Vladimirov. The general theory of relativity Maxwell equations for the electromagnetic field are transformed into equations for CRI quantities. It is postulated that the CRI components of vectors and tensors are the physically measurable quantities of the general theory of relativity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 110–115, February, 1992.The author is grateful to Yu. S. Vladimirov for useful discussions and interest in this work.     

Generalized thermoelsticity of the thermal shock problem in an isotropic hollow cylinder and temperature dependent elastic moduli

In this paper, we construct the equations of generalized thermoelasicity for a non-homogeneous isotropic hollow cylider with a variable modulus of elasticity and thermal conductivity based on the Lord and Shulman theory. The problem has been solved numerically using the finite element method. Numerical results for the displacement, the temperature, the radial stress, and the hoop stress distributions are illustrated graphically. Comparisons are made between the results predicted by the coupled theory and by the theory of generalized thermoelasticity with one relaxation time in the cases of temperature dependent and independent modulus of elasticity.     

Thermal Stress Analysis of a Continuous and Pulsed End-Pumped Nd:YAG Rod Crystal Using Non-Classic Conduction Heat Transfer Theory

In this paper, temperature distribution in the continuous and pulsed end-pumped Nd:YAG rod crystal is determined using nonclassical and classical heat conduction theories. In order to find the temperature distribution in crystal, heat transfer differential equations of crystal with consideration of boundary conditions are derived based on non-Fourier’s model and temperature distribution of the crystal is achieved by an analytical method. Then, by transferring non-Fourier differential equations to matrix equations, using finite element method, temperature and stress of every point of crystal are calculated in the time domain. According to the results, a comparison between classical and nonclassical theories is represented to investigate rupture power values. In continuous end pumping with equal input powers, non-Fourier theory predicts greater temperature and stress compared to Fourier theory. It also shows that with an increase in relaxation time, crystal rupture power decreases. Despite of these results, in single rectangular pulsed end-pumping condition, with an equal input power, Fourier theory indicates higher temperature and stress rather than non-Fourier theory. It is also observed that, when the relaxation time increases, maximum amounts of temperature and stress decrease.     

Yang's Gravitational Theory

Yang's pure space equations generalize Einstein's gravitational equations, while coming from gauge theory. We study these equations from a number of vantage points: summarizing the work done previously, comparing them with the Einstein equations and investigating their properties. In particular, the initial value problem is discussed and a number of results are presented for these equations with common energy-momentum tensors.     

向列相液晶沿面到垂面排列转变的分子场理论

以摩擦基板间的液晶薄层为研究对象,用分子场理论研究了向列相液晶分子排列转变行为.分子质心固定在简单立方晶格的格点上.液晶由极性分子构成,与基板相接触的一层分子同时受到色散和极性两类表面作用.通过自洽的数值计算,获得3种相图,清楚地展示了摩擦基板间向列相出现的从高温沿面到低温垂面排列的转变;获得实现这类转变所需要的两类表面作用的参数范围.结果表明:基板的摩擦会改变基板表面色散作用,但不会影响基板表面极性作用;表面极性相互作用能引起基板间向列相液晶发生沿面到垂面排列转变.     

Hydrogen bonding effects on the (15)N and (1)H shielding tensors in nucleic acid base pairs

The results of systematic ab initio calculations of (15)N and (1)H chemical shielding tensors in the GC base pair as a function of hydrogen bond length are presented for the first time. The hydrogen bond length characterized by the distance r(N...N) between purine N1 and pyrimidine N3 was varied between 2.57 and 3.50 A and the chemical shift tensors were calculated by the sum-over-states density functional perturbation theory. It is shown that the hydrogen bond length has a strong effect on the chemical shielding tensor of both imino proton and nitrogen, on their orientation, and, as a consequence, on the relaxation properties of both nuclei. For a nitrogen nucleus not involved in hydrogen bonding, the shielding tensor is nearly axially symmetric and almost collinear with the bond vector. As the length of the hydrogen bond decreases, the least shielding component sigma(11) deflects from the N-H vector and the shielding tensor becomes increasingly asymmetric. The significance of the presented results for the analysis of relaxation data and the efficiency of TROSY effects together with a summary of the relevant shielding parameters are presented and discussed.     

Shear Viscosity and Temperature Inequalities for Multi-Species Plasmas

The first coefficients in the orthogonal expansions of the velocity distribution functions with respect to Grad's tensorial (three-dimensional) Hermite polynomials are shown to be proportional to ther-modynamic fluxes, if the weight functions are local Maxwellians centered at the mean mass velocity and widened with a mean temperature. Balance equations for the stress tensors are established and reduced to linear algebraic systems under certain restrictions. Explicit solutions for the traces and the tracefree parts of the stress tensors are given.     

Determination of the 19F NMR chemical shielding tensor and crystal structure of 5-fluoro-dl-tryptophan

5-Fluoro-dl-tryptophan (5F-Trp) is a very sensitive probe used to investigate orientation and dynamics of biomacromolecules at the in situ level. In order to establish a (19)F NMR strategy, the crystal structure and (19)F chemical shielding tensor of 5F-Trp are reported. A novel approach was developed to use F-F homonuclear dipole-dipole coupling information to analyze single-crystal NMR data without determining crystal orientations. The measured values for the principal components of the shielding tensor are sigma(11)=0.9, sigma(22)=-63.3, and sigma(33)=-82.9 ppm relative to TFA in D(2)O. The principal axes of the shielding tensors coincide with the indole ring symmetry, which makes it a straightforward and powerful tool to monitor protein alignment in oriented environments. Hartree-Fock (HF) and density functional theory (DFT) calculations of the chemical shielding tensors are also reported.