Non-minimal coupling of torsion–matter satisfying null energy condition for wormhole solutions

We explore wormhole solutions in a non-minimal torsion–matter coupled gravity by taking an explicit non-minimal coupling between the matter Lagrangian density and an arbitrary function of the torsion scalar. This coupling describes the transfer of energy and momentum between matter and torsion scalar terms. The violation of the null energy condition occurred through an effective energy-momentum tensor incorporating the torsion–matter non-minimal coupling, while normal matter is responsible for supporting the respective wormhole geometries. We consider the energy density in the form of non-monotonically decreasing function along with two types of models. The first model is analogous to the curvature–matter coupling scenario, that is, the torsion scalar with T-matter coupling, while the second one involves a quadratic torsion term. In both cases, we obtain wormhole solutions satisfying the null energy condition. Also, we find that the increasing value of the coupling constant minimizes or vanishes on the violation of the null energy condition through matter.     

Rigorous Estimates of the Tails of the Probability Distribution Function for the Random Linear Shear Model

In previous work Majda and McLaughlin, and Majda computed explicit expressions for the 2Nth moments of a passive scalar advected by a linear shear flow in the form of an integral over R ^N . In this paper we first compute the asymptotics of these moments for large moment number. We are able to use this information about the large-N behavior of the moments, along with some basic facts about entire functions of finite order, to compute the asymptotics of the tails of the probability distribution function. We find that the probability distribution has Gaussian tails when the energy is concentrated in the largest scales. As the initial energy is moved to smaller and smaller scales we find that the tails of the distribution grow longer, and the distribution moves smoothly from Gaussian through exponential and stretched exponential. We also show that the derivatives of the scalar are increasingly intermittent, in agreement with experimental observations, and relate the exponents of the scalar derivative to the exponents of the scalar.     

Parameterized post-Newtonian approximation in a teleparallel model of dark energy with a boundary term

We study the parameterized post-Newtonian approximation in teleparallel model of gravity with a scalar field. The scalar field is non-minimally coupled to the scalar torsion as well as to the boundary term introduced in Bahamonde and Wright (Phys Rev D 92:084034 arXiv:1508.06580v4 [gr-qc], 2015). We show that, in contrast to the case where the scalar field is only coupled to the scalar torsion, the presence of the new coupling affects the parameterized post-Newtonian parameters. These parameters for different situations are obtained and discussed.     

不同模式耦合下偏振模色散几率分布的研究

研究了偏振模色散的统计特性,在不同模式耦合条件下,应用蒙特-卡罗方法模拟偏振模色散矢量的几率分布,并对模拟结果进行了函数拟合。发现随着耦合次数增加差分群时延的几率分布从一个类似δ函数分布逐渐过渡到麦克斯韦分布;在一定的耦合下,几率分布可以呈现高斯分布。对偏振模矢量的两个方向余弦进行统计分析,发现随着耦合次数的增加,偏振模矢量两个方向余弦函数的分布从高斯分布和δ函数分布都变为均匀分布。     

横向激发线偏振高斯光束的非傍轴传输

文章提出一种横向激发的任意线偏振高斯光束,该光束场量的模与传统的任意线偏振高斯光束具有相同的模,在源场区,其满足自由空间无源场的场方程。同时利用瑞利—索末菲衍射积分对该高斯光束的非傍轴传输特性进行了解析研究,给出了空间光强分布、束腰和远场发散角的解析通式,发现该类光束的远场光强呈一平顶空心光束。     

Influence of conformation on electron transport properties of oligophenyleneimine molecular wires

We propose molecular wires based on oligophenyleneimine (OPI) sandwiched between two gold electrodes. The electron transport properties of molecular wires attached to side groups are investigated using steady-state theoretical model and density functional theory by using GAUSSIAN 09 software. We investigate the influence of the side group and torsion angle on the electronic properties of molecular wires. We calculate the spatial distribution of the frontier orbitals, energy gap, transmission probability and the current rectifying ratio for OPI, OPI-pyridine, OPI-pyrazine, OPI-thiophene and OPI-thiazole. The transmission spectra change remarkably depending on the type of side group and torsion angle. The current rectifying ratio will increase by increasing the difference between torsion angles depending on the type of side group. That means the OPI-side group can be employed in molecular electronics.     

Greybody factor for a scalar field coupling to Einstein's tensor

We study the greybody factor and Hawking radiation for a scalar field coupling to Einstein's tensor in the background of Reissner–Nordström black hole in the low-energy approximation. We find that the presence of the coupling terms modifies the standard results in the greybody factor and Hawking radiation. Our results show that both the absorption probability and Hawking radiation increase with the coupling constant. Moreover, we also find that for the stronger coupling, the charge of black hole enhances the absorption probability and Hawking radiation of the scalar field, which is different from those of ones without coupling to Einstein's tensor in the black hole spacetime.     

Statistics of tumbling of a single polymer molecule in shear flow

We present experimental results on statistics of polymer orientation angles relative to the shear plane and tumbling times in shear flow with thermal noise. The strong deviation of the probability distribution functions (PDFs) of the orientation angles from Gaussian PDFs was observed in good accord with theory. A universal exponential PDF tail for the tumbling times and its predicted scaling with Wi (that is, the dimensionless shear rate normalized by the polymer relaxation time) are also tested experimentally against numerics. The scaling relations of PDF widths for both angles as a function of Wi are verified and compared with numerics.     

天文光纤机械扰模器调制环形光场的实验研究

光纤入射光束的角度和位置的变化对光纤出射光束的远场光强分布有较大影响。通过分析光纤出射光场的光强分布,研究了斜光束的偏轴角对光纤出射光场的影响。光纤耦合理论说明光纤的宏弯曲会使光纤内部模式相互耦合,根据这一原理设计一种能使光纤宏弯曲并以此来改善光纤出射场分布的机械扰模器。在实验中,对不同偏轴角入射及处于不同扰模程度的光斑进行中值滤波、高斯拟合等处理,得到光斑的径向光强分布曲线、高斯拟合度、不同出射焦比范围的能量变化等参数,以此分析机械扰模器的扰模效果。     

The gauge-invariant N=2 supersymmetric σ-model with general scalar potential

We construct the supersymmetric σ-model, in six dimensions, for an arbitrary hyper-Kähler manifold, and its minimal coupling to super-Yang-Mills theory. Non-trivial reduction to five or four dimensions yields the corresponding five- or four-dimensional N = 2 supersymmetric model with general scalar potential. We discuss briefly the coupling to supergravity in six dimensions and we give the on-shell supergravity torsion constraints.     

Determination of the backbone torsion psi angle by tensor correlation of chemical shift anisotropy and heteronuclear dipole-dipole interaction

We demonstrate that the backbone torsion psi angle of a uniformly labeled residue can be determined accurately by correlating the chemical shift anisotropy of the carbonyl carbon and the 13C-1H heteronuclear dipole-dipole interaction of the alpha carbon. To obtain the highest sensitivity for the psi angle determination, the following conditions are desired: (i) the recoupling pulse sequences for the CSA and the heteronuclear dipolar interactions are gamma encoded, in which the spatial parts of m=2 are selected; (ii) the homonuclear polarization transfer is based on the scalar spin-spin coupling. Experimental data were obtained for [U-13C, 15N]-alanine and N-acetyl-[U-13C, 15N]-d,l-valine under magic-angle spinning at 25kHz. Only three data points are required for the measurements and the dihedral angles determined are in excellent agreement with the diffraction data.     

Sources of and solutions to problems in the refinement of protein NMR structures against torsion angle potentials of mean force

It is often the case that a substantial number of torsion angles (both backbone and sidechain) in structures of proteins and nucleic acids determined by NMR are found in physically unlikely and energetically unfavorable conformations. We have previously proposed a database-derived potential of mean force comprising one-, two-, three-, and four-dimensional potential surfaces which describe the likelihood of various torsion angle combinations to bias conformational sampling during simulated annealing refinement toward those regions that are populated in very high resolution (< or =1.75 A) crystal structures. We now note a shortcoming of our original implementation of this approach: namely, the forces it places on atoms are very rough. When the density of experimental restraints is low, this roughness can both hinder convergence to commonly populated regions of torsion angle space and reduce overall conformational sampling. In this paper we describe a modification that completely eliminates these problems by replacing the original potential surfaces by a sum of multidimensional Gaussian functions. Structures refined with the new Gaussian implementation now simultaneously enjoy excellent global sampling and excellent local choices of torsion angles.     

Probability Distribution Function of Passive Scalars in Shell Models

A shell-model version of passive scalar problem is introduced, which is inspired by the model of K. Ohkitani and M. Yakhot [K. Ohkitani and M. Yakhot, Phys. Rev. Lett. 60 (1988) 983; K. Ohkitani and M. Yakhot, Prog. Theor. Phys. 81 (1988) 329]. As in the original problem, the prescribed random velocity field is Gaussian and δ correlated in time. Deterministic differential equations are regarded as nonlinear Langevin equation. Then, the Fokker-Planck equations of PDF for passive scalars are obtained and solved numerically. In energy input range (n<5, n is the shell number.), the probability distribution function (PDF) of passive scalars is near the Gaussian distribution. In inertial range (5≤n≤16) and dissipation range (n≥17), the probability distribution function (PDF) of passive scalars has obvious intermittence. And the scaling power of passive scalar is anomalous. The results of numerical simulations are compared with experimental measurements.     

An Explicit Family of Probability Measures for Passive Scalar Diffusion in a Random Flow

We explore the evolution of the probability density function (PDF) for an initially deterministic passive scalar diffusing in the presence of a uni-directional, white-noise Gaussian velocity field. For a spatially Gaussian initial profile we derive an exact spatio-temporal PDF for the scalar field renormalized by its spatial maximum. We use this problem as a test-bed for validating a numerical reconstruction procedure for the PDF via an inverse Laplace transform and orthogonal polynomial expansion. With the full PDF for a single Gaussian initial profile available, the orthogonal polynomial reconstruction procedure is carefully benchmarked, with special attentions to the singularities and the convergence criteria developed from the asymptotic study of the expansion coefficients, to motivate the use of different expansion schemes. Lastly, Monte-Carlo simulations stringently tested by the exact formulas for PDF’s and moments offer complete pictures of the spatio-temporal evolution of the scalar PDF’s for different initial data. Through these analyses, we identify how the random advection smooths the scalar PDF from an initial Dirac mass, to a measure with algebraic singularities at the extrema. Furthermore, the Péclet number is shown to be decisive in establishing the transition in the singularity structure of the PDF, from only one algebraic singularity at unit scalar values (small Péclet), to two algebraic singularities at both unit and zero scalar values (large Péclet).     

Is turbulent mixing a self-convolution process?

Experimental results for the evolution of the probability distribution function (PDF) of a scalar mixed by a turbulent flow in a channel are presented. The sequence of PDF from an initial skewed distribution to a sharp Gaussian is found to be nonuniversal. The route toward homogeneization depends on the ratio between the cross sections of the dye injector and the channel. In connection with this observation, advantages, shortcomings, and applicability of models for the PDF evolution based on a self-convolution mechanism are discussed.     

Variational analysis of Er:Ti:LiNbO3 waveguide lasers based on Gaussian/two-half Gaussian mode field distribution

Starting with two dimensional, scalar wave equation, a variational equation was established for the fundamental TE and TM modes guided in Ti:LiNbO₃ waveguides on the basis of assuming a symmetric Gaussian mode field function in the width direction and two-half Gaussian trial functions in the depth direction. The controllable waveguide fabrication parameters, including channel width, diffusion temperature, initial Ti-strip thickness and diffusion time, dependent of fundamental mode size, effective pump area, coupling efficiency between pump and laser modes, and the coupling loss between a Ti:LiNbO₃ waveguide and a fiber were numerically calculated for Z-cut Er:Ti:LiNbO₃ channel waveguide lasers at three possible emission wavelengths 1532,1563 and 1576 nm and two possible pump wavelengths 1480 and 980 nm. The calculated results were compared with those of Gaussian/Hermite–Gaussian mode field distribution in detail.     

Chiral Asymmetry and the Spectral Action

We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter.     

Universal statistics of the critical depinning force of elastic systems in random media

We study the rescaled probability distribution of the critical depinning force of an elastic system in a random medium. We put in evidence the underlying connection between the critical properties of the depinning transition and the extreme value statistics of correlated variables. The distribution is Gaussian for all periodic systems, while in the case of random manifolds there exists a family of universal functions ranging from the Gaussian to the Gumbel distribution. Both of these scenarios are a priori experimentally accessible in finite, macroscopic, disordered elastic systems.