The Newest Release of the Ortocartan Set of Programs for Algebraic Calculations in Relativity

The program Ortocartan for algebraic calculations in relativity has just been implemented in the Codemist Standard Lisp and can now be used under the Windows 98 and Linux operating systems. The paper describes the new facilities and subprograms that have been implemented since the previous release in 1992. These are: the possibility to write the output as Latex input code and as Ortocartan's input code, the calculation of the Ellis evolution equations for the kinematic tensors of flow, the calculation of the curvature tensors from given (torsion-free) connection coefficients in a manifold of arbitrary dimension, the calculation of the lagrangian from a given metric by the Landau-Lifshitz method, the calculation of the Euler–Lagrange equations from a given lagrangian (only for sets of ordinary differential equations) and the calculation of first integrals of sets of ordinary differential equations of second order (the first integrals are assumed to be polynomials of second degree in the first derivatives of the functions).     

Mode analysis of axially-asymmetric optical resonators

The characteristics of an axially-asymmetric optical resonator(AAOR)areanalysed by using the variable reference plane method.The positions of the beam waist andthe plane wavefront are obtained.The variation of the beam size ellipse and wavefront curva-ture ellipse are also discussed.     

Vibrational spectroscopy of SnBr4 and CCl4 using Lie algebraic approach

The stretching and bending vibrational energies of SnBr₄ and CCl₄ are calculated in the one-dimensional framework. The dynamical symmetry group of tetrahedral molecule was taken into consideration to construct the model Hamiltonian in this framework. Casimir and Majorana invariant operators were also determined accordingly. Using the model Hamiltonian so constructed, we reported the vibrational energy levels of SnBr₄ and CCl₄ molecules accurately.      

Distinguishing between evidence and its explanations in the steering of atomic clocks

Quantum theory reflects within itself a separation of evidence from explanations. This separation leads to a known proof that: (1) no wave function can be determined uniquely by evidence, and (2) any chosen wave function requires a guess reaching beyond logic to things unforeseeable. Chosen wave functions are encoded into computer-mediated feedback essential to atomic clocks, including clocks that step computers through their phases of computation and clocks in space vehicles that supply evidence of signal propagation explained by hypotheses of spacetimes with metric tensor fields.     

Dynamics of fronts in optical media with linear gain and nonlinear losses

The dynamics of fronts, or kinks, in dispersive media with gain and losses is considered. It is shown that the front parameters, such as the velocity and width, depend on initial conditions. This result is not typical for dissipative systems. For exponentially decreasing initial conditions, the relations for the front parameters are found. A presence of the global bifurcation, when a soliton solution is replaced by the front solution, is demonstrated. It is also shown that in order to observe fronts, the front velocity should be larger than the characteristic velocity of the modulational instability.     

Spectral and temporal changes of optical pulses propagating through time-varying linear media

We present universal formulas for the spectral and temporal output optical fields from a linear traveling-wave medium whose refractive index changes during its propagation within the medium. These formulas agree with known changes in central wavelength and energy that are associated with adiabatic wavelength conversion (AWC). Moreover, they reveal new changes to the optical pulses that have not been noticed, such as pulse compression and spectral broadening. Most significantly, we find that AWC alters the pulse power, pulse chirp, and pulse delay. All of these effects depend on whether the central wavelength is blueshifted or redshifted, the first sign of asymmetry to be reported for AWC. These findings impact the applications of AWC to optical signal processing in microphotonic and nanophotonic structures as well as in lightwave systems.     

Causal and conformal structures of two-dimensional globally hyperbolic spacetimes

The group of conformal diffeomorphisms and the group of causal automorphisms on two-dimensional globally hyperbolic spacetimes are clarified. It is shown that if two-dimensional spacetimes have non-compact Cauchy surfaces, then the groups are subgroups of that of two-dimensional Minkowski spacetime, and if two-dimensional spacetimes have compact Cauchy surfaces, then the groups are subgroups of that of two-dimensional Einstein’s static universe. Also, the groups of such spacetimes are explicitly calculated by use of universal covering spaces.     

Outer curvature and conformal geometry of an imbedding

The differential geometry of an imbedded (e.g. string or membrane world sheet) surface in a higher-dimensional background is shown to be conveniently describable (except in the null limit case) in terms of what are designated as its first, second, and third fundamental tensors, which will have the respective symmetry properties η_μν = η_(μν) as a trivial algebraic identity, K_μν^ρ = K_(μν)^ρ as the “generalised Weingarten identity”, which is the (Frobenius type) integrability condition for the imbedding, and Ξ_λμν^ρ = Ξ_(λμν)^ρ as a “generalised Codazzi equation”, which depends on the background geometry being flat or of constant curvature, needing replacement by a more complicated expression for a generic value of the background curvature B_κλ^μ_ν. The “generalised Gauss equation” expressing the dependence on this background curvature of the internal curvature tensor R_κλ^μ_ν of the imbedded surface is converted into terms of the first and second fundamental tensors, and it is thereby demonstrated that the vanishing of the (conformally invariant) “conformation tensor”, i.e. the trace free part C_μν^ρ of the second fundamental tensor K_μv^ρ, is a sufficient condition for conformal flatness of the imbedded surface (and thus in particular for the vanishing of its (Weyl type) conformal curvature tensor C_κλ^μ_ν) provided the background is itself conformally flat. In a trio of which the first two members are the generalised Gauss and Codazzi equations, the “third” member is shown to give an expression in terms of C_μν^ρ for the (trace free, conformally invariant) “outer curvature” tensor Ω_κλ^μ_ν whose vanishing is the condition for feasibility of the natural generalisation of the Walker frame transportation ansatz. The vanishing of C_μν^ρ is shown to be sufficient in a conformally flat background for the vanishing also of Ω_κλ^μ_ν.     

用可变阶数的代数方法研究双原子体系的完全振动能谱和离解能

不同双原子分子电子态的势能(或振动能谱)的展开性质可能不同,文章将固定阶数的代数方法(AM)改进为可变阶数的代数方法,使得该方法可以研究各种不同性质(不同能量展开阶数)的双原子分子电子态,也可以解决光谱计算中可能出现的"蝴蝶效应"问题。利用阶数可变的AM方法研究了原来固定阶数的AM方法难以给出正确结果的N2-a′1Σu-,Li2+-2 2Σg+,4 He D+-X1Σ+和39 K85 Rb-(2)3Σ+等不同双核体系的完全振动能谱与离解能,不但得到了与实验数据精确相符的理论结果,还正确地预言了许多由于实验条件与技术原因而未能测得的物理数据。研究表明阶数可变的AM方法能够更广泛地用于研究各类双核电子态体系的完全振动能谱和体系离解能。     

On classification and construction of algebraic Frobenius manifolds

We develop the theory of generalized bi-Hamiltonian reduction. Applying this theory to a suitable loop algebra we recover a generalized Drinfeld–Sokolov reduction. This gives a way to construct new examples of algebraic Frobenius manifolds.     

Surface solitons at the interface between semi-infinite linear and thermal nonlinear optical media

We investigate numerically surface-wave solitons occurring at the interface between semi-infinite linear and thermal nonlinear optical media, with the refractive index of the linear medium being greater than that of the nonlinear medium (in the absence of light). We find that the threshold energy flows of the existence of the surface solitons depend on the linear refractive index difference of the two media. Their fitting empirical formula has been obtained. Furthermore, we elucidate that the optical beams propagating in thermal nonlinear optical media, either as a single surface soliton or as a dipole surface soliton, can be attracted to the surface, even when launched from far away.     

On Matter and Metric in Affine Theory of Gravity

The affine theory was conceived as a geometric model, wherein the connection field is the primary structure of the space-time. According to the program lying on the basis of this theory, metric and some sort of matter are somehow to be deduced from the connection field. In the present paper, we point out classical ways to a realization of this program. It is shown that, even in that case where the introduction of the metric seems to exclude the coupling of gravity to matter, the situation is not so hopeless as one may assume. In particular, for a symmetric Einstein tensor, it is answered the old question as to a self-consistent introduction of a metric and a metrical energy-momentum tensor controversially debated by Einstein, Eddington, and Weyl.     

Dielectric tensor and optical spectra of quaterthiophene crystals

We present an approach to the microscopic calculation of the dielectric tensor near the resonances of mechanical Frenkel excitons in a vibronic coupling regime with one effective mode. The model, applied to the prototypical quaterthiophene crystal, is based on a discrete distribution of charges for the evaluation of the molecular transition moment, whilst the coulombic interactions responsible for the exciton delocalization in the crystal are calculated by the Ewald method. From the calculated tensor we simulate absorbance and reflectance spectra and by a direct comparison with the experimental ones, we identify the origin of some shoulders present in the spectra.     

Analytic perturbative classification and assignment of eigenstates of algebraic vibrational Hamiltonians

We show how a classification and assignment for highly excited molecular vibrational states obtained previously by wave function inspection can also be obtained by analytic perturbative methods. This gives additional insight into the meaning of the classification. In addition it allows one to predict beforehand in which region of the spectrum which class of states is to be expected. As examples we present the class of states in DCO which are based on the coupling of the bend with the DC stretch, the class of states of DCO without any coupling and the bend vibrational states of acetylene at both ends of the spectrum within a given polyad. Thereby we learn the exact definition and meaning of the transverse quantum numbers. As a byproduct we get for the nonintegrable original Hamiltonian, integrable approximations which are valid in a restricted region of the phase space classically or for one class of states quantum mechanically.     

Ab-initio calculation of band structure and linear optical properties of SbSI in para- and ferroelectric phases

An ab-initio pseudopotential calculation has been performed by using density functional methods within the local density approximation (LDA) to investigate the band structure and optical properties of the ferroelectric-semiconductor SbSI in the para- and ferroelectric phases. It has been shown that SbSI has an indirect gap in both phases (1.45 eV and 1.49 eV in the para- and ferroelectric phases respectively) and that the smallest direct gap is at the S point of the Brillouin zone (1.56 eV and 1.58 eV in the para- and ferroelectric phases respectively). Furthermore, it is shown that first-order phase transition, from the paraelectric phase to the ferroelectric phase (the transiton temperature is about 22 °C), does not change the nature of the band gap. Moreover, the linear frequency dependent dielectric function, including self-energy effects, has been calculated along the c-polar axis in the para- and ferroelectric phases.      

基于局部线性嵌入的特征融合方法在岩石破裂 状态分类的应用*

为了获取岩石破裂过程有效的声发射信号特征,更好的对岩石破裂状态进行分类,提出一种基于流形学习算法的LLE特征融合方法进行数据降维。以红砂岩为研究对象设计室内单轴压缩实验采集信号,然后对原始声发射信号预处理并对信号进行特征提取,以时域、频域下的特征向量重新组合成一组新的多维特征向量,采用线性主元(PCA)和流形学习LLE算法分别进行降维。比较两种算法降维后融合特征的聚类效果二维和三维分布图,使用LLE算法降维后,四种状态分布相对更近,呈一条水平线趋势,且各状态交叉混叠数目较少,第一状态没有一个样本错判,且四个状态相比于PCA降维后的聚类效果更集中。再比较两种算法降维后融合特征的敏感度之和,LLE算法融合特征敏感度之和远大于PCA算法,说明经过LLE算法降维后得到的融合特征更多地表征了原始信号包含的局部信息同时证明了LLE算法相比PCA算法具有更好的聚类效果。最后经LLE特征融合下的砂岩破裂状态分类实验验证,融合特征后的识别率相对单一的时域特征识别提高了6%。表明该方法能显著提高岩石破裂状态分类的识别率,降维性能相对突出。