主动光学技术在制造标准大反射镜中的应用

介绍了利用主动光学技术校正大型标准反射镜残余面形误差和重力变形的方法 ,研制了用于施加局部作用力的工具———机械式作动器的结构与性能 ,作用力的测定方法 ;位于不同位置的作用力引起的镜面变形量的测定与分析 ,与镜面最小面形误差对应的作动器作用力控制矩阵的求解等。对一块Φ2 30mm、中心厚 18mm、R880mm、玻璃材料为K 9的标准球面镜进行了面形误差校正实验 ,取得了较明显的校正效果。     

Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes

A new technique is introduced in order to solve the following question:When is a complete spacelike hypersurface of constant mean curvature in a generalized Robertson-Walker spacetime totally umbilical and a slice? (Generalized Robertson-Walker spacetimes extend classical Robertson-Walker ones to include the cases in which the fiber has not constant sectional curvature.) First, we determine when this hypersurface must be compact. Then, all these compact hypersurfaces in (necessarily spatially closed) spacetimes are shown to be totally umbilical and, except in very exceptional cases, slices. This leads to proof of a new Bernstein-type result. The power of the introduced tools is also shown by reproving and extending several known results.     

Tensor ABCD law for partially coherent twisted anisotropic Gaussian-Schell model beams

A 4 x 4 complex curvature tensor M>(-1) is introduced to describe partially coherent anisotropic Gaussian-Schell model (GSM) beams. An analytical propagation formula for the cross-spectral density of partially coherent anisotropic GSM beams is derived. The propagation law of M(-1) that is also derived may be called partially coherent tensor ABCD law. The analytical formulas presented here are useful in treating the propagation and transformation of partially coherent anisotropic GSM beams, which include previous results for completely coherent Gaussian beams as special cases.     

Raychaudhuri equation in quantum gravitational optics

The equation of Raychaudhuri is one of the key concepts in the formulation of the singularity theorems introduced by Penrose and Hawking. In the present article, taking into account QED vacuum polarization, we study the propagation of a bundle of rays in a background gravitational field through the perturbative deformation of Raychaudhuri’s equation. In a sense, this could be seen as another semiclassical study in which geometry is treated classically but matter (which means the photon here) is allowed to exhibit quantum characteristics that are encoded in its coupling to the background curvature.      

Polarization phase shifting shearography for optical metrological applications

We present here a different and modified configuration in order to obtain the curvature fringes by incorporating phase shifting and image processing techniques. Optical fibers are used for obtaining shear fringes in which we have used Wollaston prism as the shear element.     

Non‐linear Realizations and Higher Curvature Supergravity

We focus on non‐linear realizations of local supersymmetry as obtained by using constrained superfields in supergravity. New constraints, beyond those of rigid supersymmetry, are obtained whenever curvature multiplets are affected as well as higher derivative interactions are introduced. In particular, a new constraint, which removes a very massive gravitino is introduced, and in the rigid limit it merely reduces to an explicit supersymmetry breaking. Higher curvature supergravities free of ghosts and instabilities are also obtained in this way. Finally, we consider direct coupling of the goldstino multiplet to the super Gauss–Bonnet multiplet and discuss the emergence of a new scalar degree of freedom.     

Phase aberration compensation of digital holographic microscopy based on least squares surface fitting

Digital holographic microscopy allows the numerical reconstruction of the complex wavefront of samples, especially biological samples such as living cells. In digital holographic microscopy, a microscope objective is introduced to improve the transverse resolution of the sample; however a phase aberration in the object wavefront is also brought along, which will affect the phase distribution of the reconstructed image. We propose here a numerical method to compensate for the phase aberration of thin transparent objects with a single hologram. The least squares surface fitting with points number less than the matrix of the original hologram is performed on the unwrapped phase distribution to remove the unwanted wavefront curvature. The proposed method is demonstrated with the samples of the cicada wings and epidermal cells of garlic, and the experimental results are consistent with that of the double exposure method.     

Dark energy,curvature, and cosmic coincidence

The fact that the energy densities of dark energy and matter are similar currently, known as the coincidence problem, is one of the main unsolved problems of cosmology. We present here a model in which a spatial curvature of the universe can lead to a transition in the present epoch from a matter dominated universe to a scaling dark energy dominance in a very natural way. In particular, we show that if the exponential potential of the dark energy field depends linearly on the spatial curvature density of a closed universe, the observed values of some cosmological parameters can be obtained assuming acceptable values for the present spatial curvature of the universe, and without fine tuning in the only parameter of the model. We also comment on possible variations of this model, and realistic scenarios in which it could arise.     

异质结构的应变和应力分布模型研究

基于组合杆的平衡条件，分别建立了晶格失配、热失配以及由两者共同导致的异质结构应变 和应力分布模型，并获得了异质结构的晶格失配应变、热失配应变、弯曲应变以及曲率半径 的分析解. 同时，运用所建的模型，计算了HgCdTe/CdZnTe异质结构的应变和应力分布.结果 表明：应力最大值均在界面处，而中性面仅是材料厚度和弹性参数的函数，与晶格失配、晶 格弛豫、热失配等参数无关，且该异质结构的曲率半径是衬底厚度的函数，随衬底厚度的减 小而减小，而要保证HgCdTe/CdZnTe器件在液氮温度下不发生断裂，衬底的厚度必须大于临界值. 关键词： 异质结构 应变分布模型 应力分布模型 晶格失配     

The effects of strain and curvature on the mass burning rate of premixed laminar flames

The Markstein number characterizes the effect that flame stretch has on the burning velocity. Different expressions for this number are deduced from integral analysis. According to a phenomenological law, the Markstein number can be separated into a part for the curvature of the flame and a part for the straining of the flow. This separation is analysed here. It appears that the Markstein number for curvature and the combined one for both curvature and strain are unique. It is, however, not possible to introduce a separate and unique Markstein number for the flow straining that can be used to describe its influence in different combustion situations. The theoretical and numerical analysis is applied to flat steady counterflow flames as well as to steady, imploding and expanding spherical flames.     

On Curvature Decay in Expanding Cosmological Models

Consider a globally hyperbolic cosmological spacetime. Topologically, the spacetime is then a compact 3-manifold in cartesian product with an interval. Assuming that there is an expanding direction, is there any relation between the topology of the 3-manifold and the asymptotics? In fact, there is a result by Michael Anderson, where he obtains relations between the long-time evolution in General Relativity and the geometrization of 3-manifolds. In order to obtain conclusions however, he makes assumptions concerning the rate of decay of the curvature as proper time tends to infinity. It is thus of interest to find out if such curvature decay conditions are always fulfilled. We consider here the Gowdy spacetimes, for which we prove that the decay condition holds. However, we observe that for general Bianchi VIII spacetimes, the curvature decay condition does not hold, but that some aspects of the expected asymptotic behaviour are still true.     

Least-squares estimation for hybrid curvature wavefront sensors

In this paper general purpose weighted least-squares algorithms are introduced for use with hybrid sensors that provide slope and full curvature measurements, including the twist curvature. The algorithms are formulated for the traditional Fried and Southwell sampling geometries, as well as for a novel geometry specific to hybrid sensors. The estimation accuracy of the hybrid and Shack-Hartmann sensors are compared through simulations performed on phase screens that obey Kolmogorov turbulence theory.     

First-principle calculations of the Berry curvature of Bloch states for charge and spin transport of electrons

Recent progress in wave packet dynamics based on the insight of Berry pertaining to adiabatic evolution of quantum systems has led to the need for a new property of a Bloch state, the Berry curvature, to be calculated from first principles. We report here on the response to this challenge by the ab initio community during the past decade. First we give a tutorial introduction of the conceptual developments we mentioned above. Then we describe four methodologies which have been developed for first-principle calculations of the Berry curvature. Finally, to illustrate the significance of the new developments, we report some results of calculations of interesting physical properties such as the anomalous and spin Hall conductivity as well as the anomalous Nernst conductivity and discuss the influence of the Berry curvature on the de Haas-van Alphen oscillation.     

A generalization of the concept of constant mean curvature and canonical time

Some compact spaces of achronal hypersurfaces are constructed in various types of space-time. A variational principle is introduced on these spaces, smooth extremals of which are spacelike hypersurfaces of constant mean curvature. The integrand of the variational principle is shown to be upper semicontinuous and the direct methods of the calculus of variations are applied to obtain aC ⁰ extremal, which is defined to be a spacelike hypersurface of generalized constant mean curvature. The family of such hypersurfaces generated by altering the value of the mean curvature is discussed and the mean curvature itself is shown to have many of the properties of a canonical time coordinate.     

A MODEL OF CURVATURE,TORSION AND STRONG GRAVIEY

In this paper the stress-energy tensors of curvature and of torsion are introduced.We may derived a model of strong gravity from Einstein's equation with the stress-energy tensor of torsion,while Einstein's equation with the stressenergy tensor of curvature is an inconsistent equation.This conclusion is different from the Poincare gauge theories of gravitation,in which the curvature is directly proportional to the strong coupling.     

Determination of the metric from the curvature

A method of calculating the metric from the curvature is presented. Assuming that a tensor with the symmetry properties of a type D curvature tensor is given in an orthonormal tetrad, we use the Bianchi identities and the relationship between the connection and the tetrad in order to calculate, under certain assumptions, the corresponding metric. Some well-known metrics are derived from the curvature by using the method given here.     

A spectrally refined interface approach for simulating multiphase flows

This paper presents a novel approach to phase-interface transport based on pseudo-spectral sub-grid refinement of a level set function. In each flow solver grid cell, a set of quadrature points is introduced on which the value of the level set function is known. This methodology allows to define a polynomial reconstruction of the level set function in each cell. The transport is performed using a semi-Lagrangian technique, removing all constraints on the time step size. Such an approach provides sub-cell resolution of the phase-interface and leads to excellent accuracy in the transport, while a reasonable cost is obtained by pre-computing some of the metrics associated with the polynomials. To couple this approach with a flow solver, an converging curvature computation is introduced. First, a second order explicit distance to the sub-grid interface is reconstructed on the flow solver mesh. Then, a least squares approach is employed to extract the curvature from this distance function. This technique is found to combine the high accuracy and good conservation found in the particle level set method with the converging curvature usually obtained with classical high order PDE transport of the level set function. Tests are presented for both transport as well as two-phase flows, that suggest that this technique is capable of retaining the thin liquid structures that are expected in turbulent atomization of liquids.     

A Complete Classification of Curvature Collineations of Cylindrically Symmetric Static Metrics

Curvature collineations are symmetry directions for the Riemann tensor, as isometries are for the metric tensor and Ricci collineations are for the Ricci tensor. Complete listings of many metrics possessing some minimal symmetry have been given for a number of symmetry groups for the latter two symmetries. It is shown that a claimed complete listing of cylindrically symmetric static metrics by their curvature collineations [1] was actually incomplete and is completed here. It turns out that in this complete list, unlike the previous claim, there are curvature collineations that are distinct from the set of isometries and of Ricci collineations. The physical interpretation of some of the metrics obtained is given.     

Remarks on a New Possible Discretization Scheme for Gauge Theories

We propose here a new discretization method for a class of continuum gauge theories which action functionals are polynomials of the curvature. Based on the notion of holonomy, this discretization procedure appears gauge-invariant for discretized analogs of Yang-Mills theories, and hence gauge-fixing is fully rigorous for these discretized action functionals. Heuristic parts are forwarded to the quantization procedure via Feynman integrals and the meaning of the heuristic infinite dimensional Lebesgue integral is questioned.     

Relativistic Quantum Field Inertia and Vacuum Field Noise Spectra

The equivalence statements for quantum scalar field vacuum states that havebeen used for the thermal-like Hawking effect and Unruh effect are surveyed.An important ingredient in this framework is the concept of a vacuum field noisespectrum, by which one can obtain information about the curvature invariants ofclassical worldlines (relativistic classical trajectories). It is argued, in the spiritof the free-fall-type universality, that the preferred quantum field vacua withrespect to accelerated worldlines should be chosen from the class of all thosepossessing stationary spectra for their quantum fluctuations. For scalar quantumfield vacua there are six stationary cases, as shown by Letaw some time ago,and reviewed here. However, nonstationary vacuum noises can be treated by afew mathematical methods that are mentioned as well. Since the informationabout the kinematical curvature invariants of the worldlines is of radiometricorigin, suggestions are given on the more useful application of such an academicformalism to radiation and beam radiometric standards for high-energyaccelerators and in astrophysics. We conclude with a look at related axiomaticquantum field topics and some other recent work.