麦克斯韦鱼眼球透镜的一种复合结构

麦克斯韦鱼眼球形透镜对近距物点以最小像差成像时，往往要求较大的折射率差值△ｎ￣［１］，目前的离子交换制作工艺尚难达此技术水平。为解决此困难，本文提出将此类球透镜置于低折射率均匀介质内组成复合结构，可在保持最小像差的提前下，大幅度减小其对折射率的差值△ｎ的要求。     

Magnetization curves for general cylindrical samples in a transverse field

Using the recent results for the surface current density on cylindrical surfaces of arbitrary cross-section producing uniform interior magnetic field we propose a method for obtaining solutions of Bean’s critical state model for general cylindrical samples. The method uses the technique of conformal mapping to express the sample surface and the flux-fronts in terms of a set of coefficients that depend on a parameter. The flux-fronts are to be determined by solving a system of nonlinear ordinary differential equations for the coefficients. Retaining only a certain finite number of leading coefficients we get an approximate solution. The procedure is illustrated by considering two cyclindrical samples — one with an elliptical cross-section and the other with a non-elliptical cross-section. The virgin curve and small and large magnetization hysteresis loops for the two samples are obtained.     

Registering spherical navigators with spherical harmonic expansions to measure three-dimensional rotations in magnetic resonance imaging

Subject motion remains a challenging problem to overcome in clinical and research applications of magnetic resonance imaging (MRI). Subject motion degrades the quality of MR images and the integrity of experimental data. A promising method to correct for subject motion in MRI is the spherical navigator (SNAV) echo. Spherical navigators acquire k-space data on the surface of a sphere in order to measure three-dimensional (3D) rigid-body motion. Analysis begins by registering the magnitude of two SNAVs to determine the 3D rotation between them. Several different methods to register SNAV data exist, each with specific capabilities and limitations. In this study, we assessed the accuracy, precision and computational requirements of measuring rotations about all three coordinate axes by correlating the spherical harmonic expansions of SNAV data. We compare the results of this technique to previous SNAV studies and show that, although computationally expensive, the spherical harmonic technique is a highly accurate, precise and robust method to register SNAVs and detect 3D rotations in MRI. A key advantage to the spherical harmonic technique is the ability to optimize the accuracy, precision, processing time and memory requirements by adjusting parameters used in the registration. While present developments are aimed at improving the programming efficiency and memory handling of the algorithm, this registration technique is currently well suited for retrospective motion correction applications, such as removing motion-related image artifacts and aligning slices within a high-resolution 3D volume.     

The analysis of thermoluminescence glow curves

Information about the behavior of traps in a luminescent material is usually derived by fitting the glow curves in the thermoluminescence spectrum of the material to a general formula. From the fit one seeks to obtain values for the depth of the traps, the frequency factors governing the release of electrons from the traps, and some indication of the rates of trapping and retrapping. This study investigates how successful this fitting process is in providing reliable values for the trap parameters. The relevant rate equations are used to numerically generate simulated glow curves for specific values of trap parameters. These glow curves are then analyzed by the usual fitting process, and values for the trap parameters are derived from the fitting process. We comment on the comparison between the derived parameter values and the correct values. From these comparisons we attempt to obtain some useful insights to assist in the interpretation of experimentally observed thermoluminescence spectra.     

Navier–Stokes spectral solver in a sphere

The paper presents the first implementation of a primitive variable spectral method for calculating viscous flows inside a sphere. A variational formulation of the Navier–Stokes equations is adopted using a fractional-step time discretization with the classical second-order backward difference scheme combined with explicit extrapolation of the nonlinear term. The resulting scalar and vector elliptic equations are solved by means of the direct spectral solvers developed recently by the authors. The spectral matrices for radial operators are characterized by a minimal sparsity – diagonal stiffness and tridiagonal mass matrix. Closed-form expressions of their nonzero elements are provided here for the first time, showing that the condition number of the relevant matrices grows as the second power of the truncation order. A new spectral elliptic solver for the velocity unknown in spherical coordinates is also described that includes implicitly the Coriolis force in a rotating frame, but requires a minimal coupling between the modal velocity components in the Fourier space. The numerical tests confirm that the proposed method achieves spectral accuracy and ensures infinite differentiability to all orders of the numerical solution, by construction. These results indicate that the new primitive variable spectral solver is an effective alternative to the spectral method recently proposed by Kida and Nakayama, where the velocity field is represented in terms of poloidal and toroidal functions.     

Relativistic fluid sphere on pseudo-spheroidal space-time

A new exact closed form solution of Einstein's field equations is reported describing the space-time in the interior of a fluid sphere in equilibrium. The physical 3-space,t=constant of its space-time has the geometry of a 3-pseudo spheroid. The suitability of this solution for describing the model of a relativistic superdense star is discussed and the stability of the model under radial pulsations is examined.     

Null Cartan Bertrand curves of AW(k)-type in Minkowski 4-space

This Letter considers the curvature conditions of AW(k)-type (k=1,2,3)$(k=1,2,3)$ null Cartan curves, and investigates null Cartan Bertrand curves. We show that null Cartan Bertrand curves are AW(k)-type (k=1,2,3)$(k=1,2,3)$ curves in Minkowski 4-space.     

目标场法在悬浮超导球体的球形线圈设计中的应用

文中把目标场法引入到悬浮超导球体的球形线圈设计中,根据目标场法产生均匀磁场的原理,通过离散化绕组来近似处理球形线圈在超导球体和球形线圈的间隙内产生均匀磁场的电流密度分布规律。利用有限元分析和验证,在超导球体与球形线圈之间的间隙内产生了具有很好均匀性的悬浮磁场,这会明显提高超导球体悬浮的刚度和稳定性。     

High-performance high-resolution semi-Lagrangian tracer transport on a sphere

Current climate models have a limited ability to increase spatial resolution because numerical stability requires the time step to decrease. We describe a semi-Lagrangian method for tracer transport that is stable for arbitrary Courant numbers, and we test a parallel implementation discretized on the cubed sphere. The method includes a fixer that conserves mass and constrains tracers to a physical range of values. The method shows third-order convergence and maintains nonlinear tracer correlations to second order. It shows optimal accuracy at Courant numbers of 10–20, more than an order of magnitude higher than explicit methods. We present parallel performance in terms of strong scaling, weak scaling, and spatial scaling (where the time step stays constant while the resolution increases). For a 0.2° test with 100 tracers, the implementation scales efficiently to 10,000 MPI tasks.     

Closed time-like curves in flat Lorentz space–times

We consider the region of closed time-like curves (CTCs) in three-dimensional flat Lorentz space–times. The interest in this global geometrical feature goes beyond the purely mathematical one. Such space–times are lower-dimensional toy models of sourceless Einstein gravity or cosmology. In three dimensions all such space–times are known: they are quotients of Minkowski space by a suitable group of Poincaré isometries. The presence of CTCs would indicate the possibility of “time machines”, a region of space–time where an object can travel along in time and revisit the same event. Such space–times also provide a testbed for the chronology protection conjecture, which suggests that quantum back reaction would eliminate CTCs. In particular, our interest in this note will be to find the set free of CTCs for , where is modeled on Minkowski space and γ is a Poincaré transformation. We describe the set free of CTCs where γ is hyperbolic, parabolic, and elliptic.     

Low field anomaly in magnetization curves

We present a calculation of the isothermal magnetization hysteresis curves appropriate to highT _csuperconductors. We discuss the nature of the low field anomaly as one goes from this strong pinning case to the weak pinning case. We show that the shape of the equilibrium (thermodynamic) magnetization curve is recovered in the limit ofJ _capproaching zero.     

On phases and length of curves in a cyclic quantum evolution

The concept of a curve traced by a state vector in the Hilbert space is introduced into the general context of quantum evolutions and its length defined. Three important curves are identified and their relation to the dynamical phase, the geometric phase and the total phase are studied. These phases are reformulated in terms of the dynamical curve, the geometric curve and the natural curve. For any arbitrary cyclic evolution of a quantum system, it is shown that the dynamical phase, the geometric phase and their sums and/or differences can be expressed as the integral of the contracted length of some suitably-defined curves. With this, the phases of the quantum mechanical wave function attain new meaning. Also, new inequalities concerning the phases are presented.     

Spiral galaxies rotation curves with a logarithmic corrected newtonian gravitational potential

We analyze the rotation curves of 10 spiral galaxies with a newtonian potential corrected with an extra logarithmic term. The logarithmic correction can have its origin from fundamental frameworks, like string theories or effective models of gravity due to quantum effects. There is also a connection with some toy models resulting from TeVeS. We represent the spiral galaxies as a thin disk. There is a new constant associated with the extra term in the potential. The rotation curve of the chosen sample of spiral galaxies is well reproduced for a narrow range of the new constant. The compatibility of this correction with local physics is discussed.     

A class of deformational flow test cases for linear transport problems on the sphere

A class of new benchmark deformational flow test cases for the two-dimensional horizontal linear transport problems on the sphere is proposed. The scalar field follows complex trajectories and undergoes severe deformation during the simulation; however, the flow reverses its course at half-time and the scalar field returns to its initial position and shape. This process makes the exact solution available at the end of the simulation, and facilitates assessment of the accuracy of the underlying transport scheme. A procedure to eliminate possible cancellations of errors when the flow reverses is proposed.     

Rotation curves of galaxies: Missing mass or missing physics

The rotation curves of galaxies are modelled using very special properties of an hydrodynamically turbulent fluid possessing helicity fluctuations. The development of correlations among these fluctuations leads to the formation of organized structures characterized by a new flat branch of the spatial energy spectrum in addition to the well known Kolmogorov spectrum. It is proposed that the flat nature of the rotation curves of galaxies may be a result of the energy cascading processes occuring in turbulent galactic atmospheres. Thus, in this model, there is no need of invoking dark matter to account for the flat rotation curves of galaxies.     

Properties of period integrals of complex algebraic curves

The period integrals of non-singular complex algebraic curves in are shown to satisfy a set of polynomial relations that can be used to formulate the corresponding the Picard-Fuchs equations. Their derivation employs elementary mathematical techniques that have also application in the context of Seiberg-Witten theories.     

Elliptic PDE formulation and boundary conditions of the spherical harmonics method of arbitrary order for general three-dimensional geometries

The inherent complexity of the radiative transfer equation makes the exact treatment of radiative heat transfer impossible even for idealized situations and simple boundary conditions. Therefore, a wide variety of efficient solution methods have been developed for the RTE. Among these solution methods the spherical harmonics method, the moment method, and the discrete ordinates method provide means to obtain higher-order approximate solutions to the equation of radiative transfer. Although the assembly of the governing equations for the spherical harmonics method requires tedious algebra, their final form promises great accuracy for any given order, since it is a spectral method (rather than finite difference/finite volume in the case of discrete ordinates). In this study, a new methodology outlined in a previous paper on the spherical harmonics method (P_N) is further developed. The new methodology employs successive elimination of spherical harmonic tensors, thus reducing the number of first-order partial differential equations needed to be solved simultaneously by previous P_N approximations (=(N+1)²). The result is a relatively small set (=N(N+1)/2) of second-order, elliptic partial differential equations, which can be solved with standard PDE solution packages. General boundary conditions and supplementary conditions using rotation of spherical harmonics in terms of local coordinates are formulated for the general P_N approximation for arbitrary three-dimensional geometries. Accuracy of the P_N approximation can be further improved by applying the “modified differential approximation” approach first developed for the P₁-approximation. Numerical computations are carried out with the P₃ approximation for several new two-dimensional problems with emitting, absorbing, and scattering media. Results are compared to Monte Carlo solutions and discrete ordinates simulations and a discussion of ray effects and false scattering is provided.     

Magnetization curves for non-elliptic cylindrical samples in a transverse field

Using recent results for the surface current density on cylindrical surfaces of arbitrary cross-section producing uniform interior magnetic field and an assumed set of flux-fronts, solutions of Bean’s critical state model for cylindrical samples with non-elliptic cross-section are presented. Magnetization hysteresis loops for two cross-sections with different aspect ratios are obtained. A comparison with some exact results shows the limitations of this approach.