ANALYTIC EXPRESSION OF MAGNETIC FIELD DISTRIBUTION OF RECTANGULAR PERMANENT MAGNETS

From the molecular current viewpoint,an analytic expression exactly describing magnetic field distribution of rectangular permanent magnets magnetized sufficiently in one direction was derived from the Biot-Savart's law. This expression is useful not only for the case of one rectangular permanent magnet bulk,but also for that of several rectangular permanent magnet bulks. By using this expression,the relations between magnetic field distribution and the size of rectangular permanent magnets as well as the magnitude of magnetic field and the distance from the point in the space to the top (or bottom) surface of rectangular permanent magnets were discussed in detail. All the calculating results are consistent with experimental ones. For transverse magnetic field which is a main magnetic field of rectangular permanent magnets,in order to describe its distribution,two quantities,one is the uniformity in magnitude and the other is the uniformity in distribution of magnetic field,were defined. Furthermore,the relations between them and the geometric size of the magnet as well as the distance from the surface of permanent magnets were investigated by these formulas. The numerical results show that the geometric size and the distance have a visible influence on the uniformity in magnitude and the uniformity in distribution of the magnetic field.

3-D rheologic model of earthquake preparation (I)—Displacement field

Based on the three-dimensional ela stic inclusion model proposed by Dobrovolskii, we developed a three-dimensional rheologic inclusion model and theory to study the earthquake preparation process. By using correspondence principle in the theory of rheologic mechanics, we derived the analytic expression of the viscoelas-tic displacement at an arbitrary point (x, y, z) in three directions of x, y and z-axes (i. e., U(r, t), V*(r, t) and W(r, t)) produced by a three-dimension inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model.

Analytical Expression for the MIMO Channel Capacity

This paper presents analytical expressions for the multiple-input multiple-output （MIMO） channel capacity in frequency-flat Rayleigh fading environments. An exact analytical expression is given for the ergodic capacity for single-input multiple-output （SIMO） channels. The analysis shows that the SIMO channel capacity can be approximated by a Gaussian random variable and that the MIMO channel capacity can be approximated as the sum of multiple SIMO capacities. The SIMO channel results are used to derive approximate closed-form expressions for the MIMO channel ergodic capacity and the complementary cumulative distribution function （CCDF） of the MIMO channel capacity （outage capacity）. Simulations show that these theoretical results are good approximations for MIMO systems with an arbitrary number of transmit or receive antennas. Moreover, these analytical expressions are relatively simple which makes them very useful for practical computations.

EFFECT OF THE POISSON RATIO ON THE PERFECTLY PLASTIC STRESS FIELD AT A STATIONARY PLANE-STRAIN CRACK TIP

Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode I, Mode II and Mixed-Mode I-II plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.

Impact of Wind on Tide-Induced Advective Salt Transport in A Well- Mixed Estuary

The tide-induced net advective salt flux in well-mixed estuaries consists of five terms according to the method from Kjerfve.The term resulted from the vertical variation in salinity can be negligible in well-mixed estuaries with four tide-induced salt flux terms,known as F1−F4.To explore the effects of wind on these salt fluxes,the current-salinity analytical model combined with the perturbation analysis is extended by including wind.Analytical expressions for the four salt fluxes are derived separately in the present model.Under the assumption that only the M_(2) tidal component is accounted for and the salt flux generated by diffusion is not studied,the tide-induced net advective salt flux Q_(sx) is in the seaward direction without the wind effect.By applying the Western Scheldt estuary case,the wind influence on the tidal advection salt flux(TASF)distribution in the F4 term was investigated.The phase difference between zero-order velocity and first-order salinity(Δφ)at the surface layer of the estuary is larger than 90°and smaller than 90°at the bottom layer,which leads to landward TASF in the surface layer and seaward TASF in the bottom layer.The distribution ofΔφis not uniform in the horizontal direction with wind included,which differs from the result without wind.In the case of seaward wind with the speed of 18 m/s,the decrease in the zeroth-order velocity phase(φu)at the surface layer is larger than that of the first-order salinity phase(φs)downstream,which leads to an abnormal seaward TASF in this region.Owing to the surface stress caused by wind,the Stokes compensation flow in the middle and lower reaches increases/decreases with the increase of the landward/seaward wind,while the upstream situation is opposite.Thus,the first-order velocity in the middle and lower reaches increases/decreases with the increase of the landward/seaward wind,while the upstream situation is also opposite.The first-order salinity also increases/decreases with the increase of landward/seaward wind,while the upstream salinity tends to zero.Therefore,the tide-induced net advective salt flux Q_(sx) increases/decreases with the increase of the landward/seaward wind,which is contrary to the usual recognition.

The Transient Solution of Plane Progressive Waves

Generated by an ideal sinusoidal motion of the vertical plate, the simplest linear solution in time domain for two-dimensional regular waves is derived. The solution describes the propagation process of the plane progressive wave with a front, and will approach the linear steady- state solution as the oscillation time of the plate approaches infinity. The solution presented in this paper can be used to provide an incident wave model with analytical expression for solving the problems of diffraction and response of floating bodies in time domain.

Near-field properties of diffraction through a circular subwavelength-size aperture

Analytical nonparaxial vectorial electric field expressions for both Gaussian beams and plane waves diffracted through a circular aperture are derived by using the vector plane angular spectrum method for the first time, which is suitable for the subwavelength aperture and the near-field region. The transverse properties of intensity distributions and their evolutions with the propagating distance, and the power transmission functions for diffracted fields containing the whole field, the evanescent field and the propagating field are investigated in detail, which is helpful for understanding the relationship between evanescent and propagating components in the near-field region and can be applied to apertured near-field scanning optical microscopy.

3-D rheologic model of earthquake prepa-ration (III): Precursor field

On the basis of the theory of viscoelastic displacement and strain field for the three-dimensional rheologic model of earthquake preparation, this paper mainly studies the theoretical solution of precursor field for the three-dimensional rheologic model of earthquake preparation. We derive the viscoelastic analytical expressions of the ground tilt, underground water level, earth resistivity at an arbitrary point （x, y, z） in the rheologic medium, and analyzed the earth resistivity preliminarily, providing a certain theoretical basis for the precursor analysis of seismogenic process.

Application of generalized impedance boundary conditions to sommerfeld half-space problem

Generalized impedance boundary conditions are employed to simplify the solution of the Sommerfeld half-space problem. An analytical expression is derived for the Hertz potential of a vertical electric dipole over the earth’s surface, in which the earth is assumed to be a layered media or homogeneous dissipative half-space. A Sommerfeld type integral in the potential function is expressed as the sum of two parts: a zeroth order Hankel function and an absolutely convergent series of Bessel functions. In addition, two expressions in closed form are obtained as the far-field and near-field approximation of the present result.

Study on Electrical Potential by Buried Source Electrode within the Horizontally Layered Half-space Model

The paper first studies the analytical expression of electrical potential by a point current source in a uniform half-space medium,and then focuses on the distribution of electrical potential in a horizontally layered half-space model by a point current source within the surface layer or the bottom layer.Finally,the electrical potential by a source electrode in any layer of a layered half-space model is presented.

Quantum Discord in any Mixture of Two Bi-Qubit Arbitrary Product States

Quantum discord in any mixture of two bi-qubit arbitrary product states is studied with two different approaches. In the first approach the maximM classicM correlations are obtained via numerical computations, while in the second approach they are analytically derived. Quantum correlations captured with both approaches completely coincide, as is in accord with the conclusion of Cen et al. [Phys. Rev. A 83 （2011） 054101]. The symmetry reduction of the concerned states concerning quantum correlations is accomplished. The captured discords are amply analyzed so that some inherent distinct properties are revealed.