A-E equation of potential field transformations in the wavenumber domain and its application

A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.

Linear Transformation Theory of Quantum Field Operators and Its Applications

We extend the linear quantum transformation theory to the case of quantum field operators. The corresponding general transformation expressions of CPT transformations and gauge field transformations are considered as its applications.

COUPLED NUMERICAL SIMULATION ON COLD ROLLER'S TEMPERATURE FIFLD-PHASE TRANSFORMATION - STRESS FIELD DURING ITS QUENCHING PSOCESS

Complicated changns occur inside the steel parts during quenching process. The abruptly changed boundary conditions make the temperature field,micro - structure and stress field change dramatically in very short time, and these variables take a contact interactions in the whole process. In this paper, a three dimensional non - linear mathematical model for queeching process has been founded and the numerical simulation on temperature field,microstructre and stress field has been realized.In the FEM analysis, the incremental iteration method is used to deal with such complicated nonlinear as boundary nonlinear, physical property nonlinear,transformation nonlinear etc.The effect of stress on transformation kinetics has been considered in the calculation of microstructure. In the stress field anal- ysis,a thermo- elasto - plastic model has been founded, which considers such factors as transforma- tion strain,transformation plastic strain, themal strain and the effect of temperature and transforma- tion on mechanical propertier etc. The transient temperature field, microstructure distribution and stress field of the roller on any time can be displayed vividly,and the cooling curve and the changes of stress on any position can also be given.

Three-dimensional transformation of magnetization direction and magnetic field component at low latitudes based on vertical relationship

The transformation of the magnetization direction and the magnetic fi eld component is one of the important methods in magnetic data processing and transformation,which can be conducted in both wavenumber and spatial domains.The transformation method in the wavenumber domain has simpler processing expression and higher processing effi ciency than in the spatial domain;however,they are unstable at low latitude.In this paper,the conclusion that the sum is 0 of two vertical magnetic fi eld components(magnetization inclinations are also perpendicular)in 2D is used for the 3D transformation of the magnetization direction and the magnetic field component.In addition,the transformation method at low latitudes based on vertical relationship(VMT)is proposed,which is an iterative algorithm that converts the transformation of the magnetization direction and the magnetic field component at the low latitude into the high latitude.This method restrains the instability of transformation of constant and variable magnetization direction and magnetic fi eld components in low latitudes.The accuracy,stability,and practicality are verifi ed from synthetic models and real data.

Phase Transformation and Enhancing Electron Field Emission Properties in Microcrystalline Diamond Films Induced by Cu Ion Implantation and Rapid Annealing

Cu ion implantation and subsequent rapid annealing at 500℃ in N2 result in low surface resistivity of 1.611 ohm/sq with high mobility of 290 cm2 V-1S-1 for microcrystalline diamond （MCD） films. Its electrical field emission behavior can be turned on at Eo = 2.6 V/μm, attaining a current density of 19.5μA/cm2 at an applied field of 3.5 V/#m. Field emission scanning electron microscopy combined with Raman and x-ray photoelectron mi- croscopy reveal that the formation of Cu nanoparticles in MCD films can catalytically convert the less conducting disorder/a-C phases into graphitic phases and can provoke the formation of nanographite in the films, forming conduction channels for electron transportation.

A Sound Field Separation and Reconstruction Technique Based on Reciprocity Theorem and Fourier Transform

We show a method to separate the sound field radiated by a signal source from the sound field radiated by noise sources and to reconstruct the sound field radiated by the signal source. The proposed method is based on reciprocity theorem and the Fourier transform. Both the sound field and its gradient on a measurement surface are needed in the method. Evanescent waves are considered in the method, which ensures a high resolution reconstruction in the near field region of the signal source when evanescent waves can be measured. A simulation is given to verify the method and the influence of measurement noise on the method is discussed.

FAST FOURIER TRANSFORMS ON BINARY FIELDS

We give a unified treatment of Fast Fourier Transforms for UDMD systems which contains, as special cases, Fast Fourier algorithms for character groups of many subgroups associated with binary fields.

Modeling effective viscosity reduction behaviour of solid suspensions

Under a simple shearing flow, the effective viscosity of solid suspensions can be reduced by controlling the inclusion particle size or the number of inclusion particles in a unit volume. Based on the Stokes equation, the transformation field method is used to model the reduction behaviour of effective viscosity of solid suspensions theoretically by enlarging the particle size at a given high concentration of particles. With a lot of samples of random cubic particles in a unit cell, our statistical results show that at the same higher concentration, the effective viscosity of solid suspensions can be reduced by increasing the particle size or reducing the number of inclusion particles in a unit volume. This work discloses the viscosity reduction mechanism of increasing particle size, which is observed experimentally.

Orthogonal transformation operation theorem of a spatial universal uniform rotating magnetic field and its application in capsule endoscopy

According to the anti-phase sine current superposition theorem, the orientation, the magnetic flux density, the angular speed and the rotational direction of the spatial universal rotating magnetic field (SURMF) can be controlled within the tri-axial orthogonal square Helmholtz coils (TOSHC). Nevertheless, three coupling direction angles of the normal vector of the SURMF in the Descartes coordinate system cannot be separately controlled, thus the adjustment of the orientation of the SURMF is difficult and the flexibility of the robotic posture control is restricted. For the dimension reduction and the decoupling of control variables, the orthogonal transformation operation theorem of the SURMF is proposed based on two independent rotation angular variables, which employs azimuth and altitude angles as two variables of the three-phase sine current superposition formula derived by the orthogonal rotation inverse transformation. Then the unique control rules of the orientation and the rotational direction of the SURMF are generalized in each spatial quadrant, thus the scanning of the normal vector of the SURMF along the horizontal or vertical direction can be achieved through changing only one variable, which simplifies the control process of the orientation of the SURMF greatly. To validate its feasibility and maneuverability, experiments were conducted in the animal intestine utilizing the innovative dual hemisphere capsule robot (DHCR) with active and passive modes. It was demonstrated that the posture adjustment and the steering rolling locomotion of the DHCR can be realized through single variable control, thus the orthogonal transformation operation theorem makes the control of the orientation of the SURMF convenient and flexible significantly. This breakthrough will lay a foundation for the human-machine interaction control of the SURMF.

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.

Interpretation of the short period variations in geomagnetic anomalies of Shaanxi region

A temporary profile from Shiquan in the southern part of Shaanxi Province to Ningxian in Gansu Province for observation of geomagnetic short period variations was set up. The characteristics of geomagnetic short period variations in the profile region was analyzed through geomagnetic transfer functions at measurement sites (Fan, et al, 1998). According to the theory of multi-scale analysis of wavelet transform, the components affected by regional origin in the region is extracted in this paper. The components of regional origin is used as original data in the inversion study for investigation of 2-D conductivity structure corresponding to the regional origin. The inversion method (Zhdanov, Traynin, 1997) which is based on the minimum of the total energy of the residual field between observational electro-magnetic field and the calculated theoretical field of conductivity model and the conception of migrated residual field is introduced into our inversion of the data of magneto-variation sounding. The result of the inversion gives the underground conductivity structure in depth range of 100 km beneath the profile, and shows that a high conductivity area is located under Wugong and Qianling. The main characteristics of the inversion method is briefly discussed, that is, it can reflect the depth and the distribution of anomalous conductivity area comparatively well, and large number of parameters of inversion model is allowed to be used in the Inversion.