Time-marching numerical schemes for the electric field integral equation on a straight thin wire

We derive and analyse four algorithms for computing the current induced on a thin straight wire by a transient electric field. They all involve solving the thin wire electric field integral equations (EFIEs) and consist of a very accurate differential equations solver together with various schemes to approximate the vector potential integral equation. We carry out a rigorous numerical stability analysis of each of these methods. This has not previously been done for solution schemes for the thin wire EFIEs. Each scheme is shown to be stable and convergent provided the radius of the wire is small enough for the thin wire equations to be a valid model.     

Lipschitz classes on local fields

The Lipschitz class Lipαon a local field K is defined in this note,and the equivalent relationship between the Lipschitz class Lipαand the Holder type space C~α(K)is proved.Then,those important characteristics on the Euclidean space R~n and the local field K are compared,so that one may interpret the essential differences between the analyses on R~n and K.Finally,the Cantor type fractal functionθ(x)is showed in the Lipschitz class Lip(m,K),m＜(ln 2/ln 3).     

Energy crisis or a new soliton in the noncommutative CP(1) model?

The non-commutative (NC) CP(1) model is studied from field theory perspective. Our formalism and definition of the NC CP(1) model differs crucially from the existing one [Phys. Lett. B 498 (2001) 277, hep-th/0203125, hep-th/0303090].

Due to the U(1) gauge invariance, the Seiberg–Witten map is used to convert the NC action to an action in terms of ordinary spacetime degrees of freedom and the subsequent theory is studied. The NC effects appear as (NC parameter) θ-dependent interaction terms. The expressions for static energy, obtained from both the symmetric and canonical forms of the energy momentum tensor, are identical, when only spatial noncommutativity is present. Bogomolny analysis reveals a lower bound in the energy in an unambiguous way, suggesting the presence of a new soliton. However, the BPS equations saturating the bound are not compatible to the full variational equation of motion. This indicates that the definitions of the energy momentum tensor for this particular NC theory (the NC theory is otherwise consistent and well defined), are inadequate, thus leading to the “energy crisis”.

A collective coordinate analysis corroborates the above observations. It also shows that the above mentioned mismatch between the BPS equations and the variational equation of motion is small.     

Deposition conditions in tailoring the morphology of highly porous reticular films prepared by electrostatic spray deposition (ESD) technique

Spongy-like reticular structure is a unique morphology fabricated by electrostatic spray deposition (ESD) technique. The effects of solvent, substrate temperature, precursor feeding rate, static electric field strength, and deposition time on tailoring the reticular structure were investigated. Scanning electron microscopy was used to observe the film morphology. MnO_x or LiMn₂O₄ were selected as the model materials. It is found that in addition to the conventional solvent butyl carbitol, other kinds of solvents such as ethylene glycol and propylene glycol can also be used to obtain reticular films at a suitable substrate temperature. Porous films with a low cross-linking degree pore structure can be prepared by increasing precursor feeding rate or decreasing substrate temperature. Increasing the deposition time or the electric field strength helps to obtain reticular films with more homogeneous pore size distribution. In addition, the addition of a high boiling-point solvent in mixed alcohol solvent results in the increase of proper substrate temperature. It is concluded that the fluidity of the spray droplets on the surface of a hot substrate is an important factor to form a reticular film.     

Asymptotics in the Baum—Katz formula for random fields

In 1996, D. Deng established an analog of the Baum—Katz theorem on the convergence rate in the law of large numbers for multi-indexed random variables. The series describing the convergence rate depends, in a natural way, on the parameter characterizing the excess of the normalized sums over some level. In this paper, we find the precise asymptotics of the sum of this series with respect to the above-mentioned parameter. Thus, a generalization of a recent result due to A. Gut and A. Spataru is obtained.     

Nanophotonics and nanometrology with planar X-ray waveguide-resonator

The mechanism of X-ray waveguide-resonance propagation or the radiation superstream model, which can become the ground of X-ray nanophotonics, is discussed briefly. Some attention is devoted to features consideration of the simplest devices characterized by the waveguide-resonance transportation of X-ray beams. The experimental data showing the user possibilities of a simplest waveguide-resonators application for diffractometry are presented. We discuss the main reasons to improve the metrological characteristics for total reflection X-ray fluorescence (TXRF) analytical method in case when the target exciting beam is formed by a waveguide-resonator. Some problems appearing during the waveguide-resonator application are formulated.     

Mössbauer effect study of the decagonal quasicrystal Al65Co15Cu20

The ⁵⁷Fe Mössbauer effect study at 5.0 K and in an external magnetic field of 9.0 T on a high-quality stable decagonal quasicrystal Al₆₅Co₁₅Cu_19.9Fe_0.1 is presented. It is shown that the iron atoms are located in two distinct classes of sites. The values of the principal component of the electric field gradient tensor and the asymmetry parameter at these sites are, respectively, ?1.90(10)?×?10²¹ V/m², 0.97(15) and ?3.95(12)?×?10²¹ V/m², 0.00(17).     

The Nature of Electronic Charge

Advances in gauge theories and unified theories have not thrown light on the meaning of electron. The problem of the origin of electronic charge is made precise, new insights gained from Weyl space are summarized, and the origin of charge in terms of fractional spin is suggested. A new perspective on the abelian Chern-Simons theory is presented to explain charge.     

Preparation and characterization of ZnO nanorods from NaOH solutions with assisted electrical field

ZnO naorods on ZnO-coated seed substrates were fabricated by solution chemical method from Zn(NO₃)₂/NaOH under assisted electrical field. The working mechanism of electrical field was analyzed and the factors affecting the rod growth such as potential, precursor concentration and growth temperature were elucidated. The structural and optical properties are characterized by SEM, TEM, XRD, HRTEM and UV-vis. The results indicated that the nanorods have wurtzite structure without electrical field and are primarily of zincite structure under electrical field; when the electrical field is 1.1-1.3 V, not only the elevation of ion diffusion and adsorption lower the crystallite/solution interfacial energy and then the crystal nucleation barrier by increasing charge intensity, but also the production of H⁺ through oxidation of OH⁻ increases properly the degree of solution supersaturation near the substrate, and thus lowers the activation energy. Both the two processes do favor to rod growth. With increasing precursor concentration in this system, the average diameter and length of ZnO nanorods increase, leading to decreasing of optical transmittance. The maximum rod growth rate at given concentration of Zn²⁺ occurs at a specific temperature.     

核磁共振成像一维空间编码教学实验

利用梯度磁场实现检测信号的空间编码,是核磁共振成像(MRI)的关键技术.本文采用ccc系列样品将二维问题简化为一维,使用超小型教学用核磁共振成像仪进行了一维空间编码实验研究,并对实验过程及实验结果进行了计算模拟和分析.