Molecular Orbital Calculations on 2, 4, 6-Trinitrotoluene

Three ab initio calculations (HF/6-3IG, HF/6-3IG*, and HF/6-3IG**) on 2,4,6-trinitrotoluene were made, The results compare well with xray data, except dihedral angles of NO₂ relative to the plane of the benzene ring. The deviations are attributed to packing forces and steric effects in the crystal. The most stable structure was a torsional angle 10° of the methyl top with the benzene ring, unlike toluene. The rotational barriers of the methyl top and the 4-nitro group are small. Hydrogen bonding, dipole moments and total atomic charges arc calculated.     

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.     

HIGH ACCURACY NUMERICAL METHOD OF THIN-FILM PROBLEMS IN MICROMAGNETICS

In this paper, a new high accuracy numerical method for the thin-film problems of micron and submicron size ferromagnetic elements is proposed. For the computation of stray field, we use the finite element method(FEM) by introducing a semi-discrete artificial boundary condition [1, 2]. In our numerical experiments about the domain patterns and their movement, we can see that the results are accordant to that of experiments and other numerical methods. Our method are very convenient to deal with arbitrary shape of thin films such as a polygon with high accuracy.     

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.     

Geometrically qualified ESPI vibration analysis of an engine

This paper presents an application in the automotive industry where a combination of electronic speckle-pattern interferometry and laser doppler velocimetry were used at a critical stage in the design process of an internal combustion engine. Combined deformation and surface relief measurements were used to study the phase and amplitude of deformation of a vibrating engine. The relief data was combined with the interferometer geometry and used to geometrically correct the deformation data, in an effort to improve accuracy. The measurements allowed rapid identification and quantification of design weaknesses, particularly those causing undesirable resonances. This led to a significant reduction in the design time and lowering of costs, when compared with existing design optimisation methods.     

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).