Hamilton operator and the semiclassical limit for scalar particles in an electromagnetic field

We successively apply the generalized Case-Foldy-Feshbach-Villars (CFFV) and the Foldy-Wouthuysen (FW) transformation to derive the Hamiltonian for relativistic scalar particles in an electromagnetic field. In contrast to the original transformation, the generalized CFFV transformation contains an arbitrary parameter and can be performed for massless particles, which allows solving the problem of massless particles in an electromagnetic field. We show that the form of the Hamiltonian in the FW representation is independent of the arbitrarily chosen parameter. Compared with the classical Hamiltonian for point particles, this Hamiltonian contains quantum terms characterizing the quadrupole coupling of moving particles to the electric field and the electric and mixed polarizabilities. We obtain the quantum mechanical and semiclassical equations of motion of massive and massless particles in an electromagnetic field. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 398–411, September, 2008.     

Study on a hidden protein-DNA binding in salmon sperm DNA sample by dynamic kinetic capillary isoelectric focusing

Nuclease P1 is an important enzyme that hydrolyzes RNA or single-stranded DNA into nucleotides, and complete digestion is an essential basis for assays based on this enzyme. To digest a doubled-stranded DNA, the enzyme is usually combined with heat denaturing, which breaks doubled-stranded DNA into single strands. This paper presents an un-expected phenomenon that nuclease P1, in combination with heat denaturing, fails to completely digest a DNA sample extracted from salmon sperm. Under the experimental conditions used, at which nuclease P1 can completely digest calf thymus DNA, the digestion yield of salmon sperm DNA was only 89.5%. Spectrometric measurement indicated that a total protein of 4.7% is present in the DNA sample. To explain the reason for this phenomenon, the dynamic kinetic capillary isoelectric focusing (DK-CIEF) approach proposed previously, which allows for the discrimination of different types of protein-DNA interactions and the measurement of the individual dissociation rate constants, was modified and applied to examine possible protein-DNA interactions involved. It was found that a non-specific DNA-protein binding occurs in the sample, the dissociation rate constant for which was measured to be 7.05 ± 0.83 × 10⁻³ s⁻¹. The formation of DNA-protein complex was suggested to be the main reason for the incomplete digestion of the DNA sample. The modified DK-CIEF approach can be applied as general DNA samples, with the advantages of fast speed and low sample consumption.     

Some results on 4<Superscript><Emphasis Type="Italic">m</Emphasis></Superscript>2<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript> designs with clear two-factor interaction components

Clear effects criterion is one of the important rules for selecting optimal fractional factorial designs, and it has become an active research issue in recent years. Tang et al. derived upper and lower bounds on the maximum number of clear two-factor interactions (2fi’s) in 2 ^n−(n−k) fractional factorial designs of resolutions III and IV by constructing a 2 ^n−(n−k) design for given k, which are only restricted for the symmetrical case. This paper proposes and studies the clear effects problem for the asymmetrical case. It improves the construction method of Tang et al. for 2 ^n−(n−k) designs with resolution III and derives the upper and lower bounds on the maximum number of clear two-factor interaction components (2fic’s) in 4 ^m 2 ⁿ designs with resolutions III and IV. The lower bounds are achieved by constructing specific designs. Comparisons show that the number of clear 2fic’s in the resulting design attains its maximum number in many cases, which reveals that the construction methods are satisfactory when they are used to construct 4 ^m 2 ⁿ designs under the clear effects criterion. This work was supported by the National Natural Science Foundation of China (Grant Nos. 10571093, 10671099 and 10771123), the Research Foundation for Doctor Programme (Grant No. 20050055038) and the Natural Science Foundation of Shandong Province of China (Grant No. Q2007A05). Zhang’s research was also supported by the Visiting Scholar Program at Chern Institute of Mathematics.     

Period interaction on diffraction efficiency of blazed transmission gratings

The period interaction on diffraction of the blazed transmission gratings is analyzed with a modified extended scalar theory. For one certain period, the lights reflected from the neighboring structures can be refracted by the grating facets and form two extra fields on the bottom facet of blazed transmission gratings. The effects of this period interaction versus several diffraction orders for a fixed fabrication error of blazed transmission gratings with intermediate structures are discussed for both TE and TM polarizations. The results have been compared with those obtained with finite-difference time-domain method.     

The dynamical properties of Rydberg hydrogen atom near a metal surface

The dynamical properties of Rydberg hydrogen atom near a metal surface are presented by using the methods of phase space analysis and closed orbit theory. Transforming the coordinates of the Hamiltonian, we find that the phase space of the system is divided into vibrational and rotational region. Both the Poincaré surface of section and the closed orbit theory verify the same conclusion clearly. In this paper we choose the atomic principal quantum number asn=20. The dynamical character of the exited hydrogen atom depends sensitively on the atom-surface distanced. Whend is sufficiently large, the atom-surface potential can be expressed by the traditional van der Waals force and the system is integrable. Whend becomes smaller, there exists a critical valued _c. Ford>d _c, the system is near-integrable and the motion is regular. While chaotic motion appears ford<d _c, and the system tends to be non-integrable. The trajectories become unstable and the electron might be captured onto the metal surface.     

Studies on drug–DNA complexes,adriamycin–d‐(TGATCA)2 and 4′‐epiadriamycin–d‐(CGATCG)2, by phosphorus‐31 nuclear magnetic resonance spectroscopy

The complexes of adriamycin–d‐(TGATCA)₂ and 4′‐epiadriamycin–d‐(CGATCG)₂ are studied by one‐ and two‐dimensional ³¹P nuclear magnetic resonance spectroscopy (NMR) at 500 MHz in the temperature range 275–328 K and as a function of drug to DNA ratio (0.0–2.0). The binding of drug to DNA is clearly evident in ³¹P? ³¹P exchange NOESY spectra that shows two sets of resonances in slow chemical exchange. The phosphate resonances at the intercalating steps, T1pG2/C1pG2 and C5pA6/C5pG6, shift downfield up to 1.7 ppm and that at the adjacent step shift downfield up to 0.7 ppm, whereas the central phosphate A3pT4 is relatively unaffected. The variations of chemical shift with drug to DNA ratio and temperature as well as linewidths are different in each of the two complexes. These observations reflect change in population of B_I/B_II conformation, stretching of backbone torsional angle ζ, and distortions in O? P? O bond angles that occur on binding of drug to DNA. To the best of our knowledge, there are no solution studies on 4′‐epiadriamycin, a better tolerated drug, and binding of daunomycin or its analogue to d‐(TGATCA)₂ hexamer sequence. The studies report the use of ³¹P NMR as a tool to differentiate various complexes. The specific differences may well be the reasons that are responsible for different antitumor action of these drugs due to different binding ability and distortions in DNA. Copyright © 2009 John Wiley & Sons, Ltd.     

Sliding mesh algorithm for CFD analysis of helicopter rotor–fuselage aerodynamics

The study of rotor–fuselage interactional aerodynamics is central to the design and performance analysis of helicopters. However, regardless of its significance, rotor–fuselage aerodynamics has so far been addressed by very few authors. This is mainly due to the difficulties associated with both experimental and computational techniques when such complex configurations, rich in flow physics, are considered. In view of the above, the objective of this study is to develop computational tools suitable for rotor–fuselage engineering analysis based on computational fluid dynamics (CFD). To account for the relative motion between the fuselage and the rotor blades, the concept of sliding meshes is introduced. A sliding surface forms a boundary between a CFD mesh around the fuselage and a rotor‐fixed CFD mesh which rotates to account for the movement of the rotor. The sliding surface allows communication between meshes. Meshes adjacent to the sliding surface do not necessarily have matching nodes or even the same number of cell faces. This poses a problem of interpolation, which should not introduce numerical artefacts in the solution and should have minimal effects on the overall solution quality. As an additional objective, the employed sliding mesh algorithms should have small CPU overhead. The sliding mesh methods developed for this work are demonstrated for both simple and complex cases with emphasis placed on the presentation of the inner workings of the developed algorithms. Copyright © 2008 John Wiley & Sons, Ltd.     

Synthesis and characterization of new meso -substituted unsymmetrical metalloporphyrins

The synthesis and characterization of new meso-substituted unsymmetrical metalloporphyrins has been described. A new modified Adler method was used for the synthesis of two unsymmetrical porphyrins. Reactions of these unsymmetrical porphyrins with metal acetates afforded the corresponding metalloporphyrins in high yields with excellent purity. These porphyrins and their metal derivatives were characterized by spectroscopic methods. However, the copper complexes were further studied by ESR spectra and zinc complex by fluorescence spectrum.     

Proton Orbital [541]1/2 and Backbending in 178W

The microscopic mechanism of nine experimentally observed bands in ^178W is investigated using the particle-number conserving method of the cranked shell model with monopole and quadrupole paring interactions. The experimental results, including the moments of inertia and angular momentum alignments of nine bands in ^178W, are reproduced well by the particle-number conserving calculations, in which no free parameter is involved. Calculations demonstrate that occurrence of sharp backbending comes mainly from the contribution of high-j intruder orbitals vi13/2 or πh11/2 and their interference effect with orbitals near the Fermi surface. Theω variation of the occupation probability of each cranked orbital and the contribution to moment of inertia from each cranked orbital are analyzed.