Shear flow in the two-body Boltzmann gas. II. Small and large γ expansion of the shear viscosity

In two and three dimensions, the relaxation time Boltzmann equation can be solved analytically for the distribution function for a system of two hard particles subject to isothermal shear. The previous solutions of Morriss, and Ladd and Hoover are shown to be formally equivalent. The integral representation for the average of each of the elements of the pressure tensor in the steady state is obtained for both sllod and dolls tensor equations of motion. Rigorous equations are derived which relate the viscosity and the normal stress differences in these two methods. We obtain asymptotic expansions for each element of the pressure tensor for both small and large. For high shear rates, the viscosity is found to vanish as ^–2 log in both two and three dimensions.     

Nonperturbative effect in the β functions and the equations of motion for the string

We study systematically how to calculate the β functions nonperturbatively in the sigma model which describes the string propagation in arbitrary background fields. In particular, we calculate explicity the β functions for a tachyon and massless background fields up to the three-string tree interactions and also the four-tachyon tree interactions.     

Perturbative series and the 1/N expansion for the QED β-function

A comparison of the 5-loop perturbative series and the 1/N expansion for the QED renormalization group β-function in the Minimal Subtraction scheme is performed. The good agreement between two expansions is found which proves that the MS β-function is adequately described by both series.     

The anisotropic phenomenon in the β decay of radioactive elements and in other processes in nature

Results from experimental studies of a new hypothetical interaction in nature based on analyzing fluctuations in the intensity of the ?? decay of radioactive elements are presented. One possible explanation of the results, based on a hypothesis as to the global anisotropy of physical space caused by the existence of cosmological vector potential $\vec A_g $ , is given. It is shown that vector $\vec A_g $ has the following coordinates in the second equatorial coordinate system: right ascension ?? = 293° ± 10°; declination ?? = 36° ± 10°.     

The super-heat-kernel expansion and the renormalization of the pion–nucleon interaction

A recently proposed super-heat-kernel technique is applied to heavy baryon chiral perturbation theory. A previous result for the one-loop divergences of the pion–nucleon system to is confirmed, giving at the same time an impressive demonstration of the efficiency of the new method. The cumbersome and tedious calculations of the conventional approach are now reduced to a few simple algebraic manipulations. The present computational scheme is not restricted to chiral perturbation theory, but can easily be applied or extended to any (in general non-renormalizable) theory with boson–fermion interactions. Received: 21 July 1998 / Published online: 5 October 1998     

The effect of γ radiation on the determination of the antineutrino angular distribution from experiments on the β decay of polarized neutrons

In experiments on the β decay of polarized neutrons where only the electron and proton momentum distributions are observed and the γ radiation is not registered, the asymmetry factor B of the antineutrino angular distribution cannot be obtained rigorously — the value of B is only estimated on the average by taking into consideration the expectation (mean) value 〈B〉 and the rms deviation ΔB. The resulting unavoidable ambiguities in the determination of B amount to several percent, which is significant for the present-day experimental attempts to obtain B to very high precision ∼(0.1–1)%. Pis’ma Zh. éksp. Teor. Fiz. 69, No. 10, 681–685 (25 May 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

The parton distribution functions of the photon and the structure functionF 2 γ (x,Q 2)

We present new parametrisations of the parton distribution functions of the photon including the first parametrisation in next-to-leading order QCD. We take into account some recent theoretical considerations pertaining to the gluon content of the photon,g ^γ. We argue that if an evolution is started at very lowQ ² and a fit to allF ₂ ^γ data performed with no constraints on the gluon distribution, then physically unreasonable gluon distributions may result. Our results support recent indications thatQ ₀ ² ≤1 GeV² is too low a value from which to start a perturbative evolution. Starting our evolution atQ ₀ ² =5.3 GeV², we evolve up inQ ² using a modified version of Rossi's Ansatz. The limited lever arm inQ ² leads to limited sensitivity to the QCD scale parameter Λ, though there is a preference for low values in the 0.1–0.2 GeV range. We also present new parametrisations of the singular asymptotic quark and gluon distribution functions of the photon which we believe are more accurate than those in current use.     

The β - and γ -Form Distributions of Isotactic Polypropylene Injection Molding Controlled via Melt Vibration

The effect of melt vibration on the crystal form of isotactic Polypropylene (iPP) samples prepared by low-frequency Vibration-Assisted Injection Molding (VAIM) was investigated. The distribution of crystal forms through the thickness was investigated under different VAIM processing conditions, with Conventional Injection Molding (CIM) for comparison. Wide-Angle X-ray Diffraction (WAXD) showed that the content of β -form crystals decreases from the surface to the core region in the CIM and VAIM samples. The β -form distribution through the thickness is controlled by the VAIM processing conditions. The occurrence of γ -form crystals was found in the VAIM samples produced at relatively low vibration frequency and relatively large pressure vibration amplitude.     

Theoretical study of spectral parameters for the γ and β band systems of NO for atmosphere and high temperature

Highly correlated ab initio calculations were performed for accurate determination of γ (A²Σ⁺-X²П) and β (B²П-X²П) band systems of NO molecule. Highly accurate multi-reference configuration interaction approach was used to investigate the potential energy curves (PECs) and transition dipole moment curves. We correctly and fully described their diffuse wave functions by the obvious balance between the valence and Rydberg character of the X²П, A²Σ⁺, B²П, C²П and D²Σ⁺ states. The PECs of the three states (X²П, A²Σ⁺ and B²П) by using the aug-cc-pV5Z (aV5Z) basis set for N and O atoms agreed well with the Rydberg–Klein–Rees potential. Moreover, the Einstein A coefficients were calculated to predict the lifetimes, where the vibrational bands included v′ = 0–8, v″ = 0–29 for γ system and v′ = 0–11, v″ = 0–31 for β system. The spectral line intensities of the γ and β systems for atmosphere and high temperature were provided.     

Borel summability of the 1/N expansion for theN-vector [O(N) non-linear σ] models

We construct an analytic interpolation in 1/N for theN-vector [O(N) non-linear ] models withN-component fields on a lattice. This interpolation, valid at sufficiently high temperatures, extends over a large domain in the complex plane containing the half plane Re(1/N)>0. We use this result to show that the 1/N expansion of the free energy density and of the correlation functions is Borel summable in the thermodynamic limit and at high temperature.On leave from C.P.T., Ecole Polytechnique, F-91128 Palaiseau Cédex, France     

BEEM-π calculations for a series of pyridines and their 14N N.Q.R.

The ⁵⁷Fe Mössbauer spectrum of a powdered sample of phthalocyanine-iron(II) in an applied magnetic field of 3·0 teslas has been measured as a function of temperature in the range 4·2 K to 100 K. Measurements have also been made at 4·2 K with 6·0 teslas applied, and on a single crystal specimen at 4·2 K with 3·0 teslas applied. Independent computer fits to the three measurements taken at 4·2 K were found to be consistent with one another, and showed that detailed information concerning magnetic anisotropy can be obtained even from powdered samples of paramagnets by Mössbauer spectroscopy. Although the asymmetry parameter in the electric field gradient tensor was found to be small, there was a significant departure from tetragonal symmetry in the magnetic properties of the molecule. The magnetic hyperfine field at the ⁵⁷Fe nucleus was found to be positive in all directions, indicating that all three electronic g values are significantly greater than 2·0.     

New comprehension of the Taylor series expansion ②——Addition formulas and multiplications formulas of special functions

作为对泰勒展开公式的新认识,本文由泰勒展开公式出发,系统地导出了常用特殊函数的倍乘公式与加法公式.得到了大约50个公式,绝大多数在现有的几本主要工具书中都未能检得.     

The Removability of the Topological Term in the CP1 Model and θ Vacuum

In this paper, the removability of the topological term in the 1+1 dimension CP¹ model is studied. The unitary transformation which removes the topological term in the CP¹ model is obtained. The relation of the topological term to the a vacuum and geometric phase is found.     

Nucleation of the titanium α and β phases. in situ study of the dislocation role by synchrotron X-ray topography

This “in situ” and real time study is an approach to the role of matrix dislocations in the nucleation of the α or β phases in titanium single crystals. When the dislocations interact, forming tangles, subboundaries…, the residual stresses, present at the transformation temperature, trigger the new phase. If the dislocations are isolated at the transformation temperature they are destabilized by the large crystalline anisotropy resulting from the vibrational entropy dependence with the temperature. These dislocations disappear and do no act as preferential nucleation sites.