An attempt to find a connection between the atomic distribution in liquid and solid metals

The distance of nearest neighbours r ₁, as well as the ‘reduced’ densities extrapolated to 0°k of liquid and solid metals are compared. Some liquids are close-packed at 0°k. With increasing temperature the degree of atomic misfit increases while r ₁ stays constant or even decreases, contrary to the behaviour in the solid phase.     

AnSU(2)l ⊗SU(2)r symmetric Yukawa model in the symmetric phase

The lattice regularizedSU(2)l ?SU(2)r symmetric scalar fermion model with explicit mirror fermions is investigated in the phase with unbroken symmetry. In the present work numerical Monte Carlo calculations with dynamical fermions are performed on 4³·8 and 4³·16 lattices near the expected perturbative Gaussian fixed point. The bare Yukawa coupling of the mirror fermion is fixed at zero. Global symmetries of the model are discussed, and the numerical results are supported by lattice perturbation theory.     

Self-diffusion at grain boundaries with a disordered atomic structure

A change in the free energy of a grain boundary is analyzed in the case when lattice vacancies come to the boundary and are then delocalized in its disordered atomic structure. It is shown that the free energy of the boundary is minimized at some excess atomic volume Δv _b =Δv _b ^* , whose value depends on the energy of vacancy formation in the crystal lattice and the boundary energy. The formation of a metastable localized grain-boundary vacancy as a result of thermal fluctuations of the density in a group of n ₀=\gM_v/Δv _b atoms (\gM_v is the vacancy volume), followed by the jump of an adjacent atom into this vacancy, is taken as an elementary event of grain-boundary diffusion. Expressions for the activation energy of diffusion and the diffusion coefficient are derived for equilibrium (Δv _b =Δv _b ^* ) and nonequilibrium (Δv _b >Δv _b ^* ) boundaries.     

Aspects of crystal growth within carbon nanotubes

The comparative crystallisation and HRTEM imaging properties of simple binary halides formed by the alkali iodides MI (M = Li, K, Na, Rb and Cs) within single walled carbon nanotubes (SWNTs) are described. The most common structure type observed within SWNTs is the rocksalt archetype, although CsI was observed to form both bcc and rocksalt structure types. In SWNTs forming in the 1.2–1.6 nm diameter range, all of the incorporated halides showed preferred orientation, with the 〈100〉 growth direction predominating for rocksalt-type packing and 〈112〉 so far observed exclusively for bcc packing. Crystals with dimensions spanning 2–6 atomic layers thickness in projection invariably exhibited lattice expansions that were attributed predominantly to a net reduction in coordination at the crystal-carbon interface. The crystallisation behaviour of UCl₄–KCl and AgI–AgCl eutectic melts was compared in carbon nanotubes of different diameters and a pronounced ordering influence over the normally glassy melts was observed in narrower capillaries. HgI₂ crystallised within nanotubes with ultra-narrow (i.e., 0.8 nm) capillaries were observed to form helical 2 ×1 layer crystals. To cite this article: J. Sloan et al., C. R. Physique 4 (2003).     

Embedding theorem for weighted Sobolev classes on a John domain with weights that are functions of the distance to some h-set

Let Ω be a John domain, let Γ ? ?Ω be an h-set, and let g and v be weights on Ω that are distance functions to the set Γ of special form. In the paper, sufficient conditions are obtained under which the Sobolev weighted class W _p,g ^r (Ω) is continuously embedded in the space L _q,v (Ω). Moreover, bounds for the approximation of functions in W _p,g ^r (Ω) by polynomials of degree not exceeding r ? 1 in L _q,v ( $\tilde \Omega $ ) are found, where $\tilde \Omega $ is a subdomain generated by a subtree of the tree T defining the structure of Ω.     

Simulation of 4d \mathcal{N}=1 supersymmetric Yang–Mills theory with Symanzik improved gauge action and stout smearing

We report on the results of a numerical simulation concerning the low-lying spectrum of four-dimensional $\mathcal{N}=1$ SU(2) Supersymmetric Yang–Mills (SYM) theory on the lattice with light dynamical gluinos. In the gauge sector the tree-level Symanzik improved gauge action is used, while we use the Wilson formulation in the fermion sector with stout smearing of the gauge links in the Wilson–Dirac operator. The ensembles of gauge configurations were produced with the Two-Step Polynomial Hybrid Monte Carlo (TS-PHMC) updating algorithm. We performed simulations on large lattices up to a size of 24³?48 at β=1.6. Using QCD units with the Sommer scale being set to r ₀=0.5 fm, the lattice spacing is about a?0.09 fm, and the spatial extent of the lattice corresponds to 2.1 fm. At the lightest simulated gluino mass the spin-1/2 gluino–glue bound state appeared to be considerably heavier than its expected super-partner, the pseudoscalar bound state. Whether supermultiplets are formed remains to be studied in upcoming simulations.     

MeanM-subshell fluorescence yields atZ=88, 90, 92, and 94

M x-ray —L x-ray coincidence measurements with high resolution, cooled Si(Li) x-ray detectors were made on transitions following the alpha decays of²²⁸Th,²³²U,²³⁸Pu, and²⁴⁴Cm, in order to determine the meanM-subshell fluorescence yields. The values obtained are:v ₄ ^M =0.032±0.002, andv ₅ ^M =0.024±0.002 atZ=88;v ₁ ^M =0.038±0.003,v ₄ ^M =0.042±0.002, andv ₅ ^M =0.038±0.002 atZ=90;v ₁ ^M =0.047±0.002,v ₄ ^M =0.048±0.002, andv ₅ ^M =0.044±0.002 atZ=92;v ₁ ^M =0.066±0.002,v ₄ ^M =0.062±0.002, andv ₅ ^M =0.063±0.002 atZ=94. The quantityΩ ₁ ^M +f ₁₂ ^MΩ ₂ ^M was measured as (56±10)×10^?4, (62±12)×10^?4, (99±18) ×10^?4, and (93±15)×10^?4 forZ=88, 90, 92, and 94, respectively, which agree well with the calculations of McGuire. The radiativeL ₁-L ₃ transition intensity was measured for the four atomic numbers and found to be consistently less than the calculations of Scofield by about 45 percent.     

Franck-Condon Factors and r-Centroids for the (B [sbnd] X) and (C [sbnd] X) Bands of the 107Ag 109Ag Molecule

Arrays of Franck-Condon factors q(v′, v″) and r-centroids r(v′, v″) were computed using Morse potentials for C¹Π [sbnd] X¹Σ⁺ _g and B O⁺ _u [sbnd] X¹Σ⁺ _g bands of the ¹⁰⁷Ag ¹⁰⁹Ag molecule.     

Spin Chains with Dynamical Lattice Supersymmetry

Spin chains with exact supersymmetry on finite one-dimensional lattices are considered. The supercharges are nilpotent operators on the lattice of dynamical nature: they change the number of sites. A local criterion for the nilpotency on periodic lattices is formulated. Any of its solutions leads to a supersymmetric spin chain. It is shown that a class of special solutions at arbitrary spin gives the lattice equivalents of the $\mathcal{N}=(2,2)$ superconformal minimal models. The case of spin one is investigated in detail: in particular, it is shown that the Fateev-Zamolodchikov chain and its off-critical extension possess a lattice supersymmetry for all its coupling constants. Its supersymmetry singlets are thoroughly analysed, and a relation between their components and the weighted enumeration of alternating sign matrices is conjectured.     

Ab initio calculation of force constants and equilibrium geometries in polyatomic molecules

The force constants and equilibrium geometry of water were calculated ab initio from Hartree-Fock self-consistent field wavefunctions using the force method, and a 53/31, a 73/3 + 1 and a 95/41 + 2 gaussian lobe basis set. The force method proved to be very economic and numerically accurate.

The calculated values agree well with the experimental ones. Especially good is the agreement for the interaction constant F_rα . Calculated force constants for the 95/41 + 2 basis are: F_r = 9·158 mdyn/å, F_α = 0·8513 mdyn/å, F_rα = +0·3007, F_rr = -0·1724; the experimental values from isotope frequencies are: F_r = 8·456, F_α = 0·762, F_rα = +0·246, F_rr = -0·100 mdyn/å. The agreement in the geometry is also good for the 95/41 + 2 basis r _e = 0·9518 å, α = 107·49°, and the experimental r _e = 0·9572 å, α = 104·52°.

Force constants were found to be quite insensitive to variation in the basis functions, all three sets giving almost the same result. On the other hand, the dipole moment derivative is very sensitive.     

Embedding theorem for weighted Sobolev classes with weights that are functions of the distance to some h-set

The paper continues the first part (Russ. J. Math. Phys. 20 (3), 360–373). Let Ω be a John domain, let Γ ? ?Ω be an h-set, and let g and υ be weights on Ω that are distance functions to the set Γ of special form. In the paper, sufficient conditions are obtained under which the Sobolev weighted class W _p,g ^r (Ω) is continuously embedded in the space L _q,v (Ω). Moreover, bounds for the approximation of functions in W _p,g ^r (Ω) by polynomials of degree not exceeding r ? 1 in L _q,v ( $\tilde \Omega $ ) are found, where $\tilde \Omega $ is a subdomain generated by a subtree of the tree T defining the structure of Ω.     

Grain Boundary Grooving as an Indicator of Grain Boundary Phase Transformations

The atomic force microscopy (AFM) was used to study the grain boundary (GB) groove profiles far away from the melting temperature T _m. It is shown that AFM allows one to measure the temperature dependence of the GB energy in a rather broad temperature interval (from 0.85 T _m to T _m). The GB energy and GB segregation of Bi were measured at 1123 K in the interval of the Bi bulk concentration x ^v _Bi from 5 to 140 ppm Bi. The transition from monolayer to multilayer adsorption is observed for the 19a GB at 1123 K and x ^v _Bi = 60 at. ppm Bi. At the same point (1123 K and x ^v _Bi = 60 at. ppm Bi) a discontinuity of the first derivative of the GB energy is observed. These features were explained using the model of GB prewetting phase transformation developed previously.     

Metal-insulator transition in Bi-doped,amorphous Ga:Ar mixtures: Influence of spin-orbit scattering

Doping amorphous Ga_xAr_1?x mixtures with the strong spin-orbit scatterer Bi has a dramatic effect on the metal-insulator transition (MIT) occurring in this system at a critical metal atomic concentration x_c: (i) the MIT is shifted from x′_c = 0.36 ± 0.01 (corresponding to a critical metal volume fraction v′_c = 0.19 ± 0.01) of the undoped system to a lower value of x_c = 0.25 ± 0.01 (v_c = 0.14 ± 0.01) for (Ga_0.9Bi_0.1)_xAr_1?x and (ii) the critical exponent v and g of the dc conductivity and Hall coefficient, respectively, change from v′ = 0.5 ± 0.1 and g′ = 0 for the undoped samples to v = 1.3 ± 0.3 and g = 0.5 ± 0.1 for (Ga_0.9Bi_0.1)_xAr_1?x.     

The vector coupling α V((r) and the scales r 0, r 1 in the background perturbation theory

We study the universal static potential V _st(r) and the force, which are fully determined by two fundamental parameters: the string tension σ = 0.18 ± 0.02 GeV² and the QCD constants \(\Lambda _{\overline {MS} } (n_f )\) , taken from pQCD, while the infrared (IR) regulator M _B is taken from the background perturbation theory and expressed via the string tension. The vector couplings α _V(r) in the static potential and α _F(r) in the static force, as well as the characteristic scales, r ₁(n _f = 3) and r ₀(n _f = 3), are calculated and compared to lattice data. The result \(r_0 \Lambda _{\overline {MS} } (n_f = 3) = 0.77 \pm 0.03\) , which agrees with the lattice data, is obtained for M _B = (1.15 ± 0.02) GeV. However, better agreement with the bottomonium spectrum is reached for a smaller \(\Lambda _{\overline {MS} } (n_f = 3) = (325 \pm 15)\) MeV and the frozen value of α _V = 0.57 ± 0.02. The mass splittings \(\bar M(1D) - \bar M(1P)\) and \(\bar M(2P) - \bar M(1P)\) are shown to be sensitive to the IR regulator used. The masses M(1 ³ D ₃) = 10169(2) MeV andM(1 ³ D ₁) = 10155(3) MeV are predicted.     

On the trace and the relativistic scalar products involving Dirac matricesγ i and the 4 × 4 unit matrix

In this paper we have dealt with the relativistic scalar products likeγ _i uγ _i,Tr(γ _i u) Tr(γ _i v) and Tr(γ _i γ _j v). Here any string likeu andv involve Dirac matrices in the manneru=Π _n ^r=1 a _r where the element \(a_r = a_{r_i } \gamma _i + ia_{r_5 }\) i.e.,a _r in general involves a term \(ia_{r_5 }\) which is multiplied by a 4 × 4 unit matrix. We have further evaluated Tr (γ _b u) Tr (γ _b v) where the suffix ‘b’, unlike the dummy suffixesi andj, does not imply any summation and can assume any specific value from 1 to 5. Some reduction formulae for the evaluation of Tr (γ₅ u) and Tr(u) have been obtained in this paper.     

Investigation of N 2 + (C 2Σ u + → X 2Σ g + fluorescence excited through auger decay of the 1s −1π* resonance

A theoretical investigation of N ₂ ⁺ (C ²Σ _u ⁺ → X ²Σ _g ⁺ molecular fluorescence excited through the Auger decay of the 1s ^?1π* resonance is carried out. The fluorescence cross sections are calculated with due regard for the dependence of the matrix element of the C → X dipole transition on the internuclear distance, the interference between channels of excitation via different vibrational levels v _r of the 1s ^?1π* resonance, the rotational structure of the fluorescence band, and the predissociation of the N ₂ ⁺ C ²Σ _u ⁺ v′ ≥3) states. The calculated cross sections are in good agreement with the experimental results of recent measurements. The results of the calculations have demonstrated that the observed dependence of the cross section of the (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″) fluorescence on the excitation energy and the fluorescence wavelength for a group of bands with equal values of the difference Δv = v′ ? v″ is associated with transitions between the vibrational levels of the electronic states involved in the excitation and subsequent cascade decay of the 1s ^?1π* resonance: N₂ (v ₀ = 0) → N*₂(1s ^?1π*(v _r)) ? N ₂ ⁺ : (C ²Σ _u ⁺ (v′) → X ²Σ _g ⁺ (v″).     

Neutrino production of same-sign dimuons at the Fermilab Tevatron

The rate of neutrino- and antineutrino-induced prompt same-sign dimuon production in steel was measured using a sample of μ^?μ^? events and 25 μ⁺μ⁺ events withP _μ>9 GeV/c, produced in 1.5 millionv _μ and 0.3 million \(\overline {v_\mu }\) induced charged-current events with energies between 30 GeV and 600 GeV. The data were obtained with the Chicago-Columbia-Fermilab-Rochester (CCFR) neutrino detector in the Fermilab Tevatron Quadrupole Triplet Neutrino Beam during experiments E 744 and E 770. After background subtraction, the prompt rate of same-sign dimuon production is (0.53±0.24)×10^?4 perv _μ charged-current event and (0.52±0.33)×10^?4 per \(\overline {v_\mu }\) charged-current event. The kinematic distributions of the same-sign dimuon events after background subtraction are consistent with those of the non-prompt background due to meson decays in the hadron shower of a charged-current event. Calculations ofc \(\bar c\) gluon bremsstrahlung, based on improved measurements of the charm mass parameter and nucleon structure functions by the CCFR collaboration, yield a prompt rate of (0.09±0.39)×10^?4 perv _μ charged-current event. In this case,c \(\bar c\) gluon bremsstrahlung is probably not an observable source of prompt same-sign dimuons.     

Al表面的"类液"结构及其自扩散通道

应用分子动力学方法,采用嵌入势模型在熔点下和熔点上对Al(001),(110)和(111)表面的原子结构和自扩散现象进行研究.发现这些表面的第一层原子在低于熔点时,Al(110)面在700±10 K,Al(001)面在 860±10 K,Al(111)面在 930±10 K呈现明显自扩散且最终转变为"类液"结构,而其余各层仍保留有序状态.对这种"类液"结构进行均方位移、结构有序参数、径向分布函数和z向粒子密度分析,发现其结构和扩散行为与熔化的Al表面不同,并能在一定温度区间稳定存在.在"类液 关键词： 表面结构 分子动力学 自扩散     

Solid-state morphology and mechanical properties of Kevlar 29 fiber

Kevlar 29 is an aromatic polyamide fiber spun from the polymer poly(p-phenylene terephthalamide). It has a paracrystalline structure with a lattice distortion parameter g = 5.9% and an a? constant = 0.51. The equatorial x-ray “crystallinity” is 68%; the microparacrystal (mPC) sizes are D ₀₀₂ = 50 nm, D ₁₁₀ = 4.4 nm, and D ₂₀₀ = 3.6 nm. The mPCs are well oriented; the orientation parameter 2ψ₂₀₀> = 0.047. The small-angle x-ray diffraction pattern indicated that the fiber has nc chain folding. It has high tenacity (2.81 GNm^?2), close to the tenacity of steel; high Young's modulus (63.9 GNm^?2); small breaking strain (3.8%); and a very high melting point (600°C). Wide- and small-angle x-ray diffraction techniques, differential scanning calorimetry (DSC), and an Amsler tensile tester have been used to characterize the fiber and to assess the effect of annealing on its morphology and mechanical properties.