标定X射线粉末照相指数的新图解法,推广于正交晶系与单斜晶系

本文叙述了X射线粉末照相指数的新图解法在正交晶系与单斜晶系中的应用。由于在这两个晶系中所须确定的原始参量多于2,所以不可能像在四方晶系或六角晶系的情形,一次用图解法在平面上求得晶胞的所有初基参量。本文分析了正交晶系与单斜晶系的一些特殊情形,可用新图解法对粉末照相上一些特殊情形下的衍射线指数进行标定。为方便起见,图解法是尽量用线坐标进行的。     

Mass distribution in n—polymer stochastic aggregation and large—mass behaviour

The exact solutions of the rate equations of the n-polymer stochastic aggregation involving two types of clusters, active and passive for the kernel \dprⁿ_k=1s_(ik)(s_(ik)=i_k) and \dsumⁿ_k=1s_(ik)(s_(ik)=i_k), are obtained. The large-mass behaviours of the final mass distribution of the active and passive clusters have scaling-like forms, although the models exhibit different properties. Respectively, they have different decay exponents γ=\dfrac{2n+1}{2(n-1)} and γ=q+\dfrac{2n+1}{2(n-1)} for \dprⁿ_{k=1}s(ik)(s(ik)=ik) and γ=\dfrac 3{2(n-1)} and γ=q+\dfrac 3{2(n-1)} for \dsumⁿk=1}s(ik)(s(ik)=ik), which include exponents of two-polymer stochastic aggregation. We also find that gelation is suppressed for kernel \dprⁿk=1s(ik)(s(ik)=ik) which is different from the deterministic aggregation.}     

Non-linear oscillators and solitons of maxwell—Bloch equations

The Maxwell-Bloch equations of non-linear optics are represented as a continuous chain of C. Neumann oscillators onS ³. This representation enables us to find explicitely one-soliton solutions of the Maxwell-Bloch equations. These solutions form a two-parameter family and they correspond to the homoclinic orbits of the magnetic spherical pendula on the two-sphere.     

Magnetovacs in gauged N = 4 supergravity

A two-parameter family of supersymmetric background field solutions of the recently formulated version of gauged N = 4 supergravity is found. This constitutes strong evidence that the theory has stable vacua, despite energy densities that are unbounded below. The background geometries are metric products of (AdS)₂ × S₂, and there are covariantly constant magnetic and electric fields. For a special choice of parameters the (AdS)₂ factor becomes a flat Minkowski space and electric fields vanish.     

Isolation and quantization of the two degrees of freedom of the electromagnetic potential for any gauge

The true dynamical degrees of freedom (TDDF) of the electromagnetic potential are found for any gauge. They are the components of the Fourier transform of the electromagnetic potential on a two-dimensional spacelike plane orthogonal to the lightlike momentum vector for k² = 0 and vanish for k² ≠ 0. Gauge invariance is related to the (two-parameter) indeterminacy of this spacelike plane and the arbitrariness of the component of the electromagnetic potential along the momentum vector. By direct quantization of the TDDF for any gauge (compatible with the equations of motion), some of the well-known problems of the usual treatments are avoided. For instance, the constraint div E = 0 is a c-number (agrees with the commutation relations) without choosing a gauge, there appears no need for an indefinite metric in the space of state amplitudes, the commutators for creation and annihilation operators of every component of the electromagnetic potential (timelike, longitudinal, and transverse) have the same sign, and the energy of the electromagnetic field is positive for any gauge. When gauges are chosen, the results of the literature are recovered. In our treatment, gauge fixation and quantization commute.     

Critical binding of diatomic molecules

The behaviour of two bodies that are just bound or nearly bound is discussed. A class of potentials is given for which Schrödinger's equation has exact solutions at critical binding (zero binding energy). This class includes the known solution for the 6–10 potential. For a general potential characterized by a coupling parameter α, it is shown that the bound state energy tends to zero as -(α - α₀)², where α₀ is the critical value of the coupling parameter. Small energy scattering of atoms which are near critical binding (e.g. helium atoms) is examined. It is shown that determination of the total cross-section up to terms of order k ² is in principle sufficient to distinguish between bound and virtual states of the diatomic molecule.     

Calculation of the wave functions of the ground and weakly excited states of helium II

The wave functions of the ground (Ψ₀) and the first excited (Ψ_k) states of He II in the second-order approximation, i.e., up to the first two corrections to the corresponding solutions for a weakly nonideal Bose gas, are determined by the collective variable method, which was proposed by Bogolyubov and Zubarev and developed in the studies by Yukhnovskii and Vakarchuk. The functions Ψ₀ and Ψ_k = ψ_kΨ₀ are determined as the eigenfunctions of the N-particle Schrödinger equation from a system of coupled equations for Ψ₀, Ψ_k, and the quasiparticle spectrum E(k) of helium II. The results consist in the following: (1) these equations are solved numerically for a higher order approximation compared with those investigated earlier (the first-order approximation), and (2) Ψ₀ and ψ_k are derived from a model potential of interaction between He⁴ atoms (rather than from the structure factor as earlier) in which the potential barrier is joined with the attractive potential found from experiment. The height V ₀ of the potential barrier is a free parameter. Except for V ₀, the model does not have any free parameters or functions. The calculated values of the structure factor, the ground-state energy E ₀, and the quasiparticle spectrum E(k) of He II are in agreement with the experimental values for V ₀ ≈ 100 K. The second-order correction to the logarithm of Ψ₀ significantly affects the value of E ₀ and provides the asymptotics E(k → 0) = ck, while the second-order correction to ψ_k slightly affects the E(k). The second-order corrections to Ψ₀ and ψ_k have a smaller effect on the results compared with the first-order corrections, whereby the theory is in agreement with experiment; therefore, one may assume that the truncated Ψ₀ and ψ_k well describe the microstructure of He II. Thus, the series for Ψ₀ and Ψ_k can be truncated in spite of the fact that the expansion parameter is not very small (～1/2).     

The bond force constants of graphene and benzene calculated by density functional theory

Stretching (k_r) and bending (k_θ) bond force constants appropriate to describe the bond stiffness of graphene and benzene are calculated using density functional theory. The effect of employing different exchange-correlation functionals for the calculation of k_r and k_θ is discussed using the generalised gradient approximation (GGA) and the local density approximation (LDA). For benzene, k_r = 7.93 mdyn Å^-1 and k_θ = 0.859 mdyn Å rad^-2 using LDA, while k_r = 7.67 mdyn Å^-1 and k_θ = 0.875 mdyn Å rad^-2 using GGA. For graphene, k_r = 7.40 mdyn Å^-1 and k_θ = 0.769 mdyn Å rad^-2 using LDA, while k_r = 6.88 mdyn Å^-1 and k_θ = 0.776 mdyn Å rad^-2 using GGA. This means the difference between the bond force constants for benzene and graphene can be as large as ～12%. The comparison between these two systems allows for elucidation of the effect of periodicity and substitution of carbon atoms by hydrogen in the stiffness of C–C bonds. This effect can be explained by a different redistribution of the charge density when the systems are subjected to strain. The parameters k_r and k_θ computed here can serve as an input to molecular mechanics or finite element codes of larger carbon molecules, which in the past had frequently assumed the same bond force constants for graphene, benzene or carbon nanotubes.     

Radiative and radiationless processes of Eu3+ in dimethyl sulfoxide

Solutions of Eu³⁺ in dimethyl sulfoxide (DMSO) exhibit a considerable enhancement in the intensities of bands associated with ?J = 2 both in the absorption and in the emission spectra. This effect is so strong that addition of considerable amounts of either D₂O or H₂O has no effect at all. Contrary to that, addition of very small quantities of DMSO in solutions of Eu³⁺ in D₂O is accompanied by drastic changes in the appropriate transition probabilities. In solutions of Eu³⁺ in DMSO containing relatively small [H₂O] or [D₂O], the primary solvation sphere appears to consist mainly of DMSO. Secondary and primary fluorescence quenching rate constants have been determined such as: k^sec_D2O ? 5.1 M^-1s^-1; k^sec_DMSO ? 20 M^-1s^-1 and k_fl + k^≈_h ? 4.5 × 10²s^-1.     

Calculation of gauge couplings and compact circumferences from self-consistent dimensional reduction

We consider a system of gravity plus free massless matter fields in 4 + N dimensions, and look for solutions in which N dimensions form a compact curved manifold, with the energy-momentum tensor responsible for the curvature produced by quantum fluctuations in the matter fields. For manifolds of sufficient symmetry (including spheres, CP^N, and manifolds of simple Lie groups) the metric depends on only a single multiplicative parameter ?², and the field equations reduce to an algebraic equation for ?, involving the potential of the matter fields in the metric of the manifold. With a large number of species of matter fields, the manifold will be larger than the Planck length, and the potential can be calculated using just one-loop graphs. In odd dimensions these are finite, and give a potential of form C_N/?⁴. Also there are induced Yang-Mills and Einstein-Hilbert terms in the effective 4-dimensional action, proportional to additional numerical coefficients, D_N and E_N. General formulas are given for the gauge coupling g² in terms of C_N and D_N, and the ratio ?²/8πG in terms of C_N and E_N. Numerical values for C_N, D_N, and E_N are obtained for scalar and spinor fields on spheres of odd dimensionality N. It is found that the potential, g² and ?²/8πG can all be positive but only when the compact manifold has N = 3 + 4 k dimensions. (The positivity of the potential is needed for stability of the sphere against uniform dilations or contractions). In this case, solutions exist either for spinor fields alone or for suitable mixes of spinor and scalar fields provided the ratio of the number of scalar fields to the number of fermion fields is not too large. Numerical values of the O(N + 1) gauge couplings and 8φG/?² are calculated for illustrative values of the numbers of spinor fields. It turns out that large numbers of matter fields are needed to make these parameters reasonably small.     

Regularities of energy transfer in aqueous solutions of Ln(III) ions upon formation of their bridged complexes via the CO 3 2− and OH− anions

The influence of the solvent pH and of the presence of carbonic acid anions on the energy transfer from the Eu(III) and Tb(III) ions to a large namber of Ln(III) ions, as well as on the concentration quenching of the Dy(III) ions, is studied. It is shown that, when the anions are present in solution at a concentration by 2–4 orders of magnitude lower than that of the lanthanide ions, the energy transfer rates increase by 2–4 orders of magnitude, but the luminescence decay remains exponential. It is established that the rate constant for energy transfer (k _t ) via the hydroxyl bridge increases with decreasing concentration of lanthanide ions in solution. In an alkalinized solution, (k _t ) depends weakly on the initial water pH, because the concentration of hydroxo groups is governed by hydrolysis of water under the action of the lanthanide ions introduced into it. It is found that, at the 10^?2 M concentration of lanthanide ions in solution, the values of (k _t ) change by almost two orders of magnitude depending on the choice of an ion pair; however, these changes in no way correlate with the overlap integrals of spectra, calculated by adopting the Forster mechanism, and the inclusion of an interaction of higher multipoles does not improve the agreement with the experimental data. It is shown that, when the energy is transferred via the OH^? bridge in solutions with a total concentration of Ln(III) ions of 10^?4 M, the value of (k _t ) increases up to 10⁷ M^?1 s^?1 and becomes independent of the choice of pairs of Ln(III) ions. The dependence of (k _t ) on the ratio of the dissociation constant for a binuclear complex and the probability of energy transfer between the ions within this complex are discussed. It is concluded that the change in this ratio explains the disappearance of the dependence of (k _t ) on the choice of ions as their concentration in solution decreases, but does not explain all the observed changes in (k _t ) if only the dipole-dipole mechanism of energy transfer between the ions in bridged complexes is considered.     

Baxterization of ther-matrix for the adjoint representation of U q [D(2, 1;α)]

The Baxterization procedure is applied to the Braid group representation arising from the adjoint representation of the quantum supergroup U _q [D(2, 1;)]. This yields a two-parameter family of solutions to the (parameter dependent) Yang-Baxter equation of interest in supersymmetric lattice models.     

极化激元系统时间演化的量子涨落特性和非经典统计行为

将极化激元系统约化成模型单模光子-TO声子有效相互作用系统， 在此基础上以解析形式讨论了系统的力学量、压缩态、量子涨落特性以及亚泊松分布等非经典效应的动力学演化行为.结果表明，光子场与极化波量子场彼此交换能量过程随时间演化呈振荡性质，光子场和声子场都可以演化成压缩态，其二阶压缩度随时间演化成复杂周期振荡特性，这种非经典特性是非线性相互作用的结果并且以k₁项和k₂项同时存在并相互关联为前提.而此时光子和声子统计分布随时间演化呈现介于超Poison分布和亚Poison分布之间复杂周期振荡的新结果，非线性作用k₁项和k₂项对这种非经典统计行为都有贡献. 关键词： 极化激元系统动力学演化 单模光场-TO声子有效模型哈密顿量 量子涨落与压缩态 亚泊松分布     

幂函数叠加势的径向薛定谔方程的解析解

研究多种正幂势函数与逆幂势函数紧密耦合条件下薛定谔径向方程解析解的求解方法.对势函数为V（r）=α₁r⁸＋α₂r³+α₃r²+β₃r^-1＋β₂r^-3＋β₁r^-4的径向薛定谔方程存在解析解的条件以及精确的解析解进行了研究. 根据量子系统波函数必须满足单值、有界和连续的标准条件,首先求出径向坐标r→∞以及r→0时的渐近解,然后采用非正则奇点邻域附近的波函数级数解法与求得的渐近解相结合,通过幂级数系数比较法得到径向薛定谔方程在势函数系数紧密耦合条件下的一系列定态波函数解析解以及相应的能级结构,并作适当讨论与结论. 关键词： 级数解法 幂势函数 径向波函数 渐近解     

Multidimensional elastic waves excited by oscillating domain walls

Magnetoelastic excitations with a fine structure in the 50kHz range have been observed in the study of the domain wall resonance (DWR) in magnetic garnet thin films. DWR excites standing transverse elastic waves which have a resonance frequency given by $\text{f=}\text{nv}\text{2d}$, where f is the frequency, n is an integer, v=3.5×10⁵ cm/sec is the transversal velocity of the elastic wave, and d=0.05 cm is thickness of the film/substrate system. A fine structure associated with each of these modes has been identified as due to two dimensional bulk elastic waves by using a set of parallel microstrip lines. The dispersion relation of these elastic waves is ω²=v²(k²₁+k²₂), where ω is the radial frequency, k₁ and k₂ are the wave vectors in the orientation perpendicular and parallel to the sample surface respectively. In the case of k₁?k₂, $\text{f=}\text{f}{}_0\text{+v}{}^2\text{k}{}^2{}_2\text{f}{}_0$, where f₀ is the resonance when k₂=0. The experimental results are in excellent agreement with this model. A linear dispersion, observed when using a shorted slot-line structure, is understood as the excitation of three dimensional modes due to the complex structure of the slot-line and the sample geometry.     

Valley splitting in an n-channel (100) inversion layer on p-type silicon

The extended zone effective mass theory is proposed and is applied to the investigation of the valley splitting in an n-channel (100)Si inversion layer. The splitting is due to a tunnelling effect in k-space, and is given approximately as ΔE ≈ 0.15 (N_inv + g^?1N_depl) meV (N_inv and N_depl in units of 10¹² cm^?2$\text{g =}\text{11}\text{32}$). When the strain exists, or when k_x and k_y are both non-zero, the splitting is a little larger than this value. The enhancements of the Zeeman splittings and the valley splittings caused by the many body effects under strong magnetic fields are taken into account. The theory predicts the structure and line shape of the transverse magnetoconductivity oscillations, and the results show a very good agreement with the experiment including the cusps at the peak of the Landau levels in the indices N ? 3.     

Emission secondaire de petits agregats NipCn par des carbures de nickel

The intensities of emission of Ni_pC_n⁺(p = 1–3) and NiC_n^? secondary ions given by two alloys: Ni₃C and NiC 5% at. C, show off a saw-toothed behaviour according to the parity of the number n of carbon atoms. Maxima occur when n is odd for NiC_n⁺ ions and when n is even in the other cases (p = 2, 3; negative ions). Besides, the influence of the carbon concentration in the alloy can be observed.The alternations of NiC_n⁺ and Ni₂C_n⁺ ions can be interpreted from Pitzer and Clementi model (the clusters are supposed to be linear). Thus it can be found greater stabilities for NiC_2k+1 and Ni₂C_2k chains than for NiC_2k and Ni₂C_2k+1 chains respectively, which very well agrees with the “correspondence rule” between the emissions of different species of ions and their electronic properties.     

Transport damping by fluctuations and cluster-type expansions in kinetics

A mechanism of transport damping by fluctuations is proposed and analyzed in detail for the thermal diffusivity of a one-dimensional gas in the case when the externally induced temperature gradient is weaker than fluctuating gradients. Thermal diffusivity is calculated as a function of parameters of a one-dimensional gas characterized by a homogeneous potential of interaction between particles: for the potential V(x)=Q/|x|^k, thermal diffusivity is χ ∼ (Qn ^k/T)^1/(k−1)ν_T/n. The nonanalytic form of thermal diffusivity as a function of concentration is elucidated. The nonanalytic behavior of thermal diffusivity as a function of concentration is explained by a nontrivial symmetry of the problem under analysis at long times, after the initial fluctuations have dissipated. It is shown that spontaneous generation of macroscopic structures developing through selective growth of fluctuations of a certain type in a medium with an externally induced temperature gradient controls the transport properties of the medium when k≈1.     

On the layering transition of an SOS surface interacting with a wall. I. Equilibrium results

We consider the model of a 2D surface above a fixed wall and attracted toward it by means of a positive magnetic fieldh in the solid-on-solid (SOS) approximation when the inverse temperature is very large and the external fieldh is exponentially small in . We improve considerably previous results by Dinaburg and Mazel on the competition between the external field and the entropic repulsion with the wall, leading, in this case, to the phenomenon of layering phase transitions. In particular, we show, using the Pirogov-Sinai scheme as given by Zahradník, that there exists a unique critical valueh _k ^* () in the interval (1/4e ^–4k , 4e ^–4k ) such that, for allh(h _k+1 ^* ,h _k ^* ) and large enough, there exists a unique infinite-volume Gibbs state. The typical configurations are small perturbation of the ground state represented by a surface at heightk+1 above the wall. Moreover, for the same choice of the thermodynamic parameters, the influence of the boundary conditions of the Gibbs measure in a finite cube decays exponentially fast with the distance from the boundary. Whenh=h _k ^* () we prove instead the convergence of the cluster expansion for bothk andk+1 boundary conditions. This fact signals the presence of a phase transition. In the second paper of this series we will consider a Glauber dynamics for the above model and we will study the rate of approach to equilibrium in a large finite cube with arbitrary boundary conditions as a function of the external fieldh. Using the results proven in this paper, we will show that there is a dramatic slowing down in the approach to equilibrium when the magnetic field takes one of the critical values and the boundary conditions are free (absent).     

Nucleophilic reactivity of thiolate, hydroxide and phenolate ions towards a model O-arylated diazeniumdiolate prodrug in aqueous and cationic surfactant media

The kinetics of aromatic nucleophilic substitution of the nitric oxide‐generating diazeniumdiolate ion, DEA/NO, by thiols (L ‐glutathione, L ‐cysteine, DL ‐homocysteine, 1‐propanethiol, 2‐mercaptoethanol, and sodium thioglycolate) from the prodrug, DNP‐DEA/NO, has been examined in aqueous solution and in solutions of cationic DOTAP vesicles. Second‐order rate constants in buffered aqueous solutions (k_RS‐ = 3.48–30.9 M^?1 s^?1; 30 °C) gave a linear Brønsted plot (β_nuc = 0.414 ± 0.068) consistent with the rate‐limiting S_NAr nucleophilic attack by thiolate ions. Cationic DOTAP vesicles catalyze the thiolysis reactions with rate enhancements between 11 and 486‐fold in Tris‐HCl buffered solutions at pH 7.4. The maximum rate increase was obtained with thioglycolate ion. Thiolysis data are compared to data for nucleophilic displacement by phenolate (k_PhO‐ = 0.114 M^?1 s^?1) and hydroxide (k_OH‐ = 1.82 × 10^?2 M^?1 s^?1, 37 °C) ions. The base hydrolysis reaction is accelerated by CTAB micelles and DODAC vesicles, with the vesicles being ca 3‐fold more effective as catalysts. Analysis of the data using pseudo‐phase ion‐exchange (PIE) formalism implies that the rate enhancement of the thiolysis and base hydrolysis reactions is primarily due to reactant concentration in the surfactant pseudo‐phase. Copyright © 2009 John Wiley & Sons, Ltd.