Coordinate space form of interacting reference response function ofd-dimensional jellium

Summary The interacting reference response functionX _I ^[3](k) of three-dimensional jellium ink space was defined by Niklasson in terms of the momentum distribution of the interacting electron assembly. Here the Fourier transformF _I ^[d](r) ofX _I ^[d] (k) is studied for the jellium model withe ²/r interactions in dimensionalityd=1,2 and 3, in an extension of recent work by Holas, March and Tosi for the cased=3. The small-r and large-r forms ofF _I ^[d] (r) are explicitly evaluated from the analytic behaviour of the momentum distributionn _d(p). In the appendix, a model ofn _d (p) is constructed which interpolates between these limits.     

Monte Carlo evidence for the deviation from the Alexander-Orbach rule in three-dimensional percolation

Computer simulation is used to study the diffusion at the percolation threshold on large simple cubic lattices. The exponentk for the rms displacementr witht inr t_k is found to be smaller than 0.2, while the Alexander-Orbach 4/3 rule for the spectral dimension predictsk=0.201 ± 0.002.on leave from Minnesota Supercomputer Institute and School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota 55455.     

Correction method for the self‐absorption effects in fluorescence extended X‐ray absorption fine structure on multilayer samples

A novel correction method for self‐absorption effects is proposed for extended X‐ray absorption fine structure (EXAFS) detected in the fluorescence mode on multilayer samples. The effects of refraction and multiple reflection at the interfaces are fully considered in this correction method. The correction is performed in k‐space before any further data analysis, and it can be applied to single‐layer or multilayer samples with flat surfaces and without thickness limit when the model parameters for the samples are known. The validity of this method is verified by the fluorescence EXAFS data collected for a Cr/C multilayer sample measured at different experimental geometries.     

Diffusion in three-dimensional random systems at their percolation thresholds

Extensive Monte Carlo simulations of theant-in-the-labyrinth problem on randomL* L* L simple cubic lattices are performed, forL up to 960 on a CRAY-YMP supercomputer. The exponentk for the rms displacementr witht inrt ^k is found to bek=0.190±0.003. As a second approach, large percolation clusters with chemical shells up to 300 are generated on a simple cubic lattice at criticality. The diffusion equation is then solved by using the exact enumeration technique. The corresponding critical exponentd ^w is found to be 1/d ^w =0.250±0.003.On leave from I. Institut für Theoretische für Physik, Universität Hamburg, D-2000 Hamburg, Federal Republic of Germany.     

Effective action in higher derivative (Super)gravities

'The one-loop effective action (EA) with an accuracy up to linear curvature terms ind=4R ²-gravity, conformal gravity, andN=1,d=4 conformal supergravity on the backgroundR ₄×T_4–k,k=1, 2, 3 is calculated. (Here,R _k is thek-dimensional curved space, T_n is then-dimensional torus). The one-loop EA in multidimensionalR ²-gravity and ind=10 conformal supergravity on the backgroundR ₄ ×T _d–4 is also obtained. The mechanism of inducing the Einstein gravity from the EA of considered theories of higher derivative (super)gravity is presented.We are grateful to I. L. Bukhbinder for the numerous discussions of considered questions.     

The coloured Jones function

The invariantsJ _K,k of a framed knotK coloured by the irreducibleSU(2) _q -module of dimensionk are studied as a function ofk by means of the universalR-matrix. It is shown that whenJ _K,k is written as a power series inh withq=e ^h , the coefficient ofh ^d is an odd polynomial ink of degree at most 2d+1. This coefficient is a Vassiliev invariant ofK. In the second part of the paper it is shown that ask varies, these invariants span ad-dimensional subspace of the space of all Vassiliev invariants of degreed for framed knots. The analogous questions for unframed knots are also studied.Partially supported by NSF Grant DMS-9123657     

Conformal blocks and generalized theta functions

LetSU _X r be the moduli space of rankr vector bundles with trivial determinant on a Riemann surfaceX. This space carries a natural line bundle, the determinant line bundleL. We describe a canonical isomorphism of the space of global sections ofL ^k with the space of conformal blocks defined in terms of representations of the Lie algebrasl _r (C((z))). It follows in particular that the dimension ofH ⁰(SU _X r,L ^k ) is given by the Verlinde formula.Both authors were partially supported by the European Science Project Geometry of Algebraic Varieties, Contract no. SCI-0398-C(A)     

Lift order problems for ordinary differential equations on manifolds

Fork≥0, let ττ_k:T ^k+1(M)=T(T ^k(M))→T ^k(M) denote the (k+1)th iterated tangent bundle in relation to a base manifoldT ⁰(M)=M. LetV represent a possibly nonstationary vector field overT ^k(M), and letQ be a subset/submanifold inT ^k(M). Sufficient conditions (and, whenV is completely integrable inQ, necessary and sufficient conditions) are established to ensure that all solutionsg toy′=V(t, y) lying entirely inQ have the formG=f ^[k], wheref ^[k] is thekth-order differential lift of a curvef lying inM. The relevance of the issue for higher order dynamical systems (especially in mechanics) is discussed. Higher order involutions and complete vector field lifts are examined from the viewpoint of the differential equations they present. Collateral results on the general solvability of initial value problems are obtained and numerous examples are discussed in detail. To the memory of my teacher and friend M. Kuga (1928–1990).     

Performance optimization analysis of a thermoelectric refrigerator with two resonances

Based on electron transport theory,the performance of k x and k r filtered thermoelectric refrigerators with two resonances are studied in this paper.The performance characteristic curves between the cooling rate and the coefficient of performance are plotted by numerical calculation.It is shown that the maximum cooling rate of the thermoelectric refrigerator with two resonances increases but the maximum coefficient of performance decreases compared with those with one resonance.No matter which resonance mechanism is used(k x or k r filtered),the cooling rate and the performance coefficient of the k r filtered refrigerator are much better than those of the k x filtered one.     

The effect of statistical noise on structural parameters in EXAFS data analysis

Summary We analyse the effect of the statistical noise on the physical parameters derived from an EXAFS spectrum. Two separate classes of experimental cases are discussed, namely heavy and light backscatterers. The weight of the noise in the two cases is, in fact, quite different, depending on thek range useful for the analysis of the data. We find that for heavy backscatterers the statistical noise can usually be neglected, while for light backscatterers it can be one of the main limitations in obtaining reliable results from EXAFS. Paper presented at the Workshop on ?EXAFS Data Analysis in Disordered Systems?, held in Parma, October 5–7, 1981.     

Design of sharp transmission filters using band-edge resonances in one-dimensional photonic crystal hetero-structures

This paper presents a design of sharp transmission filters using band edge resonance effects in a hetero-structure composed of one-dimensional photonic crystals with different periods. Assuming that the photonic crystals are made of identical pairs of transparent materials, the band-edge resonance occurs when the periods are distributed in a geometrical progression with a common ratio, r=r _c , where r _c is a known function of refractive-index modulation, incident angle and the polarization of light. The band-edge resonance results in sharp resonant peaks in the transmission spectrum, with the full width at half maximum of the peaks increasing with an increase in the number of unit cells in each photonic crystal. Furthermore, if M photonic crystals are used to construct the hetero-structure, M−1 resonant peaks with the spacing between kth (1<k<M) and (k−1)th peaks equal to the band gap of the kth photonic crystal form in the transmission spectrum.     

In situ observation of Ni–Mo–S phase formed on NiMo/Al2O3 catalyst sulfided at high pressure by means of Ni and Mo K‐edge EXAFS spectroscopy

To obtain direct evidence of the formation of the Ni–Mo–S phase on NiMo/Al₂O₃ catalysts under high‐pressure hydrodesulfurization conditions, a high‐pressure EXAFS chamber has been constructed and used to investigate the coordination structure of Ni and Mo species on the catalysts sulfided at high pressure. The high‐pressure chamber was designed to have a low dead volume and was equipped with polybenzimidazole X‐ray windows. Ni K‐edge k³χ(k) spectra with high signal‐to‐noise ratio were obtained using this high‐pressure chamber for the NiMo/Al₂O₃ catalyst sulfided at 613 K and 1.1 MPa over a wide k range (39.5–146 nm^?1). The formation of Ni–Mo and Mo–Ni coordination shells was successfully proved by Ni and Mo K‐edge EXAFS measurement using this chamber. Interatomic distances of these coordination shells were almost identical to those calculated from Ni K‐edge EXAFS of NiMo/C catalysts sulfided at atmospheric pressure. These results support the hypothesis that the Ni–Mo–S phase is formed on the Al₂O₃‐supported NiMo catalyst sulfided under high‐pressure hydrodesulfurization conditions.     

Higher order differential lift equations over manifolds

LetM be a differentiable manifold modeled on a Banach space overK=R or C. LetT ^k(M) be thekth iterated tangential extension ofM, and letk ^M be thekth Bowman (=restricted tangential) extension ofM. It is shown that there is an embedding ϕ_k:k ^{→T k}(M), and that such embeddings constitute a natural transformation of functors. LetQ be a subset/submanifold inT ^k(M), and letV:Q→T(Q) be a differentiable vector field. CallV k-suitable if everyK-curveg inQ satisfyingg′=V° g has the formg=f ^[k], wheref ^[k] denotes thekth iterated differential lift of aK-curvef inM. It is shown thatV isk-suitable if and only if: (a) , where is a subset/submanifold ink ^M, and (b) , where isk-suitable relative to restricted tangentialK-curve liftsf ^(k). Interpretive consequences for motion problems are discussed.     

Neighborhood preferences in random matching problems

We consider a class of random matching problems where the distance between two points has a probability law which, for a small distance l, goes like l^r. In the framework of the cavity method, in the limit of an infinite number of points, we derive equations for p_k, the probability for some given point to be matched to its kth nearest neighbor in the optimal configuration. These equations are solved in two limiting cases: r = 0 -- where we recover p _k = 1/2^k, as numerically conjectured by Houdayer et al. and recently rigorously proved by Aldous -- and r→ + ∞. For 0 < r < + ∞, we are not able to solve the equations analytically, but we compute the leading behavior of p_k for large k. Received 14 February 2001     

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.     

The pH dependence of Am(III) complexation with acetate: an EXAFS study

The complexation of acetate with Am(III) is studied as a function of the pH (1–6) by extended X‐ray absorption fine‐structure (EXAFS) spectroscopy. The molecular structure of the Am(III)–acetate complexes (coordination numbers, oxygen and carbon distances) is determined from the raw k³‐weighted Am L_III‐edge EXAFS spectra. The results show a continuous shift of Am(III) speciation with increasing pH value towards the complexed species. Furthermore, it is verified that acetate coordinates in a bidentate coordination mode to Am(III) (Am—C distance: 2.82 ± 0.03 Å). The EXAFS data are analyzed by iterative transformation factor analysis to further verify the chemical speciation, which is calculated on the basis of thermodynamic constants, and the used structural model. The experimental results are in very good agreement with the thermodynamic modelling.     

An EXAFS spectroscopic study of Am(III) complexation with lactate

The pH dependence (1–7) of Am(III) complexation with lactate in aqueous solution is studied using extended X‐ray absorption fine‐structure (EXAFS) spectroscopy. Structural data (coordination numbers, Am—O and Am—C distances) of the formed Am(III)–lactate species are determined from the raw k³‐weighted Am L_III‐edge EXAFS spectra. Between pH 1 and pH 6, Am(III) speciation shifts continuously towards complexed species with increasing pH. At higher pH, the amount of complexed species decreases due to formation of hydroxo species. The coordination numbers and distances (3.41–3.43 Å) of the coordinating carbon atoms clearly point out that lactate is bound `side‐on' to Am(III) through both the carboxylic and the α‐hydroxy function of lactate. The experimentally determined coordination numbers are compared with speciation calculations on the basis of tabulated thermodynamic stability constants. Both EXAFS data and thermodynamic modelling are in very good agreement. The EXAFS spectra are also analyzed by iterative transformation factor analysis to further verify the determined Am(III) speciation and the used structural model.     

Data analysis method to achieve sub‐10 pm spatial resolution using extended X‐ray absorption fine‐structure spectroscopy

Obtaining sub‐10 pm spatial resolution by extended X‐ray absorption fine structure (EXAFS) spectroscopy is required in many important fields of research, such as lattice distortion studies in colossal magnetic resistance materials, high‐temperature superconductivity materials etc. However, based on the existing EXAFS data analysis methods, EXAFS has a spatial resolution limit of π/2Δk which is larger than 0.1 Å. In this paper a new data analysis method which can easily achieve sub‐10 pm resolution is introduced. Theoretically, the resolution limit of the method is three times better than that normally available. The method is examined by numerical simulation and experimental data. As a demonstration, the LaFe_1–xCr_xO₃ system (x = 0, 1/3, 2/3) is studied and the structural information of FeO₆ octahedral distortion as a function of Cr doping is resolved directly from EXAFS, where a resolution better than 0.074 Å is achieved.     

核物质状态方程中动量相关作用可能的探针

研究了动量相关作用对于中子-质子比动能谱rb(Ek)的效应,发现rb(Ek)灵敏的依赖于动量相关作用而弱的依赖于介质中核子-核子碰撞截面和对称势.因此rb(Ek)是提取重离子碰撞中动量相关作用信息的可能探针.同时,对于丰中子弹核和相同质量稳定弹核在相同入射道条件下,丰中子碰撞系统明显加强了动量相关作用对rb(Ek)的效应.故两个碰撞系统rb(Ek)结果的比较为在重离子碰撞中提取动量相关作用的知识提供了另一个重要的判据。     

Diagonal and Off-Diagonal Recursion Relation for the General Potential V(r) = Arp

A recursion relation is derived for the potential V(r) = Ar ^p. Generally, this connects off-diagonal matrix elements of r ^k–2, r ^k+p, r ^k, and r ^k+2. The diagonal case is obtained by setting m = n in this relation. The relation is derived by elementary methods and without recourse to specific properties of the eigenstates. Finally, this relation is studied for the familiar potentials p = –1, 1, 2.