Chem1D: a software package for electronic structure calculations on one-dimensional systems

We present a preliminary version of a software package, Chem1D, that performs molecular orbital calculations on one-dimensional atoms and molecules using the unadorned Coulomb operator 1/|x₁ ? x₂|. We describe methods for computing the necessary one- and two-electron integrals and outline the overall structure of the package. We use Chem1D to perform calculations on a set of small molecules and show that one-dimensional chemistry differs in a number of interesting ways from three-dimensional chemistry.     

Few-Projection Tomography. I. Radio-Astronomical Approach for the Problem and the 2-CLEAN DSA Method

We develop the radio-astronomical approach for solving the few-projection tomography problem. It is shown that the 2-CLEAN DSA method proposed for determination of the permissible solution area is an efficient way for solving this problem. The method is based on solving the deconvolution problem with allowance for the synthesized beam or the synthesized Green's function. The distortions due to the sidelobe responses of the synthesized transfer function are eliminated by using two realizations of the well-known iterative radio-astronomical CLEAN algorithm with nonlinear constraints. The proposed 2-CLEAN DSA method allows one to decrease the number of projections required for two-dimensional reconstruction by a factor of about 10 as compared with the conventional tomography approach, provided that a wide spatial-frequency spectrum limited from above is reconstructed. The method can easily be adapted to introducing additional constraints. Examples of astrotomography reconstruction are presented. We show that the proposed method is promising for a large number of remote sensing applications and compare it with other well-known reconstruction techniques. The papers by radio astronomers, who contributed significantly to the development of components of the method, are pointed out.     

Dynamically based fitting law for cross-sections of vibrational energy transfer

A three-dimensional semiclassical analytical model for cross-sections of vibrational energy transfer in collisions between an atom and a diatomic molecule has been developed. The model is based on the Bessel uniform approximation for transition probabilities valid for highly excited states of a molecule represented by the Morse oscillator. Three fitting parameters of the model are expressed in terms of the features characterizing the anisotropic intermolecular potential. The accuracy and validity of this law are tested by comparison with large Δn transitions and isotope effects in the crossed beam inelastic scattering of I₂ from He, H₂ and D₂.     

The role of heat-conducting walls in the measurement of heat and mass transport in transient grating experiments

We present a two-dimensional model to account for the role of heat-conducting walls in the measurement of heat transport and Soret-effect-driven mass transport in transient holographic grating experiments. Heat diffusion into the walls leads to non-exponential decay of the temperature grating. Under certain experimental conditions it can be approximated by an exponential function and assigned an apparent thermal diffusivity D_{th, app} < D_{th, s}, where D_th,s is the true thermal diffusivity of the sample. The ratio D_{th, app}/D_{th, s} depends on only three dimensionless parameters, d /l_s, κ_s/κ_w, and D_{th, s}/D_{th, w}. d is the grating period, l_s the sample thickness, κ_s and κ_w the thermal conductivities of sample and wall, respectively, and D_th,w the thermal diffusivity of the wall. If at least two measurements are performed at different d /l_s, both D_th,s and κ_s can be determined. Instead of costly solving PDEs, D_th,s can be obtained by finding the zero of an analytic function. For thin samples and large grating periods, heat conduction into the walls plays a predominant role and the concentration grating in binary mixtures is no longer one-dimensional. Nevertheless, the normalized heterodyne diffraction efficiency of the concentration grating remains unaffected and the true thermal and collective diffusion coefficient and the correct Soret coefficient are still obtained from a simple one-dimensional model.     

One-dimensional configuration sums in vertex models and affine Lie algebra characters

We study the local state probabilities of the vertex models in the face formulation associated with the simple Lie algebras X _n =A _n, B _n, C _n, D _n. The corner transfer matrix method expresses them in terms of one-dimensional configuration sums. We show that the latter are the string functions of X _n ⁽¹⁾ modules. We also present similar results for the restricted face models of types B _n ⁽¹⁾, C _n ⁽¹⁾, D _n ⁽¹⁾.     

A six-dimensional approach to microtexture analysis

A mathematical framework is presented for microtexture derivation and analysis. A six-dimensional space is introduced, defined as the product of direct space (x, y, z) and orientation space, parametrized by the Rodrigues vector (r ₁, r ₂, r ₃). The framework is adapted to diffraction experiments, where orientation information from many grains or deformation microstructures is recorded in parallel, with the prime aim of allowing fast measurements and thus the ability to study microstructure dynamics. Assuming the use of a monochromatic beam the geometry of the projection surfaces is deduced. The derivation of the microtexture is formulated as an inverse problem similar to reconstruction problems in absorption or emission tomography. The applicability of the two major types of reconstruction algorithm, namely transform methods and algebraic methods, is discussed. An explicit solution in terms of the iterative algebraic reconstruction technique algorithm is given. The choice of basis function is discussed. Furthermore, the framework is applied to a number of important simplifying cases. These include grain-by-grain reconstruction, classical pole figure inversion and the generation of three-dimensional maps of non-deformed grains.     

Sizing Polydisperse Dispersions by Focused Beam Reflectance and Small Angle Static Light Scattering

In this work, two different methods for particle characterization, namely focused beam reflectance and small angle static light scattering, are quantitatively compared. The results are presented in the form of moment ratios of the particle size distribution, i.e., the number weighted diameter, D_1/0, and the volume weighted diameter, D_4/3, for a broad range of particle size distributions ranging from 20 to 400 μm. Various aqueous dispersions including narrow, broad, and bimodal particle size distributions of spherical shaped ceramic beads were used in the comparison. It was found that the moment ratios obtained by focused beam reflectance measurements and small angle static light scattering correlate well, in the case of spherical particles. Furthermore, it was found that the D_1/0 values obtained by focused beam reflectance measurements are more sensitive to the presence of a small fraction of fine particles in a bimodal distribution than those obtained by small angle static light scattering.     

Investigation of superexcited states in molecular deuterium

A high-resolution VUV laser absorption spectroscopy is used to investigate the photon-induced ion-pair formation in D₂ in the spectral region from 140117.4 to 140732.0 cm^?1. We report determination of photoionization efficiency in ortho-para D₂ in supersonic molecular beam with energy resolution of 0.1 cm^?1. The assignment of the superexcited D₂ Rydberg states is done based on the quantum defect theory.     

A new transition for projections of multifractal measures and random maps

Typical projections of simple multifractal measures with generalized dimensionsD _q onto subspaces of dimensionD are considered. It is known that forD _o > D almost all projections have Euclidean support. Here it is shown that if in additionD increases beyondD, a typical projection changes from a singular continuous distribution to an absolutely continuous measure with a squareintegrable, or even differentiable density, and thus from a multifractal to an ordinary distribution with trivial singularity spectrum. Since projections of strictly self-similar measures can be regarded as invariant distributions of iterated function systems, such a transition is found also there and is expected to occur in related systems.     

D<Subscript>sJ</Subscript>(2860) and D<Subscript>sJ</Subscript>(2715)

Recently the Babar Collaboration reported a new cs̄ state, D_sJ(2860), and the Belle Collaboration observed D_sJ(2715). We investigate the strong decays of the excited cs̄ states using the ³ P ₀ model. After comparing the theoretical decay widths and decay patterns with the available experimental data, we are inclined to conclude that: (1) D_sJ(2715) is probably the 1^-(1³ D ₁) cs̄ state, although the 1^-(2³ S ₁) assignment is not completely excluded; (2) D_sJ(2860) seems unlikely to be the 1^-(2³ S ₁) and 1^-(1³ D ₁) candidate; (3) to consider D_sJ(2860) either as a 0⁺(2³ P ₀) or as a 3^-(1³ D ₃) cs̄ state is consistent with the experimental data; (4) the experimental search of D_sJ(2860) in the channels D_sη, DK^*, D^*K and D_s ^*η will be crucial to distinguish the above two possibilities. PACS 13.25.Ft; 12.39.-x     

一维金属-介质周期结构的自准直特性和亚波长成像

计算了一维金属-介质周期结构(1DMD)的色散曲线，利用传输矩阵法模拟了该结构对入射高斯光束的自准直作用，着重讨论了金属层吸收的影响；对该结构在半波长厚度时近场成像特性进行了分析，单光源的成像分辨率为λ/8，达到亚波长分辨效果；分辨率随着光源逐渐远离近场范围而降低. 双狭缝的成像模拟进一步验证了1DMD结构的近场亚波长成像能力，分辨率达到λ/3.     

Minimal Informationally Complete Measurements for Pure States

We consider measurements, described by a positive-operator-valued measure (POVM), whose outcome probabilities determine an arbitrary pure state of a D-dimensional quantum system. We call such a measurement a pure-state informationally complete (PS I-complete) POVM. We show that a measurement with 2D−1 outcomes cannot be PS I-complete, and then we construct a POVM with 2D outcomes that suffices, thus showing that a minimal PS I-complete POVM has 2D outcomes. We also consider PS I-complete POVMs that have only rank-one POVM elements and construct an example with 3D−2 outcomes, which is a generalization of the tetrahedral measurement for a qubit. The question of the minimal number of elements in a rank-one PS I-complete POVM is left open.     

Analytical Polarization and Coherence Transfer Functions for Three Dipolar Coupled Spins

Analytical polarization and coherence transfer functions are presented for a spin system consisting of three dipolar coupled homonuclear spins under energy matched conditions. Based on these transfer functions, optimal durations of Hartmann–Hahn mixing periods can be determined for arbitrary dipolar coupling constants D₁₂, D₁₃, and D₂₃. In addition, the dependence of the transfer efficiency on the relative size of the dipolar coupling constants is illustrated.     

Deshaping of the laser beam observed on the collisionally induced fluorescence of Na atoms in the nozzle expansion

The excitation spectrum ofD ₁ fluorescence and collisionally inducedD ₂ fluorescence of sodium in the early stage of the beam formation near the nozzle is studied. We observe strong reabsorption and imprisonment ofD ₁ photons influencing collisionally inducedD ₂ fluorescence. For high pressure of sodium vapour the excitation profile ofD ₂ fluorescence is dominated by the collisional broadening effect and shows unusual maxima and minima. These we connect with the laser beam focusing and defocusing effect, changing the number of photons penetrating the high density region.     

Stabilization mechanism of turbulent premixed flames in strongly swirled flows

The stabilization of turbulent premixed flames in strongly swirled flows undergoing vortex breakdown is studied in the case of the ALSTOM En-Vironmental (EV) double cone burner using a simple one-dimensional boundary layer type model and computational fluid dynamics, mainly at the level of large-eddy simulation. The analysis shows that, due to flame curvature effects, the flame speed on the combustor axis is 2 D _t/R _F lower than the turbulent burning rate, where D _t is a characteristic turbulent diffusion coefficient and R _F the flame radius of curvature. Flame propagation with negative speed observed in the experiments, i.e. the flame completely embedded in the central recirculation zone on the symmetry axis, is explained with the one-dimensional model as caused by the factor 2 D _t/R _F being larger than the characteristic turbulent burning rate. A peculiar sudden displacement of the flame anchoring location deep into the burner, which takes place experimentally at a critical value of the equivalence ratio, cannot however be explained with the present one-dimensional approach due to the modelling assumptions. The mathematical analysis is supported in this case with large-eddy simulation which can accurately reproduce the flame behaviour across the full operating range. It is finally shown that steady RANS methods cannot cope with the problem due to their inability to correctly predict the velocity flowfield in this burner.     

Localization for Random Unitary Operators

We consider unitary analogs of one-dimensional Anderson models on defined by the product U _ω=D _ω S where S is a deterministic unitary and D _ω is a diagonal matrix of i.i.d. random phases. The operator S is an absolutely continuous band matrix which depends on a parameter controlling the size of its off-diagonal elements. We prove that the spectrum of U _ω is pure point almost surely for all values of the parameter of S. We provide similar results for unitary operators defined on together with an application to orthogonal polynomials on the unit circle. We get almost sure localization for polynomials characterized by Verblunsky coefficients of constant modulus and correlated random phases Mathematics Subject Classification. 82B44, 42C05, 81Q05     

Investigating asymptotic suction boundary layers using a one-dimensional stochastic turbulence model

The turbulent asymptotic suction boundary layer is studied using a one-dimensional turbulence (ODT) model. ODT is a fully resolved, unsteady stochastic simulation technique. While flow properties reside on a one-dimensional domain, turbulent advection is represented using mapping events whose occurrences are governed by a random process. Due to its reduced spatial dimensionality, ODT achieves major cost reductions compared to three-dimensional (3D) simulations. A comparison to recent direct numerical simulation (DNS) data at moderate Reynolds number (Re = u_∞ / v₀ = 333, where u_∞ and v₀ are the free stream and suction velocity, respectively) suggests that the ODT model is capable of reproducing several velocity statistics, i.e. mean velocity and turbulent kinetic energy budgets, while peak turbulent stresses are under-estimated by ODT. Variation of the Reynolds number in the range Re ∈ [333,400,500,1000] shows that ODT can reproduce various trends observed as a result of increased suction in turbulent asymptotic suction boundary layers, i.e. the reduction of Reynolds stresses and enhanced skin friction. While up to Re = 500 our results can be directly compared to recent LES data, the simulation at Re = 1000 is currently not feasible through full 3D simulations, hence ODT may assist the design of future DNS or LES simulations at larger Reynolds numbers.     

Measurement of isotope shifts,fine and hyperfine structure splittings of the lithium D lines

The lithium D lines were studied using a diode laser that was frequency modulated by an electro-optic modulator, to excite an atomic beam. The transmission of part of the laser beam through an etalon was monitored to correct for the nonlinearity of the laser scan. The results for the ^6,7Li 2 S _1/2 and 2 P _1/2 hyperfine splittings agree very well with the best existing data while those for the D1 isotope shift and ^6,7Li fine structure splittings disagree significantly from data obtained by a previous laser atomic beam experiment. Our result for the D1 isotope shift is very close to the latest value computed using Hylleraas variational theory. Received 8 April 2002 / Received in final form 26 June 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: wvw@yorku.ca     

Development of three-dimensional turbulent separation in the neighborhood of incident crossing shock waves

The results are presented for experimental investigation of the peculiarities of the development of three-dimensional turbulent separated flows on a flat surface for the Mach number M_∞ = 4 and the Reynolds number Re₁ ∼ 55·10⁶ m⁻¹ under the conditions of the flow around two identical cylindrical bodies of revolution of diameter D = 50 mm and the body aspect ratio L _b/D = 5 with conical forebodies with semi-apex angles β_c = 30, 20, 15, and 10° located above plate in parallel to one another and to the flow. The typical stages of the three-dimensional separation development are considered under the reducing distance between the axes of the bodies within the range of Z = Δz/D = 1.06–3.0 at their fixed distance from the surface (Y = Δy/D = 0.96). The topology of limiting streamlines and the peculiarities of pressure fields on the surface as well as the gasdynamic structure of separated flows arising at the interaction of crossing bow shocks propagating from the bodies and at the interaction of secondary disturbances with the boundary layer are analysed.     

An algorithm for computed tomography image reconstruction from limited-view projections

<正>With the development of the compressive sensing theory,the image reconstruction from the projections viewed in limited angles is one of the hot problems in the research of computed tomography technology.This paper develops an iterative algorithm for image reconstruction,which can fit most cases.This method gives an image reconstruction flow with the difference image vector,which is based on the concept that the difference image vector between the reconstructed and the reference image is sparse enough.Then the l_2-norm minimization method is used to reconstruct the difference vector to recover the image for flat subjects in limited angles.The algorithm has been tested with a thin planar phantom and a real object in limited-view projection data.Moreover,all the studies showed the satisfactory results in accuracy at a rather high reconstruction speed.