bluuebunny/crossref_metadata_2025 huggingface dataset:
Effect of shear on cubic phases in gels of a diblock copolymer
Authors: Hamley I. W. , Pople J. A. , Fairclough J. P. A. , Terrill N. J. , Ryan A. J. , Booth C. , Yu G.-E. , Diat O. , Almdal K. , Mortensen K. , Vigild M.
Published: July 2002

The effect of shear on the orientation of cubic micellar phases formed by a poly(oxyethylene)–poly(oxybutylene) diblock copolymer in aqueous solution has been investigated using small-angle x-ray scattering (SAXS) and small-angle neutron scattering (SANS). SAXS was performed on samples oriented in a Couette cell using steady shear, and SANS was performed on samples subject to oscillatory shear in situ in a rheometer with a shear sandwich configuration. A body-centered-cubic (bcc) phase observed for gels with concentrations greater than 30 wt % copolymer was found to orient into a polydomain structure, with the close-packed {110} planes both parallel and perpendicular to the shear plane. For gels with 30 wt % copolymer or less, a face-centered-cubic (fcc) phase was observed, and this was also observed on heating the more concentrated gels that formed a bcc phase at room temperature. The fcc phase could be oriented to form a highly twinned structure, with a significant deviation from the ABCABC… stacking sequence of the ideal structure due to random sequences resulting from slip of {111} hexagonal-close-packed planes. For the lower concentration gels, a transition from hard to soft gel on increasing temperature was found to be characterized by a change in the susceptibility of the sample to macroscopic shear orientation, as probed using SAXS. The hard gel could be oriented by shear into a twinned fcc structure, whereas the soft gel comprised a fcc phase with a small grain size, which could not be sheared to form a macroscopically oriented domain. Shear only homogenized the sample, producing a powder SAXS pattern from a fcc structure.
The electronic, vibrational and rotational contributions to the dipole moment, polarizability, and first and second hyperpolarizabilities of the BH molecule
Authors: Ingamells Victoria E. , Papadopoulos Manthos G. , Handy Nicholas C. , Willetts Andrew
Published: July 2002

Electronic, vibrational and rotational contributions to the dipole moment μ, polarizability α, and first and second hyperpolarizabilities, β and γ, are presented for the boron hydride molecule; static and dynamic rovibrational properties are reported for the first time. The electronic contributions are computed ab initio by finite differencing the electronic energy computed at the Hartree–Fock level of theory, and using various sophisticated correlated methods. Specifically these are Mo/ller–Plesset perturbation theory at second order, and fourth order (including single, double, triple and quadruple substitutions), and the Brueckner variant of the coupled-cluster method including triple excitations; density functional theory with the B3LYP functional is used for comparison. Vibrational (and rotational) contributions to the properties are calculated at the Hartree–Fock level of theory; for the vibrational properties, electron correlation is partially included using second order Mo/ller–Plesset theory. Basis set and electron correlation effects on both electronic and vibrational contributions are assessed and discussed. The dependence of the vibrational properties on the mechanical and electrical anharmonicity is examined, and the two methods used in its computation — a finite difference approach and a perturbation theoretic method — are compared and contrasted. A brief analysis of the frequency dependence of vibrational contributions to α(−ωσ;ω1), β(−ωσ;ω1,ω2) in the electro-optic Pockels and second harmonic generation effects, and γ(−ωσ;ω1,ω2,ω3) in the electro-optic Kerr and electric-field-induced second harmonic generation effects, is presented. The electronic results are compared with literature values believed to the best currently available; agreement is shown to be acceptable.
Dynamics of reduced density matrices: Classical memory versus quantum nonlocality
Authors: Makri Nancy
Published: July 2002

The nonlocality in the path integral description of the reduced density matrix for a system interacting with a classical harmonic bath can be eliminated through the introduction of auxiliary variables, leading to Markovian equations. By contrast, the presence of an imaginary part in quantum mechanical response functions appears to prohibit similar approaches, necessitating explicit treatment of quantum nonlocality.
Ion imaging studies of the Cl(2PJ) and Br(2PJ) atomic products resulting from BrCl photodissociation in the wavelength range 235–540 nm
Authors: Cooper Martin J. , Jackson Peter J. , Rogers Leon J. , Orr-Ewing Andrew J. , Ashfold Michael N. R. , Whitaker Benjamin J.
Published: July 2002

The near ultraviolet (UV) and visible photodissociation dynamics of BrCl have been explored using the technique of photofragment ion imaging at 26 wavelengths in the range 235 to 540 nm. Ion images of the Cl(2P3/2), Cl(2P1/2), Br(2P3/2) and Br(2P1/2) photofragments reveal both the angular distributions of photofragment velocities (characterized by anisotropy parameters, β) and which of the four possible photofragment pathways are active at different wavelengths. The anisotropy parameters show extensive variation both with wavelength and for the different fragmentation channels, and these variations are interpreted largely in terms of excitations to the A 3Π(1), B 3Π(0+), C 1Π(1) and D(0+) states as the wavelength is reduced. At wavelengths between 235 and 262 nm, the Br(2P1/2)+Cl(2P3/2) channel is dominant and β=2.0±0.1 at 235 nm, characteristic of a parallel parent transition (ΔΩ=0) and supporting previous assignments of the absorption in this wavelength range being due to the D(0+)–X 1Σ+(0+) transition. A minor channel forms Cl(2P1/2)+Br(2P3/2) with an anisotropy indicative of the involvement of an underlying perpendicular absorption (ΔΩ=±1) to a state with Ω=1. Br(2P3/2)+Cl(2P3/2) and Br(2P1/2)+Cl(2P1/2) fragmentation channels are not observed. Excitation in the wavelength range 320 nm to 410 nm results in Cl(2P3/2)+Br(2P3/2) products with an anisotropy parameter of β=−1.0±0.1, consistent with assignment of the strong parent absorption to the C 1Π(1)–X 1Σ+(0+) transition. For photolysis wavelengths longer than 400 nm, the Cl(2P1/2)/Cl(2P3/2) branching ratio increases [with β∼1.0 to 1.4 for the Cl(2P1/2)], β for Cl(2P3/2) becomes less negative (and for λ⩾450 nm, values lie in the range 0 to −0.2) and Br(2P3/2) β-parameters also increase. No formation of Br(2P1/2) is observed. These observations are, in part, consistent with absorption via the B 3Π(0+)–X 1Σ+(0+) transition, although the nonlimiting β-parameter values imply a significant perpendicular contribution to the absorption spectrum. The measured anisotropy parameters for λ⩾410 nm are interpreted in terms of excitation both to an Ω=0 state [B 3Π(0+)] and an Ω=1 state [A 3Π(1) or C 1Π(1)], together with transfer of dissociating flux between states during the dissociation.
Molecular-dynamics simulation of polymer ordering. I. Crystallization from vapor phase
Authors: Yamamoto Takashi
Published: July 2002

We investigate the molecular mechanism of secondary nucleation on a growth surface of the polymer crystal. We adopt a simplified model of polyethylene molecule made of 500 beads connected by springs, and consider the crystallization from a vapor phase neglecting surrounding molecules. A strongly collapsed chain in a vacuum is placed near the infinitely wide lateral surface of the polymer crystal, and the molecular processes of adsorption and ordering are investigated by molecular-dynamics simulation. It is found that the polymer chain is quickly adsorbed, in a stepwise manner, to form a layer structure: A multilayered at lower temperature and a monolayered at higher temperature. The chain segments adsorbed to the surface align parallel with each other and gradually, within several ns, grow into a neat chain folded lamella with predominantly adjacent-reentry folds. The thickness of the lamella sensibly depends on the crystallization temperature and shows a rapid increase around the melting point. It is found that the polymer ordering on the surface is not a sequential process from the chain-end but a rather cooperative process of many segments. Furthermore, we investigate the effect of finite thickness of the substrate crystal, and find that the limited thickness of the substrate gives rise to the frequent generation of chain loops at and the segregation of chain entanglements toward the lamella surfaces.
Photodissociation dynamics of 1,1-difluoroethylene at 157 nm excitation
Authors: Lin J. J. , Wu S. M. , Hwang D. W. , Lee Y. T. , Yang X.
Published: July 2002

Photodissociation of 1,1-difluoroethylene (F2CCH2) at 157 nm has been investigated using photofragment translational spectroscopy. Five dissociation channels have been experimentally observed; molecular HF elimination, H atom elimination, molecular hydrogen (H2) elimination, F atom elimination, and double bond breaking. Molecular HF elimination and H atom elimination channels are found to be the two major dissociation pathways in photodissociation of F2CCH2 at 157 nm excitation. Molecular hydrogen (H2) elimination and double bond cleavage are also significant, while F atom elimination is a minor process. Product translational energy distributions for all dissociation channels have also been measured. All translational energy releases are peaked at energies away from zero, indicating that the dissociation of F2CCH2 at 157 nm excitation most likely occurs with exit barriers on the ground electronic potential surface through internal conversion from the initially excited electronic state. Branching ratios and averaged energy partitions for different channels have also been estimated.
An integral equation study of a simple point charge model of water
Authors: Lombardero M. , Martı́n C. , Jorge S. , Lado F. , Lomba E.
Published: July 2002

We present an extensive integral equation study of a simple point charge model of water for a variety of thermodynamic states ranging from the vapor phase to the undercooled liquid. The calculations are carried out in the molecular reference-hypernetted chain approximation and the results are compared with extensive molecular dynamics simulations. Use of a hard sphere fluid as a reference system to provide the input reference bridge function leads to relatively good thermodynamics. However, at low temperatures the computed microscopic structure shows deficiencies that probably stem from the lack of orientational dependence in this bridge function. This is in marked contrast with results previously obtained for systems that, although similarly composed of angular triatomic molecules, do not tend to the tetrahedral coordinations that are characteristic of water.
Analytic potential energy surfaces and their couplings for the electronically nonadiabatic chemical processes Na(3p)+H2→Na(3s)+H2 and Na(3p)+H2→NaH+H
Authors: Hack Michael D. , Truhlar Donald G.
Published: July 2002

High-level ab initio electronic structure calculations are presented for the ground and first excited state of the NaH2 system. These calculations include full configuration interaction (FCI) theory, second-order Mo/ller–Plesset perturbation (MP2) theory, and coupled cluster (CC) theory at a wide range of geometries including those near the conical intersection between the ground and first excited state, points in the excited-state potential energy well (exciplex), and the long-range van der Waals wells, and geometries in regions where the interaction energy is dominated by long-range forces. A 2×2 diabatic potential energy matrix function is fit to the high-level ab initio points. Special attention is paid to the form that the diabatic coupling should take and to the method used to fit this coupling. Long-range multipole and dispersion forces, including the quadrupole–quadrupole interaction, are included in the diagonal elements of the potential energy matrix. The matrix potential and its eigenvalues are compared to results that have appeared in the literature previously.
Spatial distribution of N2, N2O, and NO desorbing from a Pd(211) surface
Authors: Ikai Masamichi , Tanaka Ken-ichi
Published: July 2002

The spatial distributions of NO, N2, and N2O desorbing from Pd(211), Pd(S)-[3(111)×(100)], in temperature programmed desorption (TPD) and that of N2 produced in the temperature programmed reaction (TPR) of NO+H2 have been studied. The spatial distribution of N2 desorbing at 510 K in the TPD had a maximum intensity at θ=−25–−30 deg (down the steps) in the [1 1̄ 1̄] direction, which is almost normal to the (100) steps, and is described by 2.4 cos12(θ+26 deg). Taking account of the fact that NO molecules are preferentially adsorbed on the (111) terraces of a Pd(211) surface at low coverage, it is deduced that the NO adsorbed on the (111) terraces undergoes migration to the (100) steps, where N2 is produced. An isotopically labeled angle-resolved TPD experiment showed that N2 was produced by the NO+N reaction. On the other hand, the desorption of NO is normal to the crystal surface. This phenomenon indicates that NO desorbs via a predesorption state, where NO molecules forget their memory of the previous adsorption sites. In contrast, the spatial distribution of N2 given by the catalytic reaction in a flow of NO+H2 at 650 K, was completely different from that of N2 produced by NO+N reaction at around 500 K. It is concluded that the spatial distribution reflects the reaction or desorption mechanisms, especially the reaction coordinate on the surface.
Intermolecular forces from density functional theory. III. A multiproperty analysis for the Ar(1S)-CO(1Σ) interaction
Authors: Gianturco F. A. , Paesani F. , Laranjeira M. F. , Vassilenko V. , Cunha M. A.
Published: July 2002

The full anisotropic interaction between one Ar atom and the CO(1Σ) molecule treated as a rigid rotor (RR) at its equilibrium geometry is evaluated using density functional theory (DFT) to describe the short-range repulsive region (and its orientational anisotropy) as well as the well region and its angular dependence. The long-range dispersion forces are added from the results of perturbation theory and a scaling procedure is suggested for their correct matching with the DFT data. The computational results are found to agree very well with more sophisticated calculations and to improve on earlier empirical estimates. An extensive comparison with available transport property measurements is also carried out and using, among others, new experimental data for thermal diffusion [Shashkov et al., Inzh. Fiz. Zh. 71, 182 (1998)] analyzed in this work for the first time. The present modifications of DFT treatment of the interaction using the correct dispersion terms therefore appears to provide a realistic description of the Ar–CO potential and of several dynamical properties of this molecular mixture in the gas phase.
Sedimentation potential of a concentrated spherical colloidal suspension
Authors: Lee Eric , Chu Jhih-Wei , Hsu Jyh-Ping
Published: July 2002

The sedimentation behavior of a concentrated suspension of charged spherical particles is investigated theoretically. The sedimentation potential is evaluated taking the effect of double layer polarization into account. A cell model is adopted to describe the present multientities system, and a pseudospectral numerical scheme is used to solve the governing electrokinetic equations, which comprise a Navior–Stokes equation for flow field and a Poisson equation for electric field. Several interesting phenomena, which are absent if double layer polarization is neglected, are observed. For example, the ratio (E*/U*), E*, and U* being, respectively, the scaled sedimentation potential and the scale velocity, has a minimum if the electrical potential is low, and has a maximum if it is high.
High resolution infrared spectroscopy of single SF6 molecules in helium droplets. II. The effect of small amounts of He4 in large He3 droplets
Authors: Harms Jan , Hartmann Matthias , Sartakov Boris , Toennies J. Peter , Vilesov Andrei F.
Published: July 2002

The rotationally resolved infrared spectra of single SF6 molecules embedded in large He3 droplets have been studied as a function of mean sizes between N̄3=2×103 and 105 atoms by the cluster beam depletion technique. The observed frequency shifts and line broadening of the dopant spectra are interpreted in terms of the small impurity of about 30–50 He4 atoms, which because of their lower zero point energy completely surround the SF6 molecule. For the largest droplets, the observed rotational structure is similar to that observed in pure He4 droplets but the rotational temperature as determined from the relative line intensities is Trot=0.15(1) K, which is about a factor 2.5 lower than in pure He4 droplets. The lower temperature is expected on the basis of the lower heat of evaporation of the He3 atoms on the outside of the droplet. Mixed He/43He droplets produced by increasing the He4 concentration in the source gas to 1.2 and 4% of the He3 were found to have temperatures between that for the almost pure He3 droplets and that for pure He4 droplets.
On the frequency dependence of ultrasonically induced birefringence in isotropic phase of liquid crystal: 5CB (p-n-pentyl p′-cyanobiphenyl)
Authors: Matsuoka Tatsuro , Yasuda Keiji , Koda Shinobu , Nomura Hiroyasu
Published: July 2002

Theoretical expressions for the ultrasonically induced birefringence of liquids are obtained in the frame work of de Gennes’ phenomenological theory. The intensity and frequency dependence of ultrasonically induced birefringence in the isotropic phase of p-n-pentyl p′-cyanobiphenyl (5CB) was measured in order to examine the usefulness of birefringence measurements for investigating dynamical properties liquids. The observed birefringence was proportional to the square root of ultrasonic intensity. The birefringence divided by the square root of ultrasonic intensity increases with increasing frequency and appears to saturate when the ultrasonic frequency approaches the relaxation frequency of molecular reorientation. The observed values of birefringence were reproduced satisfactorily by the expression derived in this paper.
The role of the attractive and the repulsive interactions in the nonpolar solvation dynamics in simple fluids from the gas-like to the liquid-like densities
Authors: Yamaguchi T. , Kimura Y. , Hirota N.
Published: July 2002

We have performed molecular dynamics (MD) simulations of the nonpolar solvation dynamics in simple fluids composed of particles interacting through the Lennard-Jones (LJ) 12–6 potential or its repulsive part. The attractive or the repulsive part of the solute–solvent interaction is assumed to change on the excitation of a solute. We have followed the transition energy fluctuation of the solute by the equilibrium simulation. The division of the LJ potential followed the method of WCA [J. W. Weeks, D. Chandler, and H. C. Andersen, J. Chem. Phys. 54, 5237 (1971)]. We have surveyed over a wide solvent density region from gas-like to liquid-like densities at the constant temperature. When the attractive part changes, the relaxation becomes faster with an increase of the solvent density. This result contradicts with previous theories that treat the nonpolar solvation dynamics in terms of the diffusion of solvent particles. The time scale of the initial part of the relaxation is well correlated with the static fluctuation divided by the static average, which suggests the importance of the curvature of the free energy surface in the initial part of the solvation. When the repulsive part changes, the initial part of the relaxation is almost density independent, determined by the binary motion between solute and solvent. It is consistent with the result that the static fluctuation is almost proportional to the static average, which indicates the absence of the static correlation between solvent particles. On the other hand, the solvation correlation function shows rather complicated density dependence at the longer time scale. In the case of the binary mixture solvent, the relaxation time is inversely proportional to the diffusion coefficient. On the basis of the nonpolar solvation dynamics, the validity of the isolated binary collision model for the vibrational energy relaxation is also discussed, and the recent hydrodynamic theory on the vibrational energy relaxation [B. J. Cherayil and M. D. Feyer, J. Chem. Phys. 107, 7642 (1997)] is critically examined.
Product quantum-state-dependent anisotropies in photoinitiated unimolecular decomposition
Authors: Demyanenko A. V. , Dribinski V. , Reisler H. , Meyer H. , Qian C. X. W.
Published: July 2002

Angular distributions of state-selected NO and O products in the photoinitiated unimolecular decomposition of jet-cooled NO2 have been measured by using both the photofragment ion imaging technique with velocity map imaging and ion time-of-flight translational spectroscopy. The recoil anisotropy parameter of the photofragments, β, depends strongly on the rotational angular momentum of the photoproduct. O(3Pj=2,0) angular distributions are recorded at photolysis wavelengths 371.7, 354.7, and 338.9 nm. At these wavelengths, respectively, vibrational levels v=0, v=0,1 and v=0–2 of NO are generated. In addition, β values for NO(v=2) in specific high rotational levels are determined at ∼338 nm. The experimental observations are rationalized with a classical model that takes into account the transverse recoil component mandated by angular momentum conservation. The model is general and applicable in cases where fragment angular momentum is large, i.e., a classical treatment is justified. It is applied here both to the experimental NO2 results, and results of quantum calculations of the vibrational predissociation of the Ne–ICl van der Waals complex. It is concluded that deviations from the limiting β values should be prominent in fast, barrierless unimolecular decomposition, and in certain dissociation processes where a large fraction of the available energy is deposited in rotational excitation of the diatom. The application of the model to NO2 dissociation suggests that the nuclear dynamics leading to dissociation involves a decrease in bending angle at short internuclear separations followed by a stretching motion. This interpretation is in accord with recent theoretical calculations.
Thermodynamic fragility and kinetic fragility in supercooling liquids: A missing link in molecular liquids
Authors: Ngai K. L. , Yamamuro Osamu
Published: July 2002

Ito, Moynihan, and Angell [Nature 398, 492 (1999)] compared the kinetic and thermodynamic measures of a glassformer’s “fragility.” For the liquids they considered which include molecular, covalent, and ionic substances, thermodynamic fragility and kinetic fragility follow the same order, suggesting that the thermodynamic data alone may be sufficient to determine the kinetic fragility of a liquid. Here we restrict the comparison to a large number of molecular glass-forming liquids, and find breakdowns of the proposed correlation. The absence of an immediate connection between thermodynamic and kinetic fragilities at least in molecular liquids may be due to the effect of kinetic factors and cooperative many-body molecular dynamics. The development of a relation between them requires taking into consideration the cooperative many-body molecular dynamics. The latter governs, in conjunction with thermodynamics, the kinetics of glass-forming liquids, and thus is the missing link between the two.
Kinetics study on the hydrogen atom-induced abstraction and associative desorption of deuterium adatoms from the Si(100) surface at 573 K
Authors: Shimokawa S. , Namiki A. , Ando T. , Sato Y. , Lee J.
Published: July 2002

Hydrogen atom-induced deuterium adatom abstraction has been studied on the Si(100) surface from a desorption point of view. Abstraction of HD as well as collision-induced D2 desorption are observed on the D/Si(100) surface during H beam exposure at 573 K. For 1 ML Dad precoverage, about 30% of the desorbed D atoms are ejected as collision-induced D2 desorption at the very beginning of H(g) exposure. It is found that the decay of the HD and D2 rates are affected by the total coverage, θH+D. The decay rate of the HD rate is much lower in the low coverage regime than in the high coverage regime. The nominal cross section of the former is 2.3±1.0 Å2, while for the latter 7.2±0.5 Å2. The HD rate curves show that the abstraction obeys nearly first-order kinetics towards D coverage, θD. On the other hand, the D2 rate curves show that the collision-induced desorption obeys nearly fourth-order kinetics towards θD. Such HD abstraction is also observed on an oxygen-deposited D/Si(100) surface where the oxygen atoms are known to be incorporated between Si atoms. The observed decay rate of the HD rate is extremely low, with a cross section of 1.5±1.0 Å2. The reaction kinetics are well understood by adopting the kinetics model recently proposed by Flowers et al. [Surf. Sci. 396, 227 (1998)]. The abstraction of HD may be due to an Eley–Rideal mechanism rather than to a hot atom mechanism. Collision-induced D2 desorption may take place upon encounter of two dideuteride species via an isomerization reaction at quasiequilibrium.
Ab initio study of the hydroxide ion–water clusters: An accurate determination of the thermodynamic properties for the processes nH2O+OH−→HO−(H2O)n (n=1–4)
Authors: Pliego Josefredo R. , Riveros José M.
Published: July 2002

Clusters of hydroxide ion, HO−(H2O)n=1–4, have been studied by high level ab initio calculations in order to better understand the first coordination shell of OH− ions. Geometry optimizations were performed at Hartree–Fock, density functional theory and second order Møller–Plesset perturbation theory levels using the 6-31+G(d,p) basis set. Single point energy calculations were carried out on the optimized geometries using the more extended 6-311+G(2df,2p) basis set and a higher level of electron correlation, namely fourth-order Møller–Plesset perturbation theory. For the n=1–3 clusters, only structures with the hydroxide ion hydrogen bonded to all waters molecules were considered. For the n=4 cluster, three minima were found; the most stable species has all four waters directly bound to the hydroxide ion, while the other two clusters have only three waters in the first coordination shell. In addition, the transition state connecting the cluster containing four waters in the first coordination shell to the species having three waters in the coordination shell was characterized. The barrier for this rearrangement is very low (1.82 kcal/mol), and we predict this process to occur on the picosecond time scale. The thermodynamic properties (enthalpy, entropy and Gibbs free energy) for the formation of the clusters have been calculated for all the species (including the fully deuterated clusters). Comparison of our calculations with experimental data reveals good agreement in the free energy. Nevertheless, our ab initio results suggest that for the n>1 clusters, both −ΔH0 and −ΔS0 are larger than those reported from experiment and new experiments may be necessary to obtain accurate experimental values.
On hypersurface-homogeneous space-times
Authors: Hajj-Boutros J.
Published: July 2002

We propose a new method to build exact solutions of Einstein field equations in case of ‘‘hypersurface-homogeneous space-times.’’ The energy-momentum tensor is of perfect fluid type. Starting from SE solutions we are able to build new classes of solutions which add to the rare solutions not satisfying the equation of state p=(γ−1)μ. We study the geometrical and physical properties of some of the solutions obtained.
Separability of the Killing–Maxwell system underlying the generalized angular momentum constant in the Kerr–Newman black hole metrics
Authors: Carter B.
Published: July 2002

The concept of a Killing–Maxwell system may be defined by the relation Â[μ;v];ρ =(4π/3)ĵ[μgν]. In such a system the one-form Âμ is interpretable as the four-potential of an electromagnetic field F̂μv, whose source current ĵ μ is an ordinary Killing vector. Such a system determines a canonically associated duality class of source-free electromagnetic fields, its own dual being a Killing–Yano tensor, such as was found by Penrose [Ann. N.Y. Acad. Sci. 224, 125 (1973)] (with Floyd) to underlie the generalized angular momentum conservation law in the Kerr black hole metrics, the existence of the Killing–Yano tensor being also a sufficient condition for that of the Killing–Maxwell system. In the Kerr pure vacuum metric and more generally in the Kerr–Newman metrics for which a member of the associated family of source-free fields is coupled in gravitationally, it is shown that the gauge of the Killing–Maxwell one-form may be chosen so that it is expressible (in the standard Boyer–Lindquist coordinates) by 1/2 (a2 cos 2 θ−r2)dt+ 1/2 a(r2−a2)sin2 θ dφ, the corresponding source current being just (4π/3)(∂/∂t). It is found that this one-form (like that of the standard four-potential for the associated source-free field) satisfies the special requirement for separability of the corresponding coupled charged (scalar or Dirac spinor) wave equations.
Nonlinear equations with superposition formulas and the exceptional group G2. II. Classification of the equations
Authors: Beckers J. , Hussin V. , Winternitz P.
Published: July 2002

Nonlinear equations with superposition formulas are obtained, corresponding to the action of the complex and real forms of the exceptional Lie group G2 on the homogeneous spaces G2/H. The isotropy group of the origin H is taken as one of the maximal parabolic subgroups of G2, or as one of the maximal reductive subgroups, leaving some vector space V∈C7 (or V∈R7) invariant. The parabolic subgroups, as well as the simple subgroups SL(3,C), SU(3), SL(3,R) or SU(2,1) lead to equations with quadratic or quartic nonlinearities. The semisimple subgroups SL(2,C)⊗SL(2,C), SU(2)⊗SU(2), and SU(1,1)⊗SU(1,1) lead to equations with quadratic nonlinearities and additional nonlinear constraints on the independent variables.
Deformation of algebras and solution of self-duality equation
Authors: Leznov A. N. , Mukhtarov M. A.
Published: July 2002

The solutions of the self-duality equation depending on a set of functions of three independent variables are constructed in an explicit way. The obtained solutions are shown to be connected with two-dimensional systems determined by the operators of the Lax pair.
Unitary measurements of discrete quantities in quantum mechanics
Authors: Beltrametti Enrico G. , Cassinelli Gianni , Lahti Pekka J.
Published: July 2002

The pure measurements of discrete physical quantities are characterized within quantum theory of measurement and their unitary representations are given. Probabilistic aspects of measurements related to the so-called strong correlation conditions and a probabilistic characterization of the first kind measurements are examined. The problem of the objectification of the measurement result is analyzed in terms of a classical behavior of the measuring apparatus. As a by-product a generalization of the Wigner–Araki–Yanase theorem is given.
Phaseless inverse scattering and the phase problem in optics
Authors: Klibanov Michael V. , Sacks Paul E.
Published: July 2002

Two related problems are considered: (i) the inverse scattering problem for a potential V(x) supported on the half-line {x≥0}, when the given data is ‖R−(k)‖, the amplitude of the reflection coefficient and (ii) determination of a function g(t) supported on the half-line {t≥0} when the given data is ‖ĝ(k)‖, the amplitude of the Fourier transform of g. Under certain conditions on V or g, uniqueness theorems are proved and computational methods are developed. A numerical example of recovery of V(x) from ‖R−(k)‖ is given.
Mellin transform methods applied to integral evaluation: Taylor series and asymptotic approximations
Authors: Sasiela Richard J. , Shelton John D.
Published: July 2002

Mellin transform methods have been used to obtain Taylor series or asymptotic approximations to definite integrals whose integrands consist of the product of two generalized hypergeometric functions. This approach has proved extremely useful in many applied physics problems including the analysis of electromagnetic propagation in a turbulent medium. The main result in this article is a generalization of the method to integrands containing the product of an arbitrary number of hypergeometric functions providing a very powerful and general technique for integral evaluation with many applications in physics.
Entropy of orthogonal polynomials with Freud weights and information entropies of the harmonic oscillator potential
Authors: Van Assche W. , Yáñez R. J. , Dehesa J. S.
Published: July 2002

The information entropy of the harmonic oscillator potential V(x)=1/2λx2 in both position and momentum spaces can be expressed in terms of the so-called ‘‘entropy of Hermite polynomials,’’ i.e., the quantity Sn(H):= −∫−∞+∞H2n(x)log H2n(x) e−x2dx. These polynomials are instances of the polynomials orthogonal with respect to the Freud weights w(x)=exp(−‖x‖m), m≳0. Here, a very precise and general result of the entropy of Freud polynomials recently established by Aptekarev et al. [J. Math. Phys. 35, 4423–4428 (1994)], specialized to the Hermite kernel (case m=2), leads to an important refined asymptotic expression for the information entropies of very excited states (i.e., for large n) in both position and momentum spaces, to be denoted by Sρ and Sγ, respectively. Briefly, it is shown that, for large values of n, Sρ+1/2logλ≂log(π√2n/e)+o(1) and Sγ−1/2log λ≂log(π√2n/e)+o(1), so that Sρ+Sγ≂log(2π2n/e2)+o(1) in agreement with the generalized indetermination relation of Byalinicki-Birula and Mycielski [Commun. Math. Phys. 44, 129–132 (1975)]. Finally, the rate of convergence of these two information entropies is numerically analyzed. In addition, using a Rakhmanov result, we describe a totally new proof of the leading term of the entropy of Freud polynomials which, naturally, is just a weak version of the aforementioned general result.
Lévy flight applied to random media problems
Authors: Uchaikin V. , Gusarov G.
Published: July 2002

A random-medium model being the correlated distribution of points positioned in E-dimensional Euclidean space is considered. The construction of the medium starts from noncorrelated (Poisson) uniform distribution of parent particles; each of them initiates the finite Marcov chain of its descendants. The complete collection of correlation functions of all orders within the scope of the model has been obtained. The use of three-dimensional stable laws (Lévy laws) as transition probability density allows one to express the correlation functions of all orders in terms of two point ones only. Some numerical results are presented and discussed in connection with fractal structure simulation.
On the concept of Einstein–Podolsky–Rosen states and their structure
Authors: Arens Richard , Varadarajan V. S.
Published: July 2002

In this paper the notion of an EPR state for the composite S of two quantum systems S1,S2, relative to S2 and a set 𝒪 of bounded observables of S2, is introduced in the spirit of the classical examples of Einstein–Podolsky–Rosen and Bohm. We restrict ourselves mostly to EPR states of finite norm. The main results are contained in Theorems 3–6 and imply that if EPR states of finite norm relative to (S2,O) exist, then the elements of 𝒪 have discrete probability distributions and the Von Neumann algebra generated by 𝒪 is essentially imbeddable inside S1 by an antiunitary map. The EPR states then correspond to the different imbeddings and certain additional parameters, and are explicitly given by formulas which generalize the famous example of Bohm. If 𝒪 generates all bounded observables, S2 must be of finite dimension and can be imbedded inside S1 by an antiunitary map, and the EPR states relative to S2 are then in canonical bijection with the different imbeddings of S2 inside S1; moreover they are then given by formulas which are exactly those of the generalized Bohm states. The notion of EPR states of infinite norm is also explored and it is shown that the original state of Einstein–Podolsky–Rosen can be realized as a renormalized limit of EPR states of finite quantum systems considered by Weyl, Schwinger, and many others. Finally, a family of states of infinite norm generalizing the Einstein–Podolsky–Rosen example is explicitly given.
Analogies between finite-dimensional irreducible representations of SO(2n) and infinite-dimensional irreducible representations of Sp(2n,R). I. Characters and products
Authors: King R. C. , Wybourne B. G.
Published: July 2002

The analogy between the finite-dimensional spin representation Δ of SO(2n) and the infinite-dimensional representation Δ̃ of Sp(2n,R) is made precise. It is then shown that this analogy can be extended so as to provide a precise link between each finite dimensional unitary irreducible representation of SO(2n) and a corresponding infinite-dimensional unitary irreducible representation of Sp(2n,R). The analogy shows itself at the level of the corresponding characters and difference characters, and involves the use of Schur function methods to express both characters and difference characters of SO(2n) and Sp(2n,R) in terms of characters of irreducible representations of their common subgroup U(n). The analogy is extended still further to cover the explicit decomposition of not only tensor products of Δ and Δ̃ with other unitary irreducible representations of SO(2n) and Sp(2n,R), respectively, but also arbitrary tensor powers of Δ and Δ̃.
Resistive relaxation processes in oxygen-deficient single crystals of YBa2Cu3O7−δ
Authors: Obolenskii M. A. , Bondarenko A. V. , Vovk R. V. , Prodan A. A.
Published: July 2002

The effect of low-temperature annealing on the superconducting transition temperature and electrical resistance of single crystals of YBa2Cu3O7−δ with an oxygen deficiency δ=0.5–0.6 quenched from temperatures of 620–650 °C is considered. The transition temperature increases during annealing, while the resistance decreases. The isothermal relaxation of resistance is measured and used for estimating the activation energy of the relaxation process, which coincides with the activation energy of oxygen diffusion. The obtained results are attributed to oxygen ordering in Cu-O planes without changing its concentration. The observed step form of resistive transitions to the superconducting state is interpreted as the formation of clusters characterized by different oxygen concentrations and ordering. The cluster size is estimated.
The evolution of the double-diffusive instability: Salt fingers
Authors: Shen Colin Y.
Published: July 2002

The finite-amplitude growth of finger convection at an interface of two uniform solutions is studied to determine the processes that govern the scale and amplitude of the convection, the growth of the fingering interface, and the transition of the convection to turbulence. A conceptual model of fingering processes is provided and details are studied by means of direct numerical simulation. The simulations obtain full finger convection and turbulence for ratios of viscosity to diffusivities in the range between 1 and 10. The study shows that the evolution of finger convection in its entirety is characterized by the scale and amplitude of the fastest growing finger mode. In the parameter range studied, the growth of the fingering interface is found to be controlled mostly by molecular diffusion. Convective flux divergence only plays a secondary role. The growth of the interface is shown to have the effect of increasing the horizontal scale of the convection while decreasing the buoyancy flux. However, the kinetic and potential energies remain statistically stationary for fully developed finger convection. Density inversion developed within finger convection is shown to play an important role in the breakup of finger structures into turbulence. The significance of ‘‘collective’’ instability in determining this transition is not substantiated by the simulation for the parameter values studied here.
A comparison of the turbulence structure of subsonic and supersonic boundary layers
Authors: Smits A. J. , Spina E. F. , Alving A. E. , Smith R. W. , Fernando E. M. , Donovan J. F.
Published: July 2002

A comparison of the turbulence structure of subsonic and supersonic boundary layers reveals that, despite broad similarities, significant differences exist. The length scales derived from space-time correlations indicate that the spanwise scales are almost identical but that the streamwise scales in the supersonic flow are about half the size of those in subsonic flow. The large-scale structures in the subsonic boundary layer appear to move slightly slower, and lean more toward the wall than those observed in supersonic flows, and their shear stress content is distributed differently among the four quadrants. These observations should have a strong impact on deriving turbulence models for high Reynolds number supersonic flows.
Empirical and Stokes eigenfunctions and the far-dissipative turbulent spectrum
Authors: Foias C. , Manley O. , Sirovich L.
Published: July 2002

It is shown that the Stokes eigenfunctions and their corresponding spectra, frequently used in mathematical investigations of the Navier–Stokes equations, provide estimates on the spectrum of the two-point spatial covariance tensor. This, in turn, is used to estimate the far-dissipative turbulent spectrum. An exponential falloff is predicted and evidence given which implies that this is a sharp estimate.
Ignition and structure of a laminar diffusion flame in a compressible mixing layer with finite rate chemistry
Authors: Grosch C. E. , Jackson T. L.
Published: July 2002

In this paper the ignition and structure of a reacting compressible mixing layer lying between two streams of reactants with different free-stream speeds and temperatures using finite rate chemistry are considered. Numerical integration of the governing equations show that the structure of the reacting flow can be quite complicated depending on the magnitude of the Zeldovich number. In particular, for sufficiently large Zeldovich number, the three regimes first described by Linan and Crespo [Combust. Sci. Technol. 14, 95 (1976)]; i.e., ignition, deflagration, and diffusion flame, occur in supersonic as well as in subsonic flows. An analysis of both the ignition and diffusion flame regimes is presented using a combination of large Zeldovich number asymptotics and numerics. This allows an analysis of the behavior of these regimes as a function of the parameters of the problem. For the ignition regime, a well-defined ignition point will always exist provided the adiabatic flame temperature is greater than either free-stream temperature. For the diffusion flame regime, the location of the flame changes significantly with changes in the equivalence ratio and the Schmidt numbers.
Scale transition of double-diffusive finger cells
Authors: Shen Colin Y. , Veronis George
Published: July 2002

The processes that bring about the change of cell size in the evolution of salt-finger convection are investigated with a numerical model of the convection in a Hele–Shaw cell. It is shown that the increase of cell width during the convection is produced by the vertical penetration of increasingly wider cells from the edges of the finger zone into the interior, as has been observed in a laboratory experiment. The increase of scale is also shown to occur through the merging process in which narrow finger cells merge to form wider cells. Occasionally, transition from wide to narrow scale can occur, in which case the wide finger cell splits to form two or more narrow cells. The scale transition produced by the merging, penetration, and splitting processes is shown to have the effect of maximizing the buoyancy flux generation in an evolving finger convection. This maximization is also interpreted in terms of the most rapidly growing finger mode. The effect of the scale transition on the actual magnitude of the buoyancy flux is related to the energy dissipation of fingers.
The dissipation-range spectrum and the velocity-derivative skewness in turbulent flows
Authors: Smith L. M. , Reynolds W. C.
Published: July 2002

In order to determine the best representation of the turbulence spectrum in the dissipation range, the dynamical equation for the rate of energy dissipation ℰ is used, together with a model spectrum of the form E[k] = CKℰ2/3k−5/3 exp[ − σkm], to obtain a prediction for the velocity derivative skewness S̄ at high Reynolds number: S̄ = S̄[CK,m]. The skewness data suggest that m=2 is the best model for laboratory-scale flows.
Statistical properties of MHD turbulence and turbulent dynamo
Authors: Kida Shigeo , Yanase Shinichiro , Mizushima Jiro
Published: July 2002

Statistical properties of MHD turbulence and the mechanism of turbulent dynamo are investigated by direct numerical simulations of three-dimensional MHD equations. It is assumed that the turbulent field has a high symmetry and that the fluid has hyperviscosity and hypermagnetic diffusivity. An external force is exerted on the fluid as kinetic energy and helicity sources. The main concern of the present study is whether magnetic fields of scales comparable to the dominant fluid motions can be generated or not. It is shown that the turbulent dynamo is effective if hypermagnetic diffusivity is smaller than a critical value. The total energy spectrum is close to the k−5/3 power law in the inertial range. The energy transfer between kinetic and magnetic fields is discussed.
Formation of head–tail structure in a two-dimensional uniform straining flow
Authors: Kida S. , Takaoka M. , Hussain F.
Published: July 2002

The formation of head–tail structure, which is commonly observed in the interaction of vortex tubes, is investigated by direct numerical simulation of a two-dimensional Navier–Stokes flow. A head–tail structure is created in the course of evolution of the Batchelor dipole in a uniform straining flow. By noting that the Batchelor dipole is steady if there is no external flow and that the dipole is deformed before viscous effect appears, it is concluded that the relative strength of the straining flow plays an important role in the head–tail formation.
Viscous fingering with permeability heterogeneity
Authors: Tan C.-T. , Homsy G. M.
Published: July 2002

Viscous fingering in miscible displacements in the presence of permeability heterogeneities is studied using two-dimensional simulations. The heterogeneities are modeled as stationary random functions of space with finite correlation scale. Both the variance and scale of the heterogeneities are varied over modest ranges. It is found that the fingered zone grows linearly in time in a fashion analogous to that found in homogeneous media by Tan and Homsy [Phys. Fluids 31, 1330 (1988)], indicating a close coupling between viscous fingering on the one hand and flow through preferentially more permeable paths on the other. The growth rate of the mixing zone increases monotonically with the variance of the heterogeneity, as expected, but shows a maximum as the correlation scale is varied. The latter is explained as a ‘‘resonance’’ between the natural scale of fingers in homogeneous media and the correlation scale.
Comment on the dissipation-range spectrum in turbulent flows
Authors: Sanada Tsutomu
Published: July 2002

Recently, Smith and Reynolds [Phys. Fluids A 3, 992 (1991)] suggested that the turbulent energy spectrum with exponential decaying form E(k)=CKε2/3k−5/3 exp(−σk) (CK is Kolmogorov constant, ε is the energy dissipation rate, and σ is some constant) may be a poor model, because it does not give velocity derivative skewness in good agreement with experimental value. On the other hand, some direct numerical simulations of the Navier–Stokes equation demonstrate the above exponential form in the dissipation range. This disagreement is resolved by considering a model spectrum based on direct numerical simulation.