bluuebunny/crossref_metadata_2025 huggingface dataset:
Theory of fluorescence excitation spectra using anharmonic-coriolis coupling in S1 and internal conversion to S. I. General formalism
Authors: Helman Adam , Marcus R. A.
Published: July 2002

A treatment of one- or two-photon fluorescence excitation spectra is described using the vibration–rotation coupling of zeroth order states in the excited electronic state and nonadiabatic coupling to the ground state. Using perturbation theory, experimental harmonic frequencies, an anharmonic force field, and various theoretical Coriolis coupling constants, a quasistationary molecular eigenstate in an excited electronic state S1 is first calculated. The S1 eigenstate is then coupled via the nonadiabatic nuclear kinetic energy operator (internal conversion) to rovibronic states in the ground state manifold, the latter states approximated in a simple manner. A search algorithm is used to select the S1 dark states and the S0 states. Both the perturbation theory coefficient and the Franck–Condon factors are employed in the evaluation function used in the search. The results are applied in part II to the channel three problem in benzene.
Homogeneous nucleation rates for water
Authors: Viisanen Y. , Strey R. , Reiss H.
Published: July 2002

We have investigated homogeneous nucleation of water droplets in the vapor phase. Nucleation in water vapor has been previously studied a number of times using various experimental techniques. The nucleation pulse technique used here allows accurate measurements of homogeneous nucleation rates J vs supersaturation S in the range from 105 to 109 cm−3 s−1. The advance reported here consists of the fact that the J–S curves are measured at a selectable constant temperature. We determined the nucleation rates in supersaturated water vapor mixed with various carrier gases as functions of supersaturation and temperature (217<T/K<259). Nucleation is found to be nondependent of the nature of the carrier gas. Data analysis was carried out in four steps. First, we observed quantitative agreement in the range of overlap with experimental results by Miller et al. [J. Chem. Phys. 78, 3204 (1983)]. Second, experimental nucleation rates were compared with the predictions of classical nucleation theory. Systematic deviations from that theory were observed as in the case of other systems (e.g., alcohols, nonane) studied previously. Third, comparison with a new version of Fisher’s droplet model reveals remarkable agreement between experiment and theory. Finally, we implemented a model-independent determination of the average nucleus size directly from the slopes of the isothermal J–S curves.
Erratum: Raman linewidths and rotationally inelastic collision rates in nitrogen [J. Chem. Phys. 98, 257 (1993)]
Authors: Green Sheldon
Published: July 2002

A computer program error led to erroneous results in the titled paper. Corrected generalized IOS cross sections are significantly changed, especially at lower collision energies. These changes tend to cancel in predicted Raman linewidths; there is a systematic increase of 10–15 %, changing quantitative, but not qualitative, comparisons with experimental data.
Integral cross sections and rate constants for the reaction OH+H2→H2O+H: A semiclassical wave packet approach
Authors: Balakrishnan N. , Billing G. D.
Published: July 2002

A semiclassical wavepacket method has been introduced to study diatom–diatom exchange reactions of the type AB+CD→ABC+D; ABD+C using purely inelastic coordinates. The vibrations of the two reagent molecules are treated quantum mechanically by an exact solution of the time-dependent Schrödinger equation. The rotational motions as well as the relative translational motion of the two molecules are treated classically. The coupling between the quantal and classical degrees of freedom is described within an effective Hamiltonian approach. The method has been illustrated for the exothermic reaction OH+H2→H2O+H by computing integral cross sections and rate constants. The computed integral cross sections are in reasonable accord with existing quasiclassical trajectory results, but in significant disagreement with recently reported approximate quantum mechanical calculations. The calculated rate constants for the ground vibrational states of the reagents are in good agreement with experimental rate constants in the temperature range 300≤T≤700 K. Comparisons of the rate constants are also made with various theoretical results, including a recently reported six-dimensional quantum mechanical calculation.
Dissociation of H2 on Cu(100): Dynamics on a new two-dimensional potential energy surface
Authors: Wiesenekker G. , Kroes G. J. , Baerends E. J. , Mowrey R. C.
Published: July 2002

A two-dimensional (2-D) potential energy surface (PES) has been calculated for H2 interacting with the (100) face of copper. The PES is for H2 approaching with its internuclear axis parallel to the surface and dissociating over a bridge site into neighboring hollow sites. The density functional calculations were performed both within the local density approximation (LDA) and within a generalized gradient approximation (GGA). The LDA surface shows no barrier to chemisorption, but the GGA surface has a barrier of height 0.4 eV. A fit of the GGA surface has been used to calculate reaction probabilities for H2 in its v=0 and v=1 vibrational states, employing a wave packet method. The 2-D wave packet results for the v=0 and v=1 thresholds are consistent with experiment, indicating that the barrier height calculated within the GGA used is accurate. The GGA results for the value of the barrier height are also consistent with the GGA value (0.5 eV) recently obtained for H2+Cu(111) by Hammer et al. [Phys. Rev. Lett. 73, 1400 (1994)], but the GGA value recently computed for H2+Cu(100) (0.9 eV) by White et al. is too high [Phys. Rev. Lett. 73, 1404 (1994)].
Calculating atomic properties using variational Monte Carlo
Authors: Alexander S. A. , Coldwell R. L.
Published: July 2002

Using variational Monte Carlo and the explicitly-correlated wave function forms optimized by Schmidt and Moskowitz, we compute a number of properties for the atoms He–Ne. The expectation value of the Hamiltonian using these wave functions contains between 70.0% and 99.8% of the correlation energy for the neutral atoms (17 parameters), 60.8% and 99.1% for selected cations (9 parameters), and 73.9% and 89.4% for selected anions (17 parameters). For those properties which sample the valence region, our results are in good agreement with previous calculations (where available). Because of a defect in the wave function form, a substantial error is found in those properties which two electrons that are in close proximity.
Kinetics of crystallizing D2O water near 150 K by Fourier transform infrared spectroscopy and a comparison with the corresponding calorimetric studies on H2O water
Authors: Hage Wolfgang , Hallbrucker Andreas , Mayer Erwin , Johari G. P.
Published: July 2002

Crystallization kinetics of hyperquenched D2O liquid has been studied by Fourier transform infrared spectroscopy by determining the irreversible change in the spectra of stretching vibrations of the decoupled OH oscillator in ≊12 mol % HOD in D2O. The kinetics follows an almost exponential behavior with time. The exponent to the crystallization time, n, increases from its value of 1.0 at 152 K to 1.2 at 147 K and its value is slightly lower than that of H2O. The combined results of H2O and D2O indicate that temperature rather than the mass of the molecules determines n. Interpretation of n in terms of the morphology of grains formed seems inconsistent in view of the observed temperature effect. It is suggested that an alternative interpretation of n in terms of distribution of diffusion times, or time independent activation energy (barrier height to crystallization), is more appropriate. Calorimetric measurements for the crystallization of H2O yield results consistent with those from infrared spectroscopic study.
Molecular dynamics simulations of a Gay–Berne nematic liquid crystal: Elastic properties from direct correlation functions
Authors: Stelzer Joachim , Longa Lech , Trebin Hans-Rainer
Published: July 2002

We report molecular dynamics simulations of a Gay–Berne nematic liquid crystal at constant temperature and density/pressure using the generalization of an algorithm recently proposed by Toxvaerd [Phys. Rev. E 47, 343 (1993)]. On the basis of these simulations the absolute values of the Oseen–Zöcher–Frank elastic constants K11, K22, and K33 as well as the surface constants K13 and K24 have been calculated ab initio within the framework of the direct correlation function approach of Lipkin et al. [J. Chem. Phys. 82, 472 (1985)]. The angular coefficients of the direct pair correlation function, which enter the final equations, have been determined from the computer simulation data for the pair correlation function of the nematic by combining the Ornstein–Zernike relation and the Wiener–Hopf factorization scheme. The unoriented nematic approximation has been assumed when constructing the reference state of Lipkin et al. By an extensive study of the model over a wide range of temperatures, densities and pressures, very detailed information is provided on the elastic behavior of the Gay–Berne nematic. Interestingly, it is found that the results for the surface elastic constants are qualitatively different from those obtained with the help of analytical approximations for the isotropic direct pair correlation function. For example, the values of the surface elastic constants are partly negative and an order of magnitude smaller than the bulk elasticity. The negative values of the surface constant K13 indicate on the possibility of surface instabilities of the director pattern in a thin, free standing or weakly anchored Gay–Berne nematic liquid crystal.
Polymers below the theta point: Renormalization group considerations
Authors: Biswas Parbati , Paramekanti Arun , Cherayil Binny J.
Published: July 2002

The average size of long chains below the theta point is discussed in terms of a continuum model in which the chain is viewed as a collapsed phase perturbed by repulsive pair interactions. The representation of the collapsed phase makes use of the path integral formulation of a colored noise process introduced in an earlier paper [J. Chem. Phys. 99, 9230 (1993)], while the pair interactions are approximated as delta function pseudopotentials of strength v0. By treating the excluded volume perturbatively, the model can be described (at first order in v0) by renormalization group (RG) methods using dimensional regularization, ε expansion and minimal subtraction of poles. The nature of the fixed points of the RG transformation suggests that the collapse transition may be first order.
Rotationally resolved photodissociation spectroscopy of Mg+–Ar
Authors: Scurlock C. T. , Pilgrim J. S. , Duncan M. A.
Published: July 2002

The metal ion-complex 24Mg+–Ar has been prepared in a pulsed nozzle/laser vaporization source, mass selected with a reflection time-of-flight mass spectrometer and studied with photodissociation spectroscopy at high resolution. The (5,0) band of the A 2Πr←X 2Σ+ transition has been rotationally analyzed and the rotational constants, B″=0.1409(7) cm−1 and B′=0.1836(8) cm−1, and spin–orbit constant, A′=73.94(2) cm−1, have been determined. The bond distances in the ground and excited states of the complex (r0″=2.88 Å, r5′=2.52 Å) compare well with the values predicted by theory, and they confirm the suspected nature of the electrostatic bonding in this system.
Use of dimension-dependent potentials for quasibound states
Authors: Germann Timothy C.
Published: July 2002

Dimensional perturbation theory is applied to the calculation of complex energies for quasibound (resonance) eigenstates, using a modified dimension-dependent potential so that the infinite-dimensional limit better reflects the physical (three-dimensional) nature of the resonant eigenstate. Using the previous approach of retaining the D=3 form of the potential for all spatial dimension D, highly accurate results are obtained via Padé–Borel summation of the expansion coefficients when they are complex, but a lesser degree of convergence is found when quadratic Padé summation is applied to real expansion coefficients. The present technique of using a dimension-dependent potential allows complex expansion coefficients to be obtained in all cases, and is demonstrated to provide a marked improvement in convergence. We illustrate this approach on the Lennard-Jones potential and the hydrogen atom in an electric field.
Solvent effect on conformational equilibrium: A Monte Carlo study of 1,2-dichloroethane in carbon tetrachloride
Authors: Vilaseca Eudald
Published: July 2002

The Monte Carlo method is applied to the study of the dilute solution of 1,2-dichloroethane in CCl4 in order to explain the conformational change of the solute that is inferred from dipole moment measurements and predicted by reference interaction site model calculations. Several simulations are performed employing different types of solute–solvent interaction potentials. The results show that the conformational change can be correctly explained only when the interaction between the dipole moment of solute and the dipole moment induced in the solvent molecules is considered. This polarization effect is introduced in the calculation of the energy of each solute–solvent dimer. The results obtained contrast with the overestimations due to the reaction field theory. It is also found that a potential model without net charges in the Lennard-Jones interaction sites does not cause any solute alteration and that the addition to these sites of the corresponding net charges yields a very small conformational change in the opposite sense. Additional energetic and structural data is included for the polarization model simulation.
Investigating conformation dependence and nonadiabatic effects in the photodissociation of allyl chloride at 193 nm
Authors: Myers T. L. , Kitchen D. C. , Hu B. , Butler L. J.
Published: July 2002

The experiments presented here investigate the competing photodissociation pathways for allyl chloride upon excitation of the nominally ππ*(C=C) transition at 193 nm. The measured photofragment velocity distributions evidence C–Cl bond fission and HCl elimination. The recoil kinetic energy distribution for the HCl products is bimodal, indicating two primary processes for HCl elimination. The experimental measurements show C–Cl bond fission dominates, giving an absolute branching ratio of HCl:C–Cl=0.12±0.03 when the parent molecule is expanded through a nozzle at 200 °C. The branching ratio depends on the nozzle temperature; at 475 °C, the absolute branching ratio measured is HCl:C–Cl=0.24±0.03. We analyze the experimental results along with supporting ab initio calculations and earlier photodissociation studies of vinyl chloride in order to examine the potential influence of nonadiabaticity along the C–Cl fission reaction coordinate and its dependence on molecular conformation.
Dissociation dynamics of quasibound levels in the g 3Σg+ state of H2: Characterization of the continuum
Authors: Wouters E. R. , Buijsse B. , Los J. , van der Zande W. J.
Published: July 2002

Decay pathways and photofragment anisotropy parameters have been determined for a series of rovibrational levels of the g 3Σg+ state in molecular hydrogen using fast-beam photofragment spectroscopy. The g 3Σg+(v=4) levels are found to be weakly predissociated by homogeneous interaction with the lower lying n=2 a 3Σg+ state and by rotational coupling with the i 3Πg state. The observed photofragment anisotropy reveals fine and hyperfine structure depolarization. The decay of g 3Σg+(v=5) levels is dominated by barrier tunneling. The anisotropy parameters identify the symmetry of the continuum to be of mixed Σg and Πg character, which implies that hydrogen molecules can tunnel through two different barriers. The determination of the kinetic energy and the anisotropy parameter of the photofragments have resulted in a number of spectral reassignments.
A high-resolution analysis of the C̃ A12–X̃ A12 transition of CaNH2: Pure precession in polyatomic molecules
Authors: Morbi Zulfikar , Zhao Chunfeng , Bernath Peter F.
Published: July 2002

The high resolution spectrum of the 000 vibronic band of the C̃ A12–X̃ A12 transition of CaNH2 was recorded with a laser ablation/supersonic molecular beam spectrometer. Approximately 140 lines of the Ka′=0←Ka″=0 and the Ka′=1←Ka″=1 sub–bands were measured and combined with the previous Ã B22–X̃ A12 and B̃ B12–X̃ A12 results. A global fit of the data was carried out and the effective spectroscopic constants for the X̃, Ã, B̃, C̃ states are reported. A complete set of spin–rotation constants (εαα’s) are now available for the Ã B22, B̃ B12 and C̃ 2A1 states. The unpaired electron in these three excited states can be considered to be located in three p–orbitals (px,py,pz) centered on the metal atom. The simple pure precession model provides estimates for the 9 spin–rotation parameters in the Ã, B̃, and C̃ states.
Association and isotopic exchange reactions of CH(CD)[X 2Π]+CO
Authors: Taatjes Craig A.
Published: July 2002

The reaction rates for CH12 and CD12 with normal isotopic abundance CO and CO13 have been studied at 293 K for pressures between 12.5 and 500 Torr and at 100 Torr for temperatures be-tween 293 and 650 K. The pressure and temperature dependence of the addition reaction of CH with CO have been measured. The addition rate coefficient can be fit to the expression 7.2±0.3×10−12(T/293)−2.4±0.2 cm3 molecule−1 s−1 at 100 Torr total pressure (He buffer). A fit of the pressure dependence to a Troe expression with Fc=0.6 yields a low-pressure rate constant (k0) of 2.4±0.3×10−30 cm6 molecule−2 s−1. The rate for carbon atom exchange has been measured by comparison of the C13 labeled and unlabeled reaction rates. The isotopic exchange reaction is 1.0±0.2×10−12 cm3 molecule−1 s−1 at 20 Torr. The deuterium isotope effect on the exchange rate is large, with an inverse kinetic isotope effect (kH/kD)=0.28±0.08 at 20 Torr. This inverse isotope effect reflects the competition between collisional stabilization and isomerization, and is a convolution of isotope effects for the isomerization, unimolecular dissociation, and stabiliza-tion rates. The experimental results are consistent with a mechanism for exchange that in-volves isomerization of an HCCO adduct via an oxiryl intermediate, and indicate that insertion into the C–O bond is not important in this reaction.
Evolution of dissipative processes via a statistical thermodynamic approach. I. Generalized Mori–Heisenberg–Langevin equations
Authors: Madureira Justino R. , Vasconcellos Áurea R. , Luzzi Roberto , Casas-Vázquez José , Jou David
Published: July 2002

Within the scope of a nonequilibrium statistical ensemble formalism we derive a hierarchy of equations of evolution for a set of basic thermo-hydrodynamic variables, which describe the macroscopic nonequilibrium state of a fluid of bosons. This set is composed of the energy density and number density and their fluxes of all order. The resulting equations can be considered as far-reaching generalizations of those in Mori’s approach. They involve nonlocality in space and retro-effects (i.e. correlations in space and time respectively), are highly nonlinear, and account for irreversible behavior in the macroscopic evolution of the system. The different contributions to these kinetic equations are analyzed and the Markovian limit is obtained. In the follow up article we consider the nonequilibrium thermodynamic properties that the formalism provides.
Calculating frequency-dependent hyperpolarizabilities using time-dependent density functional theory
Authors: van Gisbergen S. J. A. , Snijders J. G. , Baerends E. J.
Published: July 2002

An accurate determination of frequency-dependent molecular hyperpolarizabilities is at the same time of possible technological importance and theoretically challenging. For large molecules, Hartree–Fock theory was until recently the only available ab initio approach. However, correlation effects are usually very important for this property, which makes it desirable to have a computationally efficient approach in which those effects are (approximately) taken into account. We have recently shown that frequency-dependent hyperpolarizabilities can be efficiently obtained using time-dependent density functional theory. Here, we shall present the necessary theoretical framework and the details of our implementation in the Amsterdam Density Functional program. Special attention will be paid to the use of fit functions for the density and to numerical integration, which are typical of density functional codes. Numerical examples for He, CO, and para-nitroaniline are presented, as evidence for the correctness of the equations and the implementation.
State-to-state vibrational predissociation dynamics of the acetylene-HF complex
Authors: Oudejans L. , Moore D. T. , Miller R. E.
Published: July 2002

The vibrational predissociation of the acetylene-HF complex has been studied by probing the final state distributions of the photofragments, including the intermolecular scalar correlations. Results are presented for excitation of both the asymmetric C–H stretching vibration of the acetylene and the H–F stretch. In the latter case, the primary dissociation channel is V–R, resulting in highly rotationally excited HF produced in coincidence with ground vibrational state acetylene. Excitation of the asymmetric C–H stretch results in intramolecular V–V energy transfer to the C–C stretch excited state of the acetylene. The dissociation energy of the complex is determined to be 1088 cm−1±2 cm−1.
Z-vector formalism for the Fock space multireference coupled cluster method: Elimination of the response of the highest valence sector amplitudes
Authors: Ajitha D. , Pal Sourav
Published: July 2002

In this paper we present Z-vector formalism for the Fock space multireference coupled cluster framework. We present detailed equations describing the derivative effective Hamiltonian, where the response amplitudes of the highest Fock sector are eliminated. We discuss the conditions and approximations under which the formalism is possible. We also discuss the implications and comparison with the similar formalism in the single reference framework. The computational advantages and feasibility are also commented upon in this paper.
Experimental distinction between phase shifts and time delays: Implications for femtosecond spectroscopy and coherent control of chemical reactions
Authors: Albrecht Allison W. , Hybl John D. , Gallagher Faeder Sarah M. , Jonas David M.
Published: July 2002

Two different definitions of phase shifts and time delays are contrasted and shown to match different experimental methods of generating delayed pulses. Phase shifts and time delays are usually defined in terms of a carrier wave in magnetic resonance, but definitions based on the envelope of a single pulse are useful in optics. It is demonstrated experimentally that a frequency domain measurement using spectral interferometry can simultaneously measure phase shifts with an accuracy of 0.1 rad (2σ) and time delays with a precision of 40 attoseconds (2σ) for 25 femtosecond optical pulses. Envelope time delays are generated by pathlength differences in an interferometer. Constant spectral phase shifts are demonstrated by diffracting pulses from a variable phase volume diffraction grating. Experimental requirements for phase-resolved spectroscopy are outlined. The theory of phase-locked pulse pair techniques is reexamined, and it is concluded that linear experiments with phase-locked pulse pairs are completely equivalent to Fourier transform absorption spectroscopy and do not measure the refractive index or real part of the susceptibility. It is shown that Fourier sine and cosine transformations of truncated time domain signals which do not match the symmetry of the complete signal can produce a false dispersive susceptibility because they are equivalent to Kramers–Kronig inversion of finite bandwidth absorption data. A procedure for shifting π/2 phase-locked transients by a quarter cycle of delay to generate a transient with a π/2 spectral phase shift is given. Equations used to calculate femtosecond nonlinear optical signals have assumed carrier wave delays. Modifications to these equations are required when envelope delays are generated by interferometer pathlength differences and modified equations are given. The modified equations yield significantly different results for phase-resolved or interferometric experiments. In particular, the modified equations are needed to calculate indirectly (interferometrically) detected frequencies and the real and imaginary parts of two-dimensional Fourier transform spectra. The role of the refractive index and real part of the frequency domain susceptibility in nonlinear experiments with phase-locked pulse pairs is explored. It is concluded that experiments such as the heterodyne detected stimulated photon echo are insensitive to nonlinear refractive index changes under some circumstances. Finally, modifications of some equations used in the theory of coherent control are needed to match theory with experimental practice.
Surface-rheological measurements on glass forming polymers based on the surface tension driven decay of imprinted corrugation gratings
Authors: Hamdorf Marc , Johannsmann Diethelm
Published: July 2002

We report on surface-rheological experiments on glass forming polymers making use of the decay of imprinted surface corrugation gratings. Whereas the grating is frozen in at temperatures below the glass temperature Tg, surface tension drives its decay once the sample is heated to above Tg. From the balance between surface tension and viscous stress, the near-surface shear modulus G(ω) is derived. For polystyrene a marked dependence on chain length is found. While the near-surface moduli agree with the bulk values for highly entangled samples, an increase of the apparent stiffness by a factor of 10 compared to the bulk is found for chains shorter than the entanglement length.
Geometric phase effects in the H+D2→HD+D reaction
Authors: Kendrick Brian K.
Published: July 2002

The general vector potential (gauge theory) approach for including geometric phase effects in accurate three-dimensional quantum scattering calculations in symmetrized hyperspherical coordinates is applied to the H+D2(v,j)→HD(v′,j′)+D reaction at 126 values of total energy in the range 0.4–2.4 eV. State-to-state reaction probabilities, integral, and differential cross sections are computed using both the Boothroyd–Keogh–Martin–Peterson (BKMP2) and the Liu–Siegbahn–Truhlar–Horowitz potential energy surfaces for the first six values of total angular momentum (J⩽5). Calculations are performed on each surface both with and without the geometric phase. Due to symmetry, the effects of the geometric phase are shown to cancel out when contributions from even and odd values of J are added together for both the integral and differential cross sections, at all energies, and independent of which surface is used. These results are consistent with recent experimental results which are in good agreement with theoretical treatments which do not include the geometric phase. Relatively broad transition state resonances are observed in the rotationally resolved integral and differential cross sections.
Group theoretical analysis of the Hartree–Fock–Bogoliubov equation. I. General theory
Authors: Ozaki Masa-aki
Published: July 2002

This paper describes a general group theoretical analysis of the temperature–Hartree-Fock–Bogoliubov (HFB) equation and its solution. The action of the symmetry group G0 of the system on the HFB Hamiltonian, the HFB density matrix, and the HFB Green function are defined. It is shown that the HFB equation and its solution is classified by a subgroup G of G0, which is the invariance group of the HFB Hamiltonian, the HFB density matrix, and the HFB Green function corresponding the solution. General expression of the instability of a solution and its decomposition into R-rep (single-valued irreducible representation over the real number field) components of the invariance group of the solution are obtained. The self-consistent field (SCF) condition is decomposed into R-rep components of G0.
The relation of a theory of countable sets to the field equations of physics
Authors: BenDaniel D. J.
Published: July 2002

The systematic development of mathematics is based on the theory of sets. We present an axiom system in which, in contradistinction to the usual theories, it seems possible to define formal provability yet some useful mathematics can be derived. Some features of the theory suggest that these axioms can provide a possible new foundation for mathematical physics.
Spherically symmetric perfect fluid solutions in isotropic coordinates
Authors: Hajj-Boutros Joseph
Published: July 2002

A method of generating solutions of Einstein’s field equations for static fluid spheres is presented. This new method has a very clear advantage since it bypasses the direct resolution of the field equations. One of the solutions obtained is then studied in some detail; it verifies an equation of state of the form p≂αρ+βρ1+1/n.
Symmetric tensor spherical harmonics on the N-sphere and their application to the de Sitter group SO(N,1)
Authors: Higuchi Atsushi
Published: July 2002

The symmetric tensor spherical harmonics (STSH’s) on the N-sphere (SN), which are defined as the totally symmetric, traceless, and divergence-free tensor eigenfunctions of the Laplace–Beltrami (LB) operator on SN, are studied. Specifically, their construction is shown recursively starting from the lower-dimensional ones. The symmetric traceless tensors induced by STSH’s are introduced. These play a crucial role in the recursive construction of STSH’s. The normalization factors for STSH’s are determined by using their transformation properties under SO(N+1). Then the symmetric, traceless, and divergence-free tensor eigenfunctions of the LB operator in the N-dimensional de Sitter space-time which are obtained by the analytic continuation of the STSH’s on SN are studied. Specifically, the allowed eigenvalues of the LB operator under the restriction of unitarity are determined. Our analysis gives a group-theoretical explanation of the forbidden mass range observed earlier for the spin-2 field theory in de Sitter space-time.
Symmetries of static, spherically symmetric space-times
Authors: Bokhari Ashfaque H. , Qadir Asghar
Published: July 2002

In this paper it is shown that reduction from maximal to minimal static, spherical symmetry of a space-time occurs in only one step reducing the number of independent Killing vector fields from 10 to 4. Maximal symmetry corresponds only to the de Sitter, anti-de Sitter, and Minkowski metrics, without reference to the Einstein field equations.
Quantum motion on a half-line connected to a plane
Authors: Exner P. , Šeba P.
Published: July 2002

In this paper, the free motion of a particle on a manifold that consists of a one-dimensional and a two-dimensional part connected in one point is discussed. The class of admissible Hamiltonians is found using the theory of self-adjoint extensions. Particular attention is paid to those Hamiltonians that allow the particle to pass through the point singularity; the reflection coefficient and other quantities characterizing scattering on the connection point are calculated. A possible application is also discussed.
Liouville theorem for the Yang–Mills self-duality equations
Authors: Majid Shahn
Published: July 2002

It is shown that under certain conditions one may associatively matrix-multiply Lie-algebra-valued matrices with a componentwise Lie bracket. Using this, a simple algebraic constraint on a Lie-algebra-valued antisymmetric n×n matrix F, which in n=4 is essentially self-duality or anti-self-duality, is described. Somewhat in analogy with Liouville’s theorem for the Cauchy–Riemann equations in n=2, it is shown that, for n>4, the constraint implies that the Lie subalgebra generated by the matrix elements {Fμν } decomposes into copies of S_O_(n) plus a few degenerate cases. The result may be relevant to the structure of the quantum chromodynamic vacuum.
Expressions for the zeta-function regularized Casimir energy
Authors: Elizalde E. , Romeo A.
Published: July 2002

The expansion of the Casimir energy for a scalar field with mass m, in a space where one dimension has been compactified into a circle of length a, leads to a double-infinite series that can be regularized by analytic continuation in the space dimension. The dimensionally regularized sum is then expressed as a power series in am by means of zeta-function expansions. The two possibilities of odd and even space dimensions are distinguished. In the odd space dimension we give a power expansion for small am, in addition to the asymptotic behavior. For the even space dimension, an expansion valid for any value of am is obtained. The contribution of higher-order terms is studied and, for the three-dimensional space, results for different values of the compactification length are shown.
Generalized Holstein–Primakoff realizations and quantum group-theoretic coherent states
Authors: Chang Zhe
Published: July 2002

A set of deformed k-boson operators are defined and it is shown that the nonlinear transformations from the usual deformed oscillator operators to the deformed k-boson operators form an Abelian group. It is shown that the multiboson operators satisfy quantum Weyl–Heisenberg group. The generalized Holstein–Primakoff realizations in terms of these multibosons operators are used to define the quantum group-theoretic coherent states of SUq(1,1) and SUq(2). The uncertainties ΔX(k′,q) and ΔP(k′,q) with respect to those group-theoretic and generalized coherent states are computed explicitly and the results show that these coherent states are squeezed.
On Wick algebras with braid relations
Authors: Marcinek Wl/adysl/aw , Ral/owski Robert
Published: July 2002

The general theory of deformed commutation relations for creation and annihilation operators of particles equipped with arbitrary braid statistics (Ψ-statistics) is studied in terms of Wick algebras. The construction and examples of such algebras are given.
Exact solutions of the Einstein equations with sources from linearized solutions
Authors: Torres del Castillo G. F.
Published: July 2002

It is shown that if (gμν,Fμν) is an exact solution of the Einstein–Maxwell equations and lμ is a principal null direction of Fμν then (gμν+2Hlμlν,Fμν) is also an exact solution of the Einstein–Maxwell equations if and only if (2Hlμlν,0) satisfies the Einstein–Maxwell equations linearized about (gμν,Fμν). It is also shown that an analogous result applies in the case of the Einstein–Weyl equations if lμ is parallel to the flux vector of the neutrino field.
Augmented temporal logic formalism for histories-based generalized quantum mechanics
Authors: Dass Tulsi , Joglekar Yogesh
Published: July 2002

An axiomatic development of dynamics of systems in the framework of histories is given which contains the history versions of classical and traditional quantum mechanics as special cases. We consider theories which admit a quasitemporal structure (a generalization of the concept of time using partial semigroups) and whose “single time” propositions have the mathematical structure of a logic; isomorphism of logics at different “instants of time” is not assumed. The concept of directed partial semigroup is introduced to incorporate the concept of direction of flow of time in quasitemporal theories. Starting with a few simple axioms, the space of history propositions is explicitly constructed and shown to be an orthoalgebra (as envisaged in the scheme of Isham and Linden [J. Math. Phys. 35, 5452–5476 (1994)]); its subspace consisting of history filters (“homogeneous histories”) is a meet semilattice. The partial semigroups employed allow semi-infinite irreducible decompositions.
Precession of a freely rotating rigid body. Inelastic relaxation in the vicinity of poles
Authors: Efroimsky Michael
Published: July 2002

When a solid body is freely rotating at an angular velocity Ω, the ellipsoid of constant angular momentum, in the space Ω1,Ω2,Ω3, has poles corresponding to spinning about the minimal-inertia and maximal-inertia axes. The first pole may be considered stable if we neglect the inner dissipation, but becomes unstable if the dissipation is taken into account. This happens because the bodies dissipate energy when they rotate about any axis different from principal. In the case of an oblate symmetrical body, the angular velocity describes a circular cone about the vector of (conserved) angular momentum. In the course of relaxation, the angle of this cone decreases, so that both the angular velocity and the maximal-inertia axis of the body align along the angular momentum. The generic case of an asymmetric body is far more involved. Even the symmetrical prolate body exhibits a sophisticated behavior, because an infinitesimally small deviation of the body’s shape from a rotational symmetry (i.e., a small difference between the largest and second largest moments of inertia) yields libration: the precession trajectory is not a circle but an ellipse. In this article we show that often the most effective internal dissipation takes place at twice the frequency of the body’s precession. Applications to precessing asteroids, cosmic-dust alignment, and rotating satellites are discussed.
Elastohydrodynamic collision and rebound of a flat plate from a planar surface due to body and fluid inertia
Authors: Weinbaum S. , Chen L. , Ganatos P.
Published: July 2002

It is generally assumed in the collision and rebound of a blunt object from a planar surface at high Re that the air in the intervening fluid gap plays an insignificant role in the elastic rebound because of its negligible mass and that the classical theory of Hertz [A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1927) 4th ed.] for the contact deformation in a vacuum can be applied. In this paper the prototype problem of the elastohydrodynamic collision and rebound of an elastic plate or disk from a rigid planar wall is considered , and it is shown that the fluid motion and pressure forces in the gap are instrumental in determining the elastic deformation of the body and its rebound. A new theoretical framework is developed to examine the dynamics of the near collision process and the conditions necessary for elastic recoil to occur. This theory predicts that there is a minimum critical initial velocity for rebound and that there is a wide range of conditions from which the plate will rebound without actually touching the wall. The rebound of the edge and center of the plate do not occur simultaneously and the criterion for the edge to just make contact with the wall is derived. The analysis also shows that the rebound and the acceleration of the air in the gap is so rapid that the unsteady viscous boundary layers are only of secondary importance. Thus the intertia of the body and the air and the instantaneous deformation geometry determine the dynamic pressure forces in the gap. Despite the inherent nonlinearity of the problem, it is possible to develop an asymptotic analysis in which closed form solutions can be obtained for many of the important results by treating the instantaneous lowest-order solution for the gap height rather than time as the independent variable. The present theory is valid up to and slightly beyond the point of rebound where the fluid at the edge of the plate experiences negligible pressure recovery.
Linear stability of stagnation flow
Authors: Thompson Charles , Manley Martin G.
Published: July 2002

The linear stability of a steady stagnation flow over a cylindrical body is examined. Special consideration is given to the influence oscillatory modulation of the steady flow has on the bifurcation of three-dimensional vortical disturbances from stability. It is shown that such modulations result in a fixed bifurcation point according to linear stability theory. The sensitivity of the bifurcation point to the time-harmonic modulation and steady flow speed is considered in the analysis. It is shown that stagnation flow exhibits instability if unsteadiness is introduced into the basic state of the flow. Analytical results are compared to experimental data.
A simple nonlinear model for the return to isotropy in turbulence
Authors: Sarkar Sutanu , Speziale Charles G.
Published: July 2002

A quadratic nonlinear generalization of the linear Rotta model for the slow pressure-strain correlation of turbulence is developed for high Reynolds number flows. The model is shown to satisfy realizability and to give rise to no stable nonzero equilibrium solutions for the anisotropy tensor in the case of vanishing mean velocity gradients. In order for any model to predict a return to isotropy for all relaxational flows, it is necessary to ensure that there is no nonzero stable fixed point that attracts realizable initial conditions. Both the phase space dynamics and the temporal behavior of the model are examined and compared against experimental data for the return to isotropy problem. It is demonstrated that the quadratic model successfully captures the experimental trends which clearly exhibit nonlinear behavior. Comparisons are also made with the predictions of the linear Rotta model, the quasilinear Lumley model, and the nonlinear model of Shih, Mansour, and Moin. The simple quadratic model proposed in this study does better than the Rotta model as anticipated, and also compares quite favorably with the other more complicated nonlinear models.
On dynamic excitation of Marangoni instability
Authors: Gershuni G. Z. , Nepomnyashchy A. A. , Velarde M. G.
Published: July 2002

For a liquid layer parametrically excited with a time harmonically varying heat flux imposed normal to the free surface, threshold values for the onset of convective thermocapillary instability are provided. Both the critical Marangoni number and the critical wave number are given as functions of the Prandtl number. Also provided here are some numerical estimates for possible experimental test of the theoretical predictions.
The modulational instability of coupled waves
Authors: McKinstrie C. J. , Bingham R.
Published: July 2002

The collinear propagation of an arbitrary number of finite-amplitude waves is modeled by a system of coupled nonlinear Schrödinger equations; one equation for each complex wave amplitude. In general, the waves are modulationally unstable with a maximal growth rate larger than the modulational growth rate of any wave alone. Moreover, waves that are modulationally stable by themselves can be driven unstable by the nonlinear coupling. The general theory is then applied to the relativistic modulational instability of two laser beams in a beat-wave accelerator. For parameters typical of a proposed beat-wave accelerator, this instability can seriously distort the incident laser pulse shapes on the particle-acceleration time scale, with detrimental consequences for particle acceleration.
Generalized gyrokinetics
Authors: Bernstein Ira B. , Catto Peter J.
Published: July 2002

A nonlinear gyrokinetic formalism is developed which admits mean velocities comparable to thermal speeds in arbitrary magnetic field geometry. The theory is fully electromagnetic and does not employ an eikonal ansatz. The moments of the gyrokinetic distribution function, as well as the gyrokinetic equation it satisfies, are derived to first order in the guiding center expansion parameter. This large mean velocity formulation is important whenever the E×B drift over the thermal speed cannot be ordered small. For example, upon summing over all species, the moment description yields a set of generalized magnetohydrodynamic equations which are valid to one order higher in the expansion parameter.
Experimental studies in vortex pair motion coincident with a liquid reaction
Authors: Karagozian A. R. , Suganuma Y. , Strom B. D.
Published: July 2002

An experimental examination of the coincidence of a liquid reaction (acid/base) with the formation of a vortex pair structure is described in which emphasis is placed on the evolution of the strained diffusion layer and reacted core structures. Flow visualization of the reaction process is achieved via the technique of chemically sensitive laser-induced fluorescence. The observed growth of reacted core structures associated with each vortex is compared with theoretically predicted behavior published recently [Recent Advances in the Aerospace Sciences (Plenum, New York, 1985), p. 395; Combust. Sci. Technol. 49, 185 (1986)]. Vortex pair separation is also compared with theoretical correlations, and the relevance of the analogy between a fast liquid reaction (Sc≫1) and a gaseous reaction (Sc∼1) is discussed.
Linear stability of plane Poiseuille flow of two superposed fluids
Authors: Yiantsios Stergios G. , Higgins Brian G.
Published: July 2002

Stability of two superposed fluids of different viscosity in plane Poiseuille flow is studied numerically. Conditions for the growth of an interfacial wave are identified. The analysis extends Yih’s results [J. Fluid Mech. 27, 337 (1967)] for small wavenumbers to large wavenumbers and accounts for differences in density and thickness ratios, as well as the effects of interfacial tension and gravity. Neutral stability diagrams for the interfacial mode are reported for a wide range of the physical parameters describing the flow. The analysis shows also that the flow is linearly unstable to a shear mode instability. The dependence of the critical Reynolds number for the shear mode on the viscosity ratio is reported. Theoretical predictions of critical Reynolds numbers for both modes of instability are compared with available experimental data.
Studies of Raman scattering from overdense targets irradiated by several kilojoules of 0.53 μm laser light
Authors: Drake R. P. , Turner R. E. , Lasinski B. F. , Williams E. A. , Phillion D. W. , Estabrook K. G. , Kruer W. L. , Campbell E. M. , Manes K. R. , Hildum J. S. , Johnston T. W.
Published: July 2002

In this paper a study of stimulated Raman scattering (SRS) from relatively planar plasmas irradiated with short-wavelength (0.53 μm) laser light is reported. The Novette Laser Facility [Laser Part. Beams 3, 173 (1985)] produced several kilojoules of light in 1 nsec, which allowed it to irradiate a large spot with enough intensity to produce significant Raman scattering. These experiments measured the fluence, angular distribution, spectrum, and timing of the Raman light, as a function of the average laser intensity. Reductions in the Raman fluence at low laser intensity are attributed to collisional damping. The measured SRS fluence was larger than that predicted from convective amplification of bremsstrahlung noise, as calculated using the average properties of the laser beam and the plasma. Possible contributions to the observed scattering from enhanced noise, Raman scattering within filaments, and the absolute Raman instability at density extrema are discussed.
Funnel-shaped vortical structures in wall turbulence
Authors: Kaftori D. , Hetsroni G. , Banerjee S.
Published: July 2002

The structure of the turbulent boundary layer in a horizontal open channel was investigated experimentally by means of laser Doppler anemometry (LDA) and by flow visualization synchronized with the LDA. These experiments indicate that the dominant structures in the wall region are large scale streamwise vortices which originate at the wall and grow and expand into the outer flow region. The shape of the vortices is that of an expanding spiral, wound around a funnel which is laid sideways in the direction of flow. Most of the observations of wall turbulence phenomena made over the years, such as quasistreamwise vortices, ejections, and sweeps seem to be part of these funnel-shaped vortices.