bluuebunny/crossref_metadata_2025 huggingface dataset:
Thermal rate constants of the N2+O→NO+N reaction using ab initio 3A″ and 3A′ potential energy surfaces
Authors: Bose Deepak , Candler Graham V.
Published: July 2002

Theoretical determinations of the thermal rate constants and product energy distributions of the N2+O→NO+N reaction, which plays a crucial role in hydrocarbon air combustion and high temperature air chemistry, are carried out using a quasiclassical trajectory method. An analytical fit of the lowest 3A′ potential energy surface of this reaction based on the CCI ab initio data is obtained. The trajectory study is done on this surface and an analytical 3A″ surface proposed by Gilibert et al. [J. Chem. Phys. 97, 5542 (1992)]. The thermal rate constants computed from 3000 to 20 000 K are in good agreement with the available experimental data. In addition, the dependence of the rate constant on the N2 internal state is studied. It is found that a low vibrational excitation can reduce the rate constant of this reaction by a factor of 3. Also, we investigate the effect of the N2 vibrational state on the product NO vibrational distribution, and it is found that at low N2 vibrational states, the NO vibrational distribution is nearly Boltzmann. However, at N2(v≳10), the product distribution is almost uniform at low energy levels.
Current-voltage characteristics of molecular wires: Eigenvalue staircase, Coulomb blockade, and rectification
Authors: Mujica Vladimiro , Kemp Mathieu , Roitberg Adrian , Ratner Mark
Published: July 2002

We have studied the current vs voltage curves (I–V characteristics) of a mesoscopic device consisting of two electrodes and a molecular wire. The wire Hamiltonian includes both electronic tunneling and Coulomb repulsion within a Hubbard model that is treated at the Hartree–Fock level. The inclusion of electron repulsion is an extension of our previous work that only considered the case of noninteracting electrons. We have found several important features in the calculated characteristics of the wire. These include (1) a staircaselike structure that strongly resembles that associated with Coulomb blockade in heterostructures and quantum dots, but that in the case of the wire is associated with the discrete nature of the molecular resonances; (2) regions of negative differential resistance associated with increased localization of the molecular resonances. Our theoretical model includes a consistent treatment of the conduction in the linear and nonlinear regimes which remains valid even when the device is operated close to resonance. These results can be particularly relevant for a comparison with recent experiments on molecular wires.
Interaction of gas-phase atomic deuterium with the Ru(001)–p(1×2)–O surface: Kinetics of hydroxyl and water formation
Authors: Schick M. , Xie J. , Mitchell W. J. , Weinberg W. H.
Published: July 2002

The deuteration of oxygen adatoms on the Ru(001) surface has been investigated by means of temperature programmed desorption and high-resolution electron energy loss spectroscopy. Exposure of gas-phase atomic deuterium to the p(1×2) oxygen overlayer with a fractional adatom coverage of oxygen of 0.5 leads to the production of water at a surface temperature as low as 90 K. After exposure to molecular deuterium, no reaction is observed, suggesting that a direct Eley–Rideal (ER) reaction occurs between the impinging deuterium atoms and the preadsorbed oxygen. Only after a very low exposure of deuterium was it possible to isolate chemisorbed OD groups on the surface, implying that OD formation is the rate-limiting step in the formation of water via ER kinetics on Ru(001). Estimates of the ER reaction cross sections were made, and for the deuteration of adsorbed oxygen and hydroxyls, the cross sections were found to be (7.0±0.3)×10−17 cm2 and (2.2±0.1)×10−15 cm2, respectively. In addition to the ER mechanism, the chemisorbed OD groups could also react with coadsorbed deuterium adatoms via Langmuir–Hinshelwood (LH) kinetics at surface temperatures near 170 K, suggesting an activation barrier that is less than 9 kcal/mol. This implies that OD formation is also the rate-limiting step in the formation of water via LH kinetics on Ru(001).
Orientational correlation functions and polarization selectivity for nonlinear spectroscopy of isotropic media. I. Third order
Authors: Tokmakoff A.
Published: July 2002

The contribution of orientational relaxation to the tensor components of the third-order nonlinear polarization is evaluated for off-resonance Raman and dipole resonant experiments in the perturbative limit. Orientational correlation functions are calculated within the model of orientational diffusion for all third-order tensor components relevant to isotropic media. General expressions for polarization geometries that are selective to particular components of the signal, i.e., magic angles, are derived for collinear and crossed-beam excitation geometries. It is shown that although limited selectivity exists for Raman spectroscopies, no combination of polarizations will give complete selectivity to the isotropic, anisotropic, or nonresonant contributions to the Raman polarizability tensor. For resonant spectroscopies, the four-time correlation function that describes the orientational polarization decay can be written as the product of three two-time correlation functions. While magic angles for orientational relaxation will exist for experiments that probe population dynamics, such as pump–probe and transient grating spectroscopies, orientational relaxation cannot be removed from coherence experiments such as the photon echo.
Tunable vacuum ultraviolet laser spectroscopy of XeAr and XeNe near 68 000 cm−1: Interatomic potentials mediated by a 6s Rydberg electron
Authors: Pibel Charles D. , Ohde Kyoko , Yamanouchi Kaoru
Published: July 2002

The laser induced fluorescence spectra of XeAr and XeNe have been measured near the Xe 6s[3/2]°1−1S0 transition at 68 045.663 cm−1. In XeAr, nine discrete peaks were observed, attributed to excitation to vibrational levels of the excited Ω=0+ electronic state, merging into a continuum. From a Franck–Condon analysis, the potential for the excited Ω=0+ state of XeAr was determined. It was found that this potential has a shallow minimum at long range [De′=28(1) cm−1, re′=5.44(7) Å] with a shallow repulsive wall. The shallow repulsive wall is attributed to the influence of the XeAr+ ion core at short range. The role of the 6s Rydberg electron of Xe in determining the shape of the interatomic potentials of excited XeRg (Rg=a rare gas atom) is discussed on the basis of a simple model potential, in which the interatomic potential is described as the sum of a diatomic ion core (XeRg+) potential term and a term representing the exchange repulsion between the Rydberg electron and the rare gas moiety. For XeNe, only continuum spectra were observed, indicating that the upper states are not bound.
The structure and binding energy of K+–ether complexes: A comparison of MP2, RI-MP2, and density functional methods
Authors: Feller David , Aprà Edoardo , Nichols Jeff A. , Bernholdt David E.
Published: July 2002

The structures and binding energies of several cation:ether complexes (K+:dimethyl ether, K+:dimethoxyethane, K+:12-crown-4 and K+:18-crown-6) were determined with second and fourth order perturbation theory using correlation consistent basis sets. Several of these are the largest correlated calculations yet attempted on crown ethers. The observed systematic convergence to the complete basis set limit provides a standard by which the accuracy of previous studies can be measured and facilitates the calibration of density functional methods. Recent Fouier transform ion cyclotron resonance experiments predicted K+:18-crown-6 binding energies which were significantly smaller than ab initio calculations. None of the potential sources of error examined in the present study were large enough to explain this difference. Although the 6-31+G* basis set used in an earlier theoretical study was smaller than the smallest of the correlation consistent basis sets, with suitable correction for basis set superposition error, it appears capable of yielding binding energies within several kcal/mol of the basis set limit. Perturbation theory calculations exploiting the ‘‘resolution of the identity’’ approximation were found to faithfully reproduce binding energies and conformational differences. Although the cation–ether interaction is dominated by classical electrostatics, the accuracy of density functional techniques was found to be quite sensitive to the choice of functionals. The local density SVWN procedure performed well for binding energies and conformational differences, while underestimating K+O distances by up to 0.08 Å. The gradient-corrected Becke–Lee–Yang–Parr functional underestimated the K+:12c4 binding energy by 4–7 kcal/mol or 15%.
Peristaltic instability of cylindrical gels
Authors: Barrière Benoı̂t , Sekimoto Ken , Leibler Ludwik
Published: July 2002

We investigate here the stability of a gel cylinder subject to a strong surface tension. Both the criteria for the occurrence of a peristaltic instability and its dynamical evolution are determined within linear elasticity. Shrinking gels may show such an instability, as has been reported by Matsuo and Tanaka [Nature 358, 482 (1992)]. Considering approximate values of the relevant parameters, we find results in qualitative agreement with their experiments.
The hydroperoxyl radical dimer: Triplet ring or singlet string?
Authors: Fermann Justin T. , Hoffman Brian C. , Tschumper Gregory S. , Schaefer III Henry F.
Published: July 2002

In order to determine the lowest energy isomer of the hydroperoxyl radical dimer, H2O4, ab initio quantum mechanical methods were employed to predict the geometrical structures, relative energies, harmonic vibrational frequencies, and associated IR intensities of both open chain and cyclic isomers. Two minima were located on the open chain potential energy surface, one of C2 symmetry and one of C1 symmetry. The relative energies of the different H2O4 structures vary strongly with level of theory. The most reliable treatment used in the present study predicted that the global minimum is the closed-shell C1 chain isomer which is lower in energy than the planar C2h triplet cyclic isomer by 1.6 kcal mol−1 including zero point vibrational energy corrections. It is argued that both structures should be observable, depending on the method of preparation.
Analysis of the hydrogen-bonded structure of water from ambient to supercritical conditions
Authors: Jedlovszky P. , Brodholt J. P. , Bruni F. , Ricci M. A. , Soper A. K. , Vallauri R.
Published: July 2002

The structure of water has been analyzed at eight different thermodynamic states from ambient to supercritical conditions both by molecular dynamics (MD) and Reverse Monte Carlo (RMC) simulation. MD simulations have been carried out with two different potential models, a polarizable potential and one of the most successful nonpolarizable models, i.e., the well known Simple Point Charge potential in its revised version labeled by E (SPC/E). It has been found that, although the polarizable model can reproduce the experimental partial pair correlation functions at the high temperature states better than the nonpolarizable one, it still cannot account for all the features of the measured functions. The experimental partial pair correlation functions have been well reproduced by the RMC simulations at every state point. The resulting structures have been analyzed in detail. It has been found that the tetrahedral orientation of the hydrogen bonded neighbors is already lost at 423k, whereas the hydrogen bonds themselves remain preferentially linear even above the critical point. In investigating the properties of the hydrogen-bonded clusters of the molecules it has been found that the space-filling percolating network, present under ambient conditions, collapses around the critical point.
Transition states for chemical reactions I. Geometry and classical barrier height
Authors: Malick David K. , Petersson G. A. , Montgomery John A.
Published: July 2002

A new computational procedure for the characterization of transition states for chemical reactions is proposed and tested. Previous calculations have frequently employed a single point high-level energy calculation at a transition state geometry obtained with a less expensive computational method, Energy[Method(1)]//Geom[Method(2)]. If we instead search the “inexpensive” intrinsic reaction coordinate (IRC) for the maximum of Energy[Method(1)] along this reaction path, the resulting “IRCMax method”, Max{Energy[Method(1)]}//IRC{Geom[Method(2)]}, reduces errors in transition state geometries by a factor of 4 to 5, and reduces errors in classical barrier heights by as much as a factor of 10. When applied to the CBS-4, G2(MP2), G2, CBS-Q, and CBS-QCI/APNO model chemistries, the IRCMax method reduces to the standard model for the reactants and products, and gives rms errors in the classical barrier heights for ten atom exchange reactions of 1.3, 1.2, 1.0, 0.6, and 0.3 kcal/mol, respectively.
A rapid monotonically convergent iteration algorithm for quantum optimal control over the expectation value of a positive definite operator
Authors: Zhu Wusheng , Rabitz Herschel
Published: July 2002

A new iteration method is presented for achieving quantum optimal control over the expectation value of a positive definite operator. Theoretical analysis shows that this new algorithm exhibits quadratic and monotonic convergence. Numerical calculations verify that for this new algorithm, within a few steps, the optimized objective functional comes close to its converged limit.
Does solvation cause symmetry breaking in the I3− ion in aqueous solution?
Authors: Lynden-Bell R. M. , Kosloff R. , Ruhman S. , Danovich D. , Vala J.
Published: July 2002

We seek to answer the question posed in the title by simulation of the tri-iodide ion in water, modeling the intermolecular interactions by classical potentials. The decrease in solvation free energy as a function of the dipole moment of the ion is calculated using an extended dynamics simulation method. This decrease is approximately quadratic in the ion dipole. Symmetry breaking occurs if this decrease is greater than the energy required to polarize the ion. We use ab initio calculations on an isolated ion to find the electronic and vibrational contributions to the polarizability, from which the polarization energy can be calculated. The solvated ion is found to be more stable when displaced along the asymmetric stretching coordinate, due to contributions of this deformation to the molecular dipole. As a test of the model’s reliability, it is used to derive solvation force autocorrelation functions from which time scales for vibrational energy and phase relaxation are estimated. The results are demonstrated to agree well with experimentally obtained values for these phenomena, vindicating reliability of the theoretical approach.
Synthesis of a cubic Ge3N4 phase at high pressures and temperatures
Authors: Serghiou G. , Miehe G. , Tschauner O. , Zerr A. , Boehler R.
Published: July 2002

The two known phases of germanium nitride (Ge3N4) have hexagonal and trigonal symmetries and consist of three-dimensional networks of corner-connected Ge–N tetrahedra. A new cubic spinel phase (space-group Fd3m, a0=8.3 Å, Z=8, ρ=6.36 g/cm3) containing Ge–N octahedra and tetrahedra in a 2:1 ratio was synthesized from elemental germanium and molecular nitrogen starting materials in a laser-heated diamond-anvil cell above 14 GPa. This phase is isostructural to the recently discovered cubic spinel phase of Si3N4.
Non-Markovian stochastic Schrödinger equation
Authors: Gaspard P. , Nagaoka M.
Published: July 2002

We report a study of a stochastic Schrödinger equation corresponding to the Redfield master equation with slipped initial conditions, which describes the dynamics of a slow subsystem weakly coupled to a fast thermal bath. Using the projection-operator method of Feshbach, we derive a non-Markovian stochastic Schrödinger equation of the generalized Langevin type, which simulates the time evolution of the quantum wave functions of the subsystem driven by the fluctuating bath. For δ-correlated baths, the non-Markovian stochastic Schrödinger equation reduces to the previously derived Markovian one. Numerical methods are proposed to simulate the time evolution under our non-Markovian stochastic Schrödinger equation. These methods are illustrated with the spin-boson model.
The viscoelastic response of Brownian suspensions
Authors: Lowe C. P. , Masters A. J.
Published: July 2002

In a simple model for the long-time dynamical behavior of Brownian suspensions, particles diffuse independently while simultaneously undergoing direct interactions with each other. Despite its simplicity, this model forms the basis of both the Brownian dynamics computer simulation technique and apparently successful theories. Here we use the approach to study numerically the viscoelastic response of a suspension of hard spheres. At low volume fractions (10%) we find that the frequency dependence of the viscosity is in agreement with theoretical calculations based on solving the two-particle Smoluchowski equation. At a higher volume fraction (45%) we find that the model is not well described by various extensions of low density theory that have been proposed. Including hydrodynamics in a minimal way (by allowing the particles to diffuse with the short-time diffusion coefficient) and comparing with experiment, the model successfully reproduces the viscoelastic response over an intermediate range of frequencies. However, at low frequencies a significant disagreement emerges. A “slowing down” of the dynamics of the particles at longer times, more apparent in the simulations than in the experimental results, appears to be the cause of this discrepancy. Ultimately, this leads to a significant overestimate of the zero frequency (Newtonian) viscosity. The reason theories based on the approach yield such excellent agreement with experiment, we can only conclude, is because they fail to describe the model adequately.
On the computer simulation of a hydrophobic vitreous silica surface
Authors: Bakaev V. A. , Steele W. A.
Published: July 2002

The experimental evidence that the surface of pure vitreous silica can be hydrophobic imposes strong limitations on possible atomic configurations at that surface. This is due primarily to the fact that the electric field of the partially ionic SiO2 can have very strong interactions with adsorbed polar molecules and with water in particular. The simulations reported here indicate that a surface structure consisting of a random net of almost regular corner-sharing SiO4 tetrahedra with a low concentration of defects such as nonbridging oxygen atoms is capable of producing hydrophobicity. It is shown that the defects as well as distortion of the SiO4 tetrahedra as measured by their dipole and quadrupole moments give rise to hydrophilic adsorption sites on the surface. Computer simulation of such a random net at a surface runs into a general problem typical of computer simulations of amorphous solids: at temperatures near to but above the glass transition temperature, the time scale of the molecular dynamics is many orders of magnitude less than the experimental structural relaxation times of the material. A solution to this problem was obtained here by imposing a constraint on the molecular dynamics simulation that directs the chain of simulated configurations toward one without nonbridging oxygens. This is demonstrated by showing that the binding energies of a water molecule over the surface of this solid are smaller than the energy liquefaction, which is taken here as the criterion for hydrophobicity.
On the configurational temperature of simple fluids
Authors: Baranyai András
Published: July 2002

Using the formalism of liquid-state statistical mechanics, we study the properties of the recently derived configurational temperature [H. H. Rough, Phys. Rev. Lett. 78, 772 (1997)]. We show that the configurational temperature expression derived in the microcanonical ensemble is valid for open equilibrium systems as well. We also present a special way of deriving the configurational temperature for dilute gases. The same approach connects the pair-correlation function and the pair potential in the form of a sum rule which can be utilized in the integral equation theory of liquids.
Approximate calculation of femtosecond pump–probe spectra monitoring nonadiabatic excited-state dynamics
Authors: Dilthey Stefan , Hahn Susanne , Stock Gerhard
Published: July 2002

An approximate theory of femtosecond spectroscopy of nonadiabatically coupled electronic states is developed. Neglecting the commutators of vibrational Hamiltonians pertaining to different diabatic electronic states, the formulation represents a generalization of the semiclassical Franck–Condon approximation to the case of nonadiabatic dynamics. Explicit expressions for various time- and frequency-resolved spectra are derived which allow for a simple interpretation of femtosecond spectroscopy of vibronically coupled molecular systems. Employing multidimensional model problems describing (i) the nonadiabatic cis–trans isomerization of an electronic two-state system, and (ii) the S2→S1 internal conversion of pyrazine, exact reference data are compared to approximate calculations of transient absorbance and emission as well as time-resolved photoelectron spectra. In all cases considered, the approximation is shown to be appropriate for probe–pulse durations that are shorter than the period of the fastest relevant vibrational mode of the molecular system. Reducing the numerical costs of pump–probe simulations to the costs of a standard time-dependent wave-packet propagation, the approximate theory leads to substantial computational savings.
Coupling between the internal rotation of the methyl group and proton/deuteron transfer in jet-cooled 5-methyl-9-hydroxyphenalenone(OH) and 5-methyl-9-hydroxyphenalenone(OD): Tunneling rate dependence of coupling potential
Authors: Nishi Kaori , Sekiya Hiroshi , Mochida Tomoyuki , Sugawara Tadashi , Nishimura Yukio
Published: July 2002

The energy levels and the potentials arising from coupling between the two large amplitude motions, the internal rotation of the methyl group, and the proton/deuteron transfer have been investigated by measuring the fluorescence excitation, dispersed fluorescence, and hole-burning spectra in the S1-S0 region of jet-cooled 5-methyl-9-hydroxyphenalenone(OH)/5-methyl9-hydroxyphenalenone(OD) and 5-methyl-9-hydroxyphenalenone(OD)–water 1:1 complex. The symmetry of the potential functions for the internal rotation of the methyl group have been analyzed by a one-dimensional periodic potential V=V3/2(1−cos 3φ)+V6/2(1−cos 6φ), where Vn is the barrier height for n-fold symmetry and φ is the rotational angle. The internal rotation of the methyl group in the S0 and S1 states of the 5-methyl-9-hydroxyphenalenone(OD)–water complex has been described well by three-fold potentials. The potential for the S0 state of 5-methyl9-hydroxyphenalenone(OD) is three-fold, whereas that for the S1 state of 5-methyl9-hydroxyphenalenone(OD) is six-fold. The potentials for the S1 and S0 states of 5-methyl9-hydroxyphenalenone(OH) are suggested to be six-fold. It has been shown that the coupling of the two motions reduces the symmetry of the tunneling potential when the tunneling rate is slow and decreases the tunneling rate, but the symmetry of the tunneling potential does not change and only provides a small effect on the rate of proton transfer when the tunneling rate is very fast. The tunneling rates for 5-methyl-9-hydroxyphenalenone(OH)/5-methyl-9-hydroxyphenalenone-(OD) are much larger than those for 5-methyltropolone(OH)/5-methyltropolone(OD) reported previously. The difference in the coupling between these molecules has been discussed.
Super- and subcritical hydration of nonpolar solutes. I. Thermodynamics of hydration
Authors: Matubayasi Nobuyuki , Nakahara Masaru
Published: July 2002

Hydration thermodynamics of nonpolar solutes in high-temperature water is investigated by computer simulations. The excess chemical potentials of the methane and hard sphere solutes are evaluated over a wide range of density and temperature, and the thermodynamic origin of the enhanced affinity of the nonpolar solute for super- and subcritical water is identified. It is shown that when the density is medium to high in the high-temperature conditions, the enhanced affinity results from the elevated temperature and represents the nonspecific aspect of super- and subcritical water. The excess chemical potentials are further decomposed into the enthalpic and entropic components. It is found that when the system is moved from the ambient state to a high-temperature state, the accompanying change is unfavorable for the enthalpic component and is favorable for the entropic component. The thermodynamics of cavity formation is also pursued in connection to the size distribution of cavities in pure solvent water. The utility of the scaled-particle theory is then demonstrated over a wide range of thermodynamic conditions, and the effective diameter of the water molecule is assigned within the framework of the scaled-particle theory.
Density functional calculations of nuclear quadrupole coupling constants in the zero-order regular approximation for relativistic effects
Authors: van Lenthe Erik , Jan Baerends Evert
Published: July 2002

The zeroth-order regular approximation (ZORA) is used for the evaluation of the electric field gradient, and hence nuclear quadrupole coupling constants, in some closed shell molecules. It is shown that for valence orbitals the ZORA-4 electron density, which includes a small component density (“picture-change correction”), very accurately agrees with the Dirac electron density. For hydrogen-like atoms exact relations between the ZORA-4 and Dirac formalism are given for the calculation of the electric field gradient. Density functional (DFT) calculations of the electric field gradients for a number of diatomic halides at the halogen nuclei Cl, Br, and I and at the metallic nuclei Al, Ga, In, Th, Cu, and Ag are presented. Scalar relativistic effects, spin–orbit effects, and the effects of picture-change correction, which introduces the small component density, are discussed. The results for the thallium halides show a large effect of spin–orbit coupling. Our ZORA-4 DFT calculations suggest adjustment of some of the nuclear quadrupole moments to Q(79Br)=0.30(1) barn, Q(127I)=−0.69(3) barn, and Q(115In)=0.74(3) barn, which should be checked by future highly correlated ab initio relativistic calculations. In the copper and silver halides the results with the used gradient corrected density functional are not in good agreement with experiment.
Potentials of mean force of simple ions in ambient aqueous solution. II. Solvation structure from the three-dimensional reference interaction site model approach, and comparison with simulations
Authors: Kovalenko Andriy , Hirata Fumio
Published: July 2002

We applied the three-dimensional reference interaction site model (3D-RISM) integral equation theory with the 3D hypernetted chain (3D-HNC) closure or its partial linearization (3D-PLHNC) to obtain the potentials of mean force (PMFs) and the solvation structure of sodium chloride in ambient water. The bulk solvent correlations are treated by the dielectrically consistent site–site RISM/HNC theory (DRISM/HNC) to provide a proper description of the dielectric properties of solution and to include the case of a finite salt concentration. The PMF is calculated as a difference in the solvation free energy of an ion pair and of individual ions. We obtained and analyzed in detail the PMFs and solvation structure for ion pairs of NaCl at infinite dilution and a concentration of 1 M. The results are in reasonably good agreement with molecular dynamics simulations for the same model of the solution species. Positions and orientations of water molecules in the first solvation shell around the ion pair are deduced. The short-range hydration structure of the ion pairs at infinite dilution and at moderate concentration is very similar. Ionic ordering and clustering is found in 1 M solution.
Canonoid transformations from a geometric perspective
Authors: Cariñena José F. , Rañada Manuel F.
Published: July 2002

The concept of canonoid transformation for a locally Hamiltonian vector field is introduced, and its relation with the existence of non-Noether constants of the motion is shown from a geometrical viewpoint. The equations determining generating functions for such canonoid transformations are obtained and applications to some particular problems given.
Nth (even)-order minimum uncertainty products
Authors: Lynch Robert , Mavromatis Harry A.
Published: July 2002

This paper considers the problem of finding the quantum states that minimize the products of the (even) Nth-order fluctuation of two canonically conjugate operators. The problem is first attacked in an abstract form and an equation derived for the desired states. A consideration of the N=2 case then leads to a connection with the new concept of ‘‘squeezed states’’ of the electromagnetic field, and the usual exact solution involving the coherent state. The concept of ‘‘higher-order squeezing’’ is touched on to motivate the further discussion. The cases N=4, 6, and 8 are then taken up, and approximate solutions to them found via a new numerical technique. During these calculations, it is noted that only the first few terms in the expansion in number states figure in the solution; this observation is then exploited to find an approximate closed solution to the problem valid for all N.
A superparticle on the super Riemann surface
Authors: Matsumoto Shuji , Uehara Shozo , Yasui Yukinori
Published: July 2002

The free motion of a nonrelativistic superparticle on the super Riemann surface (SRS) of genus h≥2 is investigated. Geodesics or classical paths are given explicitly on the super Poincaré upper half-plane SH, a universal covering space of the SRS, and the paths with some suitable initial conditions yield periodic orbits on the SRS. The periodic orbits are unstable and the system is chaotic. Quantum mechanics is solved on the universal covering space SH and the heat kernel is given on the SRS. This leads to a superanalog of the Selberg trace formula. The Selberg super zeta function is introduced whose zero points and poles determine the energy spectrum on the SRS.
Lax pairs galore
Authors: Calogero F. , Nucci M. C.
Published: July 2002

A formula that yields an (apparently—but only apparently—nontrivial) Lax pair for any nonlinear evolution PDE in 1+1 dimensions possessing a local conservation law is presented. Several examples are exhibited.
Homogeneous manifolds and modified KdV equations
Authors: Guil F. , Mañas M.
Published: July 2002

Each of the equations related to the Korteweg–de Vries (KdV) equation through a Miura transformation is described in terms of a homogeneous manifold associated to the loop group of SL(2,C)-valued maps on the circle.
Precise exponential estimates in adiabatic theory
Authors: Martinez André
Published: July 2002

General adiabatic evolutions associated to Hamiltonians, which admit a holomorphic extension with respect to the time variable in a complex strip, and whose spectrum satisfies a gap condition are studied. An explicit rate of exponential decay is given, which is related to simple geometric quantities associated to the spectrum of the Hamiltonian, for the transition probability between the two parts of the spectrum when the evolution is taken from −∞ to +∞.
Continuous histories and the history group in generalized quantum theory
Authors: Isham C. J. , Linden N.
Published: July 2002

We treat continuous histories within the histories approach to generalized quantum mechanics. The essential tool is the ‘‘history group:’’ the analog, within the generalized history scheme, of the canonical group of single-time quantum mechanics.
Hamiltonian structure and Darboux theorem for families of generalized Lotka–Volterra systems
Authors: Hernández-Bermejo Benito , Fairén Vı́ctor
Published: July 2002

This work is devoted to the establishment of a Poisson structure for a format of equations known as generalized Lotka–Volterra systems. These equations, which include the classical Lotka–Volterra systems as a particular case, have been deeply studied in the literature. They have been shown to constitute a whole hierarchy of systems, the characterization of which is made in the context of simple algebra. Our main result is to show that this algebraic structure is completely translatable into the Poisson domain. Important Poisson structures features, such as the symplectic foliation and the Darboux canonical representation, rise as a result of rather simple matrix manipulations.
Spin and wave function as attributes of ideal fluid
Authors: Rylov Yuri A.
Published: July 2002

An ideal fluid whose internal energy depends on density, density gradient, and entropy is considered. Dynamic equations are integrated, and a description in terms of hydrodynamic (Clebsch) potentials occurs. All essential information on the fluid flow (including initial and boundary conditions) appears to be carried by the dynamic equations for hydrodynamic potentials. Information on initial values of the fluid flow is carried by arbitrary integration functions. Initial and boundary conditions for potentials contain only nonessential information concerning the fluid particle labeling. It is shown that the description in terms of n-component complex wave function is a kind of such description in terms of hydrodynamic potentials. Spin determined by the irreducible number nm of the wave function components appears to be an attribute of the fluid flow. Classification of fluid flows by the spin appears to be connected with invariant subspaces of the relabeling group.
The action operator for continuous-time histories
Authors: Savvidou K.
Published: July 2002

We define the action operator for the consistent histories formalism, as the quantum analog of the classical action functional, for the simple harmonic oscillator case. We conclude that the action operator is the generator of time transformations, and is associated with the two types of time evolution of the standard quantum theory: the wave-packet reduction and the unitary time evolution. We construct the corresponding classical histories and demonstrate the relevance with the quantum histories. Finally, we show the relation of the action operator to the decoherence functional.
Transformations of quadrilateral lattices
Authors: Doliwa Adam , Santini Paolo Maria , Mañas Manuel
Published: July 2002

Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogs: the multidimensional quadrilateral lattices, i.e., lattices x:ZN→RM, N⩽M, whose elementary quadrilaterals are planar. Our investigation is based on the discrete analog of the theory of the rectilinear congruences, which we also present in detail. We study, in particular, the discrete analogs of the Laplace, Combescure, Lévy, radial, and fundamental transformations and their interrelations. The composition of these transformations and their permutability is also investigated from a geometric point of view. The deep connections between “transformations” and “discretizations” is also investigated for quadrilateral lattices. We finally interpret these results within the ∂̄ formalism.
Velocity–vorticity correlations related to the gradients of the Reynolds stresses in parallel turbulent wall flows
Authors: Klewicki J. C.
Published: July 2002

By using the momentum equations in ‘‘vorticity’’ form, relations between velocity–vorticity correlations and gradients of the Reynolds stresses are established for a two-dimensional turbulent channel flow. Employing these relations, the approximate formulas of Phillips [Phys. Fluids, 30, 2354 (1987)] and recently obtained experimental data allow for unmeasured velocity–vorticity correlation profiles to be deduced. The results herein indicate that the contributions to the gradients of the diagonal stresses are dominated by the correlation involving the spanwise vorticity component, while the contributions to the off-diagonal stresses are shared almost equally between the correlations involving the spanwise and normal vorticity components.
New approximate boundary conditions for large eddy simulations of wall-bounded flows
Authors: Piomelli Ugo , Ferziger Joel , Moin Parviz , Kim John
Published: July 2002

Two new approximate boundary conditions have been applied to the large eddy simulation of channel flow with and without transpiration. These new boundary conditions give more accurate results than those previously in use, and allow significant reduction of the required CPU time over simulations in which no-slip conditions are applied. Mean velocity profiles and turbulence intensities compare well both with experimental data and with the results of resolved simulations. The influence of the approximate boundary conditions remains confined near the point of application and does not affect the turbulence statistics in the core of the flow.
Spectral features of wall pressure fluctuations beneath turbulent boundary layers
Authors: Farabee Theodore M. , Casarella Mario J.
Published: July 2002

Experimental measurements of the frequency spectra and frequency cross-spectra of the wall pressure fluctuations beneath a turbulent boundary layer were made in a low-noise flow facility. The data, taken over a range of flow speeds, clearly display a dimensionless frequency (ωδ/uτ=50) at which the spectra achieve a maximum and a low-frequency range with an approximately ω2 rolloff. The scaling laws for the low-, mid-, and high-frequency regions of the spectrum are established. The cross-spectral data, obtained over a range of streamwise separations (0.21≤ξ/δ≤16.4), allow for the computations of the decay Γ(ξ,ω) and convection velocity Uc(ξ,ω) of the wall pressure field. These data show the existence of two distinct wave number groups: a high wave number group that scales on the similarity variable k1ξ=ωξ/Uc(ξ,ω) associated with turbulent sources in the log region of the boundary layer, in which eddies decay in proportion to their size, and a low wave number group that defines the cutoff for the large-scale turbulence contributors in the outer region of the boundary layer. The convection velocity data support the conjecture that the major turbulent contributions to the low and high wave number groups come from the outer and inner layers, respectively. These new results, when examined collectively, firmly establish the spectral features of the wall pressure fluctuations, including the low-frequency range, which is highly sensitive to (passive) structures in the outer flow. The locations for the turbulent sources of the wall pressure field are proposed.
An interpretation of the translation of drops and bubbles at high Reynolds numbers in terms of the vorticity field
Authors: Stone H. A.
Published: July 2002

The steady translation of a drop is reconsidered in the high Reynolds number flow limit, ℛ≫1. The standard approach for determining the drag on a spherical drop is to calculate the total energy dissipation in the fluid with the velocity field approximated using the potential flow solution outside the drop and Hill’s spherical vortex inside. Kang and Leal [Phys. Fluids 31, 233 (1988)] provide the first calculation of the drag for a spherical bubble by integrating the normal stresses over the bubble surface. Their detailed calculation shows that the drag coefficient up to O(ℛ−1) depends only on the O(1) vorticity distribution along the bubble surface and is independent of the vorticity distribution in the fluid. Here, this conclusion regarding the role of vorticity is extended to the case of any steady high Reynolds number bubble shape compatible with the steady translational speed; there is no restriction to sphericity. The results are demonstrated without explicit calculations and follow from the representation of the energy dissipation for translating drops in terms of the vorticity field.
Streaming vorticity flux from oscillating walls with finite amplitude
Authors: Wu J. Z. , Wu X. H. , Wu J. M.
Published: July 2002

How to describe vorticity creation from a moving wall is a long standing problem. This paper discusses relevant issues at the fundamental level. First, it is shown that the concept of ‘‘vorticity flux due to wall acceleration’’ can be best understood by following fluid particles on the wall rather than observing the flow at fixed spatial points. This is of crucial importance when the time-averaged flux is to be considered. The averaged flux has to be estimated in a wall-fixed frame of reference (in which there is no flux due to wall acceleration at all); or, if an inertial frame of reference is used, the generalized Lagrangian mean (GLM) also gives the same result. Then, for some simple but typical configurations, the time-averaged vorticity flux from a harmonically oscillating wall with finite amplitude is analyzed, without appealing to small perturbation. The main conclusion is that the wall oscillation will produce an additional mean vorticity flux (a fully nonlinear streaming effect), which is partially responsible for the mechanism of vortex flow control by waves. The results provide qualitative explanation for some experimentally and/or computationally observed phenomena.
Diffusional separation of gases by sinusoidal oscillations
Authors: Kurzweg U. H. , Jaeger M. J.
Published: July 2002

It is shown that gas mixtures can be separated at relatively high differential flow rates by an enhanced diffusion technique involving the oscillation of gases within a capillary bundle in the presence of axial concentration gradients. Experimental data for the diffusional separation of both He–CO2 and CO2–SF6 mixtures into an O2 carrier are presented.
Evolution and breaking of ion-acoustic waves
Authors: Rosenau Philip
Published: July 2002

A new amplitude equation governing the velocity evolution of ion-acoustic waves in a collisionless plasma is derived: Vtt+(V2)xt=[(1−V2)Vx] x+βVxxtt. From this equation the existence of a critical amplitude threshold is immediately deduced, which leads to a double layer and above which solitary waves cannot exist. Above this threshold shock waves form and density undergoes explosive growth. Multidimensional waves and waves due to the magnetic drift are also considered.
Statistics of turbulence subgrid-scale stresses: Necessary conditions and experimental tests
Authors: Meneveau Charles
Published: July 2002

Some thoughts are presented regarding the question: when can a subgrid-scale model yield correct statistics of resolved fields in a large-eddy simulation (LES) of turbulent flow. The filtered Navier–Stokes equations are used to find necessary conditions on the statistical properties of the modeled subgrid-scale stress tensor, for statistical equivalence between a ‘‘real’’ and a modeled (via LES) turbulent velocity field. When trying to formulate sufficient conditions, an unclosed hierarchy of expressions is obtained, essentially due to the ‘‘turbulence problem’’ of the resolved scales of motion. Experimental (statistical a priori) testing of subgrid-scale models is performed, based on single-probe measurements in grid turbulence and on several key assumptions. Three versions of the eddy-viscosity model are considered: constant eddy viscosity, subgrid kinetic energy, and the usual Smagorinsky eddy viscosity. Measured joint moments between filtered velocity and real or modeled subgrid scale stresses show that both energy and enstrophy dissipation can be properly captured, with a single value of the model constants over a significant range of filter widths. These results are used to examine a new subgrid model based on enstrophy equilibrium. The cross-correlation function of filtered velocity with the subgrid stress tensor is measured, which is of special importance for large-scale energy spectra. No significant differences are observed between the different models, and it is found that they predict trends in the stress-velocity cross-correlation quite well. The results show that, in nearly isotropic turbulence, the eddy-viscosity subgrid models correctly reproduce statistical trends necessary for the accurate LES prediction of energy spectra and enstrophy evolution.
Chaotic mixing by internal inertia-gravity waves
Authors: Joseph Binson
Published: July 2002

The Lagrangian transport of “passive” particles advected by inertia-gravity waves is investigated. We consider two classes of waves, namely, vertically trapped, horizontally propagating waves, and those propagating in three dimensions (3D). In the former case, it is shown that the superposition of at least two waves is necessary to produce chaotic particle paths; whereas for the latter case, at least three waves are required to initiate chaotic mixing. Liapounov exponents are used to quantify the predictability of particle trajectories in the chaotic region. Whether the chaotic mixing process is temporally uniform or intermittent is deduced from the local deviation from the Liapounov exponent. Typical estimates of Liapounov exponents give error-doubling times of the order of a few hours which roughly decreases as the amplitude of the perturbing wave (ε) increases. For waves propagating only in the horizontal, the chaotic mixing process tends to be more uniform as ε increases, while the reverse is the case for waves propagating in 3D with more intermittent mixing for larger values of ε. The chaos induced transport process is characterized from a relation of the form ΔX2(t)∼tα, for large t, where ΔX2(t) is the mean square distance traveled by a cloud of particles. For lower values of ε, the horizontally propagating case gives values of α greater than 2 and is nearly 2 for a larger value of ε. The value of α is nearly 2 for chaotically dispersing particle clouds in the 3D propagating case. Also, correlation dimensions are used to learn about the geometry of the cloud evolution. The results show that clouds originating in the chaotic zone initially spread more than like a filament, subsequently become area filling, and then proceed toward space filling behavior. This sequence of transition has been found to be faster for the 3D propagating waves than for the vertically trapped case. The implications of the results to the wave-induced mixing phenomena in geophysical flows are discussed.
Time-dependent equations governing the shape of a two-dimensional liquid curtain, Part 1: Theory
Authors: Weinstein Steven J. , Clarke Andrew , Moon Alice G. , Simister Elizabeth A.
Published: July 2002

Approximate equations have been derived that govern the time-dependent response of a two-dimensional liquid curtain falling under the influence of gravity and subjected to ambient pressure disturbances. Starting with the assumptions of potential flow and constant surface tension, and using the approximation that the curtain is long and thin, a steady-state base flow is first determined. In agreement with previous literature results, the analysis reveals that the curtain flow is essentially in free fall, where the velocity profile is only slightly curved across the curtain thickness. Then, by assuming that the disturbances to the curtain are small, the time-dependent equations are linearized about the approximated base flow. The approximate nature of the base flow necessitates a careful ordering of terms to assure that the linearization is valid. Two equations governing the curtain shape are derived: the first governs the deflection of the curtain centerline, and the second governs the thickness variations. Previous literature results regarding wave propagation and steady curtain deflections can be predicted via the derived equations. It is also found that to lowest order, pressure disturbances induce a deflection of the curtain centerline while preserving the local thickness associated with the undisturbed curtain.