bluuebunny/crossref_metadata_2025 huggingface dataset:
Vibrational energy transfer between the isotopomers of carbon monoxide at low temperatures
Authors: Turnidge M. L. , Reid J. P. , Barnes P. W. , Simpson C. J. S. M.
Published: July 2002

Rate constants have been measured for vibration to vibration energy transfer from C12O16(v=1) to the first vibrationally excited state of both C13O16 (Δν̄=47 cm−1) and C13O18 (Δν̄=100 cm−1) using the infrared laser fluorescence technique over the temperature range 50 to 270 K in the gas phase and in liquid neon, deuterium and argon solutions. Fluorescence from C12O16(v=1) was filtered out, and the time-dependence of the fluorescence intensity from the other isotopomer used to determine the rate constants for energy transfer. The results for the two isotopomeric systems are markedly different. For that with the smaller energy mismatch, C12O16–C13O16, the rate constants increase with decrease in temperature from 270 to 80 K. This is shown to be consistent with near-resonant energy transfer mediated by transition dipole-transition dipole couplings. Below 80 K, the temperature dependence of the rate constants flattens. For the C12O16–C13O18 system, the rate constants decrease with decrease in temperature from 270 to 100 K, below which they increase with further decrease in temperature. The temperature dependence in the range 270 to 100 K is shown to be consistent with energy transfer mediated by a combination of by long range and short range forces. Below 100 K, the temperature dependence of the rate constants is governed by attractive forces which influence the collision pair during their encounter. The rate constants are compared with previous studies of near-resonant vibrational energy transfer in other systems at low temperatures.
Photoelectron spectroscopy of OH−(N2O)n=1–5
Authors: Kim Joseph B. , Wenthold Paul G. , Lineberger W. C.
Published: July 2002

The 351 nm photoelectron spectra of OH−(N2O)n, n=1–5, are reported. Each spectrum is composed of a single broad feature that shifts toward higher electron binding energy as the number of solvent molecules increases. Analysis of OH−(N2O) spectra at ion temperatures of 200 and 300 K shows that there is significant intensity in the 000 transition, and that transitions to the dissociative region of the OH+N2O potential energy surface are also accessed. The electron affinity of OH(N2O) is estimated to be 2.14±0.02 eV, from which the OH–N2O bond dissociation energy is calculated as 0.39 eV. The photoelectron spectra of OH−(N2O)n>1 are accurately modeled as the convolution of the OH−(N2O) spectrum with the OH−(N2O)n−1. The anion vertical detachment energies and the adiabatic electron affinities for OH(N2O)n=2–5 are obtained and the thresholds for stepwise dissociation of N2O are located, indicating that photodetachment accesses multiple dissociation channels.
Crossed molecular beams and quasiclassical trajectory studies of the reaction O(1D)+H2(D2)
Authors: Alagia M. , Balucani N. , Cartechini L. , Casavecchia P. , van Kleef E. H. , Volpi G. G. , Kuntz P. J. , Sloan J. J.
Published: July 2002

The dynamics of the reactions O(1D)+H2→OH+H and O(1D)+D2→OD+D have been investigated in crossed molecular beam experiments with mass spectrometric detection at the collision energies of 1.9 and 3.0 kcal/mol, and 5.3 kcal/mol, respectively. From OH(OD) product laboratory angular and velocity distribution measurements, center-of-mass product translational energy and angular distributions were derived. The angular distributions are nearly backward–forward symmetric with a favored backward peaking which increases with collision energy. About 30% of the total available energy is found to be channeled into product translational energy. The results are compared with quasiclassical trajectory calculations on a DIM (diatomic-in-molecules) potential energy surface. Related experimental and theoretical works are noted. Insertion via the 1 1A′ ground state potential energy surface is the predominant mechanism, but the role of a second competitive abstraction micromechanism which should evolve on one of (or both) the first two excited surfaces 1A″ and 2 1A′ is called into play at all the investigated energies to account for the discrepancy between theoretical predictions and experimental results.
Self-diffusion of charged colloidal tracer spheres in transparent porous glass media: Effect of ionic strength and pore size
Authors: Kluijtmans Sebastiaan G. J. M. , de Hoog Els H. A. , Philipse Albert P.
Published: July 2002

The influence of charge on diffusion in porous media was studied for fluorescent colloidal silica spheres diffusing in a porous glass medium. The bicontinuous porous silica glasses were optically matched with an organic solvent mixture in which both glass and tracers are negatively charged. Using fluorescence recovery after photobleaching, the long-time self-diffusion coefficient DSL of the confined silica particles was monitored in situ as a function of the ionic strength and particle to pore size ratio. At high salt concentration DSL reaches a relatively high plateau value, which depends on the particle to pore size ratio. This plateau value is unexpectedly higher than the value found for uncharged silica spheres in these porous glasses, but still significantly smaller than the free particle bulk diffusion coefficient of the silica spheres. At low salt concentration DSL reduces markedly, up to the point where colloids are nearly immobilized. This peculiar retardation probably originates from potential traps and barriers at pore intersections due to deviations from cylinder symmetry in the double layer interactions between tracers and pore walls. This indicates that diffusion of charged particles in tortuous porous media may be very different from transport in long capillaries without such intersections.
Simulations of the adhesion between molecularly bonded surfaces in direct force measurements
Authors: Vijayendran R. , Hammer D. , Leckband D.
Published: July 2002

Biological materials often adhere via discrete cross bridges between reactive molecules on opposing surfaces. The macroscopic environment and surface properties as well as the detailed molecular characteristics of the cross bridges affect the adhesive properties of such systems. This work investigates the influence of these properties on force probe measurements of biological materials. This was done by simulating the dynamics of cross-bridge formation and rupture during a typical experiment with the surface force apparatus (SFA). These simulations show how the surface curvature of the force probe, the kinetic properties of the adhesion molecules, and the lateral mobility of the cross bridges influence the measured forces. The role of these properties in relating such microscopic quantities as the strength of individual cross bridges to macroscopically observed forces is also considered. Using the same computational methodology, we also analyzed the validity of using the Derjaguin approximation to relate measured macroscopic surface and interaction free energies to cross-bridge strengths. If the lateral motion of the cross bridges is negligible, these simulations show that this approach is valid for typical SFA experiments. For the experimentalist, our results provide a rationale for relating the strengths of individual adhesive bonds to macroscopic force probe measurements.
Using quantum rotational polarization moments to describe the stereodynamics of the H+D2(v=0,j=0)→HD(v′,j′)+D reaction
Authors: de Miranda Marcelo P. , Clary David C. , Castillo Jesus F. , Manolopoulos David E.
Published: July 2002

We present results of quantum calculations we have performed on the title reaction in order to study its stereodynamics at collision energies of 0.54 and 1.29 eV. Our theoretical model is based on a representation where directional properties are expressed in terms of real rotational polarization moments instead of magnetic quantum numbers. We analyze the physical meaning of rotational polarization moments and show that, when defined as in the present work, these quantities directly describe the reaction stereodynamics in terms of intuitive chemical concepts related to preferences in the reaction mechanism for particular planes and senses of molecular rotation. Using this interpretation, we identify two distinct regimes for the stereodynamics of the title reaction, observed when HD is formed with low or high rotational excitation. We also identify relevant characteristics of both regimes: (i) the existence and location of preferred planes and senses of molecular rotation, (ii) correlations between these preferences, the scattering angle and the reaction probability, and (iii) their dependence on the collision energy.
In pursuit of the ab initio limit for conformational energy prototypes
Authors: Császár Attila G. , Allen Wesley D. , Schaefer Henry F.
Published: July 2002

The convergence of ab initio predictions to the one- and n-particle limits has been systematically explored for several conformational energy prototypes: the inversion barriers of ammonia, water, and isocyanic acid, the torsional barrier of ethane, the E/Z rotamer separation of formic acid, and the barrier to linearity of silicon dicarbide. Explicit ab initio results were obtained with atomic-orbital basis sets as large as [7s6p5d4f3g2h1i/6s5p4d3f2g1h] and electron correlation treatments as extensive as fifth-order Mo/ller–Plesset perturbation theory (MP5), the full coupled-cluster method through triple excitations (CCSDT), and Brueckner doubles theory including perturbational corrections for both triple and quadruple excitations [BD(TQ)]. Subsequently, basis set and electron correlation extrapolation schemes were invoked to gauge any further variations in arriving at the ab initio limit. Physical effects which are tacitly neglected in most theoretical work have also been quantified by computations of non-Born–Oppenheimer (BODC), relativistic, and core correlation shifts of relative energies. Instructive conclusions are drawn for the pursuit of spectroscopic accuracy in theoretical conformational analyses, and precise predictions for the key energetic quantities of the molecular prototypes are advanced.
Molecular dynamics of polymer growth
Authors: Akkermans Reinier L. C. , Toxvaerd So/ren , Briels W. J.
Published: July 2002

The irreversible polymerization of a monomer liquid has been studied by molecular-dynamics simulation in two and three dimensions. The growth process is studied under good solvent conditions in the dilute regime and up to semidilute and concentrated regimes. In the dilute regime we observe a reaction limitation due to trapping of the growing centers, which is more pronounced in the lower dimension. At higher concentrations the presence of other chains decreases the monomer mobility and reaction rate. Conformational properties are studied by scaling analysis of end-to-end and gyration radii. A crossover from swollen conformations towards screened conformations is observed as growth proceeds.
Intramolecular vibrational energy redistribution and conformational isomerization in vibrationally excited 2-fluoroethanol: High-resolution, microwave-infrared double-resonance spectroscopy investigation of the asymmetric –CH2(F) stretch near 2980 cm−1
Authors: Green David , Hammond Sarah , Keske John , Pate Brooks H.
Published: July 2002

The asymmetric –CH2(F) stretch spectrum of 2-fluoroethanol near 2980 cm−1 has been rotationally assigned using microwave-infrared double-resonance spectroscopy methods in an electric-resonance optothermal molecular-beam spectrometer. The eigenstate-resolved infrared spectrum shows the effects of intramolecular vibrational energy redistribution (IVR) through the fragmentation of each rotational level of the vibrationally excited state into a set of transitions. From the spectrum we determine the IVR lifetime of the asymmetric –CH2(F) stretch to be 275 ps. The measured vibrational state density at 2980 cm−1 is 44 states/cm−1, and matches the value for the total state density obtained from a direct count. This agreement suggests that vibrational states of both the Gg′ and Tt conformers are coupled by the intramolecular dynamics. From measurements of the c-type pure rotational transitions of the Gg′ conformer we determine that the tunneling splitting for the Gg′ ground state is less than 35 kHz. The infrared spectrum is characterized by a large number of closely spaced infrared transitions. The clustering of vibrational energy levels is attributed to the weak interaction between the degenerate Gg′ and nondegenerate Tt vibrational states. This lifting of the effective Gg′ parity degeneracy is quantitatively investigated through the shape of the nearest-neighbor level spacing distribution. From this analysis we estimate that the isomerization lifetime for the Gg′ conformer of 2-fluoroethanol is 2 ns.
A theoretical analysis of the state-specific decomposition of OH(A 2Σ+,v′,N′,F1/F2) levels, including the effects of spin–orbit and Coriolis interactions
Authors: Parlant Gérard , Yarkony David R.
Published: July 2002

The state-specific decomposition OH(A 2Σ+,v′,N′,F1/F2)→O(3PJ)+H(2S) is investigated using multichannel scattering theory based on potential energy curves, spin–orbit couplings, and Coriolis couplings, obtained from multireference configuration interaction wave functions. The fine-structure branching fractions of the O(3PJ) fragment are determined and compared with the results of frequently used approximate models. The predissociation rates of the individual OH(A 2Σ+,v′,N′,F1/F2) levels are also computed and compared with the results of recent experiments.
A fresh look at ensembles: Derivative discontinuities in density functional theory
Authors: Chan Garnet Kin-Lic
Published: July 2002

We present a zero temperature ensemble spin density functional theory. We discuss the ensemble quantities that arise from derivative discontinuities, including the nonvanishing asymptotic potential and band gap shift, in the context of the Kohn–Sham formalism, and hybrid exact exchange theories, such as the Hartree–Fock–Kohn–Sham formalism. We describe and implement a general method of calculating these quantities in atomic and molecular systems. Finally we discuss how our results explain the deficiencies of existing functionals, and how new functionals should be constructed, illustrating our conclusions by examining the dissociation of H2+.
Melting thermodynamics of organic nanocrystals
Authors: Jiang Q. , Shi H. X. , Zhao M.
Published: July 2002

The size-dependent melting temperature and the size-dependent melting entropy of organic nanocrystals are predicted by use of our simple model being free of any adjustable parameter. The model predictions for the size-dependent melting temperature and the size-dependent melting entropy are supported by the experimental results on benzene, chlorobenzene, heptane, and naphthalene nanocrystals.
Competing reaction pathways from Y+C2H2 collisions
Authors: Stauffer Hans U. , Hinrichs Ryan Z. , Willis Peter A. , Davis H. Floyd
Published: July 2002

The crossed molecular beams method with 193 and 157 nm photoionization detection was used to study the competing reaction pathways resulting from collisions of ground state Y atoms with acetylene (C2H2). Three channels, corresponding to nonreactive decay of collision complexes, H2 elimination, and H atom elimination, were studied as a function of collision energy (〈Ecoll〉=6–25 kcal/mol). Production of YC2+H2 and decay of long-lived complexes back to reactants were observed at all collision energies studied. Product translational energy distributions for the H2 elimination channel demonstrate that a substantial fraction of excess energy available to the YC2+H2 products is channeled into relative translational energy. Analogous H2 elimination channels were studied in reactions of Zr and Nb with C2H2 at 〈Ecoll〉=6.0 kcal/mol. For these reactions, the H2 elimination product translational energy distributions were found to peak near zero kinetic energy, in contrast to the behavior observed for the YC2+H2 products. This suggests that a significant potential energy barrier exists in the exit channel of the YC2+H2 elimination step, whereas no exit channel barrier exists in forming ZrC2+H2 and NbC2+H2. The reformation of Y + C2H2 reactants following decay of long-lived collision complexes was found to transfer 40%–50% of the initial relative translational energy into C2H2 internal excitation. The YC2H+H product channel was only observed to occur above a collision energy threshold of 21.5±2.0 kcal/mol. Since YC2H+H production is fully spin-allowed and involves simple Y–H bond fission in the intermediate HYC2H complex, it is unlikely that any significant potential energy barrier is present in excess of the reaction endoergicity. Additional studies of Y+C2D2 reactions confirm that the observed collision energy threshold for the H or D atom loss channel corresponds to the energetic threshold for reaction, allowing determination of D0(Y–CCH)=110.2±2.0 kcal/mol.
Iterative evaluation of the path integral for a system coupled to an anharmonic bath
Authors: Makri Nancy
Published: July 2002

An iterative algorithm is presented for evaluating the path integral expression for the reduced density matrix of a quantum system interacting with an anharmonic dissipative bath whose influence functional is obtained via numerical methods. The method allows calculation of the reduced density matrix over very long time periods.
Theoretical interpretation of the electroabsorption spectra of polyacene crystals. II. Charge-transfer states
Authors: Slawik Michał , Petelenz Piotr
Published: July 2002

In recent articles, a two-dimensional analog of the Merrifield model of the coupling between the Frenkel and charge transfer (CT) excitations of a molecular crystal was successfully applied for the calculation of the electroabsorption (EA) spectra of polyacene crystals. Presently, the results of those calculations are rationalized in terms of a simplified two-state model, designed specifically for interpretational purposes. Particular attention is given to the CT manifold where symmetry considerations rule out the existence of eigenstates endowed with nonzero dipole moment, seemingly contradicting the existing experimental evidence of second-derivative EA signals. The apparent contradiction is resolved by analyzing EA contributions from pairs of zero-field eigenstates coupled by the modulating field. The new approach provides a bridge to the conventional interpretation rooted in the localized model of CT excitations, and allows to determine the limits of validity of the traditional analysis of EA spectra.
Electronic structure and chemical bonding between the first row transition metals and C2: A photoelectron spectroscopy study of MC2− (M=Sc, V, Cr, Mn, Fe, and Co)
Authors: Li Xi , Wang Lai-Sheng
Published: July 2002

Vibrationally resolved photoelectron spectra of MC2− (M=Sc, V, Cr, Mn, Fe, and Co) are reported at two detachment photon energies, 532 and 355 nm. All the spectra showed a well resolved vibrational progression in the ground state detachment features. Electron affinities, vibrational frequencies, and information about the low-lying electronic states were obtained for the first row transition metal dicarbide molecules. The measured electron affinities for the MC2 species show strong metal-dependence with a minimum at VC2 and a maximum at MnC2. The ground state vibrational frequencies were observed to decrease from ScC2 to a minimum in CrC2 and then increases slightly in MnC2 and FeC2. The trends of the electron affinities and vibrational frequencies for the MC2 species were found to correlate well with the corresponding monoxides, suggesting that the chemical bonding in M–C2 is analogous to that in M–O. The M–C2 bonding was thus interpreted to be quite ionic, and MC2 can be qualitatively viewed as M2+C22−, analogous to M2+O2−.
Ab initio classical trajectories on the Born–Oppenheimer surface: Updating methods for Hessian-based integrators
Authors: Bakken Vebjørn , Millam John M. , Bernhard Schlegel H.
Published: July 2002

For the integration of the classical equations of motion in the Born–Oppenheimer approach, each time the energy and gradient of the potential energy surface are needed, a properly converged wave function is calculated. If Hessians (second derivatives) can be calculated, significantly larger steps can be taken in the numerical integration of the equations of motion without loss of accuracy. Even larger steps can be taken with a Hessian-based predictor–corrector algorithm. Since updated Hessians are used successfully in quasi-Newton methods for geometry optimization, it should be possible to improve the performance of trajectory calculations using updated Hessians. The Murtagh–Sargent (MS) update, the Powell-symmetric–Broyden (PSB) update and Bofill’s update (a weighted combination of MS and PSB) were tested, and Bofill’s update was found to be the best. Slightly smaller step sizes were needed with Hessian updating to maintain good conservation of the energy, but this was more than compensated by the reduction in total computational cost. An overall factor of 3 in speed-up was obtained for trajectories of systems containing 4 to 6 heavy atoms computed at the HF/3-21G level.
Molecular dynamics studies of chainlike molecules confined in a carbon nanotube
Authors: Zhang Fei
Published: July 2002

Molecular dynamics simulations are performed on model fluids of linear decanes (C10H22) in order to investigate the structural and dynamical properties of chainlike molecules confined in a carbon nanotube. The density profiles, chain end-to-end distances, and order parameters are calculated to show that the confined liquids are strongly inhomogeneous and anisotropic. Anomalous positive peaks in the velocity correlation function perpendicular to the tube direction are observed and explained. Diffusion coefficients along the tube direction are calculated. We find that the diffusion coefficients in the inner region of the tube are greater than in the contact region, and that the diffusion coefficients averaged over the entire tube are much higher than in bulk liquids at the same temperatures and densities.
Spectral analysis of electron transfer kinetics. I. Symmetric reactions
Authors: Cao Jianshu , Jung Younjoon
Published: July 2002

A spectral analysis method is proposed to characterize multiple time scales in electron transfer processes, including vibrational relaxation, electronic coherence, activated curve crossing, or barrier crossing. Within this unified framework, observed rate behavior, biexponential and multiexponential decay, and population recurrences and oscillations are different components of the same kinetic spectrum; thus, several existing theoretical models, developed for limiting cases of electron transfer, can be analyzed, tested, and extended. In particular, the rate constant extracted from the analysis does not saturate as the electronic coupling increases but shows a crossover from the nonadiabatic to adiabatic limits, and the kinetic spectrum in the large coupling regime reveals the nature of the localization–delocalization transition as the consequence of two competing mechanisms. Though the analysis is presented in the context of electron transfer, this approach provides a different perspective for understanding dissipative dynamics and hence can be applied to study condensed-phase laser spectroscopy, quantum coherence control, energy transfer, and other charge transfer processes.
The chemical Langevin equation
Authors: Gillespie Daniel T.
Published: July 2002

The stochastic dynamical behavior of a well-stirred mixture of N molecular species that chemically interact through M reaction channels is accurately described by the chemical master equation. It is shown here that, whenever two explicit dynamical conditions are satisfied, the microphysical premise from which the chemical master equation is derived leads directly to an approximate time-evolution equation of the Langevin type. This chemical Langevin equation is the same as one studied earlier by Kurtz, in contradistinction to some other earlier proposed forms that assume a deterministic macroscopic evolution law. The novel aspect of the present analysis is that it shows that the accuracy of the equation depends on the satisfaction of certain specific conditions that can change from moment to moment, rather than on a static system size parameter. The derivation affords a new perspective on the origin and magnitude of noise in a chemically reacting system. It also clarifies the connection between the stochastically correct chemical master equation, and the deterministic but often satisfactory reaction rate equation.
Molecular packing changes of alkanethiols monolayers on Au(111) under applied pressure
Authors: Barrena E. , Ocal C. , Salmeron M.
Published: July 2002

A study of the changes of molecular packing in self-assembled monolayers of alkylthiols on Au(111) induced by external pressure is presented. Atomic force microscopy (AFM) is used to apply pressure and to measure the height of islands of alkanethiols partially covering the gold surface. The islands are made of ordered straight chain alkylthiol molecules tilted from the surface normal. Their height was found to decrease in a stepwise manner as a function of the load applied by the tip. Simultaneous stepwise increases in friction force were observed. A simple geometrical model involving the interlocking of alkyl chains at specific molecular tilt angles can explain the observations. According to the model, tilts in both the nearest neighbor and the next-nearest neighbor directions are necessary.
Confined gravitational fields produced by anisotropic fluids
Authors: Herrera L. , Ponce de León J.
Published: July 2002

A family of solutions of the Einstein equations for a spherically symmetric distribution of anisotropic matter is presented, which can be matched with the flat (Minkowskian) space-time on the boundary of the matter, although the energy density and stresses are nonvanishing within the sphere.
Moment invariants for the Vlasov equation
Authors: Holm D. D. , Lysenko W. P. , Scovel J. C.
Published: July 2002

Moment invariants [functions of the moments of a Vlasov distribution that are invariant under Sp(6)] are classified using Young diagrams. The connection between the moment invariants and the Poincaré invariants is established. An application using the moment invariants as phase space coordinates is considered for a matching section in a particle-beam accelerator, and a Lie–Poisson numerical integration algorithm for the moment dynamics is proposed.
Partial differential equations for the probability density and charge density of quantum statistical mechanics
Authors: Kostin M. D.
Published: July 2002

A partial differential equation is derived for the Slater sum of the Dirac equation. Normalization of the Slater sum gives the temperature-dependent probability density. Another partial differential equation is derived for the Slater sum of the Klein–Gordon equation. This Slater sum yields the temperature-dependent charge density. The transition from quantum theory to classical theory for the two partial differential equations is carried out and the relation between the two resulting classical equations is investigated.
Universal L operator and invariants of the quantum supergroup U
q
(gl(m/n))
Authors: Zhang R. B.
Published: July 2002

A spectral parameter-dependent solution of the graded Yang–Baxter equation is obtained, which is universal in the sense that it lives in Uq(gl(m/n))⊗End(V) with V the vector module of Uq(gl(m/n)). The invariants of this quantum supergroup are constructed using this solution.
Universal C-integrable nonlinear partial differential equation in N+1 dimensions
Authors: Calogero F.
Published: July 2002

A nonlinear partial differential equation of evolution in N+1 dimensions is exhibited, which is C integrable (namely, integrable via an appropriate Change of variables), and which also possesses an element of universality, as it is obtained by applying a limiting procedure to a class of nonlinear partial differential equations. Since this limiting procedure corresponds to physical conditions likely to prevail in some phenomenological circumstances, it is expected that this equation shall have applicative relevance; but this possibility is not pursued in this paper. The method whereby this equation has been obtained, as well as its integrable character, qualify it as a (N+1)-dimensional analog of the Eckhaus equation, to which it does indeed reduce for N=1.
On Feynman’s approach to the foundations of gauge theory
Authors: Land M. C. , Shnerb N. , Horwitz L. P.
Published: July 2002

In 1948, Feynman showed Dyson how the Lorentz force law and homogeneous Maxwell equations could be derived from commutation relations among Euclidean coordinates and velocities, without reference to an action or variational principle. When Dyson published the work in 1990, several authors noted that the derived equations have only Galilean symmetry and so are not actually the Maxwell theory. In particular, Hojman and Shepley proved that the existence of commutation relations is a strong assumption, sufficient to determine the corresponding action, which for Feynman’s derivation is of Newtonian form. In a recent paper, Tanimura generalized Feynman’s derivation to a Lorentz covariant form with scalar evolution parameters, and obtained an expression for the Lorentz force which appears to be consistent with relativistic kinematics and relates the force to the Maxwell field in the usual manner. However, Tanimura’s derivation does not lead to the usual Maxwell theory either, because the force equation depends on a fifth (scalar) electromagnetic potential, and the invariant evolution parameter cannot be consistently identified with the proper time of the particle motion. Moreover, the derivation cannot be made reparameterization invariant; the scalar potential causes violations of the mass-shell constraint which this invariance should guarantee. Tanimura’s derivation is examined in the framework of the proper time method in relativistic mechanics, and the technique of Hojman and Shepley is used to study the unconstrained commutation relations. It is shown that Tanimura’s result then corresponds to the five-dimensional electromagnetic theory previously derived from a Stueckelberg-type quantum theory in which one gauges the invariant parameter in the proper time method. This theory provides the final step in Feynman’s program of deriving the Maxwell theory from commutation relations; the Maxwell theory emerges as the ‘‘correlation limit’’ of a more general gauge theory, in which it is properly contained.
Numerical path integral techniques for long time dynamics of quantum dissipative systems
Authors: Makri Nancy
Published: July 2002

Recent progress in numerical methods for evaluating the real-time path integral in dissipative harmonic environments is reviewed. Quasi-adiabatic propagators constructed numerically allow convergence of the path integral with large time increments. Integration of the harmonic bath leads to path integral expressions that incorporate the exact dynamics of the quantum particle along the adiabatic path, with an influence functional that describes nonadiabatic corrections. The resulting quasi-adiabatic propagator path integral is evaluated by efficient system-specific quadratures in most regimes of parameter space, although some cases are handled by grid Monte Carlo sampling. Exploiting the finite span of nonlocal influence functional interactions characteristic of broad condensed phase spectra leads to an iterative scheme for calculating the path integral over arbitrary time lengths. No uncontrolled approximations are introduced, and the resulting methodology converges to the exact quantum result with modest amounts of computational power. Applications to tunneling dynamics in the condensed phase are described.
(I,q)-graded Lie algebraic extensions of the Poincaré algebra, constraints on I and q
Authors: Wills Toro Luis Alberto
Published: July 2002

The constraints on the index set I and on the function q of the (I,q)-graded Lie algebras over K containing the Poincaré Lie algebra are studied. By using the single-grading model, particular choices for I and q consistent with the found constraints are determined for K=C. Gradings are then found for which I⊆I=Z2×(Z4N×Z4N)×Gre, with N∈N and Gre an Abelian group. These gradings provide a way for algebraic extensions of the Poincaré Lie algebra beyond the Z2-gradings of supersymmetry and supergravity. In these algebraic extensions, each other commuting space–time parameter can either commute or anticommute with the further parameters of the (I,q)-graded (super) manifold. Different field representations can have—with each other—generalized commutative behavior beyond commutativity and anticommutativity.
Green’s-function approach to two- and three-dimensional delta-function potentials and application to the spin-1/2 Aharonov–Bohm problem
Authors: Park D. K.
Published: July 2002

Delta-function potentials in two- and three-dimensional quantum mechanics are analyzed by incorporating the self-adjoint extension method within the Green’s-function method. The energy-dependent Green’s functions for free particle plus delta-function potential systems are explicitly determined and similar calculations are carried out for the spin-1/2 Aharonov–Bohm system. It is found that the time-dependent propagator for the latter cannot be evaluated analytically except for a particular value of the self-adjoint extension parameter. It corresponds to the case in which the singular solution alone contributes for the partial wave defined by ‖m+α‖<1.
On stochastic diffusion equations and stochastic Burgers’ equations
Authors: Truman A. , Zhao H. Z.
Published: July 2002

In this paper we construct a strong solution for the stochastic Hamilton Jacobi equation by using stochastic classical mechanics before the caustics. We thereby obtain the viscosity solution for a certain class of inviscid stochastic Burgers’ equations. This viscosity solution is not continuous beyond the caustics of the corresponding Hamilton Jacobi equation. The Hopf–Cole transformation is used to identify the stochastic heat equation and the viscous stochastic Burgers’ equation. The exact solutions for the above two equations are given in terms of the stochastic Hamilton Jacobi function under a no-caustic condition. We construct the heat kernel for the stochastic heat equation for zero potentials in hyperbolic space and for harmonic oscillator potentials in Euclidean space thereby obtaining the stochastic Mehler formula.
On the huge Lie superalgebra of pseudo-superdifferential operators and super KP-hierarchies
Authors: Sedra M. B.
Published: July 2002

Lie superalgebraic methods are used to establish a connection between the huge Lie superalgebra Ξ of super- (pseudo-) differential operators and various super KP-hierarchies. We show in particular that Ξ splits into 5=2×2+1 graded algebras expected to correspond to five classes of super-KP-hierarchies generalizing the well-known Manin–Radul and Figueroa–Mas–Ramos supersymmetric KP-hierarchies.
Some trigonometric identities. II
Authors: Gervois A. , Mehta M. L.
Published: July 2002

Some trigonometric sums arising in the perturbative study of integrable chiral Zn quantum chains are directly evaluated.
On 3+1 decompositions with respect to an observer field via differential forms
Authors: Fecko Marián
Published: July 2002

3+1 decompositions of differential forms on a Lorentzian manifold (M,g; +−−−) with respect to arbitrary observer field and the decomposition of the standard operations acting on them are studied, making use of the ideas of the theory of connections on principal bundles. Simple explicit general formulas are given as well as their application to the Maxwell equations.
Limit analysis of the diffraction of a plane wave by a one-dimensional periodic medium
Authors: Felbacq D. , Guizal B. , Zolla F.
Published: July 2002

In this paper we address the problem of the reflection coefficient limit in a periodic stratified structure when the number of periods tends to infinity. We show that the graph of the reflected energy admits a superior envelope and we exhibit an explicit formula.
Two-particle scattering theory for anyons
Authors: Korff C. , Lang G. , Schrader R.
Published: July 2002

We consider potential scattering theory of a nonrelativistic quantum mechanical 2-particle system in R2 with anyon statistics. Sufficient conditions are given which guarantee the existence of Møller operators and the unitarity of the S-matrix. As examples the rotationally invariant potential well and the δ-function potential are discussed in detail. In case of a general rotationally invariant potential the angular momentum decomposition leads to a theory of Jost functions. The anyon statistics parameter gives rise to an interpolation for angular momenta analogous to the Regge trajectories for complex angular momenta. Levinson’s theorem is adapted to the present context. In particular we find that in case of a zero energy resonance the statistics parameter can be determined from the scattering phase.
Structure and thermal expansion of the low-temperature phase of SF6
Authors: Isakina A. P. , Prokhvatilov A. I. , Rodrı́guez-Carvajal J.
Published: July 2002

Powder x-ray and neutron diffraction studies of the crystalline structure, lattice parameters, and thermal expansion coefficients of sulfur hexafluoride SF6 are performed in the temperature range 1.64–110 K. It is shown that the low-temperature phase (at T<94.3 K) is monoclinic, space group C2/m(C2k3), with Z=6, in which 1/3 of the SF6 molecules occupy the positions of higher symmetry (2/m) and 2/3 of the molecules the lower one (m). As follows from the analysis of the structural results obtained, the availability of two types of molecular local symmetry positions is responsible for the anisotropic character of molecular rotation and the presence of features on the temperature dependences of the structural and thermodynamic properties of SF6 crystals in the low-temperature phase, especially near Tc of the orientational phase transition. A detailed comparison the present results with the known data in the literature is carried out.
Flow through rotating straight pipes
Authors: Lei U. , Hsu C. H.
Published: July 2002

Detailed numerical simulation has been carried out for fully developed laminar flow through a circular straight pipe with radius a, which is rotating with constant speed Ω about an axis perpendicular to its own axis. The flow is symmetric about a plane containing the pipe axis with its normal parallel to the rotation axis. There are four types of flow regime that result from the various effects of the secondary flow on the main stream via the convection and Coriolis term. When RΩ≤10 and RΩG≤100, the axial velocity profile is essentially axisymmetric and parabolic. Here RΩ=Ωa2/ν and G=G*a3/(ρν2), where G* is the reduced axial pressure gradient driving the flow, ρ is the fluid density, and ν is the kinematic viscosity. When RΩ<0.85(RΩG)1/3 and RΩG>100, the axial velocity profile is skewed toward the pressure side with one maximum occurring on the symmetric plane. When RΩ>1.26(RΩG)2/5 and RΩ>10, the axial velocity shows a dumbell-like profile with the ‘‘dumbell’’ center coinciding with the pipe axis and the ‘‘dumbell’’ axis perpendicular to the symmetric plane. When 0.85(RΩG)1/3≤RΩ≤1.26(RΩG)2/5 and RΩG>100, the axial velocity profile is skewed toward the pressure size but with two maxima, occurring symmetrically on both sides of the symmetric plane. The present calculation bridges most of the previous asymptotic analyses and provides a correlation formula for the friction factor ratio between the rotating and stationary pipe flow for most of the laminar regime of engineering interest.
On the interaction between first- and second-mode waves in a supersonic boundary layer
Authors: Maestrello L. , Bayliss A. , Krishnan R.
Published: July 2002

Linear stability theory predicts two or more types of unstable disturbances in a sufficiently high-speed boundary layer. These include the first mode, which is similar to the Tollmien–Schlichting waves found in low-speed flows, and the second mode, which does not depend strongly on the viscosity. Generally the most unstable first mode is three dimensional while the most unstable second mode is two dimensional. The interaction between these two spatially unstable modes are studied by direct solution of the three-dimensional Navier–Stokes equations. It is found that the two-dimensional second mode causes a significant increase in the nonlinearity and in the three-dimensionality of the flow field. The results suggest that this interaction may accelerate transition for flows where the second mode has a significant growth rate.
Stability of sliding Couette–Poiseuille flow in an annulus subject to axisymmetric and asymmetric disturbances
Authors: Sadeghi Venus M. , Higgins Brian G.
Published: July 2002

The linear stability of pressure-driven flow between a sliding inner cylinder and a stationary outer cylinder is studied numerically. Attention is restricted to axisymmetric disturbances (n=0), and asymmetric disturbances with azimuthal wave numbers n=1, 2, and 3. Neutral stability curves in the Reynolds number versus the wave-number plane are presented as a function of the sliding velocity of the inner cylinder for select values of the radius ratio κ. Overall, the sliding velocity of the inner cylinder has a net stabilizing effect on all modes studied. Results presented for κ=2 show that individual disturbance modes can be completely stabilized by increasing the sliding velocity. In particular, when the sliding velocity is approximately 25% of the maximum Poiseuille velocity, the neutral curve for the n=2 mode vanishes; at 36% of the maximum Poiseuille velocity, the neutral curve for the n=0 mode vanishes, and at 65%, the neutral curve for the n=1 mode vanishes. For a stationary inner cylinder the asymmetric modes are generally the least stable, though this conclusion does depend on the magnitude of κ. As κ→1 the axisymmetric mode is found to be the most dangerous.
Large-scale structures and molecular mixing
Authors: Broadwell James E. , Mungal M. Godfrey
Published: July 2002

Scalar mixing and chemical reactions in turbulent shear layers and jets are examined with emphasis on experimental results of high spatial and temporal resolution. Such measurements show that the notion of distinguishing fluids that are molecularly mixed from those that are simply stirred is valid and useful. Two models that seem especially suitable for implementing mixing analyses from this viewpoint are described and speculations on possible connections with the idea of chaotic advection offered.
Reaction zone structure for strong, weak overdriven, and weak underdriven oblique detonations
Authors: Powers Joseph M. , Gonthier Keith A.
Published: July 2002

A simple dynamic systems analysis is used to give examples of strong, weak overdriven, and weak underdriven oblique detonations. Steady oblique detonations consisting of a straight lead shock attached to a solid wedge followed by a resolved reaction zone structure are admitted as solutions to the reactive Euler equations. This is demonstrated for a fluid that is taken to be an inviscid, calorically perfect ideal gas that undergoes a two-step irreversible reaction with the first step exothermic and the second step endothermic. This model admits solutions for a continuum of shock wave angles for two classes of solutions identified by a Rankine–Hugoniot analysis: strong and weak overdriven waves. The other class, weak underdriven, is admitted for eigenvalue shock-wave angles. Chapman–Jouguet waves, however, are not admitted. These results contrast those for a corresponding one-step model that, for detonations with a straight lead shock, only admits strong, weak overdriven, and Chapman–Jouguet solutions.
Large departures from Boussinesq approximation in the Rayleigh–Bénard problem
Authors: Fröhlich J. , Laure P. , Peyret R.
Published: July 2002

Flows involving natural convection are generally studied employing the Boussinesq approximation of the Navier–Stokes equations. This paper deals with large departures from this limit by considering the two-dimensional, periodic Rayleigh–Bénard problem as an example. The main effect investigated here is a strong variation in the density considered primarily as a function of temperature as it is accounted for by the low Mach number equations. Additionally, the effect of temperature-dependent viscosity and heat conductivity is considered. Both types of departure are measured by the nondimensional temperature gradient. They destroy the midplane symmetry of the problem and lead to quantitative and qualitative changes of the flow, in particular in the bifurcation from the conduction state. The present study illustrates how three different approaches—by linear stability analysis, weakly nonlinear analysis, and direct simulation—permit the investigation of complementary aspects of the problem. The first is used to determine the critical Rayleigh number for the onset of convection. The second is well suited for investigating the nature of the bifurcation and shows that the flow in the form of rolls becomes subcritical if the non-Boussinesq character is strong enough. Direct simulations of the flow field confirm this behavior and permit the study of situations far from criticality. It turns out that non-Boussinesq effects are more and more confined to small parts of the domain as the Rayleigh number increases, so that their influence on mean properties of the flow diminishes.
Periodic blocking in parallel shear or channel flow at low Reynolds number
Authors: Davis A. M. J.
Published: July 2002

The two-dimensional creeping flow disturbance due to a periodic array of wall-attached barriers in either a parallel shear flow or a channel flow is determined by the use of a distribution of force singularities on each barrier. In each case, the Fredholm integral equation of the first kind, obtained by requiring no normal flow at a barrier, can be transformed into an infinite linear system of the second kind, whose coefficients involve, at most, infinite sums of elementary functions. The computed physical quantities include the displacement of the unbounded shear flow, the induced pressure gradient in the other flows, the maximum velocity in the symmetric flow through pairs of barriers, and the slip length derived by using the Maxwell slip-flow approximation to model the effect of barriers on a wall.
Electrostatic wave generation above and below the plasma frequency by electron beams
Authors: Cairns Iver H.
Published: July 2002

The growth of electrostatic waves near the plasma frequency  fp resulting from an unstable electron beam is investigated by solving the unmagnetized electrostatic dispersion equation numerically. Particular attention is given to finding the dispersion relations, frequencies of maximum growth, and resonant or nonresonant character of the waves for particular beam parameters. These numerical solutions are compared with analytic theories for reactive (or fluid-type) and kinetic versions of the beam instability, and for the O’Neil and Malmberg [Phys. Fluids 11, 1754 (1968)] connection of the beam and Langmuir modes. Conditions for these theoretical descriptions to be relevant, and conditions for growth significantly above or below  fp are given. Three general results are found: (i) the unstable waves do not have the Langmuir dispersion relation except in the limit of a very dilute beam with growth on the connected mode of O’Neil and Malmberg; (ii) the properties of the unstable mode depend strongly on beam parameters such as beam density, speed, and temperature; (iii) the frequency of maximum growth frequently lies significantly above or below  fp, and differs significantly from that predicted by the Langmuir dispersion relation. These results imply important consequences for strong turbulence theory, theories for nonlinear wave–wave processes such as the Langmuir wave decay and electromagnetic emission at multiples of  fp, and observational identifications of  fp from observed wave frequencies.