bluuebunny/crossref_metadata_2025 huggingface dataset:
Quantum cluster equilibrium theory of liquids: General theory and computer implementation
Authors: Weinhold F.
Published: July 2002

We describe a method for calculating equilibrium properties of liquids by extending the standard quantum statistical thermodynamic treatment of chemical equilibria to the analogous equilibria between molecular clusters, as characterized by modern ab initio techniques. We review the equations of quantum statistical thermodynamics in the canonical ensemble for the case of coupled cluster equilibria, and show how standard treatments of translational and electronic partition functions can be modified to account for excluded-volume and cluster–cluster interaction effects at finite densities. The resulting quantum cluster equilibrium (QCE) model is implemented in a computer program that accepts ab initio input cluster properties and calculates the cluster populations for distinct distributions (phases) satisfying the equilibrium conditions at chosen T, P. We sketch the basic equations and numerical algorithms of the QCE program for neat liquids as well as more general multi-component solution equilibria. The companion paper describes general numerical characteristics of the model, including dependencies on program parameters and cluster input.
Diffusion quantum Monte Carlo calculation of the binding energy and annihilation rate of positronium hydride, PsH
Authors: Jiang Nan , Schrader D. M.
Published: July 2002

Using the diffusion quantum Monte Carlo (DMC) method with importance sampling, we calculate the binding energy and annihilation rate of positronium hydride, PsH. We get 1.0661±0.0014 eV for the binding energy, and 2.463±0.020 ns−1 for the annihilation rate. The binding energy is in agreement with the results of the best Ritz variational calculations and the best DMC calculation reported to date, and the annihilation rate agrees with the results of the Ritz variational calculations but not that of the only other DMC result known to us. A new method for correcting expectation values calculated from mixed estimators is proposed and demonstrated.
Scattering and trapping dynamics of gas-surface interactions: Theory and experiments for the Xe-graphite system
Authors: Någård Mats B. , Andersson Patrik U. , Marković Nikola , Pettersson Jan B. C.
Published: July 2002

We report on molecular beam experiments and molecular dynamics simulations of xenon scattering with incident energies E=0.06−5.65 eV from graphite. The corrugation felt by an atom interacting with the surface is found to be influenced by both surface temperature, Ts, and E. Angular distributions are significantly broadened when Ts is increased, clearly indicating corrugation induced by thermal motion of the surface also at the highest E employed. Direct scattering dominates for high E, while trapping becomes important for kinetic energies below 1 eV. The coupling between atom translation and surface modes in the normal direction is very effective, while trapped atoms only slowly accommodate their momentum parallel to the surface plane. The very different coupling normal and parallel to the surface plane makes transient (incomplete) trapping-desorption unusually pronounced for the Xe/graphite system, and atoms may travel up to 50 nm on the surface before desorption takes place. The nonlocal and soft character of the Xe-graphite interaction compared to interactions with close packed metal surfaces explains the observed high trapping probabilities and the lack of structural corrugation effects at high kinetic energies. Experimental results and simulations are in good agreement for a wide range of initial conditions, and we conclude that the model contains the most essential features of the scattering system.
Cavity ring down spectroscopy on solid C60
Authors: Engeln Richard , von Helden Gert , van Roij André J. A. , Meijer Gerard
Published: July 2002

The light absorption of a solid sample in the 8.5 μm region is measured via cavity ring down (CRD) absorption spectroscopy, using a free electron laser (FEL) as a source of widely tunable infrared (IR) radiation. A 3 mm thick zinc-selenide (ZnSe) window is used as a substrate for a 20–30 nm thick C60 film. On top of the structureless absorption due to ZnSe (<340 ppm), one of the well-known fundamental IR absorption lines of C60 is measured with monolayer sensitivity.
Strong external field effects on electronic dephasing of molecular transitions in condensed media
Authors: Morillo M. , Cukier R. I.
Published: July 2002

We discuss the effects of a strong external field on the optical transition between two electronic states of a solute immersed in a medium. The solute states may be weakly or quite strongly coupled to the medium. The electronic dephasing process is characterized via the power absorbed by the solute. The average absorbed power P̄(t) for resonant, strong fields exhibits an oscillatory decay in time, reflecting the finite change in the population difference of the electronic states, and the dephasing arising from the coupling to the medium. The coefficients of P̄(t) depend on the detuning from resonance as well as the coupling strength between the external field and the solute’s transition dipole. Our method is nonperturbative in the external field strength and shows that the spectral line shapes can be systematically altered by the application of a strong external field. We also show that for strong but off-resonance fields, P̄(t) returns to the linear response regime.
Creep and stress relaxation in a longitudinal polymer liquid crystal: Prediction of the temperature shift factor
Authors: Brostow Witold , D’Souza Nandika Anne , Kubát Josef , Maksimov Robert
Published: July 2002

The polymer liquid crystal PLC is the PET/0.6PHB copolymer; PET=poly(ethylene terephthalate), PHB=ρ-hydroxybenzoic acid (LC): 0.6=the mole fraction of PHB. This is a multiphase system with PHB-rich islands in a PET-rich matrix. Tensile creep compliance was measured isothermally from 20 °C to 160 °C in 10 °C intervals. Master curves were determined using the time–temperature superposition for 20 °C and for the glass transition temperature of the PET-rich phase TgPET=62 °C. Experimental values of the temperature shift factor aT as a function of temperature T agree in the entire T range with those from Eq. (7) relating aT to the reduced volume ṽ and the Hartmann equation of state Eq. (10). Values of aT(T) calculated from the Williams–Landel–Ferry (WLF) formula give very large errors below Tg. A control 14 months creep experiment agrees with the theoretical predictions from Eq. (7). Stress relaxation experiments were performed under the constant strain of 0.5% from 20 °C to 120 °C, again master curves were determined for 20 °C and for TgPET and aT(T) values calculated. The stress relaxation aT(T) results agree with those from creep and with those from Eq. (7).
Crossed-beam reaction of carbon atoms with hydrocarbon molecules. V. Chemical dynamics of n-C4H3 formation from reaction of C(3Pj) with allene, H2CCCH2(X 1A1)
Authors: Kaiser R. I. , Mebel A. M. , Chang A. H. H. , Lin S. H. , Lee Y. T.
Published: July 2002

The crossed molecular beams technique was employed to investigate the reaction between ground state carbon atoms, C(3Pj), and allene, H2CCCH2(X 1A1), at two averaged collision energies of 19.6 and 38.8 kJ mol−1. Product angular distributions and time-of-flight spectra of C4H3 were recorded. Forward-convolution fitting of the data yields weakly polarized center-of-mass angular flux distributions isotropic at lower, but forward scattered with respect to the carbon beam at a higher collision energy. The maximum translational energy release and the angular distributions combined with ab initio and RRKM calculations are consistent with the formation of the n-C4H3 radical in its electronic ground state. The channel to the i-C4H3 isomer contributes less than 1.5%. Reaction dynamics inferred from the experimental data indicate that the carbon atom attacks the π-orbitals of the allenic carbon–carbon double bond barrierless via a loose, reactant-like transition state located at the centrifugal barrier. The initially formed cyclopropylidene derivative rotates in a plane almost perpendicular to the total angular momentum vector around its C-axis and undergoes ring opening to triplet butatriene. At higher collision energy, the butatriene complex decomposes within 0.6 ps via hydrogen emission to form the n-C4H3 isomer and atomic hydrogen through an exit transition state located 9.2 kJ mol−1 above the products. The explicit identification of the n-C4H3 radical under single collision represents a further example of a carbon–hydrogen exchange in reactions of ground state carbon atoms with unsaturated hydrocarbons. This channel opens a barrierless route to synthesize extremely reactive hydrocarbon radicals in combustion processes, interstellar chemistry, and hydrocarbon-rich atmospheres of Jupiter, Saturn, Titan, as well as Triton.
Critical analysis of the calculated frequency shifts of hydrogen-bonded complexes
Authors: Silvi B. , Wieczorek R. , Latajka Z. , Alikhani M. E. , Dkhissi A. , Bouteiller Y.
Published: July 2002

The frequency shift of the proton donor in hydrogen bonded complexes is an important quantity which enables to discuss the nature of the hydrogen bond. Calculations of frequency shifts by quantum chemical methods are usually performed within the harmonic approximation and therefore the comparison with experimental data is biased. We have investigated the importance of anharmonic corrections in the case of twelve complexes in which either FH or ClH is the proton donor. Hartree–Fock, Mo/ller–Plesset second and third order (MP2, MP3), density functional theory (DFT), and hybrid Hartree–Fock/DFT methods have been used for the calculations. It is shown that the anharmonic contribution to the frequency shift is rather method dependent. Its magnitude is usually 10%–20% of the total shift though it can be as large of ∼ 50% for (ClH)2. Once anharmonicity is taken into account, most methods tend to noticeably overestimate the frequency shifts. In the case of DFT related approaches this trend is interpreted in terms of a poor description of the exchange in the intermolecular region.
Quantum calculations of highly excited vibrational spectrum of sulfur dioxide. III. Emission spectra from the C̃ 1B2 state
Authors: Xie Daiqian , Ma Guobin , Guo Hua
Published: July 2002

We report quantum mechanical calculations of the X̃←C̃ emission spectra of SO2 at the red wing of the C̃ absorption band. The near equilibrium potential energy surface of the C̃ 1B2 state is deduced by fitting experimental vibrational frequencies using an exact quantum mechanical Hamiltonian. Low-lying vibrational eigenenergies on this double minimum potential agree well with experimental frequencies and the corresponding eigenstates show some interesting features. Both spectral positions and intensities of the X̃←C̃ transitions are obtained up to 16 000 cm−1 using a Chebyshev based spectral method, which does not explicitly construct vibrational eigenfunctions in the X̃ state. The emission spectra are in reasonably good agreement with experimental measurements.
Contribution of intermolecular energy transfer to heat conduction in a simple liquid
Authors: Ohara Taku
Published: July 2002

Heat conduction in a low-temperature liquid is mainly caused by interaction between molecules. The intermolecular energy transfer (IET), which contributes to macroscopic heat conduction flux, is discussed in the present paper. Intermolecular energy transfer is examined using the results of molecular dynamics (MD) simulations for a simple liquid, which is modeled using the Lennard-Jones (LJ) (12-6) potential. The intermolecular energy exchange rate (IEER) is defined as the product of the intermolecular forces acting between two molecules and the velocities of the molecules. A probability distribution of the magnitude of the IEER was obtained in an ordinary equilibrium MD simulation; such a distribution was well correlated to the intermolecular distances. The substantial contribution of the IET to heat conduction flux, which is called the intermolecular energy transfer rate (IETR) here, is given by a time average of the IEER. A model is introduced to evaluate the contribution of the IET to heat conduction flux, based on an assumption that the IETR is proportional to the magnitude of the IEER itself. To verify this model, MD simulations of heat conduction in the LJ liquid under a constant temperature gradient were performed and the IETR was obtained directly. It was found that the IETR had a strong correlation with the IEER. The direct observation of the IETR by the simulation of heat conduction also showed that energy transfer in the direction opposite to the macroscopic heat flux appears in certain regions of intermolecular distances periodically. The negative energy transfer is observed between a center molecule and molecules in the inner half shell of the second and further neighbor shells The appearance of negative energy transfer reduces the net contribution of energy transfer between molecules separated by longer distances, and consequently heat conduction in a liquid is effected only by the IET between first neighbor molecules.
Infrared spectra and pseudopotential calculations for NUO+, NUO, and NThO in solid neon
Authors: Zhou Mingfei , Andrews Lester
Published: July 2002

The title cation and molecules have been prepared by reactions of laser-ablated metal cations and atoms with NO during condensation in excess neon at 4 K. Infrared fundamentals for the NUO and NThO molecules blue shift 1.6%–2.9% on going from argon to neon matrices and are calculated from 5.8% to 0.0% too high using density functional theory, GAUSSIAN 98, and pseudopotentials on the actinide metal. The isolated NUO+ cation, formed in previous gas-phase ion–molecule reactions, is characterized by new 1118.6 and 969.8 cm−1 neon matrix absorptions. Two normal modes (isotopic frequencies) are accurately modeled by the calculations for NUO+, NUO, and NThO. The isolated NUO+ cation observed here provides a vibrational model for its important isoelectronic UO22+ analog, which has only been characterized in condensed phases where partial neutralization of the dication readily occurs.
Molecular dynamics simulation of limiting conductances for LiCl, NaBr, and CsBr in supercritical water
Authors: Lee S. H. , Cummings P. T.
Published: July 2002

We report molecular dynamics simulations of LiCl, NaBr, and CsBr in supercritical water in order to explain the experimental observations of the limiting conductances as a function of the density of water at supercritical state points. As was the case in our previous work on NaCl in supercritical water [Lee et al., Chem. Phys. Lett. 293, 289 (1998)], we find that the experimental trends in the limiting conductances as a function of water density are reproduced in our simulations—a clear change of slope from the assumed linear dependence of limiting conductances of LiCl, NaBr, and CsCl on the water density. We also found that the effect of the number of hydration water molecules around ions dominates in the higher-density region while the interaction strength between the ions and the hydration water molecules (as measured by the potential energy per hydration water molecule) dominates in the lower-density region. In the case of Cs+ and Br−, however, the latter factor in the lower-density region is not as dominant as in the cases of Na+ and Cl− since a clear difference between the potential energy per hydration water molecule at densities above and below 0.45 g/cm3 was not clearly observed in the cases. In the case of Li+, the interaction between the ions and the hydration water in the lower-density region is almost a nonfactor since the potential energy per hydration water molecule is monotonically decreased with decreasing water density, which is consistent with the linear increase of the limiting conductance for the Li+ ion with decreasing water density.
Nonequilibrium molecular dynamics simulation of transport and separation of gases in carbon nanopores. II. Binary and ternary mixtures and comparison with the experimental data
Authors: Xu Lifang , Sedigh Mehran G. , Tsotsis Theodore T. , Sahimi Muhammad
Published: July 2002

We present the results of extensive nonequilibrium molecular dynamics simulations of transport and separation characteristics of binary and ternary gas mixtures consisting of CO2, CH4, and H2 through a carbon nanopore, in the presence of an external chemical potential gradient. The gas molecules are represented as Lennard-Jones (LJ) hard spheres. The effect of the various factors, such as the temperature, feed composition, and the pore size, on the transport, adsorption, and separation characteristics is investigated in detail. The simulations’ predictions are compared with experimental data obtained with a carbon molecular-sieve membrane. In some cases, there is good agreement between the predictions and the experimental data, while in other cases the simulations’ results and the data do not agree. Possible causes for the (dis)agreement are discussed, including the crucial interplay between two main factors in gas separation in a pore space, namely, adsorption on the pores’ walls versus the morphology (the pores’ interconnectivity and size distribution) of the porous material. Improved models are thus suggested.
Mechanisms of phase transitions in sodium clusters: From molecular to bulk behavior
Authors: Calvo F. , Spiegelmann F.
Published: July 2002

The thermodynamics of sodium clusters is investigated by means of a classical empirical potential and a simple quantal tight-binding model. Neutral and singly charged clusters of sizes ranging from 8 to 147 atoms are considered. A very particular attention is paid to the optimization and sampling problems. We determine the lowest-energy structures (global minima) with the “basin-hopping” technique, and the finite-temperature simulations are improved by using the “q-jumping” method and put together with the multiple histogram method. The clusters geometries may be very different on the model used, but also on the ionic charge, up to the size of about 40 atoms. The thermodynamical analysis is performed near the solid–liquid transition by calculating the complete calorific curves (heat capacities) as well as some microscopic parameters to probe the dynamics on the energy landscapes, including the spectra of isomers found by periodic quenching, isomerization indexes and the Lindemann parameter δ. Up to the largest sizes, we find that the heat capacity generally displays several features within the two models, although structural differences in the lowest-energy isomers usually induce different calorific curves. These premelting phenomena are characteristic of isomerizations taking place in a limited part of the configuration space. The thermodynamics appears to be directly related to the lowest-energy structure, and melting by steps is favored by the presence of defects on its surface. We estimate the melting temperatures Tmelt(n) and latent heats of melting L(n), and we observe two very different behaviors of their variations with the size n. Below about 75 atoms, both Tmelt and L exhibit strong non-monotonic variations typical of geometric size effects. This “microscopic” behavior is caused by the dominating premelting effects, and is replaced by a more “macroscopic” behavior for sizes larger than about 93 atoms. The premelting phenomena become there less important, and the melting process is much like the bulk solid–liquid phase transition rounded by size effects. The continuous variations displayed by the melting temperature are the only remains of cluster size effects. The models used are discussed and criticized on the basis of the similarities and discrepancies between their predictions and the experimental data.
The structure of subcritical and supercritical methanol by neutron diffraction, empirical potential structure refinement, and spherical harmonic analysis
Authors: Yamaguchi Toshio , Benmore C. J. , Soper A. K.
Published: July 2002

Pulsed neutron diffraction with isotope substitution on the hydroxyl hydrogens (H) is used to study the structure of methanol in two supercritical conditions (253 °C, 117.7 MPa, 0.700 g cm−3 and 253 °C, 14.3 MPa, 0.453 g cm−3) as well as a subcritical state (202 °C, 73.7 MPa, 0.700 g cm−3) (Tc=240 °C, Pc=8.1 MPa, ρc=0.272 g cm−3 for methanol). From three experiments on CD3OD, CD3OH, and a CD3O(H0.28+D0.72) mixture at the three thermodynamic states, the composite partial structure factors and pair correlation functions, XX, XH, and HH, are derived, where X represents a weighted sum of correlations from carbon (C), oxygen (O), and methyl hydrogen (M) atoms on the methanol molecule. The data are used in an empirical potential structure refinement (EPSR) computer simulation of methanol at the three thermodynamics states. Model distributions of molecules consistent with these data are used to estimate the individual site-site radial distribution functions, the coefficients of the spherical harmonic expansion of the orientational pair correlation function, the details of hydrogen bonding, and the three-dimensional structure of clusters formed in subcritical and supercritical methanol. In both subcritical and supercritical states of moderate density, the hydrogen bonds remain, with the average number of hydrogen bonds of 1.6±0.1 per molecule and the average chain-length of 3.1±0.4 molecules, which are less than the 1.77±0.07 per molecule and 5.5±1.0 molecules, respectively, found under ambient conditions; however, in the subcritical and supercritical methanol at moderate density the hydrogen bonds are mostly associated with clusters of 3–5 methanol molecules, in contrast with ambient methanol in which methanol molecules are involved in a nonlinear hydrogen bonded chain structure. In the low-density supercritical methanol, the large clusters are broken to generate monomers or small oligomers; the average number of hydrogen bonds per molecule decreases to 1.0±0.1, and the chain-length is 1.8±0.2 with a maximum length up to 7. The present results are compared with those recently obtained by molecular dynamics simulations, NMR, and Raman scattering of supercritical methanol.
Theoretical study for partial molar volume of amino acids in aqueous solution: Implication of ideal fluctuation volume
Authors: Imai Takashi , Kinoshita Masahiro , Hirata Fumio
Published: July 2002

A Kirkwood–Buff equation for the partial molar volumes of polyatomic molecules in solutions is derived based on the reference interaction site model (RISM) theory of molecular liquids. The partial molar volume of the twenty amino acids in aqueous solution at infinite dilution are calculated using the equation, and the results are discussed in comparison with the experimental data. The results indicate that ionizations of the C- and N-terminus groups give negative contributions to the volume ranging from −3.2 cm3/mol to −9.7 cm3/mol depending on the amino acid. Ionization of the dissociable residues also give negative contribution which ranges from −3.0 cm3/mol to −6.0 cm3/mol. On the other hand, contribution of the fractional charges on atoms to the volume is not necessarily negative, but rather slightly positive with few exceptions. It is clarified that contribution from an atom group to the volume is largely dependent on the situation where the group is placed. Therefore, it is concluded that the conventional way of determining the partial molar volume from group contributions is not reliable. The theoretical results for the partial molar volume exhibit a systematic deviation from corresponding experimental data, which increases nearly proportionally with increasing temperature and with the number of atoms in the amino acids. In order to account for the deviation, a concept of the “ideal fluctuation volume” is proposed, which is the ideal gas contribution to the volume, originating from the intramolecular fluctuation of solute.
Efficient pseudospectral methods for density functional calculations
Authors: Murphy R. B. , Cao Y. , Beachy M. D. , Ringnalda M. N. , Friesner R. A.
Published: July 2002

Novel improvements of the pseudospectral method for assembling the Coulomb operator are discussed. These improvements consist of a fast atom centered multipole method and a variation of the Head–Gordan J-engine analytic integral evaluation. The details of the methodology are discussed and performance evaluations presented for larger molecules within the context of DFT energy and gradient calculations.
Extended similarity transformed equation-of-motion coupled cluster theory (extended-STEOM-CC): Applications to doubly excited states and transition metal compounds
Authors: Nooijen Marcel , Lotrich Victor
Published: July 2002

The diagonalization manifold in similarity transformed equation-of-motion coupled cluster (STEOM-CC) theory is extended to include doubly excited determinants. In the resulting extended-STEOM approach accurate results are obtained for doubly excited states in small model systems for which full configuration interaction (CI) benchmark results are available (∼0.1 eV errors). On the other hand, extended-STEOM results are found to be virtually identical (<0.1 eV shifts) to the original STEOM results for states that are dominated by single excitations, at least in prototypical organic molecules. The extended-STEOM method is also applied to the transition metal complexes TiCl4, Ni(CO)4, and MnO4−, and yields improved results compared to STEOM and EOM-CCSD. For highly correlated systems, like the permangenate anion, results are not yet fully satisfactory however. In these cases the dominant source of error appears to be the description of ground, ionized, and attached states that underly the similarity transformed Hamiltonian in the extended-STEOM approach.
Exact reduced density matrices for a model problem
Authors: Cohen Leon , Lee Chongmoon
Published: July 2002

The reduced density matrices of arbitrary order for the boson problem of N particles, each attracted harmonically to a central point and interacting with each other harmonically, are analytically calculated.
Use of alternative hyperspherical coordinates for three-body systems
Authors: Klar H.
Published: July 2002

Relationships between alternative sets of hyperspherical coordinate systems for the treatment of three-body systems are developed. Transformations of hyperspherical harmonics for S states under a change of intrinsic angles are derived, and applied to harmonic expansions of potential energy surfaces.
Unique shape of uniformly polarizable dielectrics
Authors: Brownstein K. R.
Published: July 2002

A homogeneous isotropic dielectric body, placed in a uniform external electric field, will acquire a polarization P(r). If the body is an ellipsoid then P is uniform. A proof is presented showing that only ellipsoidal bodies have this property.
A class of conformally flat solutions for a charged sphere in general relativity
Authors: Xingxiang Wang
Published: July 2002

In this paper a class of conformally flat interior solutions of Einstein–Maxwell equations for a charged sphere is obtained. These solutions satisfy physical conditions inside the sphere.
Algebraic invariants of the Riemann tensor in a four-dimensional Lorentzian space
Authors: Carminati J. , McLenaghan R. G.
Published: July 2002

A set of 16 scalar invariants is given of the Riemann tensor which is shown to contain complete minimal sets in the Einstein–Maxwell and perfect fluid cases. All previously known sets fail to be complete in the perfect fluid case.
Supersymmetric extensions of the nonlinear Schrödinger equation: Symmetries and coverings
Authors: Roelofs G. H. M. , Kersten P. H. M.
Published: July 2002

A construction is proposed for a supersymmetric generalization of the cubic Schrödinger equation, resulting in two supersymmetric systems, one of which contains a free parameter. Both systems are proven to admit an infinite set of (higher-order) local and nonlocal symmetries and a seemingly infinite set of conservation laws, the lowest-order terms of which are given explicitly. Moreover, the theory of coverings (equivalent to the prolongation method of Wahlquist and Estabrook) is applied to both systems. Both are seen to admit an infinite-dimensional covering algebra, the structure of which is determined explicitly, resulting in a related supersymmetric system of differential equations, as well as an auto-Bäcklund transformation for each equation. This indicates the complete integrability of both systems.
Euclidean spinor Green’s functions in the space–time of a straight cosmic string
Authors: Linet B.
Published: July 2002

The spinor Green’s function and the twisted spinor Green’s function in a Euclidean space with a conical-type line singularity are generally determined. In particular, in the neighborhood of the point source, they are expressed as a sum of the usual Euclidean spinor Green’s function and a regular term. In four dimensions, these determinations can be used to calculate the vacuum energy density and the twisted one for a massless spinor field in the space–time of a straight cosmic string. In the Minkowski space–time, the vacuum energy density for a massive twisted spinor field is explicitly determined.
SU(1,1) coherent states and associated Wick symbol calculus
Authors: Luo Shunlong
Published: July 2002

We display the relationship of Perelomov and Barut–Girardello coherent states associated with the discrete series of SU(1,1) by establishing the interwining operators. Both Perelomov and Barut–Girardello coherent states are deformations of Glauber coherent states of Heisenberg–Weyl group, but they approximate the latter from different sides and exhibit a certain duality. We also develop a symbol calculus of SU(1,1) algebra in terms of Barut–Girardello coherent states (Perelomov coherent states are not suitable for this purpose) and rederive the disentanglement (Baker–Campbell–Hausdorff) formula for SU(1,1) generators by the symbol calculus and parameter differentiation technique.
Comment on Hamiltonian structures for the n-dimensional Lotka–Volterra equations
Authors: Kerner Edward H.
Published: July 2002

Plank’s recent discussion in this Journal of Hamiltonian structure of Lotka–Volterra dynamics is shown to have roots going back many years. This is briefly sketched together with an infrastructure of the Lie–Koenigs theorem and Gibbs ensemble theory.
On the Schrödinger equation with steplike potentials
Authors: Aktosun Tuncay
Published: July 2002

The one-dimensional Schrödinger equation is considered when the potential is asymptotic to a positive constant on the right half line in a certain sense. The zero-energy limits of the scattering coefficients are obtained under weaker assumptions than used elsewhere, and the continuity of the scattering coefficients from the left are established. The scattering coefficients for the potential are expressed in terms of the corresponding coefficients for the pieces of the potential on the positive and negative half lines. The number of bound states for the whole potential is related to the number of bound states for the two pieces. Finally, an improved result is given on the small-energy asymptotics of reflection coefficients for potentials supported on a half line.
A hierarchy of nonlinear evolution equations, its bi-Hamiltonian structure, and finite-dimensional integrable systems
Authors: Engui Fan , Hongqing Zhang
Published: July 2002

An isospectral problem and the associated hierarchy of nonlinear evolution equations is presented. As a reduction, a new generalized nonlinear Schrödinger equation is obtained. It is shown that the hierarchy possesses bi-Hamiltonian structure and is integrable in Liouville sense. Moreover, the eigenvalue problem can be nonlinearized as a finite-dimensional completely integrable system under the Bargmann constraint between the potentials and the eigenvalues.
Point-contact-spectroscopy evidence of quasi-particle interactions in RNi2B2C (R=Ho, Y)
Authors: Yanson I. K. , Fisun V. V. , Jansen A. G. M. , Wyder P. , Canfield P. C. , Cho B. K. , Tomy C. V. , Paul D. McK.
Published: July 2002

The point-contact (PC) d2V/dI2-spectra of HoNi2B2C and YNl2B2C reveal structure at applied voltages corresponding to the phonon frequencies. At about 4 meV a maximum is observed in the phonon density of states by analogy to the soft-phonon structure in neutron scattering experiments for LuNi2B2C [P. Dervenagas et al., Phys. Rev. B52, R9839 (1995)]and YNl2B2C [H. Kawano et al., Czech. J. Phys. 46, S2-825 (1996), Phys. Rev. Lett. 77, 4628 (1996)]. In the Ho compound the low-energy phonon peak is suppressed by an applied magnetic field in an anisotropic way, pointing to an interaction between the phonons and the magnetic systems. Surprisingly, in the nonmagnetic Y compound the 4-meV peak is also suppressed by a magnetic field. In the Ho-compound contacts which show the 〈quasi-thermal〉 behavior, the detailed magnetic-field and temperature dependences of PC spectra suggest that the magnetic order is destroyed due to the coupled phonon-magnon subsystem which is driven out of equilibrium by electrons that pass through the contact, by analogy with the nonequilibrium phonon-induced destruction of the superconducting state in point contacts [I. K. Yanson et al., JETP Lett. 45, 543 (1987)]. The PC electron-phonon interaction (EPI) spectral functions are reconstructed and the estimates for the λ-parameter yield the values of the order of 0.1. Comparison with PC EPI spectra of nonsuperconducting and nonmagnetic LaNi2B2C. [I. K. Yanson et al., Phys. Rev. Lett. 78, 935 (1997)], as well as the comparative study of PC EPI and Andreev-reflection spectra for various contacts with superconducting Ho and Y compounds suggest that the low-energy part of the electron-quasi-particle interaction spectral function is responsible for the Cooper pairing in these materials.
Magnetic-field-induced phase transitions between helical structures in noncentrosymmetric uniaxial antiferromagnets
Authors: Bogdanov A. N. , Shestakov A. A.
Published: July 2002

Two symmetrically different types of one-dimensional modulated structures (cycloids and conical helicoids) can exist in noncentrosymmetric uniaxial antiferromagnets. An applied magnetic field induces a first-order phase transition between these phases. The equilibrium parameters of the modulated structures are determined from the solution of the corresponding differential equations, and the phase diagram of the antiferromagnet in a bias magnetic field is calculated numerically. An analysis of experimental results leads to the conclusion that the predicted phase transition occurs in Ba2CuGe2O7.
Active control of convection
Authors: Singer Jonathan , Bau Haim H.
Published: July 2002

It is demonstrated theoretically that active (feedback) control can be used to alter the characteristics of thermal convection in a toroidal, vertical loop heated from below and cooled from above. As the temperature difference between the heated and cooled sections of the loop increases, the flow in the uncontrolled loop changes from no motion to steady, time-independent motion to temporally oscillatory, chaotic motion. With the use of a feedback controller effecting small perturbations in the boundary conditions, one can maintain the no-motion state at significantly higher temperature differences than the critical one corresponding to the onset of convection in the uncontrolled system. Alternatively, one can maintain steady, time-independent flow under conditions in which the flow would otherwise be chaotic. That is, the controller can be used to suppress chaos. Likewise, it is possible to stabilize periodic nonstable orbits that exist in the chaotic regime of the uncontrolled system. Finally, the controller also can be used to induce chaos in otherwise laminar (fully predictable), nonchaotic flow.
Renormalization group analysis of the Reynolds stress transport equation
Authors: Rubinstein R. , Barton J. M.
Published: July 2002

The pressure-gradient–velocity correlation and return to isotropy term in the Reynolds stress transport equation are analyzed using the Yakhot–Orszag renormalization group. The perturbation series for the relevant correlations, evaluated to lowest order in the ε expansion of the Yakhot–Orszag theory, are infinite series in tensor product powers of the mean velocity gradient and its transpose. Formal lowest-order Padé approximations to the sums of these series produce a rapid pressure strain model of the form proposed by Launder et al. [J. Fluid Mech. 68, 537 (1975)], and a return to isotropy model of the form proposed by Rotta [Z. Phys. 129, 547 (1951)]. In both cases, the model constants are computed theoretically. The predicted Reynolds stress ratios in simple shear flows are evaluated and compared with experimental data. The possibility is discussed of deriving higher-order nonlinear models by approximating the sums more accurately.
An investigation of the influence of the size distribution of seeding particles on LDA velocity data in the vicinity of a large velocity gradient
Authors: Thomas P. J. , Bütefisch K.-A.
Published: July 2002

The influence of the properties of the size distribution of seeding particles on the results of laser Doppler anemometry (LDA) velocity measurements in the vicinity of a large velocity gradient downstream of an aerodynamic shock is studied numerically. Accounting for the differing velocity lag of particles of different sizes the average velocity and the pertaining rms values are determined in the relaxation region within which the particles adjust towards the changed flow velocity downstream of the shock. It is shown how the average velocity and the rms value depend on the mean particle size and the density of the particle material. It is demonstrated in a numerical simulation how the LDA system’s ‘‘amplitude limit,’’ which can offer a means of excluding the contribution of large particles towards the experimental results, affects the average velocity and the rms value to be measured in the relaxation region. Experimental LDA data of velocity measurements across an oblique shock are presented. A good qualitative agreement of the numerical and the experimental results is found.
Numerical evidence for nonuniversality of the soft/hard turbulence classification for thermal convection
Authors: Christie Steven L. , Domaradzki J. Andrzej
Published: July 2002

Direct numerical simulations of turbulent Rayleigh–Bénard convection have been conducted in large aspect ratio boxes to examine the characteristics of convection in the range of Rayleigh numbers corresponding to the soft turbulence regime in the Chicago group classification. A measured exponent in the power law dependence of Nusselt number on Rayleigh number is 0.274, closer to the value 2/7 found in a small aspect ratio cell at the University of Chicago for the hard turbulence regime than the 1/3 obtained there for soft turbulence. The distributions of temperature fluctuation T′ in the convective core do not exhibit a unique functional form. Gaussian, exponential, and mixed (Gaussian-exponential) forms are observed. Further, it is shown that a transition in the functional form of the T′ pdf can be produced by changing the aspect ratio of the computational box without changing Rayleigh number at all. These results are in agreement with other studies, which have indicated that the hard/soft characterization of turbulent convection may partially reflect as yet not fully understood distinctions between convective turbulence in large and small aspect ratio cells.
Theory of a high-n toroidicity-induced shear Alfvén eigenmode in tokamaks
Authors: Fu G. Y. , Cheng C. Z.
Published: July 2002

A high-n WKB-ballooning mode equation is employed to study toroidicity-induced shear Alfvén eigenmodes (TAE) in s-α space, where s=(r/q)(dq/dr) is the magnetic shear and α=−(2Rq2/B2)(dp/dr) is the normalized pressure gradient for tokamak plasmas. In the ballooning mode first stability region, TAE modes are found to exist only for α less than some critical value αc. It is found that these TAE modes reappear in the ballooning mode second stability region for bands of α values. The global envelope structures of these TAE modes are studied by the Wentzel–Kramers–Brillouin (WKB) method and are found to be bounded radially if the local mode frequency has a maximum in radius.
Nonlocal fluxes at a plasma sheath
Authors: Marchand R. , Abou-Assaleh Z. , Matte J. P.
Published: July 2002

The particle and energy fluxes of electrons at the boundary of a plasma in contact with a perfectly absorbing plate are considered. In general, the fluxes are shown not to be determined by the plasma temperature and density at the plate but rather by a convolution of the plasma profiles in the vicinity of the plate. A simple empirical expression is proposed for the nonlocal fluxes, which approximately reproduces the results of a full kinetic calculation. The implications of this, to divertor plasmas near the neutralizer plate, are discussed.
A nonperiodic Euler–Vlasov code for the numerical simulation of laser–plasma beat wave acceleration and Raman scattering
Authors: Bertrand P. , Ghizzo A. , Johnston T. W. , Shoucri M. , Fijalkow E. , Feix M. R.
Published: July 2002

Numerical simulations of stimulated Raman scattering (SRS) and beat wave acceleration (BWA) are presented, which were obtained with an Eulerian relativistic Vlasov code. Such a code provides good resolution all over phase space, including very low density regions where particle-in-cell codes simply run out of calculation particles. This resolution is important for these problems because of the intense interest in the highly accelerated electrons. In this paper the emphasis is on the development of the Vlasov code for a bounded plasma, which is much more realistic than the periodic, initial-value case treated in an earlier publication.
Relativistic hydrodynamics and thermodynamics of anisotropic plasmas
Authors: Gedalin M.
Published: July 2002

State equations for a fully relativistic anisotropic plasma are obtained which generalize the Chew–Goldberger–Low theory. These equations are also a generalization of the isentropic law onto the anisotropic case. The problem of temperature definition in the anisotropic case is discussed.
The effect of relativistic hysteresis on resonance absorption
Authors: Ma Jin-Xiu , Sheng Zheng-ming , Xu Zhi-zhan
Published: July 2002

Using a simple model, it is shown that, because of the relativistic electron-mass variation, the mode-converted electrostatic electric field exhibits hysteresis in the vicinity of the critical layer. The hysteretic effect will increase the resonance absorption of obliquely incident p-polarized light (electric field vector in the plane of incidence) in a way as to increase the large-amplitude region of the electrostatic field. When the threshold light intensity for the occurance of hysteresis is exceeded, the absorption coefficient can be appreciably above the linear results.
Algebraic nonlinear growth of the resistive kink instability
Authors: Biskamp Dieter
Published: July 2002

It is derived from a simple model that the resistive kink mode grows algebraically W∝t2 for island size W exceeding the resistive layer width. The model only uses the properties of the linear eigenfunction and of current-sheet reconnection. Because of the geometry of the inflow velocity, the usual quasisingular behavior in the current sheet edge region vanishes. The theory is in quantitative agreement with high-S number numerical simulations.
Effect of window reflection on gyrotron operation
Authors: Antonsen T. M. , Cai S. Y. , Nusinovich G. S.
Published: July 2002

A simple nonlinear theoretical model is developed to study the effects of small reflections from gyrotron output windows on gyrotron operation. The results obtained from this model show that when the product of the reflection coefficient and the delay time is small enough the gyrotron oscillates stably, and the output frequency will vary smoothly with changes in the cold cavity frequency. When the product is large, however, the output frequency jumps when the cold cavity frequency changes. Further, the reflection can, under certain conditions, cause the gyrotron to become unstable and the output frequency will have a spectrum that either consists of periodically spaced discrete lines, a dense set of narrow lines, or even a broadband spectrum. The width of this spectrum is inversely proportional to the delay time.
On the two-dimensionality of the critical disturbances for stratified viscous plane parallel shear flows
Authors: Pearlstein Arne J.
Published: July 2002

It is rigorously proved that the most critical small disturbances to a stratified viscous plane parallel shear flow between rigid horizontal boundaries must be either two-dimensional (2-D) transverse or longitudinal modes, and that there are no marginally stable flows for which truly 3-D disturbances are marginally stable. This allows the linear stability analysis to be restricted to (two classes of ) 2-D disturbances.
The electric dipole of a guiding center and the plasma momentum density
Authors: Kaufman Allan N.
Published: July 2002

Pfirsch [Z. Naturforsch., Teil A 39, 1 (1984)] has shown that the charge and current density in the guiding-center representation have contributions from electric dipole moments and magnetic dipole corrections. These moments are interpreted in terms of elementary guiding-center theory, and their role in the expression for the total momentum density is explained.
Comparison of experimental and computational techniques for plane mixing layers
Authors: Mehta R. D. , Inoue O. , King L. S. , Bell J. H.
Published: July 2002

Some studies of forced and unforced plane turbulent mixing layers have been conducted using two experimental and two computational approaches. The present paper contains an overall comparison and discussion of the measured and computed results. The experimental results include flow-visualization data using the smoke-laser technique and mean flow and turbulence measurements obtained with hot X wires and a two-component laser-Doppler velocimeter (LDV). The mean flow and turbulence results indicate that the two experimental techniques agree reasonably well for this shear flow. Two-dimensional computations of the measured mixing layers have also been conducted in a coordinated effort; one method uses the inviscid discrete vortex technique for a spatially developing layer and the other is based on an approximation to the Reynolds-averaged Navier–Stokes equations. The vortex method was found to give excellent results for the forced mixing layer while the Reynolds-averaged computations, with a modified turbulence model, were particularly successful at capturing the near-field viscous behavior that included the splitter plate wake.
Inverse moments equilibria for helical anisotropic systems
Authors: Cooper W. A. , Hirshman S. P. , Depassier M. C.
Published: July 2002

An energy functional is devised for magnetic confinement schemes that have anisotropic plasma pressure. The minimization of this energy functional is demonstrated to reproduce components of the magnetohydrodynamic (MHD) force balance relation in systems with helical symmetry. An iterative steepest descent procedure is applied to the Fourier moments of the inverse magnetic flux coordinates to minimize the total energy and thus generate anisotropic pressure MHD equilibria. Applications to straight ELMO Snaky Torus (NTIS Document No. DE-84002406) configurations that have a magnetic well on the outermost flux surfaces have been obtained.
Influence of the ion/neutral atom mass ratio on the damping of electrostatic ion-cyclotron waves
Authors: Suszcynsky D. M. , Cartier S. L. , D’Angelo N. , Merlino R. L.
Published: July 2002

The damping of electrostatic ion–cyclotron waves by ion–neutral collisions was studied in a single-ended Q machine. The amplitudes of K+ and Cs+ electrostatic ion-cyclotron waves were measured as a function of neutral pressure in helium, neon, argon, krypton, and xenon. For each ion/neutral atom combination, the electrostatic ion-cyclotron wave amplitude maximizes at a neutral pressure that scales monotonically with the m+/mn mass ratio. This result is interpreted by considering the dynamics of elastic collisions between the ions and the neutral atoms.