bluuebunny/crossref_metadata_2025 huggingface dataset:
Use of the histogram and jump-walking methods for overcoming slow barrier crossing behavior in Monte Carlo simulations: Applications to the phase transitions in the (Ar)13 and (H2O)8 clusters
Authors: Tsai C. J. , Jordan K. D.
Published: July 2002

The histogram and jump-walking algorithms are combined to deal efficiently with the problem of slow barrier crossing in Monte Carlo simulations. The utility of the histogram/jump-walking scheme is illustrated by application to the (Ar)13 and (H2O)8 clusters in their ‘‘phase transition’’ regions. Slow barrier crossing behavior is particularly acute for (H2O)8 as modeled by the TIP3P potential. Even in this case, the histogram/jump-walking algorithm proves to be quite successful at attaining equilibrium.
Electronic energy transfer in liquids. The effect of molecular dynamics
Authors: Westlund Per-Olof , Wennerström Håkan
Published: July 2002

A Liouville formalism has been developed for treating energy transfer processes within the same conceptual framework as other relaxation processes. The theory of Förster, describing energy transfer between a pair of immobile fluorescent molecules has been generalized to include the effects of molecular dynamics the static, intermediate and fast dynamic regimes. Förster’s master equation of the excitation populations is derived from the Liouville formalism and we arrive at the proper criteria for its validity within the physical model. A closed form expression is derived for the fluorescence anisotropy of a macromolecular system containing pair of pairwise interacting chromophores where one of the chromophores undergoes a two state conformational change. The expression derived is valid without assuming that the nonradiative state and the conformation dynamic is uncoupled. It is shown that when energy transfer and conformational changes occur on the same time scale, the decay times of the fluorescence anisotropy depend in a complex way on the molecular relaxation.
Statistical thermodynamics in the classical molecular dynamics ensemble. II. Application to computer simulation
Authors: Lustig Rolf
Published: July 2002

The statistical thermodynamics of the classical molecular dynamics ensemble is applied to computer simulation. The general formalism [J. Chem. Phys. 100, 3048 (1994)] is worked out for pairwise additive intermolecular potentials. Specific use is made of the multicenter n/m-Mie interaction. Cutoff corrections for arbitrary thermodynamic functions are devised.
Path-integral treatment of multi-mode vibronic coupling
Authors: Krempl Stefan , Winterstetter Manfred , Plöhn Heiko , Domcke Wolfgang
Published: July 2002

A path-integral (PI) approach to real-time quantum dynamics is developed which is suitable to treat the short-time dynamics of vibronic-coupling systems involving many degrees of freedom. The theory is formulated for the case of two electronic states which are coupled by a single active vibrational mode and whose energy separation is modulated by many so-called tuning modes. Time-dependent correlation functions are expressed as sums over all possible paths in the space of two electronic states in discretized time. For each electronic path, the multi-mode vibrational propagator factorizes into a product of single-mode propagators. Introducing the concept of classes of approximately equivalent paths, the summation over paths is replaced by a summation over classes and the computation of propagator averages within each class. It is shown that the propagator averages can efficiently be calculated by a recursive scheme. The performance of the PI method has been tested for a two-state four-mode model representing S1–S2 vibronic coupling in pyrazine. The PI results (time-dependent correlation functions and absorption spectra) are compared with numerically exact reference data which are available for this model. To demonstrate the potential of the path-integral approach for multi-mode problems, calculations are reported for a twenty-four-mode vibronic-coupling model.
Xenon diffusion on a stepped Pt(11,11,9) surface
Authors: Sneh Ofer , George Steven M.
Published: July 2002

The surface diffusion of xenon was studied on a stepped Pt(11,11,9) surface. Laser-induced thermal desorption (LITD) techniques were employed to examine the coverage dependence and anisotropy of the Xe diffusion. The coverage dependence of the Xe desorption rate was also measured using isothermal LITD and isothermal mass spectrometric methods. Both the diffusion and desorption rates of Xe on Pt(11,11,9) were independent of Xe coverage. These coverage-independent results provide no evidence for Xe trapping on step sites and are inconsistent with the existence of Xe islands. The coverage-independent desorption kinetics were similar to the kinetics on Pt(111) at low coverage with Edes=5.7 kcal/mole and νd=3.7×1010 s−1. The Xe diffusion was anisotropic and overwhelmingly parallel to the step edges. The diffusion kinetic parameters parallel to the step edges were Edif=2.8 kcal/mole and D0=50 cm2/s. This diffusion barrier is much larger than earlier theoretical predictions. The diffusion pre-exponential is also much larger than the values predicted by transition state theory. These experimental results suggest that Xe diffuses on the stepped Pt(111) surface with a multiple-site hopping mechanism. The temperature dependence of this multiple-site hop length may dominate the measured diffusion activation energy. Consequently, in accordance with recent calculations, the experimentally measured diffusion barrier may not directly reflect the underlying potential energy surface.
Double-quantum homonuclear rotary resonance: Efficient dipolar recovery in magic-angle spinning nuclear magnetic resonance
Authors: Nielsen N. C. , Bildso/e H. , Jakobsen H. J. , Levitt M. H.
Published: July 2002

We describe an efficient method for the recovery of homonuclear dipole–dipole interactions in magic-angle spinning NMR. Double-quantum homonuclear rotary resonance (2Q-HORROR) is established by fulfilling the condition ωr=2ω1, where ωr is the sample rotation frequency and ω1 is the nutation frequency around an applied resonant radio frequency (rf) field. This resonance can be used for double-quantum filtering and measurement of homonuclear dipolar interactions in the presence of magic-angle spinning. The spin dynamics depend only weakly on crystallite orientation allowing good performance for powder samples. Chemical shift effects are suppressed to zeroth order. The method is demonstrated for singly and doubly 13C labeled L-alanine.
Benzene adsorption on Cu(111): Formation of a stable bilayer
Authors: Xi Ming , Yang Michael X. , Jo Sam K. , Bent Brian E. , Stevens Paul
Published: July 2002

The structure of benzene deposited on a Cu(111) surface has been investigated by a combination of temperature-programmed desorption (TPD), high-resolution electron energy loss spectroscopy (HREELS), and near-edge x-ray absorption fine structure (NEXAFS) measurements. The results indicate that benzene forms a stable bilayer on Cu(111) at 110 K prior to multilayer formation. The TPD studies show that the second layer benzene desorbs with a peak temperature 5 K higher than that for benzene multilayers. HREELS and NEXAFS results indicate that benzene in the first layer bonds with its π ring parallel to the surface. With increasing coverage, benzene forms a second layer with its π ring significantly tilted away from the surface. The results are consistent with an approximately perpendicular configuration between the first and second layer benzene molecules, which is analogous to the structure of crystalline benzene. Isotope labeling experiments indicate there is almost complete mixing between molecules in different layers during sequential adsorption at 110 K.
A dressing for the matrix elements of the singles and doubles equation-of-motion coupled-cluster method that recovers additive separability of excitation energies
Authors: Meissner Leszek , Bartlett Rodney J.
Published: July 2002

The concept of intermediate effective Hamiltonians is employed to modify the equation-of-motion coupled-cluster method with singles and doubles (EOM-CCSD). The main goal is to eliminate the extensivity error that plagues the standard formulation of EOM-CCSD. Modification of the EOM-CCSD matrix elements (that will be called dressing here) not only eliminates the size- extensivity error but also gives some approximation to contributions from the triply excited configurations.
Estimating full configuration interaction limits from a Monte Carlo selection of the expansion space
Authors: Greer J. C.
Published: July 2002

Full configuration interaction (FCI) calculations are useful as benchmarks for approximate techniques used in quantum chemistry: they are indeed the desired goal for all energy and wave function calculations in that they are the best solution to the Schrödinger equation within a finite basis Ansatz. Application of the method is limited due to the rapid increase in the number of configurations as the basis set size is increased. Many means have been applied to limit the number of terms in the expansion with the best known method being the singles and doubles expansion CI(SD). A Monte Carlo algorithm is proposed here whereby a CI expansion is allowed to expand by randomly including new terms which interact with those terms already present in the expansion. Solution of the variational problem is then performed for these randomly chosen configurations and a selection criterium for the resulting CI coefficients is applied. Repeated application of this method allows for estimates of the FCI energy. Calculations for the water molecule are performed to demonstrate the method.
Monte Carlo simulation of the chemical potential of polymers in an expanded ensemble
Authors: Escobedo Fernando A. , de Pablo Juan J.
Published: July 2002

A new method is proposed for calculation of the chemical potential of macromolecules by computer simulation. Simulations are performed in an expanded ensemble whose states are defined by the length of a tagged molecule of variable size. A configurational-bias sampling and a preweighting scheme are introduced to facilitate transitions between such states. The usefulness of the method is illustrated by calculations of the chemical potential of hard chain molecules over a wide range of densities. The method proposed here is shown to offer significant advantages over other available methods for calculation of chemical potentials, particularly for long chain molecules at high densities.
Experimental studies of the vapor phase nucleation of refractory compounds. IV. The condensation of magnesium
Authors: Ferguson Frank T. , Nuth J. A. , Lilleleht L. U.
Published: July 2002

Magnesium nucleation was studied over the range of approximately 700 to 950 K in a gas evaporation apparatus. Measured supersaturation ratios ranged from approximately 37 to 4.2 over this temperature range, respectively. A comparison of these data and Classical Nucleation Theory shows that the two are not consistent. Although there is a good correlation between the supersaturation and the temperature data when plotted in accordance with Scaled Nucleation Theory, some of the derived parameters are slightly below the limits predicted by the theory.
New Rydberg–Rydberg transitions of the ArH and ArD molecules. I. Emission from np states of ArD
Authors: Dabrowski I. , Tokaryk D. W. , Vervloet M. , Watson J. K. G.
Published: July 2002

The ground electronic state of argon hydride has a repulsive potential apart from a long-range van der Waals minimum, but the Rydberg excited states have bound potentials similar to those of the ion ArH+. These states can be described approximately in terms of united-atom quantum numbers nl. We report here rotational analyses of the bands 5p→5s, 5p→6s, and 6p→5s of ArD, which help to further characterize the np Rydberg series. In ArH the bands 5p→5s and 6p→5s have broad lines because of predissociation in the lower state, and 5p→6s is difficult to analyze without further information. The present data are fitted with a Hund’s case (d) effective Hamiltonian. In previous work the 4p state was found to have a very small σ-π splitting, but this does not hold for the higher np states, and is probably due to an accidental cancellation between electrostatic and polarizability contributions. On the other hand, the spin–orbit coupling decreases monotonically with n. Features of the rotational levels are discussed in terms of the high-J limiting quantum numbers lJ=N−R and sJ=J−N, where R≡N+, in particular the effect of spin–orbit coupling on the levels with (lJ,sJ)=(−1,1/2) and (0,−1/2), which produces a tendency to Hund’s case e behavior in 4p, and a sharp avoided crossing in 6p. The corresponding avoided crossing in 5p would occur beyond the present range of observed J values.
The liquid crystalline phase behavior of dimerizing hard spherocylinders
Authors: McGrother Simon C. , Sear Richard P. , Jackson George
Published: July 2002

The phase behavior of dimerizing (associating) rigid particles is studied by both theory and computer simulation. The model molecule comprises a hard spherocylinder of length L and diameter D with a terminal square well bonding site embedded in one of the hemispherical caps. This model mimics the properties of simple hydrogen bonding mesogens; for example, mesogens with a carboxylic acid end group which are capable of forming dimers. A recently proposed theory of the isotropic (I)-nematic (N) phase transition for long hard spherocylinders with an attractive site at one end [R. P. Sear and G. Jackson, Mol. Phys. 82, 473 (1994)] is extended to shorter molecules. In the original theory the free energy is truncated at the level of the second virial coefficient. We now include the higher virial coefficients in an approximate manner with a Parsons type scaling. The accuracy of the theory is demonstrated by comparison with novel Monte Carlo simulation data for the same model. Excellent agreement is found for densities, pressures and degrees of association especially at the liquid crystalline phase transition. In comparing the results for the L/D=5 associating system with those for its nonassociating analogue, the nematic phase is seen to be stabilized relative to the isotropic phase, while the nematic (N)-smectic-A (SmA) transition occurs at approximately the same density. The I-N transition for the dimerizing system is clearly first order, while the N-SmA is essentially continuous. The smectic-A phase has a monolayer structure which is similar to that formed by the nonassociating system. Furthermore, a system of otherwise nonmesogenic molecules with L/D=3 has a stable liquid crystal phase when dimerization is made possible with the inclusion of the terminal bonding sites. Rather than being a nematic phase, this phase is surprisingly found to have the layered structure of a smectic-A phase. We discuss our results in terms of the increase in the ‘effective’ aspect ratio as a result of association.
Nanostructured silicon films obtained by neutral cluster depositions
Authors: Mélinon P. , Kéghélian P. , Prével B. , Perez A. , Guiraud G. , LeBrusq J. , Lermé J. , Pellarin M. , Broyer M.
Published: July 2002

Nanosize neutral silicon clusters produced using a laser vaporization source were analyzed in the gas phase and deposited on various substrates at room temperature in ultrahigh vacuum. Nanostructured thin films with thickness around 100 nm resulting from this nearly ballistic deposition process were subsequently characterized by several complementary electron spectroscopy techniques to investigate the electronic structure. The film properties are comparable to those of a disordered phase but different from the properties of conventional amorphous or nanoporous silicon. The specific features observed in the Si-cluster assembled films cannot be simply interpreted on the basis of quantum confinement effects and are rather attributed to the presence of odd-membered rings in the incident-free cluster structure. Some Si-cluster geometries in the subnanometric size range are proposed and discussed on the basis of the experimental results and a tight binding scheme.
Similarity transformed equation-of-motion coupled-cluster theory: Details, examples, and comparisons
Authors: Nooijen Marcel , Bartlett Rodney J.
Published: July 2002

The similarity transformed equation-of-motion coupled-cluster (STEOM-CC) method is presented in full detail. Comparisons are made with the Fock space coupled-cluster (FSCC) method and the equation-of-motion coupled-cluster (EOM-CC) scheme. The role of implicit triple excitations and, relatedly, charge transfer separability in STEOM is discussed. The dependence on the choice of active space in STEOM is addressed and criteria for the selection of the active space are given. The evaluation of properties within STEOM is outlined and a large number of illustrative examples of STEOM is presented.
Thermal stimulation of the surface termination of LaAlO3{100}
Authors: Yao J. , Merrill P. B. , Perry S. S. , Marton D. , Rabalais J. W.
Published: July 2002

The surface termination, structure, and morphology of the LaAlO3{100} surface has been studied as a function of temperature by means of time-of-flight scattering and recoiling spectrometry (TOF-SARS), atomic force microscopy (AFM), low-energy electron diffraction (LEED), Auger electron spectroscopy (AES), and x-ray photoelectron spectroscopy (XPS). The results show that the surface is terminated in a Al–O layer from room temperature up to ∼150 °C and a La–O layer at temperatures above ∼250 °C. The surfaces are terminated exclusively in either Al–O or La–O layers, with mixed terminations observed only in the intermediate region of 150–250 °C. These surfaces exhibit ordered (1×1) LEED patterns and stepped AFM images with step heights of 3.9±0.5 Å and terrace widths of ∼1000 Å. A mechanism is proposed for this low-temperature surface stoichiometry change which is linked to the observation of the creation of surface oxygen deficiencies upon heating. The oxygen deficient Al–O terminating layer transforms to a La–O terminating layer, creating a near-surface vacancy in the twelve coordinate site of the perovskite structure.
A selected-ion-flow-drift-tube study of charge transfer processes between atomic, molecular, and dimer ion projectiles and polyatomic molecules ethane, propane, and n-butane
Authors: Praxmarer C. , Hansel A. , Lindinger W. , Herman Z.
Published: July 2002

Charge transfer processes of Ar+, Kr+, Xe+, N2+, CO+, Ar2+, Kr2+, and N4+ with the alkanes ethane, propane, and n-butane were investigated using the selected-ion-flow-drift-tube (SIFDT) technique. The relative abundances of molecular and fragment hydrocarbon product ions can be explained using the breakdown pattern of the hydrocarbon molecular ion in question and assuming that the recombination energy of the projectile ions is deposited in the quasi continuum of the energy levels of the polyatomic molecular ions in a resonant way. The observed increase of the fragment ion yields with increasing collision energy is due to collision induced excitation up to the dissociation limit of the hydrocarbon ions in collisions with the helium buffer gas atoms rather than to inelastic charge transfer from hyperthermal projectile ions.
Structures and electronic phases of the bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) clusters and κ-(BEDT-TTF) salts: A theoretical study based on ab initio molecular orbital methods
Authors: Imamura Yutaka , Ten-no Seiichiro , Yonemitsu Kenji , Tanimura Yoshitaka
Published: July 2002

Electronic and geometrical structures of bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) molecules are studied using ab initio molecular orbital methods. The optimized structure of a BEDT-TTF monomer is close to the experimental one within errors of 0.02 Å and 0.5 deg in bond length and angle, respectively, except the ethylene group. Ab initio parameters such as transfer integrals and Coulomb interactions are determined from the BEDT-TTF dimer and tetramer calculations. Using model Hamiltonians with the ab initio parameters, we investigate the electronic states based on the exact diagonalization method. The results show that the ground state has antiferromagnetic correlation which is consistent with experimental results. We study the effects of long-range Coulomb interactions employing the 2-D extended Hubbard model with the Hartree–Fock approximation. It is found that the ground state shows various phases; antiferromagnetic, charge ordering, and paramagnetic ones, controlled by the long-range interactions.
Initial stages of nucleation in phase separating polymer blends
Authors: Lefebvre A. A. , Lee J. H. , Jeon H. S. , Balsara N. P. , Hammouda B.
Published: July 2002

The initial stages of nucleation during liquid–liquid phase separation in mixtures of high molecular weight polymers was studied by time-resolved small angle neutron scattering. Phase separation was induced either by decreasing temperature or by increasing pressure. One of the blend components was labeled with deuterium to obtain sufficient scattering contrast between the components. The general features of nucleation were independent of quench depth and the nature of the quench (temperature quench versus pressure quench). The early stages of nucleation consisted of amplification of concentration fluctuations. During this stage, the scattered intensity (I) in the low scattering vector (q) limit was consistent with the Ornstein–Zernike equation. This enabled the determination of the characteristic length scale of the growing fluctuations, ξ. The I vs q behavior at intermediate scattering vectors (q>1/ξ) could be described by a power law (I∼q−d). We demonstrate the existence of a time–temperature superposition principle during nucleation: The time dependence of d at different quench depths could be superimposed by a lateral shift of the data along the time axis (log scale). In analogy to the shift factor for viscoelastic behavior of polymers, we define a nucleation shift factor, aN, which describes the slowing down of nucleation kinetics with decreasing quench depth. Similarly, nucleation after pressure quenches can be described by a time–pressure superposition law. For each quench, we find that the scattering intensity is independent of time in the high q regime (q>qmerge). This implies the absence of growing structures with length scales smaller than ξcrit=1/qmerge during nucleation. This aspect of nucleation is consistent with classical theories which predict the existence of a critical nucleus size. As expected, ξcrit increases with decreasing quench depth.
Convergence of Breit–Pauli spin–orbit matrix elements with basis set size and configuration interaction space: The halogen atoms F, Cl, and Br
Authors: Nicklass Andreas , Peterson Kirk A. , Berning Andreas , Werner Hans-Joachim , Knowles Peter J.
Published: July 2002

Systematic sequences of basis sets are used to calculate the spin–orbit splittings of the halogen atoms F, Cl, and Br in the framework of first-order perturbation theory with the Breit–Pauli operator and internally contracted configuration interaction wave functions. The effects of both higher angular momentum functions and the presence of tight functions are studied. By systematically converging the one-particle basis set, an unambiguous evaluation of the effects of correlating different numbers of electrons in the Cl treatment is carried out. Correlation of the 2p-electrons in chlorine increases the spin–orbit splitting by ∼80 cm−1, while in bromine we observe incremental increases of 130, 145, and 93 cm−1, when adding the 3d, 3p, and 2p electrons to the set of explicitly correlated electrons, respectively. For fluorine and chlorine the final basis set limit, all-electrons correlated results match the experimentally observed spin–orbit splittings to within ∼5 cm−1, while for bromine the Breit–Pauli operator underestimates the splitting by about 100 cm−1. More extensive treatment of electron correlation results in only a slight lowering of the spin–orbit matrix elements. Thus, the discrepancy for bromine is proposed to arise from the nonrelativistic character of the underlying wave function.
Inherent structure of a molten salt
Authors: La Violette Randall A. , Budzien Joanne L. , Stillinger Frank H.
Published: July 2002

We calculated the inherent structure of a model melt of zinc (II) bromide over a wide range of densities. Stable, metastable, and unstable branches were obtained for the zero temperature pressure–volume isotherm of the inherent structure. The pressure–volume isotherm, the void distribution, and the structure factor were used to identify the spinodal, independent of any model equation of state.
SL(3,R) as the group of symmetry transformations for all one-dimensional linear systems
Authors: Aguirre M. , Krause J.
Published: July 2002

The converse problem of similarity analysis is solved in general for the finite symmetry transformations of any inhomogeneous ordinary linear differential equation of the second order ẍ+f2(t)ẋ+f1(t)x =f0(t). The eight-parameter realizations of the symmetry group are obtained in the form ℱ−1𝒫2 ℱ, where ℱ stands for transformations of (t,x) that depend exclusively on the fundamental solutions of the equation, and where 𝒫2 is an arbitrary projective transformation in the plane. Thus it is shown that the full point symmetry group corresponds to SL(3,R) indeed, without recourse to the Lie algebra. Also, a technique is obtained for calculating the finite point symmetry realization of SL(3,R) for any given one-dimensional linear system. Some miscellaneous examples are given.
The analogy between spin glasses and Yang–Mills fluids
Authors: Holm Darryl D. , Kupershmidt Boris A.
Published: July 2002

A dictionary of correspondence is established between the dynamical variables for spin-glass fluid and Yang-Mills plasma. The Lie-algebraic interpretation of these variables is presented for the two theories. The noncanonical Poisson bracket for the Hamiltonian dynamics of an ideal spin glass is shown to be identical to that for the dynamics of a Yang–Mills fluid plasma, although the Hamiltonians differ for the two theories. This Poisson bracket is associated to the dual space of an infinite-dimensional Lie algebra of semidirect-product type.
Initial value problem for colliding gravitational plane waves. II
Authors: Hauser Isidore , Ernst Frederick J.
Published: July 2002

As a preliminary step in the development of a Hilbert problem (HP) approach to the initial value problem (IVP) for colliding gravitational plane waves with noncollinear polarizations, the IVP for colliding gravitational plane waves with collinear polarizations is reformulated in two different ways as an HP in a complex plane. The solutions of both forms of the HP are found and each of these agrees with the solution obtained by another method in the previous paper of this series [I. Hauser and F. J. Ernst, J. Math. Phys. 30, 872 (1989)]. The conditions imposed on the initial data of the IVP by the vacuum field equations are discussed in detail. Anticipating the next paper of this series, the generalization of one form of the HP to noncollinear polarizations is briefly described.
Initial value problem for colliding gravitational plane waves. III
Authors: Hauser Isidore , Ernst Frederick J.
Published: July 2002

The development of a homogeneous Hilbert problem (HHP) approach to the initial value problem (IVP) for colliding gravitational plane waves with noncollinear polarization that began in two earlier papers [I. Hauser and F. J. Ernst, J. Math. Phys. 30, 872 (1989) and 30, 2322 (1989)] is continued. After formulating the HHP, the description of how one can apply it to generate a new family of solutions of the colliding wave problem that generalizes a three-parameter family constructed by Ernst, García, and Hauser [J. Math. Phys. 29, 681 (1988)] using a double-Harrison transformation is given. Then the proof that the solution of the new HHP indeed solves the IVP that is posed is presented. A matrix Fredholm equation of the second kind that is equivalent to the HHP is also deduced. This will be used in a sequel to complete the proof of existence of solutions of the HHP and the proof that certain assumed differentiability hypotheses are in fact valid.
An asymptotic analysis and its application to the nonrelativistic limit of the Pauli–Fierz and a spin-boson model
Authors: Arai Asao
Published: July 2002

An abstract asymptotic theory of a family of self-adjoint operators {Hκ}κ>0 acting in the tensor product of two Hilbert spaces is presented and it is applied to the nonrelativistic limit of the Pauli–Fierz model in quantum electrodynamics and of a spin-boson model. It is proven that the resolvent of Hκ converges strongly as κ→∞ and the limit is a pseudoresolvent, which defines an ‘‘effective operator’’ of Hκ at κ≊∞. As corollaries of this result, some limit theorems for Hκ are obtained, including a theorem on spectral concentration. An asymptotic estimate of the infimum of the spectrum (the ground state energy) of Hκ is also given. The application of the abstract theory to the above models yields some new rigorous results for them.
Initial value problem for colliding gravitational plane waves. IV
Authors: Hauser Isidore , Ernst Frederick J.
Published: July 2002

In a preceding paper [I. Hauser and F. J. Ernst, J. Math. Phys. 31, 871 (1990)], the initial value problem for colliding gravitational plane waves was reformulated as a homogeneous Hilbert problem (HHP) in a complex plane. It is now proven that a unique solution of this HHP always exists and that any assumed differentiability or holomorphy properties of the plane-wave metrics imply corresponding properties for the scattered wave metric. This completes the demonstration, initiated in the preceding paper, that the solution of the HHP furnishes the solution of the initial value problem. A Fredholm equation that is equivalent to the HHP and that was introduced in the preceding paper is used to effect the proofs.
Properties of the Dirac–Weyl operator with a strongly singular gauge potentiala)
Authors: Arai Asao
Published: July 2002

Considered is a quantum system of a charged particle moving in the plane R2 under the influence of a perpendicular magnetic field concentrated on some fixed isolated points in R2. Such a magnetic field is represented as a finite linear combination of the two-dimensional Dirac delta distributions and their derivatives, so that the gauge potential of the magnetic field also may be strongly singular at those isolated points. Properties of the Dirac–Weyl operator with such a singular gauge potential are investigated. It is seen that some of them depend on whether the magnetic flux is locally quantized or not. Particular attention is paid to the zero-energy state. For each of the self-adjoint realizations of the Dirac–Weyl operator, the number of the zero-energy states is computed. It is shown that, in the present case, a theorem of Aharonov and Casher [Phys. Rev. A 19, 2461 (1979)], which relates the total magnetic flux to the number of zero-energy states, does not hold. It is also proven that the spectrum of every self-adjoint extension of the minimal Dirac–Weyl operator is equal to R.
Algebraic structure of parabose Fock space. I. The Green’s ansatz revisited
Authors: Macfarlane A. J.
Published: July 2002

A description of the Fock space of a parabose oscillator of order p based on commutation relations bilinear in creation and annihilation operators rather than trilinear ones is developed. A new statement of the well-known Green’s ansatz is introduced to help understand the significance of the bilinear commutation relations. It is also applied to show how all parabose oscillators of even order (respectively, odd order) can be obtained as irreducible constituents of the Fock space associated with a Green’s ansatz of two (three) terms. Analogs of the form in which the parabose Green’s ansatz is presented are provided for one parafermi oscillator and for systems of many parabose and parafermi oscillators of the same order. Methods used in the paper allow various new results for q-deformed parabose oscillators to be derived.
Universal central extensions of elliptic affine Lie algebras
Authors: Bremner Murray
Published: July 2002

Let 𝔤 be a simple complex (finite dimensional) Lie algebra, and let R be the ring of regular functions on a compact complex algebraic curve with a finite number of points removed. Lie algebras of the form 𝔤⊗CR are considered; these generalize Kac–Moody loop algebras since for a curve of genus zero with two punctures R≂C[t,t−1]. The universal central extension of 𝔤⊗R is analogous to an untwisted affine Kac–Moody algebra. By Kassel’s theorem the kernel of the universal central extension is linearly isomorphic to the Kähler differentials of R modulo exact differentials. The dimension of the kernel for any R is determined first. Restricting to hyperelliptic curves with 2, 3, or 4 special points removed, a basis for the kernel is determined. Restricting further to an elliptic curve with punctures at two points (of orders one and two in the group law) we explicitly determine the cocycles which give the commutation relations for the universal central extension. The results involve Pollaczek polynomials, which are a genus-one generalization of ultraspherical (Gegenbauer) polynomials. © 1994 American Institute of Physics.
Algebraic and spectral properties of some quasiorthogonal polynomials encountered in quantum radiation
Authors: Zarzo A. , Yáñez R. J. , Ronveaux A. , Dehesa J. S.
Published: July 2002

The nodal structure of the wavefunctions of a large class of quantum-mechanical potentials is often governed by the distribution of zeros of real quasiorthogonal polynomials. It is known that these polynomials (i) may be described by an arbitrary linear combination of two orthogonal polynomials {Pn(x)} and (ii) have real and simple zeros. Here, the three term recurrence relation, the second order differential equation and the distribution of zeros of quasiorthogonal polynomials of the classical class (i.e., when Pn(x) is a Jacobi, Laguerre or Hermite polynomial) are derived and analyzed. Specifically, the exact values of the Newton sum rules and the WKB density of zeros of these polynomials are found.
The W1+∞(gl
s)-symmetries of the s-component KP hierarchy
Authors: van de Leur Johan
Published: July 2002

Adler, Shiota, and van Moerbeke obtained for the KP and Toda lattice hierarchies a formula which translates the action of the vertex operator on tau-functions to an action of a vertex operator of pseudodifferential operators on wave functions. This relates the additional symmetries of the KP and Toda lattice hierarchy to the W1+∞−, respectively, W1+∞×W1+∞− algebra symmetries. In this paper we generalize the results to the s-component KP hierarchy. The vertex operators generate the algebra W1+∞(gls), the matrix version of W1+∞. Since the Toda lattice hierarchy is formally equivalent to the 2-component KP hierarchy, the results of this article uncover in that particular case a much richer structure than the one obtained by Adler, Shiota, and van Moerbeke.
Subalgebras with converging star products in deformation quantization: An algebraic construction for C
P
n
Authors: Bordemann M. , Brischle M. , Emmrich C. , Waldmann S.
Published: July 2002

Based on a closed formula for a star product of Wick type on CPn, which has been discovered in an earlier article of the authors, we explicitly construct a subalgebra of the formal star algebra (with coefficients contained in the uniformly dense subspace of representative functions with respect to the canonical action of the unitary group) that consists of converging power series in the formal parameter, thereby giving an elementary algebraic proof of a convergence result already obtained by Cahen, Gutt, and Rawnsley. In this subalgebra the formal parameter can be substituted by a real number α: the resulting associative algebras are infinite dimensional, except for the case α=1/K, K a positive integer, where they turn out to be isomorphic to the finite-dimensional algebra of linear operators in the Kth energy eigen- space of an isotropic harmonic oscillator with n+1 degrees of freedom. Other examples like the 2n torus and the Poincaré disk are discussed.
A study of nonlinear dynamical models of plasma turbulence
Authors: Qian S. , Lee Y. C. , Chen H. H.
Published: July 2002

A dissipative Benjamin–Ono equation is introduced to study turbulence of a magnetic two-fluid system. An exact nonlinear mode truncation method is applied in which a finite number of poles are used to represent completely the asymptotic behavior of the system. The pole dynamics exhibit a wide range of nonlinear phenomena, including periodic and chaotic orbits. Statistical properties of the resultant turbulent flows such as correlation functions and energy spectra are also studied. The results show that the system can indeed reach the strong turbulent state.
Steady-state magnetohydrodynamic clump turbulence
Authors: Tetreault David J.
Published: July 2002

The turbulent steady state of the magnetohydrodynamic (MHD) clump instability [Phys. Fluids 31, 2122 (1988)] is investigated. The steady state is determined by the balance between clump growth by turbulent mixing and clump decay by field line stochasticity. The turbulent fields driving the mixing are generated self-consistently from Ampère’s law and conserve the magnetic helicity. In the steady state, the mean current and magnetic field satisfy J0=μB0, where μ depends on the mean-square fluctuation level. Above this critical point (J0>μB0), the plasma is MHD clump unstable. MHD clump instability is a dynamical route to the force-free, Taylor state. For the steady state to exist, μ must exceed a threshold on the order of that required for B0z field reversal. Steady-state MHD clump turbulence corresponds to field reversed Taylor states. From the μ threshold condition, the steady-state fluctuation spectrum (δBrms/B) is calculated and shown to increase with mean driving current as θ3, where θ is the pinch parameter.
Intermittency and attractor size in isotropic turbulence
Authors: Kraichnan Robert H.
Published: July 2002

Qualitative arguments suggest that the Kolmogorov 1941 (K41) inertial range for space dimensionality D3 corresponds to a maximum attractor size if compared with alternative inertial ranges in which intermittency increases as a power of wavenumber. Therefore upper bounds on attractor size consistent with K41 do not either rule out or imply intermittency corrections to the −5/3 law. In contrast, the K41 inertial range corresponds to minimum attractor size if D>4.
Narrow fingers in a Hele–Shaw cell
Authors: Kopf-Sill Anne R. , Homsy G. M.
Published: July 2002

Narrow fingers that occupy much less than one-half the cell width have been observed in a carefully prepared Hele–Shaw cell. These fingers sometimes show dendritic instability. They are in most respects similar to those produced artificially by Couder et al. [Phys. Rev. A 34, 5175 (1986); Europhys. Lett. 2, 437 (1986)] and are believed to represent a new class of solutions to the shape selection problem.
Chaotic dynamics of spatially homogeneous gas mixtures
Authors: Lupini R. , Spiga G.
Published: July 2002

The transport of N gases in a background host medium can be described, in the case of constant collision frequencies, by a set of N ordinary differential equations of the Lotka–Volterra type. It is shown that for N=3 such a set exhibits chaotic dynamics generated by a sequence of period-doubling bifurcations starting from a supercritical Hopf bifurcation of the three-species equilibrium state.
On the physical accuracy of scalar transport modeling in inhomogeneous turbulence
Authors: Bernard Peter S. , Rovelstad Amy L.
Published: July 2002

Direct numerical simulations of scalar fields produced by uniform and line sources in channel flow are used as the basis for examining the accuracy of random flight and closure models in predicting turbulent scalar transport rates. Closure models of gradient form with an anisotropic eddy diffusivity tensor perform well for the uniform source flow and the far field of plumes. In the near field, the plumes are seriously distorted due to the inappropriateness of gradient transport in modeling the streamwise flux rate. Random flight models are most successful in producing a qualitative rendering of the near field of plumes, but are subject to significant quantitative inaccuracies for the low Reynolds and Schmidt number flows considered here. Ensembles of particle paths having common end points are used to explore the physics of the scalar transport correlation. For plume flows, transport in the near field is found to be primarily due to the average effect of the meandering of the turbulent fluid over the source, in which the amount of scalar dispersed by a fluid particle correlates with the local velocity fluctuation. Farther downstream, displacement transport—which may be reasonably modeled via gradient physics—emerges as the principal mechanism behind the scalar flux.
Thermocapillary flow near a cold wall
Authors: Canright D.
Published: July 2002

The thermocapillary feedback mechanism important at the edge of weld pools and other materials processes is examined through a model problem. A pool of liquid with a flat horizontal free surface is bounded on one side by a vertical solid wall, which is maintained at a cold temperature to unit depth, and at a warmer temperature below; far away the fluid is at the warmer temperature. Surface tension is a decreasing function of temperature, so that the surface thermal gradient drives flow toward the corner. When convection is vigorous, the flow compresses the thermal gradient which is driving the flow; this positive feedback results in small local length scales and high velocities near the corner. This problem is examined through a detailed scaling analysis and through numerical simulation for a range of parameters. The results show that for vigorous convection, the flow in the cold corner is locally determined.
Energy-conserving truncations for convection with shear flow
Authors: Thiffeault Jean-Luc , Horton Wendell
Published: July 2002

A method is presented for making finite Fourier mode truncations of the Rayleigh–Bénard convection system that preserve invariants of the full partial differential equations in the dissipationless limit. These truncations are shown to have no unbounded solutions and provide a description of the thermal flux that has the correct limiting behavior in a steady-state. A particular low-order truncation (containing 7 modes) is selected and compared with the 6-mode truncation of Howard and Krishnamurti [J. Fluid Mech. 170, 385 (1986)], which does not conserve the total energy in the dissipationless limit. A numerical example is presented to compare the two truncations and study the effect of shear flow on thermal transport.
Lagrangian acceleration measurements at large Reynolds numbers
Authors: Voth Greg A. , Satyanarayan K. , Bodenschatz Eberhard
Published: July 2002

We report experimental measurements of Lagrangian accelerations in a turbulent water flow between counter-rotating disks for Taylor–Reynolds numbers 900<Rλ<2000. Particle tracks were recorded by imaging tracer particles onto a position sensitive photodiode, and Lagrangian information was obtained from fits to the position versus time data. Several challenges associated with extracting Lagrangian statistical quantities from particle tracks are addressed. The acceleration variance is obtained as a function of Reynolds number and shows good agreement with Kolmogorov (1941) scaling. The Kolmogorov constant for the acceleration variance is found to be a0=7±3.
Competition of mixing and segregation in rotating cylinders
Authors: Dury Christian M. , Ristow Gerald H.
Published: July 2002

Using discrete element methods, we study numerically the dynamics of the size segregation process of binary particle mixtures in three-dimensional rotating drums, operated in the continuous flow regime. Particle rotations are included and we focus on different volume filling fractions of the drum to study the interplay between the competing phenomena of mixing and segregation. It is found that segregation is best for a more than half-filled drum due to the nonzero width of the fluidized layer. For different particle size ratios, it is found that radial segregation occurs for any arbitrary small particle size difference and the final amount of segregation shows a linear dependence on the size ratio of the two particle species. To quantify the interplay between segregation and mixing, we investigate the dynamics of the center of mass positions for each particle component. Starting with initially separated particle groups we find that no mixing of the component is necessary in order to obtain a radially segregated core.
Infrared imaging of the surface temperature field of water during film spreading
Authors: Saylor J. R. , Smith G. B. , Flack K. A.
Published: July 2002

Deposition of a spontaneously-spreading film on a clean water surface creates a front which propagates radially outward from the point of deposition. This rapidly spreading film was used as a tool to quickly change the boundary condition of a water surface from one which is shear-free, to a boundary condition which supports shear. Infrared images of a water surface experiencing evaporative convection were recorded as this film spread. These images were converted to surface temperature fields. The amount of turbulent structure present in these fields changes dramatically across the front. Ahead of the front, significant variations at large and small spatial scales are evident, while behind the front the small scale structures are eliminated. The time scale at which this damping occurs is short and has not been reported on heretofore. In addition to being relevant to free surface turbulence, these results demonstrate the utility of infrared imaging in the study of spreading films.
An investigation of the flow regimes resulting from splashing drops
Authors: Morton David , Rudman Murray , Jong-Leng Liow
Published: July 2002

Numerical simulations have been used to investigate the flow regimes resulting from the impact of a 2.9 mm water drop on a deep water pool at velocities in the range 0.8–2.5 m/s. The results were used to identify the conditions leading to the formation of vortex rings, entrapment of a bubble during cavity collapse and the formation of vertical Rayleigh jets. Bubble entrapment and the associated growth of a thin high speed jet were shown to be the result of a capillary wave that propagates down the walls of the crater resulting from drop impact. Although the existence of a capillary waves is a necessary condition for bubble entrapment, bubbles will only occur when the wave speed and maximum crater size is such that the wave reaches the bottom of the crater before collapse has resulted in the formation of a thick Rayleigh jet. Simulations also clarified the conditions for which drop impact leads to axi-symmetric vortex rings. Results not reported previously, include the observation that a single drop can produce multiple vortex rings and that vortex rings can occur for conditions that lead to broad Rayleigh jets. Based on these results, it was concluded that the formation of vortex rings depends on the time at which vorticity is generated and the nature of its subsequent transport.