bluuebunny/crossref_metadata_2025 huggingface dataset:
Photoionization spectroscopy of small mercury clusters in the energy range from vacuum ultraviolet to soft x ray
Authors: Blanc J. , Broyer M. , Dugourd Ph. , Labastie P. , Sence M. , Wolf J. P. , Wöste L.
Published: July 2002

We have measured the single and double photoionization efficiency of Hgn mass selected clusters as a function of photon energy between 30 and 110 eV for masses ranging from n=1 to 36 for the singly ionized and from n=5 to 70 for the doubly ionized clusters, using the light beam issued from a wiggler at the BESSY synchrotron. The results show in all cases a spectrum similar to the 5d→εf shape resonance previously observed in the isolated atom. In contrast, the expected 5p→6p transition allowed by hybridization of the 6s and 6p orbitals is not observed. We also compared the mass spectra of singly and doubly charged mercury clusters ionized by electron impact (30–90 eV) to those of clusters ionized by synchrotron radiation (30–70 eV). We found that the ratio Hg2+n/Hg+n was higher for photoionization at low energy and for electron impact ionization at high energy. Finally, we estimated the critical stability size of the triply charged clusters.
Bond order simulation model: Coordination dependent bimetallic bonds
Authors: Zhu Ling , DePristo Andrew E.
Published: July 2002

The variation of metal–metal bond strength or atomic site energy with number and type of atomic neighbors is described within a generalization of the bond order simulation (BOS) model, named the BOS-mixing model. The site energy for fixed coordination is expressed as a quadratic function of the number of existing mixed metal bonds. The three parameters in this functional form are (over)determined by the mixing energy as a function of composition for bulk bimetallic fcc systems. For the ten bimetallic alloys formed from Ni, Cu, Rh, Pd, and Ag, we find that the BOS-mixing model describes the composition dependence predicted by non-self-consistent electron density functional theory. Using the same BOS-mixing parameters obtained from this non-self-consistent electron density functional theory, the BOS-mixing model predicts accurately the microstructures (coordination arrangements) of clusters of Ni101Cu100, and Cu101Pd100 which are prototypical systems for bimetallic clusters. For Ni101Pd100 the BOS-mixing model displays some inaccuracies due to the atomic size mismatch of 10% which distorts the cluster shape from a perfect lattice structure. This is the same effect noted in previous applications of the BOS model and is thus expected.
Compact model potentials for ab initio embedded cluster calculations. Part I. Basic formulation
Authors: Mejías J. A. , Fernández Sanz Javier
Published: July 2002

In light of the theory of separability of many-electron systems, a methodology to perform embedded cluster calculations in order to study localized phenomena in a large electronic system is reported. A general equation for the cluster spin orbitals under the assumptions of frozen environment and cluster-environment strong orthogonality requirements is presented. The interactions between active and frozen electrons are adequately introduced through computationally convenient ab initio compact model potentials (CMPs) built up as a sum of long- and short-range terms. The short-range term, Coulomb and exchange interactions, are developed as a spectral representation in a nonorthogonal basis set. Cluster wave function, energy, and analytic geometrical derivatives calculations with CMPs have been implemented for several kinds of cluster wave functions. In order to evaluate the accuracy of the results obtained using this methodology, some simple test calculations for different hydrogen molecule-cation complexes have been performed both at the Hartree–Fock and multiconfigurational self-consistent-field levels of theory. As shown by an analysis based on the constrained space orbitals variations method, the main deviations are due to the lack of charge transfer contributions in the CMP calculations.
Spin–orbit effects in the photodissociation of ionized rare gas trimers: Comparison of He+3, Ar+3, and Xe+3
Authors: Haberland H. , Hofmann A. , Issendorff B. v.
Published: July 2002

The velocities of neutral and charged photofragments of the rare gas trimers He+3, Ar+3, and Xe+3 have been examined in a comprehensive study for photon energies ranging from 1.5 to 6 eV. For this purpose, a novel time-of-flight technique has been applied which allows the simultaneous examination of both neutral and charged fragments. The general fragmentation pattern of all three species was that of a linear trimer with a parallel transition moment and a totally repulsive excited state: In the course of the dissociation, two of the particles gain high velocities in opposite directions, while the third particle (the middle particle of the linear trimer) only obtains a small velocity. The positive charge generally localizes on one of the fast outer particles, as can be expected from the symmetry properties of the excited state. For Ar+3 and Xe+3, however, also localization of the charge on the slow particle can be observed. This effect strongly depends on the energy of the absorbed photon, and can be quenched by decreasing the vibrational excitation of the trimer. Comparison of the results with new potential energy surface calculations indicate that mainly spin–orbit coupling induced conical intersections are responsible for this charge redistribution phenomenon.
Circumstellar carbon chain molecules: A density function theory study of CnO, n=3–9
Authors: Moazzen-Ahmadi N. , Zerbetto Francesco
Published: July 2002

The infrared vibrational frequencies and intensities of the CnO linear chains, n=3–9, in their electronic ground state is predicted at the Becke–Lee–Yang–Parr (BLYP) level of theory. The computational model is assessed in three steps: (i) comparison of calculated and experimental rotational parameters for the whole series; (ii) comparison of experimental and calculated infrared frequencies, intensities and isotopic shifts for C3O (this molecule can be considered the prototype of the chains whose ground electronic state is 1Σ+); (iii) comparison of calculated and experimental infrared frequencies and intensities for C4O (this molecule can be considered the prototype of the chains whose ground electronic state is 3Σ−). The excellent agreement between experimental and computational results allows the prediction of the infrared pattern to 20 cm−1 for the frequencies and a few percent for the relative intensities. Analysis of the infrared intensities in terms of local atomic oscillators within the chains shows that while for short chains the intensity arises from the motion of the two carbon atoms nearest to the oxygen, for C7O and C9O the intensity arises in conjunction with the motion of carbon atoms close to, but not at, the other end of the molecule. For these two molecules, the infrared intensity is therefore similar in nature to that of pure carbon chains.
Rotationally resolved vibronic spectra of the van der Waals modes of benzene–Ar and benzene–Kr complexes
Authors: Riedle E. , Sussmann R. , Weber Th. , Neusser H. J.
Published: July 2002

Rotationally resolved vibronic spectra of eight van der Waals bands built onto the 610 transition of the bare molecule are reported for the complexes C6H6⋅Ar, C6D6⋅Ar, and C6H6⋅84Kr. The rotational structure of most of the bands is identified as that of a perpendicular transition with Coriolis coupling constants nearly the same as those of the 610 band of the respective complex. We therefore conclude that the excited van der Waals modes of the three complexes have a1 symmetry. Precise rotational constants are fitted to the large number of unblended lines assigned in each spectrum. In contrast, the lowest energy van der Waals bands of both C6H6⋅Ar and C6D6⋅Ar display a completely different rotational structure which can neither be explained by a genuine perpendicular nor a genuine parallel transition. This situation will be analyzed in detail in accompanying work and the final vibronic assignments deduced. The rovibronic lines in all the spectra show a linewidth of 130 MHz that is solely due to the laser linewidth and to residual Doppler broadening in the molecular jet. It is concluded that the excited vibronic combination states of intramolecular and van der Waals vibrations do not predissociate on the nanosecond time scale of our experiment. Two of the reported spectra show irregularities in the rotational structure that are explained by coupling to adjacent combination states.
Spectroscopy, polarization and nonadiabatic dynamics of electronically excited Ba(Ar)n clusters: Theory and experiment
Authors: Krylov A. I. , Gerber R. B. , Gaveau M. A. , Mestdagh J. M. , Schilling B. , Visticot J. P.
Published: July 2002

Molecular Dynamics simulations using a surface-hopping method for transitions between different electronic states are employed to study the dynamics following photoexcitation of the Ba(Ar)125 cluster. The results are used to interpret spectroscopic experiments on large, size-distributed Ba(Ar)n clusters. The dynamics of the coupled electronic-nuclear motions in the cluster involves transitions between three potential energy surfaces, corresponding to the nearly-degenerate p-states of the excited Ba atom. Ejection of excited Ba atoms, adsorbed on the surface of the cluster, can take place. The focus in comparing theory and experiment is on the emission spectrum from the excited clusters, on the polarization of this radiation, and on the polarization of light emitted by excited Ba atoms ejected from the cluster. Based on the good agreement found between theory and experiment, a comprehensive picture of the excited state dynamics is given. It is found that upon excitation, energy is rapidly redistributed in the cluster and no direct ejection of Ba occurs. Electronic relaxation to the lowest P-state occurs, and the latter dominates the cluster emission spectrum and polarization. The electronic state relaxation is mostly complete within t≲10 ps. Ejection of Ba atoms occurs as a rare and delayed event when a dynamical fluctuation creates a ‘‘hot spot’’ at the Ba site, with a non-adiabatic excitation to the highest electronic level. The results show the feasibility of near-quantitative understanding of non-adiabatic processes in large clusters.
Order-disorder transition of polystyrene-block-polyisoprene. I. Thermal concentration fluctuations in single-phase melts and solutions and determination of χ as a function of molecular weight and composition
Authors: Mori Keiji , Okawara Atsuo , Hashimoto Takeji
Published: July 2002

Small-angle x-ray scattering (SAXS) from single-phase melts and solutions of polystyrene-block-polyisoprene (SI) having various degrees of polymerization N and compositions f were analyzed on the basis of Landau-type mean-field theory developed by Leibler. The effective Flory interaction parameter χeff per segment in melts and in semidilute Θ solutions were determined from the mean-field analysis of the SAXS profiles obtained at temperatures higher than TMF, the crossover temperature above which the non-mean-field effects become less significant and the mean-field theory becomes a good approximation. It was found that χeff thus determined depends on N, f, volume fraction of the SI in the solution φp and the interaction parameter χ0 in melt: χeff=φpχ0 and χ0 is a function of f and N; χ0 at a given f is a decreasing function of N and that at a given N is approximately a quadratic function of f with a minimum at f≂1/2.
A pseudopotential hole-particle treatment of neutral rare gas excimer systems. I. Formalism
Authors: Duplàa P. , Spiegelmann F.
Published: July 2002

A pseudopotential hole-particle formalism is developed for the treatment of rare-gas excimers and excited rare-gas clusters. The formalism relies on the definition of a model Hamiltonian on the basis of single hole-particle excitations (from the neutral closed shell ground state) involving localized np hole orbitals and any orthogonal molecular orbital (MO) basis set for the excited particle. Hole contributions in the Hamiltonian matrix elements are taken into account via distance- and orientation-dependent transfer integrals (hole delocalization) and repulsion integrals like in diatomic in molecules treatments of rare gas ions, while the contribution of the excited particle is included through an explicit quantal treatment via one-electron e-Rg and averaged e-Rg+ pseudopotentials. Core-polarization pseudopotentials are also added to account for core-polarization and core-Rydberg correlation effects. Some approximated core-Rydberg two-electron integrals needed for adequate space and spin multiplicity of the excited states are also included. The possible applications and extensions of this formalism are discussed.
Molecular dynamics of linear and branched alkanes: Simulations and nuclear magnetic resonance results
Authors: Mondello Maurizio , Grest Gary S. , Garcia Armando R. , Silbernagel Bernard G.
Published: July 2002

We have extended two previously introduced models of n-alkanes to numerically investigate the liquid-state dynamics of branched alkanes. We compare our results with new experimental measurements of diffusion and 13C-NMR T1 relaxation. Significant systematic and quantitative agreement is found between simulated and experimental values. We demonstrate the role of branching in controlling the temperature dependence of diffusion and point out the effect of global single-chain relaxation processes on the local intramolecular dynamics probed by the 13C-NMR experiment.
A computational study of 13-atom Ar–Kr cluster heat capacities
Authors: Frantz D. D.
Published: July 2002

Heat capacity curves as functions of temperature were calculated using Monte Carlo methods for the series of Ar13−nKrn clusters (0≤n≤13). The clusters were modeled classically using pairwise additive Lennard-Jones potentials. J-walking (or jump-walking) was used to overcome convergence difficulties due to quasiergodicity present in the solid–liquid transition regions, as well as in the very low temperature regions where heat capacity anomalies arising from permutational isomers were observed. Substantial discrepancies between the J-walking results and the results obtained using standard Metropolis Monte Carlo methods were found. Results obtained using the atom-exchange method, another Monte Carlo variant designed for multicomponent systems, were mostly similar to the J-walker results. Quench studies were also done to investigate the clusters’ potential energy surfaces; in each case, the lowest energy isomer had an icosahedral-like symmetry typical of homogeneous 13-atom rare gas clusters, with an Ar atom being the central atom.
Primitive models of chemical association. II. Polymerization into flexible chain molecules of prescribed length
Authors: Kalyuzhnyi Yu. V. , Lin C.-T. , Stell G.
Published: July 2002

The structural properties of the totally flexible sticky two-point (S2P) model for polymerization into chain molecules of fixed length are studied. The model is represented by an n-component mixture of hard spheres of the same size with species 2,…,n−1 bearing two attractive sticky sites A and B, randomly distributed on the surface. The hard spheres of species 1 and n have only one site per particle, site B for species 1 and site A for species n. Due to the specific choice for the attractive interaction, which is present only between site B of the particles of species a and site A of the particles of species a+1, this version of the S2P model represents an associating fluid that polymerizes into freely jointed tangent hard-sphere chain molecules. The correlation functions of this model are studied at all degrees of association using a recently obtained general solution of the polymer Percus–Yevick (PPY) approximation [Yu. Kalyuzhnyi and P. Cummings, J. Chem. Phys. 103, 3265 (1995)]. Comparison of the results of the present theory in the complete association limit with corresponding computer-simulation results and results of other theories is presented and discussed. The complete-association results constitute a quantitatively successful theory of the mean monomer–monomer distribution functions for n⩽16 but for n=50 these functions are no longer quantitatively accurate.
Nonlinear electrical potential fluctuations of solvent around solutes: An integral equation study
Authors: Chong Song-Ho , Hirata Fumio
Published: July 2002

We present a theoretical formulation for the solvent force constant and the asymmetry parameter which characterize the free energy profile governing the electrical potential fluctuations of the solvent molecules around solutes. This formulation allows the calculation of these parameters via the extended reference interaction site method, an integral equation theory developed for molecular liquids and solutions. Since the method is inherently a nonlinear theory, we can shed some light on the possible nonlinear effects in the electrical potential fluctuations. The nonlinear effects in the solvent force constant and the validity of the linear approximation will be examined by a series of calculations for monatomic and diatomic solutes immersed in a simple dipolar solvent. The origin of the solute-dependent solvent force constant is discussed.
Ab initio molecular dynamics simulation of liquid hydrogen fluoride
Authors: Röthlisberger Ursula , Parrinello Michele
Published: July 2002

We have performed an ab initio molecular dynamics (MD) simulation of the structure of liquid hydrogen fluoride. Our results exhibit a strong contraction of the hydrogen bond in going from the gas to the liquid phase. The local structure of the liquid resembles that of the solid with the appearance of short lived hydrogen-bonded zig-zag chains. We have also studied the dynamical properties of the system. When compared with previous MD and Monte Carlo simulations based on empirical potentials our calculations allow us to resolve old controversies.
Thermochemistry of gaseous ZrF, ZrF2, and ZrF3
Authors: Hildenbrand D. L. , Lau K. H.
Published: July 2002

Several gaseous reaction equilibria involving the lower-valent Zr–F species were studied by mass spectrometry over parts of the range 1400 – 2400 K, and the derived reaction thermodynamics were used to evaluate the bond dissociation energies, BDE, and standard enthalpies of formation, ΔfH°298, of the gaseous species ZrF, ZrF2, and ZrF3. Emphasis was placed on correlation of the second and third law results as an aid in selecting the proper thermal functions. BDE values at 298 K, measured by reference to the molecule BaF, were found to be D(Zr–F)=149.9±2.5;D(FZr–F)=161.2±2.5;D(F2Zr–F=149.6±4.5; and D(F3Zr–F)=157.9±2.5 kcal mol−1. Corresponding values of ΔfH°298 for the gaseous species were calculated to be ZrF, 12.3±2.8;ZrF2,−129.9±3.7 and ZrF3,−260.5±2.8 kcal mol-1. The results are discussed in terms of other information in the literature. When all results are evaluated with consistent thermal functions and auxiliary data, there is reasonable agreement among derived thermochemical values.alues.
Dynamics of the hydrogen and phosphate ions in proton conducting gel/D3PO4 electrolytes: A H2 and P31 nuclear magnetic resonance study
Authors: Jeffrey K. R. , Wieczorek W. , Raducha D. , Stevens J. R.
Published: July 2002

Protonic conducting polymeric gel synthesis is motivated by its possible application in various electrochemical devices. This study focuses on the molecular motion of deuterons in gels formed with D3PO4 dissolved in propylene carbonate and a polymer matrix obtained using a free radical polymerization of methyl methacrylate with a cross-linking agent triethylene glycol dimethacrylate. Results are reported for samples containing 11, 23, and 45 mass % D3PO4. The measurements of the diffusion coefficients for deuterons and P31 show conclusively that the deuterons diffuse faster than the phosphorus carrying species. Therefore, the ionic conductivity results from a combination of the vehicular and Grotthus-type mechanisms. Species such as D2PO4−, D3PO4, or D4PO4+ are formed and the motion of the ions represents the vehicular mechanism while deuteron hopping from one species to the others constitutes the Grotthus mechanism. The nuclear magnetic resonance (NMR) spectra are consistent with the deuterons residing in a narrow distribution of sites; activation energies are similar for all samples, indicating that the barrier height to motion is independent of the concentration of D3PO4. This information reinforces the picture that the deuterons are always closely associated with PO4 groups. The correlation times determined from the deuteron nuclear relaxation times do not follow the Vogel–Tamman–Fulcher behavior observed in the conductivity measurements. The temperature dependence of the conductivity follows that of the structural relaxation or α process for T>1.2Tg, while the NMR correlation time is determined by any motion which modulates the electric field gradient at the deuteron site. Both the α and slow β processes influence the NMR correlation times.
Identifying physical clusters in bubble nucleation
Authors: Kusaka Isamu , Oxtoby David W.
Published: July 2002

We present a new approach to molecular simulation of bubble nucleation. Our approach does not involve any ad hoc criteria to define a bubble for a given instantaneous configuration of molecules. Instead, we explore the stochastic evolution of a system chosen as a small part of the liquid phase by means of an isothermal–isobaric Monte Carlo simulation aided by the umbrella sampling technique. The physical clusters relevant to nucleation, bubbles in the present case, emerge naturally as we attain a coarse-grained description of this stochastic process by introducing proper order parameters, i.e., the volume and the interaction potential of the system. Thus, the concept of cluster commonly employed to describe vapor to liquid nucleation is generalized naturally for the case of bubble nucleation. The method is applied to Lennard-Jones fluids to evaluate the free energy of bubble formation under a moderate negative pressure. The interaction potential plays a similar role to that in vapor to liquid nucleation in that it characterizes the spatial extent of the bubble. There is thus a unity in free energetics of vapor to liquid nucleation and of bubble nucleation.
The Schrödinger formulation of the Feynman path centroid density
Authors: Ramírez Rafael , López-Ciudad Telesforo
Published: July 2002

We present an analysis of the Feynman path centroid density that provides new insight into the correspondence between the path integral and the Schrödinger formulations of statistical mechanics. The path centroid density is a central concept for several approximations (centroid molecular dynamics, quantum transition-state theory, and pure quantum self-consistent harmonic approximation) that are used in path integral studies of thermodynamic and dynamical properties of quantum particles. The centroid density is related to the quasistatic response of the equilibrium system to an external force. The path centroid dispersion is the canonical correlation of the position operator, which measures the linear change in the mean position of a quantum particle upon the application of a constant external force. At low temperatures, this quantity provides an approximation to the excitation energy of the quantum system. In the zero temperature limit, the particle’s probability density obtained by fixed centroid path integrals corresponds to the probability density of minimum energy wave packets, whose average energy defines the Feynman effective classical potential.
Solvation and intramolecular reorganization in 9,9′-bianthryl: Analysis of resonance Raman excitation profiles and ab initio molecular orbital calculations
Authors: Scholes Gregory D. , Fournier Thierry , Parker Anthony W. , Phillips David
Published: July 2002

The observations of a clear solvent-dependence of resonance Raman intensities, but an absence of concommitant changes in absorption cross-sections, are reported for the molecule 9,9′-bianthryl (BA). Displacements obtained by analysis of the nonpolar solvent data are found to reproduce the absorption spectra recorded in all solvents studied, but not the resonance Raman intensities in polar solvents. Moreover, transform theory is found to be unsuccessful in reproducing the resonance Raman intensities in any solvent. These observations suggest that ultrafast relaxation dynamics (on the timescale probed by the resonance Raman experiment) are changing the displacements of the intramolecular vibrational modes. The changes in the displacements determined by analysis of the data are consistent with a correlation between the total reorganization energy accompanying the charge transfer and the solvent dielectric properties (i.e., the mode-specific reorganization is found to increase with solvent dielectric properties). In effect, the immediate free energy surface “seen” by the molecule changes dramatically with time and causes significant intramolecular reorganization, at least for the initial stages of evolution of the emissive state. These findings are supported by ab initio molecular orbital (MO) geometry optimization, analytical frequencies, and excited state calculations (CIS/3-21G*, HF/6-31G*). It is shown that most of the normal modes of the S0 state of BA are splittings of corresponding anthracene modes, however, for the relaxed S1 geometry of BA (i.e., gas phase equilibrium geometry), the modes are calculated to be red-shifted and have significantly greater splittings. Furthermore, the dipole moment of this relaxed S1 state is calculated to be 0.099 debye in the gas phase, compared to 0.00 debye for the equilibrium ground state and the vertical, unrelaxed, S1 state. The optimized S1 geometry of BA is found to be a “90°” geometry (i.e., torsion angle between the anthracene ring planes), similar to that of the ground state except for subtle asymmetries in each anthracene ring which lower the symmetry from D2. We suggest that these results provide direct evidence for the importance of solvent-dependent intramolecular reorganization in this molecule.
A comprehensive light scattering study of the glass former toluene
Authors: Wiedersich J. , Surovtsev N. V. , Rössler E.
Published: July 2002

We present depolarized light scattering data of the glass former toluene as obtained from tandem Fabry–Perot interferometry and Raman scattering covering a frequency range 0.5 GHz<v<5000 GHz. A large temperature interval of the (supercooled) liquid (Tg=117 K<T<295 K) as well as of the glass (7 K<T<117 K) is measured. Testing the scaling laws of idealized mode coupling theory (MCT) we find that MCT provides a satisfying interpolation up to the fluid regime (T/Tg=2.5) and a critical temperature Tc≅153 K is extracted. Deviations from the high-temperature MCT laws below Tc can be identified by constructing a master curve for the α-process. The deviations are attributed to spectral contributions from the high-frequency wing of the α-process and/or of the slow β-process which appear apparently only below Tc. A comparison with dielectric spectroscopy data, exhibiting a strong β-process, confirms this. Furthermore, we carry out a phenomenological analysis which assumes additivity of the susceptibility of α-process and fast dynamics. This approach allows us to single out the fast dynamics spectrum and to determine the nonergodicity parameter f. Whereas 1−f(T) is essentially constant above 160 K, a sharp decrease is observed below 160 K. This decrease stops at T=Tg and only a weak temperature dependence survives below Tg. Thus, the fast dynamics changes its characteristics at Tc and Tg. We speculate on the possibility of an ideal glass state exhibiting no relaxation any longer, and finally we comment on reasons for the large scatter of Tc data reported for some glass formers so far.
Coherence transfer by single-transition cross-polarization: Quantitation of cross-correlation effects in nuclear magnetic resonance
Authors: Ferrage Fabien , Eykyn Thomas R. , Bodenhausen Geoffrey
Published: July 2002

It is shown that selective single-transition cross-polarization (ST-CP) may be achieved in four-level systems such as encountered in NMR (nuclear magnetic resonance) of scalar-coupled two-spin systems (for example, N15–H1 groups in peptides), by employing two selective resonant fields applied to a pair of connected transitions with RF amplitudes much weaker than the separation of the parallel transitions (e.g., the scalar coupling constant JNH). The transfer benefits from differential line narrowing due to interference between the N15 chemical shift anisotropy and N15–H1 dipolar coupling, which is clearly observed in N15-labeled human ubiquitin at 600 MHz.
Graded contractions of sl(3,C)
Authors: Couture M. , Patera J. , Sharp R. T. , Winternitz P.
Published: July 2002

The Wigner–Inönü contraction is generalized to include gradings other than Z2 and the formalism is applied to obtain all toroidal contractions of sl(3,C). Examples of contractions based on nontoroidal gradings are also given.
An alternative expression for the addition theorems of spherical wave solutions of the Helmholtz equation
Authors: Clercx H. J. H. , Schram P. P. J. M.
Published: July 2002

An alternative formulation of the addition theorem for spherical wave solutions of the Helmholtz equation is presented. The 3-j symbols of Wigner, or more precisely the Gaunt coefficient (complete solid angle integral of a triple product of spherical harmonics), which appear in the formerly introduced expressions of these addition theorems are replaced by an explicit matrix expression relating the spherical wave solutions defined with respect to the different origins. The generalized Gaunt coefficients, which are complete solid angle integrals of a multiple product of spherical harmonics, can then be written in terms of a matrix product of basic matrices representing the Gaunt coefficient.
Invariant polynomials and Molien functions
Authors: Forger Michael
Published: July 2002

The Molien function associated with a finite-dimensional representation of a compact Lie group is a useful tool in representation theory because it acts as a generating function for counting the number of invariant polynomials on the representation space. The main purpose of this paper is to introduce a more general (and apparently new) generating function which, in the same sense, counts not only the number of invariant real polynomials in a real representation or the number of invariant complex polynomials in a complex representation, as a function of their degree, but encodes the number of invariant real polynomials in a complex representation, as a function of their bidegree (the first and second component of this bidegree being the number of variables in which the polynomial is holomorphic and antiholomorphic, respectively). This is obviously an additional and non-trivial piece of information for representations which are truly complex (i.e., not self-conjugate) or are pseudo-real, but it provides additional insight even for real representations. In addition, we collect a number of general formulas for these functions and for their coefficients and calculate them in various irreducible representations of various classical groups, using the software package MAPLE.
Rigorous application of the stochastic functional method to plane-wave scattering from a random cylindrical surface
Authors: Skaropoulos Nikolaos C. , Chrissoulidis Dimitrios P.
Published: July 2002

The stochastic functional method is applied to plane-wave scattering from a random cylindrical surface, whereupon the Dirichlet boundary condition is rigorously imposed. Analytical results, accurate to second and fourth order in surface roughness, are obtained for the coefficients of the Wiener–Hermite expansion of the secondary scattered wave field. The validity of approximate solutions is numerically investigated by means of the boundary condition criterion and of the energy consistency criterion. The former, which is introduced herein, states that any approximate solution should be in conformity with the boundary condition, whereas the latter pertains to the energy conservation law. The numerical investigation indicates that the rigorous application of the stochastic functional method yields more accurate results in terms of both criteria than did previous treatments of the problem under consideration. Moreover, it is suggested that applicability limits should be set through the mean boundary condition criterion instead of the energy consistency criterion; the latter may lead to underestimating deficiencies of the approximate solution under test.
Approximate inertial manifolds and effective viscosity in turbulent flows
Authors: Foias Ciprian , Manley Oscar P. , Temam Roger
Published: July 2002

The recently formulated concept of approximate inertial manifolds is exploited as a means for eliminating systematically the fine structure of the velocity field in two-dimensional flows. The resulting iterative procedure does not invoke any statistical properties of the solutions of Navier–Stokes equations. It leads to a modification of those equations, such that effective viscosity-like terms arise in a natural way. The rigorous mathematical considerations can be related to the corresponding physical concepts and intuition. The result leading to a numerical algorithm, essentially a nonlinear Galerkin method, provides a basis for large eddy simulation in which the subgrid model is derived from the properties of the Navier–Stokes equations, rather than from more or less justifiable ad hoc arguments. Some limited speculations concerning the expected results in three dimensions are also offered.
Rates, pathways, and end states of nonlinear evolution in decaying two-dimensional turbulence: Scaling theory versus selective decay
Authors: Carnevale G. F. , McWilliams J. C. , Pomeau Y. , Weiss J. B. , Young W. R.
Published: July 2002

A recently proposed scaling theory of two-dimensional turbulent decay, based on the evolutionary pathway of successive mergers of coherent vortices, is used to predict the rate and end state of the evolution. These predictions differ from those based on the selective-decay hypothesis and traditional ideas of spectrum evolution, and they are in substantially better agreement with numerical solutions at large Reynolds number.
Coherence of intense localized vorticity in decaying two-dimensional Navier–Stokes turbulence
Authors: Terry P. W. , Newman D. E. , Mattor N.
Published: July 2002

The coupled evolution of an intense localized vortex and decaying Navier–Stokes turbulence in two dimensions is examined in order to identify and describe the physical process allowing regions of intense vorticity to decouple from the eddy cascade and survive as coherent structures. It is found that the shear straining of turbulent eddies by the differential rotation of the intense vortex gives rise to vortex coherence. Dimensional analysis and analytic solution of a closure representation in the asymptotic limit of large shear are used to determine a nonuniform vortex diffusivity produced by turbulent straining, and the spatial structure of turbulence in the vortex. When the shear straining rate exceeds the appropriate measure of the ambient turbulent straining rate, turbulent fluctuations in the vortex interior localize to a narrow layer in the vortex edge. Likewise, vortex diffusion becomes weak, the vortex lifetime becomes large, and greatly exceeds the eddy lifetimes of ambient turbulence.
Finite-amplitude shear waves in a channel with compliant boundaries
Authors: Rotenberry James M.
Published: July 2002

The problem of the finite-amplitude stability of an incompressible fluid flowing in a channel with compliant walls is studied by numerically calculating the traveling wave solutions that bifurcate from plane Poiseuille flow along a neutral stability curve in the Reynolds number, wave-number plane. This curve is the zero-amplitude intersection of a neutral stability surface in amplitude, Reynolds number, and wave-number space. To determine the differences between the rigid and compliant wall flow, solutions are generated for several compliant wall models. For sufficiently compliant walls the finite-amplitude solutions are stable to two-dimensional periodic disturbances in the limit of small amplitude. However, the solutions destabilize as the amplitude increases. Since these stable solutions exist for such a small range of energy and Reynolds number, these calculations indicate that the process of transition for compliant boundaries is (at least for small amplitude) qualitatively the same as that for rigid boundaries.
Whistler-wave electron cyclotron heating in uniform and nonuniform magnetic fields
Authors: Guest G. E. , Fetzer M. E. , Dandl R. A.
Published: July 2002

Recent laboratory experiments on single-pass electron cyclotron heating employing whistler waves [Phys. Fluids B 1, 2010 (1989)] have shown direct evidence of nonlinear collective processes that can have a major effect on the properties of the resulting plasma. A theoretical interpretation of these experimental results is proposed herein, based on linear and nonlinear aspects of electron cyclotron heating. The observed increments in electron kinetic energy are shown to be consistent with a conventional linearized analysis of the gyroresonant interaction. The observed bursts of radiation in sidebands near the heating frequency are consistent with the nonlinear gyrophase bunching of resonant electrons in the whistler wave resulting in coherent excitation of unstable sidebands.
Self-similar evolution of the nonlinear magnetic buoyancy instability
Authors: Shibata K. , Tajima T. , Matsumoto R.
Published: July 2002

A new type of self-similar solution of ideal magnetohydrodynamics (MHD) in the nonlinear stage of the undular model (k∥B) of the magnetic buoyancy instability (the ballooning instability in fusion plasma physics or the Parker instability in astrophysics) is found through MHD simulation and theory. The linear theory developed agrees well with our simulation in the early (linear) stage. The nonlinear stages of the instability in the simulation show the self-similar evolution. One of the solutions obtained from the nonlinear analysis has the characteristics of nonlinear instability in Lagrangian coordinates; the fluid velocity and the Alfvén speed on each magnetic loop increase exponentially with time, because the loop is evacuated by the field-aligned motion of matter resulting from gravitational acceleration. In the later stage of the nonlinear evolution, the solution property changes from exponential to power-law time dependence. The latter corresponds to a force-free expansion solution. The later saturation of the velocity increment is also discussed.
Processes terminating radiative collapse in a hydrogen fiber Z pinch
Authors: Chittenden J. P. , Haines M. G.
Published: July 2002

The processes terminating radiative collapse, of relevance to the present generation of hydrogenic fiber Z pinch experiments, are identified and discussed. Computational analogs for these processes are developed and used to modify a basic model consisting of a one-dimensional (1-D) Lagrangian resistive magnetohydrodynamic (MHD) code, coupled to a model of a realistic external circuit. A radiation transport package, tailored to the problem, is used to simulate radiation energy transfer within the pinch. Other effects accounted for include modification of the electron transport coefficients for high electron magnetization as well as the effect of free-electron degeneracy upon electron transport coefficients, the equation of state, and the opacity. Results suggest that termination is dominated by rapid changes in the radial profiles of both degenerate electron pressure and the radiation energy loss per unit volume (the gradient of the latter profile changing sign as the high-density pinch core becomes optically thick to lower frequencies). The termination process is shown to be a hybrid of radiation transport and free-electron degeneracy effects for all line densities considered, with electron degeneracy becoming increasingly important at lower line densities.
Steady fast dynamo flows
Authors: Finn John M. , Hanson James D. , Kan Ittai , Ott Edward
Published: July 2002

The problem of whether or not steady fast kinematic dynamos exist for typical smooth velocity fields has remained an open question in the origin of magnetic fields in nature (e.g., the observed magnetic fields in stars and in galaxies). [Here by a steady flow it is meant that the fluid velocity v depends on position x but is independent of time t, i.e., v=v(x).] Recently it has been conjectured that fast kinematic dynamos are produced by flows that satisfy a certain condition. Flows satisfying this condition are called D flows. In this paper it is shown how to construct a class of steady D flows, and the properties of this class of flows are investigated. The results indicate that fast dynamo action is typical for steady chaotic flows.
Resistive drift wave and interchange turbulence in a cylindrical plasma with magnetic and velocity shear
Authors: Wakatani M. , Watanabe K. , Sugama H. , Hasegawa A.
Published: July 2002

By solving numerically the two-field nonlinear model equations for the potential and density fluctuations in the presence of a density gradient, magnetic curvature with shear, and poloidal velocity shear, turbulent spectra and diffusion rates are studied. When the adiabatic parameter (Ωe/νe)(ρs2/R2)/(κρs) is small, a trend of a dual cascade, normal cascade of the density fluctuations, and an inverse cascade of the potential fluctuations, is seen in the wave number spectra, producing a large particle flux proportional to νe1/3. Here R is the major radius, ρs is the ion Larmor radius at the electron temperature, Ωe is the electron cyclotron frequency, νe is the electron ion collision frequency, and κ is an inverse scale length of the background density gradient. Parallel wave numbers are represented by 1/R. For large (Ωe/νe)(ρs2/R2)/(κρs), the electrons become adiabatic, with a significantly reduced particle flux proportional to νe. In the presence of an externally imposed radial electric field with a negative (positive) polarity, Er<0 (Er≳0), the poloidal velocity shear in the E×B drift motion suppresses (enhances) the fluctuation level in the growth phase; however, these effects practically disappear in the saturated state. The radial electric field produced by the inverse cascade due to the convective nonlinearity is also studied; however, its effect on the particle transport is mild.
Interaction of ultrahigh laser fields with beams and plasmas
Authors: Sprangle Phillip , Esarey Eric
Published: July 2002

The nonlinear interaction of ultraintense laser pulses with electron beams and plasmas is rich in a wide variety of new phenomena. Advances in laser science have made possible compact terawatt lasers capable of generating subpicosecond pulses at ultrahigh powers (≥1 TW) and intensities (≥1018 W/cm2). These ultrahigh intensities result in highly relativistic nonlinear electron dynamics. This paper briefly addresses a number of phenomena including (i) laser excitation of large-amplitude plasma waves (wake fields), (ii) relativistic optical guiding of laser pulses in plasmas, (iii) optical guiding by preformed plasma channels, (iv) laser frequency amplification by ionization fronts and plasma waves, (v) relativistic harmonic generation, (vi) stimulated backscattering from plasmas and electron beams, (vii) nonlinear Thomson scattering from plasmas and electron beams, and (viii) cooling of electron beams by intense lasers. Potential applications of these effects are also discussed.
Ion kinetic simulations of the formation and propagation of a planar collisional shock wave in a plasma
Authors: Vidal F. , Matte J. P. , Casanova M. , Larroche O.
Published: July 2002

Ion kinetic simulations of the formation and propagation of planar shock waves in a hydrogen plasma have been performed at Mach numbers 2 and 5, and compared to fluid simulations. At Mach 5, the shock transition is far wider than expected on the basis of comparative fluid calculations. This enlargement is due to hot ions streaming from the hot plasma into the cold plasma and is found to be limited by the electron preheating layer, essentially because electron–ion collisions slow down these energetic ions very effectively in the cold upstream region. Double-humped ion velocity distributions formed in the transition region, which are particularly prominent during the shock formation, are found not to be unstable to any electrostatic mode, due to electron Landau damping. At Mach numbers of 2 and below, no such features are seen in velocity space, and there is very little difference between the profiles from the kinetic and fluid simulations.
An emerging understanding of H-mode discharges in tokamaks*
Authors: Groebner R. J.
Published: July 2002

A remarkable degree of consistency of experimental results from tokamaks throughout the world has developed with regard to the phenomenology of the transition from L-mode to H-mode confinement in tokamaks. The transition is initiated in a narrow layer at the plasma periphery where density fluctuations are suppressed and steep gradients of temperature and density form in a region with large first and second radial derivatives in the vE=(E×B)/B2 flow velocity. These results are qualitatively consistent with theories which predict suppression of fluctuations by shear or curvature in vE. The required vE flow is generated very rapidly when the magnitude of the heating power or of an externally imposed radial current exceed threshold values and several theoretical models have been developed to explain the observed changes in the vE flow. After the transition occurs, the altered boundary conditions enable the development of improved confinement in the plasma interior on a confinement time scale. The resulting H-mode discharge has typically twice the confinement of L-mode discharges and regimes of further improved confinement have been obtained in some H-mode scenarios.
Bifurcation analysis of the transverse drift-wave-envelope instability
Authors: Laedke E. W. , Spatschek K. H. , Zocha K.
Published: July 2002

One-dimensionally localized and longitudinally stable wave packets of drift waves are considered. The two-dimensional saturation of an always occurring transverse instability is calculated by a bifurcation analysis and leads to two-dimensionally localized vortices. The latter do not show a collapse. It is supposed that this process is a generation mechanism of stable vortices in inhomogeneous plasmas.
Plasma current ramp-up and Ohmic-heating transformer recharging experiments using lower-hybrid waves on a tokamak
Authors: Takase Y. , Knowlton S. , Porkolab M.
Published: July 2002

Plasma current ramp-up by lower-hybrid waves in a high-density regime (n̄e≳1×1019 m−3) is investigated on the Alcator C tokamak [Nucl. Fusion 25, 1127 (1985)]. A time-averaged conversion efficiency (Ẇ−Pext)/Prf of over 15% has been obtained at a density of n̄e ≂1×1019 m−3, where W is the poloidal field energy and Pext is the external inductive power. The maximum conversion efficiency obtainable is lower at higher densities. Ramp-up rates of over 1 MA/sec were obtained when rf current ramp-up is applied to an Ohmically maintained plasma. Lower-hybrid current drive can also be used to maintain the plasma while recharging the Ohmic-heating transformer. The conversion efficiency of 10% obtained during recharging is found to be comparable to that obtained during ramp-up under similar conditions.
Physical mechanisms of instability in a liquid layer subjected to an electric field and a thermal gradient
Authors: Pontiga F. , Castellanos A.
Published: July 2002

The linear stability of a plane layer of dielectric liquid subjected to an electric field and a thermal gradient is studied. The liquid is supposed to have a non-negligible residual conductivity and to exhibit an injection of charge from one of the electrodes. Both effects are due to the dissolution of a given salt in the liquid. The ionic mobility and the dielectric constant are temperature dependent. The stability of this configuration is studied with the help of an heuristic model and a precise discussion of the physical mechanisms of instability is made. Complete sets of the stability maps corresponding to different cases are presented.