bluuebunny/crossref_metadata_2025 huggingface dataset:
Dynamical structure of oligo(ethylene glycol)s-water solutions studied by time domain reflectometry
Authors: Sato Takaaki , Niwa Hiromu , Chiba Akio , Nozaki Ryusuke
Published: July 2002

Dielectric relaxation measurements on water solutions of ethylene glycol 200 and 400, (degree of polymerization N=4 and 9) in entire concentration region were carried out using a time domain reflectometry at 25 °C in the frequency range from 300 MHz to 20 GHz. For all the samples, only one dielectric loss peak was observed in this frequency range. Plots of the relaxation strength and logarithm of the relaxation time calculated from apparent peak frequency of dielectric loss curves against monomer unit molar fraction of ethylene glycol X give straight lines in the region of 0<X<0.35 for N=4, and 0<X<0.37 for N=9. Shapes of dispersion and absorption curves exhibit critical change at the concentration X≈0.35 for N=4 and X≈0.37 for N=9, corresponding to the ratio of one ether oxygen and 1.7 water. Analysis of these phenomena indicates that hydration complex of one ether oxygen and 1.7 water is formed, and the 1:1.7 complex behaves as one kind of component corresponding to 2.7(=1+1.7) waterlike molecules in the solution. It is suggested that ether oxygen can be inserted into water structure by replacing water oxygen. This hydration mechanism makes water structure stable. Ethylene glycol dissolves in water without much perturbation to water structure.
Site and isotope effects on the molecular hydrogen elimination from ethylene at 157 nm excitation
Authors: Lin Jim J. , Hwang Dennis W. , Lee Yuan T. , Yang Xueming
Published: July 2002

Site and isotope effects on the molecular hydrogen elimination from ethylene have been studied from the photodissociation of ethylene at 157 nm excitation. Experimental results show that there are three different types of molecular elimination processes: 1,1 elimination, 1,2-cis elimination, and 1,2-trans elimination. These elimination processes show significantly different translational energy distributions. Isotope effect on the dynamics of these molecular hydrogen elimination processes has been also investigated carefully.
The surface constraint all atom model provides size independent results in calculations of hydration free energies
Authors: Sham Yuk Yin , Warshel Arieh
Published: July 2002

Consistent approaches for calculations of solvation free energies should provide results which are independent of the size of the simulation region. Simulations that use periodic boundary conditions and a standard Ewald treatment yield size dependent results. Corrections that can overcome this problem have been formulated, but have not yet been fully validated for solutes with general charge distributions. Furthermore, Ewald treatments of proteins may involve size dependent problems whose nature has not been explored by systematic studies. Here we demonstrate that our surface constraint all-atom solvent (SCAAS) model with its spherical boundary conditions (that include special polarization constraints) provides proper size independent results. It is also pointed out that this approach lends itself to an effective treatment of long-range interactions and offers a useful way of obtaining size independent free energies in studies of electrostatic effects in proteins.
Quantum dynamics of an Eley–Rideal gas–surface reaction: Four dimensional planar model for H(D)(gas)+D(H)-Cu(111)
Authors: Dai Jiqiong , Light John C.
Published: July 2002

We present a quantum dynamical study for the abstraction reaction of hydrogen and its isotope on Cu(111) surface by a four-dimensional planar model. The rigid surface corrugation has been explicitly treated. High vibrational and rotational excitation observed in our product–state distributions indicates that the reactions occur mainly via the Eley–Rideal mechanism as suggested earlier by experiments as well as the three-dimensional flat surface model. The four-dimensional planar model using a cut through the six-dimensional LEPS (London–Eyring–Polanyi–Sato) potential energy surface essentially reproduces the isotope effects observed in experiment in the energy distributions of the reaction product. The unreacted atoms are found either to bounce back from the surface or to diffuse on the surface as atoms. A significant concentration of diffusing atoms on the surface could result in an associative desorption pathway and contribute to the experimental measurement of HD formation.
X-ray scattering from monolayers of F(CF2)10(CH2)2OH at the water–(hexane solution) and water–vapor interfaces
Authors: Zhang Zhongjian , Mitrinovic Dragoslav M. , Williams Scott M. , Huang Zhengqing , Schlossman Mark L.
Published: July 2002

Synchrotron x-ray reflectivity is used to study the structure of a monolayer of F(CF2)10(CH2)2OH self-assembled at the liquid–liquid interface from a solution in hexane placed in contact with water. It is demonstrated that this monolayer is in a high density (solid) phase below a transition temperature. This is in contrast to the conventional expectation that soluble surfactants form disordered monolayers at the liquid–liquid interface. Above the transition temperature the monolayer desorbs into the hexane solution, leaving behind an interface with a very low density of surfactants. Hysteresis in the formation of the monolayer occurs when the temperature is scanned through the transition temperature. The success of these measurements relied upon the development of a novel technique to flatten the liquid–liquid interface to the extent required for x-ray reflectivity. The measurements of F(CF2)10(CH2)2OH at the liquid–liquid interface are compared to x-ray surface diffraction measurements of monolayers of the same material spread at the water–vapor interface. A solid to disordered-phase phase transition also occurs in the spread monolayer though at a slightly higher temperature. This indicates that the hexane acts to disorder the solid monolayer at the water–hexane interface. A measurement of the thermal expansion coefficient of the monolayer at the water–vapor interface is consistent with literature values for bulk hydrocarbon rotator phases, in contrast with previous measurements on monolayers of perfluoro-n-eicosane supported on water.
Eley–Rideal and hot-atom reactions of H(D) atoms with D(H)-covered Cu(111) surfaces; quasiclassical studies
Authors: Shalashilin Dmitrii V. , Jackson Bret , Persson Mats
Published: July 2002

Quasiclassical molecular dynamics studies are made of H or D atoms incident from the gas phase onto D or H-covered Cu(111) surfaces. Two detailed model potential energy surfaces are used, both based on the results of extensive total energy calculations using the density functional method. The incident H (D) atoms can react directly to form HD via the Eley–Rideal mechanism, or trap onto the surface. These trapped hot atoms can react with the adsorbates to form HD or can eventually dissipate enough energy through collisions with the adsorbates to become immobile. We also observe the formation of D2 (H2). Probabilities for these various processes, as well as the rotational, vibrational, and translational energy distributions of the products are computed and compared with experiment. Hot-atom pathways to product formation are shown to make significant contributions. One of the potentials gives excellent agreement with experiment, while the other is less successful.
Temperature dependent rate constants for the reactions of gas phase lanthanides with N2O
Authors: Campbell Mark L.
Published: July 2002

The reactivity of gas phase lanthanide (Ln) atoms (Ln=La–Yb with the exception of Pm) with N2O from 298 to 623 K is reported. Lanthanide atoms were produced by the photodissociation of Ln(TMHD)3 (TMHD=2,2,6,6-tetramethyl-3,5-heptanato ion) and detected by laser-induced fluorescence. Large variations in the reaction rate constants are observed. The bimolecular rate constants are described in Arrhenius form by k[Ce(1G4)]=(1.9±0.5)×10−10 exp(−0.8±0.8 kJ mol−1/RT); Pr(4I9/2), (3.6±1.2)×10−10 exp(−8.0±1.2 kJ mol−1/RT); Nd(5I4), (3.4±0.4)×10−10 exp(−8.8±0.5 kJ mol−1/RT); Sm(7F0), (3.2±1.1)×10−10 exp(−11.2±1.2 kJ mol−1/RT); Eu(8S7/2), (2.7±0.4)±10−10 exp(−12.7±0.5 kJ mol−1/RT); Gd(9D2), (2.0±0.3)×10−10 exp(−6.4±0.5 kJ mol−1/RT); Tb(6H15/2), (2.9±0.5)×10−10 exp(−10.9±0.6 kJ mol−1/RT); Dy(5I8), (3.4±0.8)×10−10 exp(−16.2±0.8 kJ mol−1/RT); Ho(4I15/2), (2.9±0.5)×10−10 exp(−17.1±0.6 kJ mol−1/RT); Er(3H6), (3.3±1.2)×10−10 exp(−18.4±1.2 kJ mol−1/RT); Tm(2F7/2), (3.5±0.6)×10−10 exp(−19.5±0.6 kJ mol−1/RT); Yb(1S0), (2.5±0.2)×10−10 exp(−20.2±0.3 kJ mol−1/RT) where the uncertainties represent ±2σ. The reaction barriers are found to correlate to the energy required to promote an electron out of the 6s subshell.
Accurate excitation energies from time-dependent density functional theory: Assessing the PBE0 model
Authors: Adamo Carlo , Scuseria Gustavo E. , Barone Vincenzo
Published: July 2002

We analyze the performance of a density functional model obtained by combining the Perdew–Burke–Erzenrhof (PBE) generalized gradient functional with a predetermined amount of exact exchange for predicting vertical electronic excitation energies within a time-dependent approach. Four molecules, namely, CO, H2CO, (CH3)2CO, and C2H4, have been chosen as benchmark cases. Our results show that this model (PBE0) provides accurate excitations both to valence and Rydberg states. Furthermore, the results are numerically close to those obtained using asymptotically correct exchange-correlation functionals. The performance of the PBE0 model for predicting excitation energies in larger molecules is assessed for benzene, pyridine, and naphthalene. Here, the PBE0 model provides results which are in fairly good agreement with experimental data and of similar quality to those obtained by more sophisticated (and time-consuming) post-Hartree–Fock methods.
A unified quantal and classical description of the stereodynamics of elementary chemical reactions: State-resolved k–k′–j′ vector correlation for the H+D2(v=0, j=0) reaction
Authors: de Miranda Marcelo P. , Aoiz F. J. , Bañares Luis , Rábanos V. Sáez
Published: July 2002

We present a detailed and quantitative comparison of the quantum mechanical (QM) and quasiclassical (QCT) descriptions of the stereodynamics of elementary chemical reactions. Analogous formulations of the QM and QCT k–k′–j′ vector correlation in atom–diatom reactions have been derived and shown to be equivalent in the correspondence principle limit. The comparison between the results obtained from the application of the QM and QCT methodologies to the H+D2(v=0, j=0)→HD(v′,j′)+D reaction at a collision energy of 1.29 eV renders an almost quantitative agreement.
Basis set convergence of the interaction energy of hydrogen-bonded complexes
Authors: Halkier Asger , Klopper Wim , Helgaker Trygve , Jo/rgensen Poul , Taylor Peter R.
Published: July 2002

The Hartree-Fock and correlation contributions to the interaction energy of the hydrogen-bonded complexes (HF)2, (HCl)2, H2OHF, HCNHF, and (H2O)2 are computed in conventional calculations employing the aug-cc-pVXZ series of basis sets at the levels of Hartree-Fock theory, second-order perturbation theory, and coupled-cluster theory with single and double excitations augmented by a perturbative triples correction. The basis set convergence of the interaction energy is examined by comparison with results obtained with an explicitly correlated wave function model. The counterpoise-corrected and uncorrected Hartree-Fock interaction energies both converge very unsystematically. The convergence of the uncorrected correlation contribution is also very unsystematic because the basis set superposition error and the error from the incomplete description of the electronic Coulomb cusp both are present. Once the former has been effectively removed by the counterpoise correction, the cusp dominates and the convergence of the counterpoise-corrected correlation contribution follows an X−3 form similar to the form for the correlation energy. Two-point extrapolated values obtained with this form are close to the basis set limit and represent a significant improvement on the unextrapolated results.
Evolution of the potential energy surface with size for Lennard-Jones clusters
Authors: Doye Jonathan P. K. , Miller Mark A. , Wales David J.
Published: July 2002

Disconnectivity graphs are used to characterize the potential energy surfaces of Lennard-Jones clusters containing 13, 19, 31, 38, 55, and 75 atoms. This set includes members which exhibit either one or two “funnels” whose low-energy regions may be dominated by a single deep minimum or contain a number of competing structures. The graphs evolve in size due to these specific size effects and an exponential increase in the number of local minima with the number of atoms. To combat the vast number of minima we investigate the use of monotonic sequence basins as the fundamental topographical unit. Finally, we examine disconnectivity graphs for a transformed energy landscape to explain why the transformation provides a useful approach to the global optimization problem.
Size and number density of precrystalline aggregates in lysozyme crystallization process
Authors: Tanaka Shinpei , Ito Kohzo , Hayakawa Reinosuke , Ataka Mitsuo
Published: July 2002

Using dynamic light scattering, we investigated supersaturated aqueous solutions of hen egg white lysozyme. We could observe the formation of aggregates only in solutions, from which crystals grew within a few days. The aggregates were grouped into smaller “units” and larger “clusters.” The units consisted of a few molecules, whereas the clusters grew from about 100 nm to 1 μm. At the beginning of aggregation, the number density of the units decreased, while that of the clusters increased. At this stage, unit-cluster aggregation proceeded. At the next stage, the number density of the units became constant, while that of the clusters began to decrease, which means that the units stopped aggregating and cluster-cluster aggregation started. The aggregation mechanism for the clusters fit well with the diffusion limited cluster aggregation model, but this model alone could not explain that the aggregates separated into two groups, corresponding to units and clusters, and that the units stopped aggregating during the aggregation process. We find that the observed aggregation process has several similarities to the liquid-liquid phase separation process, which occurs metastably in protein solution. Furthermore, using both models for diffusion limited aggregation and the liquid-liquid phase separation together, we could naturally explain the process of the cluster formation.
A simulation study of the decay of the pair correlation function in simple fluids
Authors: Dijkstra Marjolein , Evans Robert
Published: July 2002

Monte Carlo simulations are used to investigate the asymptotic decay of the total pairwise correlation function h(r) for some model fluids. We determine the poles of the Fourier transform ĥ(q) from the direct correlation function c(r). The leading poles determine the ultimate, r→∞, decay of h(r). For the truncated and shifted Lennard-Jones fluid we calculate the Fisher–Widom (disorder) line in the temperature-density (T,ρ) plane where the ultimate decay of rh(r) crosses over from monotonic (exponential) to exponentially damped oscillatory decay. This line lies close to that obtained in an earlier integral-equation [hypernetted chain-soft core mean spherical approximation (HMSA)] study. For states on the monotonic side of the disorder line, h(r) has a finite number of oscillations and we determine the boundaries which mark regions in the (T,ρ) plane where h(r) has a given number of zeros using a random-phase approximation for c(r). In the case of the hard-sphere fluid, the ultimate decay of h(r) is oscillatory for all densities and we find that simulation results for the period and (exponential) decay length of the oscillations are in good overall agreement with those of Percus–Yevick theory, although there is some indication that systematic differences develop for high-density states ρ*⩾0.85.
Cl+HD
(v=1; J=1,2) reaction dynamics: Comparison between theory and experiment
Authors: Kandel S. A. , Alexander A. J. , Kim Z. H. , Zare R. N. , Aoiz F. J. , Bañares L. , Castillo J. F. , Rábanos V. Sáez
Published: July 2002

Vibrationally state-resolved differential cross sections (DCS) and product rotational distributions have been measured for the Cl+HD(v=1, J=1)→HCl(DCl)+D(H) reaction at a mean collision energy of 0.065 eV using a photoinitiated reaction (“photoloc”) technique. The effect of HD reagent rotational alignment in the Cl+HD(v=1, J=2) reaction has also been investigated. The experimental results have been compared with exact quantum mechanical and quasiclassical trajectory calculations performed on the G3 potential energy surface of Allison et al. [J. Phys. Chem. 100, 13575 (1996)]. The experimental measurements reveal that the products are predominantly backward and sideways scattered for HCl(v′=0) and HCl(v′=1), with no forward scattering at the collision energies studied, in quantitative agreement with theoretical predictions. The experimental product rotational distribution for HCl(v′=1) also shows excellent agreement with quantum-mechanical calculations, but the measured DCl+H to HCl+D branching ratio is near unity, which is at variance with the theoretical calculations that predict about 3 times larger yield of HCl+D at these collision energies. The reactivity shows a marked dependence on the direction of the HD(v=1, J=2) rotational angular momentum, and experimental measurements of this reagent alignment effect are in good agreement with theoretical predictions.
Flow, diffusion and crystallization of supercooled liquids: Revisited
Authors: Ngai K. L. , Magill J. H. , Plazek D. J.
Published: July 2002

Within the last five years, investigators using NMR and forced Raleigh scattering techniques have found that the Stokes–Einstein (S–E) relation breaks down in supercooled liquids. It has been pointed out that the shear viscosity has a significantly stronger temperature dependence than either the self-diffusion coefficient, D(T), or the translational diffusion coefficient of tracer molecules of comparable size (not shape) to the host liquid. These observations confirm our results on trinaphthylbenzene (TNB) and 1,2 diphenylbenzene (OTP), published in a series of papers more than 30 years ago. An analysis of crystal growth rate measurements on these materials demonstrated that the transport-dominated crystal growth rate, G′(T), exhibited a weaker temperature dependence than the shear viscosity, η(T). Where the expression G(T)=f(T)/η(T) is often substituted for the more basic growth rate relationship G(T)=D(T)f(T). We showed that this practice (often used) is invalid. Here, f(T) is a nucleation/growth free energy term. Reexamination of our earlier work has shown that the extent of the S–E “breakdown,” as revealed by crystal growth rate data, is consistent with the answers that are now provided by modern NMR and forced Rayleigh scattering techniques. Employing the derivative procedure of Stickel and co-workers to fit our TNB viscosity data over more than 15 orders of magnitude, requires an Arrhenius temperature dependence at high temperatures, a “crossover” to a Vogel–Fulcher–Tammann–Hesse dependence at some temperature TA, and a further “crossover” to another Vogel–Fulcher–Tammann–Hesse form at a lower temperature, TB. Below TB a disparity occurs between the temperature dependences of the transport-dominated crystal growth rate and viscosity. Where our old and the recent results coincide, the techniques represent or measure similar parameters.
Electron configuration changes in excited pyrazine molecules analyzed by femtosecond time-resolved photoelectron spectroscopy
Authors: Stert V. , Farmanara P. , Radloff W.
Published: July 2002

Using the pump–probe technique with 130 fs laser pulses near 200 nm and near 266 nm the internal conversion of the pyrazine molecule excited to the S2 state has been studied. The lifetime of the S2 state due to internal conversion to the lower electronic states is τIC(2)=(20±10) fs while the lifetime of the secondarily populated S1 state is τIC(1)=(22±1) ps. The results of femtosecond time-resolved electron spectroscopy directly demonstrate the variation of the electron configuration during the internal conversion: The electron spectrum changes significantly on the fs time scale for pyrazine ions produced by ionization via the S2 state with ππ* character and by ionization of S1 state molecules with nπ* configuration after the internal conversion, respectively. The results obtained confirm theoretical estimations of Domcke and co-workers [J. Chem. Phys. 95, 7806 (1991); J. Phys. Chem. 97, 12466 (1993)] who describe the internal conversion in the pyrazine molecule on the basis of a conical intersection of the corresponding potential energy surfaces.
Fluorine atom abstraction by Si(100) II. Model
Authors: Tate M. R. , Pullman D. P. , Li Y. L. , Gosalvez-Blanco D. , Tsekouras A. A. , Ceyer S. T.
Published: July 2002

A model is developed to describe the kinetics of the three scattering channels—unreactive scattering and dissociative chemisorption via single atom abstraction and two atom adsorption—that are present in the interaction of F2 with Si(100). The model provides a good description of the non-Langmuirian coverage dependence of the probabilities of single atom abstraction and two atom adsorption, yielding insight into the dynamics of the gas–surface interaction. The statistical model is based on the premise that the two dissociative chemisorption channels share a common initial step, F atom abstraction. The subsequent interaction, if any, of the complementary F atom with the surface determines if the overall result is single atom abstraction or two atom adsorption. The results are consistent with the orientation of the incident F2 molecular axis with respect to the surface affecting the probability of single atom abstraction relative to two atom adsorption. A perpendicular approach favors single atom abstraction because the complementary F atom cannot interact with the surface, whereas a parallel approach allows the F atom to interact with the surface and adsorb. The fate of the complementary F atom is dependent on the occupancy of the site with which it interacts. The model distinguishes between four types of dangling bond sites on the Si(100)(2×1) surface, based on the occupancy of the site itself and that of the complementary Si atom in the Si surface dimer. The results show that the unoccupied dangling bond sites on half-filled dimers are about twice as reactive as those on empty dimers, which is consistent with an enhanced reactivity due to a loss of a stabilizing π interaction between the two unoccupied dangling bonds on a dimer.
Lifetime of spatially heterogeneous dynamic domains in polystyrene melts
Authors: Wang Chia-Ying , Ediger M. D.
Published: July 2002

A photobleaching method is used to measure the rotational dynamics of tetracene and rubrene in polystyrene, and to determine the lifetime of spatially heterogeneous dynamic domains in the polystyrene matrix. It is possible to selectively photobleach subsets of probe molecules in more mobile environments and to measure the time required for the remaining slower-than-average probes to be redistributed into an equilibrium set of environments. For polystyrene, this exchange time is much longer than the α-relaxation time at temperatures very near Tg and exhibits a strong temperature dependence. These results are qualitatively consistent with previous studies on tetracene in supercooled o-terphenyl and indicate that the observation of long-lived heterogeneous dynamic domains at temperatures very near Tg is neither matrix nor probe specific.
A remarkable heavy atom isotope effect in the dissociative chemisorption of nitrogen on Ru(001)
Authors: Romm L. , Citri O. , Kosloff R. , Asscher M.
Published: July 2002

An extremely large isotope effect [Ieff=Pdiss(15N2)/Pdiss(14N2)], has been measured in the dissociative chemisorption of nitrogen molecules over Ru(001). It varies from unity at kinetic energies above 2 eV to 0.2 at Ek=1.4 eV. These observations are consistent with a barrier for direct dissociation of 1.8 eV, in agreement with previous experiments and recent ab initio density functional theory calculations. It supports earlier studies that proposed tunneling as the dissociation dynamics mechanism.
Classes of potentials of time-dependent central force fields which possess first integrals quadratic in the momenta
Authors: Leach P. G. L.
Published: July 2002

The general form for the potential of a time-dependent central force which possesses an energylike first integral is determined. In two special cases additional first integrals (apart from the angular momentum) are found. These enable the orbit equation to be determined without further quadrature. The Schrödinger equation is solved fully in these cases.
Computer-aided study of a class of Riemannian space-times
Authors: Rebouças M. J. , Åman J. E.
Published: July 2002

The Riemannian Gödel-type manifolds are examined in the light of the equivalence problem techniques by using algebraic computing. The conditions for space-time homogeneity of a Riemannian manifold with a Gödel-type metric are derived, generalizing previous work on this subject matter. A classification of the Gödel-type Riemannian manifolds based on the two relevant parameters m and Ω is formulated. It is shown that apart from the m2=4Ω2 case they are all Petrov type D with a five-parameter group of motions. The special m2=4Ω2 manifold is shown to be conformally flat and to admit a seven-parameter group of isometries. An algebraic classification of the Ricci spinor of all Gödel-type Riemannian manifolds is discussed. Possible sources for these space-times are examined. A generalization of the Rebouças–Tiomno theorem on Gödel-type manifolds is given.
A gauge theory for the quantum planar three-body problem
Authors: Iwai Toshihiro
Published: July 2002

A several-particle system is called a molecule in the Born–Oppenheimer approximation. The nonrigidity of molecules involves difficulty in molecular dynamics. Guichardet [A. Guichardet, Ann. Inst. H. Poincaré 40, 329 (1984)] showed recently that the vibration motion cannot in general be separated from the rotation motion, by using the connection theory in differential geometry. The point of his theory is the observation that a center-of-mass system is made into a principal fiber bundle with rotation group as the structure group, and is equipped with a connection by the Eckart condition of rotationless constraint. The base manifold of this bundle is called the internal space. The fact that the connection has nonvanishing curvature gives rise to the nonseparability of vibration from rotation. This is a mathematical meaning of nonrigidity of molecules. As an application of the connection theory due to Guichardet, this paper establishes a gauge theory for nonrigid molecules on the basis of the observation that the vector bundle associated with the principal fiber bundle (the center-of-mass system) provides a setting for quantum mechanics of the ‘‘internal’’ molecular motion. The interest, however, centers on planar triatomic molecules in order to put forward the gauge theory in an explicit manner. The conclusion is this: The internal space of a planar triatomic molecule is diffeomorphic with R3−{0}, and endowed with Dirac’s monopole field which may be interpreted as a Coriolis field induced by the rotation. The angular momentum eigenvalues, which are twice the quantized monopole strengths, assign the complex line bundles over the internal space. The internal states of the molecule are described as the cross sections of the complex line bundle, on which the internal Hamiltonian operator acts in minimally coupling with the monopole field.
Dirac operators with a spherically symmetric δ-shell interaction
Authors: Dittrich J. , Exner P. , Šeba P.
Published: July 2002

Dirac operators with a contact interaction supported by a sphere are studied restricting attention to the operators that are rotationally and space-reflection symmetric. The partial wave operators are constructed using the self-adjoint extension theory, a particular attention being paid to those among them that can be interpreted as δ-function shells of scalar and vector nature. The class of interactions for which the sphere becomes impenetrable is specified and spectral properties of the obtained Hamiltonians are discussed.
The abundant symmetry structure of hierarchies of nonlinear equations obtained by reciprocal links
Authors: Carillo Sandra , Fuchssteiner Benno
Published: July 2002

Explicit computation for a Kawamoto-type equation shows that there is a rich associated symmetry structure for four separate hierarchies of nonlinear integrodifferential equations. Contrary to the general belief that symmetry groups for nonlinear evolution equations in 1+1 dimensions have to be Abelian, it is shown that, in this case, the symmetry group is noncommutative. Its semisimple part is isomorphic to the affine Lie algebra A(1)1 associated to sl(2,C). In two of the additional hierarchies that were found, an explicit dependence of the independent variable occurs. Surprisingly, the generic invariance for the Kawamoto-type equation obtained in Rogers and Carillo [Phys. Scr. 36, 865 (1987)] via a reciprocal link to the Möbius invariance of the singularity equation of the Kaup–Kupershmidt (KK) equation only holds for one of the additional hierarchies of symmetry groups. Thus the generic invariance is not a universal property for the complete symmetry group of equations obtained by reciprocal links. In addition to these results, the bi-Hamiltonian formulation of the hierarchy is given. A direct Bäcklund transformation between the (KK) hierarchy and the hierarchy of singularity equation for the Caudrey–Dodd–Gibbon–Sawada–Kotera equation is exhibited: This shows that the abundant symmetry structure found for the Kawamoto equation must exist for all fifth-order equations, which are known to be completely integrable since these equations are connected either by Bäcklund transformations or reciprocal links. It is shown that similar results must hold for all hierarchies emerging out of singularity hierarchies via reciprocal links. Furthermore, general aspects of the results are discussed.
A first integral for a class of time-dependent anharmonic oscillators with multiple anharmonicities
Authors: Leach P. G. L. , Maharaj S. D.
Published: July 2002

The integrability of the equation q̈=f(t)q2+g(t)q3+h(t)q4+j(t)q5 is considered. Particular cases of this equation arise in the study of charged plasma in an axially symmetric magnetic field and in shear-free spherically symmetric gravitational fields in general relativity. The above equation with only a quadratic term arises in the study of shear-free fluids, in general [A. Krasinski, J. Math. Phys. 30, 433 (1989)]. The equation with a cubic term is applicable when there is an electromagnetic field. In special cases we reduce the solution to a quadrature that has solutions in terms of elliptic integrals. A Lie point symmetry analysis is performed and the different cases that arise are considered for the existence of a symmetry.
Contractions of the irreducible representations of the quantum algebras suq(2) and soq(3)
Authors: Gromov N. A. , Man’ko V. I.
Published: July 2002

The contractions of the irreducible representations of the unitary quantum algebra suq(2) and the orthogonal quantum algebra soq(3) in the Gel’fand–Tsetlin basis are regarded in detail with the help of the dual numbers.
Symmetries of discrete dynamical systems
Authors: Levi D. , Winternitz P.
Published: July 2002

Differential–difference equations of the form ün=Fn(t,un−1,un,un+1) are classified according to their continuous Lie point symmetry groups. It is shown that for nonlinear equations, the symmetry group can be at most seven-dimensional. The integrable Toda lattice is a member of this class and has a four-dimensional symmetry group.
The equivalence of Darmois-Israel and distributional method for thin shells in general relativity
Authors: Mansouri R. , Khorrami M.
Published: July 2002

A distributional method to solve the Einstein’s field equations for thin shells is formulated. The familiar field equations and jump conditions of Darmois-Israel formalism are derived. A careful analysis of the Bianchi identities shows that, for cases under consideration, they make sense as distributions and lead to jump conditions of Darmois-Israel formalism.
The ultrarelativistic Reissner–Nordstro/m field in the Colombeau algebra
Authors: Steinbauer R.
Published: July 2002

The electromagnetic field of the ultrarelativistic Reissner–Nordstro/m solution shows the physically highly unsatisfactory property of a vanishing field tensor but a nonzero, i.e., δ-like, energy density. The aim of this work is to analyze this situation from a mathematical point of view, using the framework of Colombeau’s theory of nonlinear generalized functions. It is shown that the physically unsatisfactory situation is mathematically perfectly defined and that one cannot avoid such situations when dealing with distributional valued field tensors.
Intrinsic characterization of the variable separation in the Hamilton–Jacobi equation
Authors: Benenti Sergio
Published: July 2002

The nonorthogonal separation of variables in the Hamilton–Jacobi equation corresponding to a natural Hamiltonian H=12gijpipj+V, with a metric tensor of any signature, is intrinsically characterized by geometrical objects on the Riemannian configuration manifold: Killing vectors, Killing tensors, and Killing webs. Comparisons with previous characterizations and some illustrative examples are given.
Existence theorems for hairy black holes in su(N) Einstein–Yang–Mills theories
Authors: Mavromatos N. E. , Winstanley E.
Published: July 2002

We establish the existence of hairy black holes in su(N) Einstein–Yang–Mills theories, described by N−1 parameters, corresponding to the nodes of the gauge field functions.
The Camassa–Holm equation as a geodesic flow on the diffeomorphism group
Authors: Kouranbaeva Shinar
Published: July 2002

Misiolek [J. Geom. Phys. 24, 203–208 (1998)] has shown that the Camassa–Holm equation is a geodesic flow on the Bott–Virasoro group. In this paper it is shown that the Camassa–Holm equation for the case κ=0 is the geodesic spray of the weak Riemannian metric on the diffeomorphism group of the line or the circle obtained by right translating the H1 inner product over the entire group. This paper uses the right-trivialization technique to rigorously verify that the Euler–Poincaré theory for Lie groups can be applied to diffeomorphism groups. The observation made in this paper has led to physically meaningful generalizations of the CH-equation to higher dimensional manifolds.
On construction of recursion operators from Lax representation
Authors: Gürses Metin , Karasu Atalay , Sokolov Vladimir V.
Published: July 2002

In this work we develop a general procedure for constructing the recursion operators for nonlinear integrable equations admitting Lax representation. Several new examples are given. In particular, we find the recursion operators for some KdV-type systems of integrable equations.
Combined side wall and bottom wall effects on the Stokes velocity of a disk moving broadside
Authors: Trahan Jeffrey F. , Folse R. F. , Hussey R. G.
Published: July 2002

The effect of a solid boundary on the Stokes velocity of a circular disk of zero thickness moving broadside is known in two cases: (i) when the boundary is an infinite plane parallel to the plane of the disk, and (ii) when the boundary is a cylindrical tube of infinite length coaxial with the disk. Results are presented of an experiment in which both boundary effects are significant and it is shown that there is a smooth transition from a region in which the cylindrical side wall is dominant to a region in which the plane bottom wall is dominant. Measurements with disks of different thickness indicate that results for zero thickness can be obtained by linear extrapolation. The recent results for a sphere obtained by Sano [J. Phys. Soc. Jpn. 56, 2713 (1987)] suggest a way of obtaining an empirical correction to the side wall effect. An empirical correction to the bottom wall effect is also presented, and the two corrections are found to overlap for a significant range.
Potential flow around a row of spheres in a circular tube
Authors: Cai Xiaolong , Wallis Graham B.
Published: July 2002

The streamfunction for the flow of an ideal fluid through a tube containing an infinite row of equidistant stationary spheres has been obtained by extending the works of Smythe [Phys. Fluids 4, 756 (1961)] and Michael [Phys. Fluids 8, 1263 (1965)]. Spheres whose separation of centers L varies from one diameter to infinity are considered, while the ratio of the tube and sphere radii R varies from one to infinity. With a relation developed by Wallis [Multiphase Sci. Technol. 5, 239 (1989)], the added (or virtual or apparent) mass coefficient per sphere has been found as a function of R and L. Direct numerical solutions of the problem using finite-element methods are in excellent agreement with the analytical results.
The decay of homogeneous isotropic turbulence
Authors: George William K.
Published: July 2002

A new theory for the decay of homogeneous, isotropic turbulence is proposed in which truly self-preserving solutions to the spectral energy equation are found that are valid at all scales of motion. The approach differs from the classical approach in that the spectrum and the nonlinear spectral transfer terms are not assumed a priori to scale with a single length and velocity scale. Like the earlier efforts, the characteristic velocity scale is defined from the turbulence kinetic energy and the characteristic length scale is shown to be the Taylor microscale, which grows as the square root of time (or distance). Unlike the earlier efforts, however, the decay rate is shown to be of power-law form, and to depend on the initial conditions so that the decay rate constants cannot be universal except possibly in the limit of infinite Reynolds number. Another consequence of the theory is that the velocity derivative skewness increases during decay, at least until a limiting value is reached. An extensive review of the experimental evidence is presented and used to evaluate the relative merits of the new theory and the more traditional views.
On the motion of small spherical bubbles in two-dimensional vortical flows
Authors: Ruetsch G. R. , Meiburg E.
Published: July 2002

The motion of small, spherical noninteracting bubbles in two-dimensional vortical flows by means of numerical simulations is investigated. After a discussion concerning the various bubble equations, bubble trajectories are calculated in a solid-body vortex, where it is found that the bubble motion can be described in terms of the location where the bubbles accumulate, or equilibrium points, and the rate of entrapment into these equilibrium points. Of importance here is that the rate of entrapment into the vortex has an optimum value for some value of the inertia parameter, or inverse Stokes number. The bubble motion in a temporally evolving shear layer is investigated, where it is found that the solid-body vortex model predicts the trends in the growth in concentration about the vortex center for the case without gravity. For the case with gravity, not all bubbles are captured by the vortex, and the percentage of bubbles captured increases with decreasing inertia parameter. Also discussed is how these factors affect the generation of the interface between regions seeded and not seeded with bubbles.
Stability of sub-Alfvénic plasma expansions
Authors: Huba J. D. , Hassam A. B. , Winske D.
Published: July 2002

A comprehensive theoretical treatment of the linear stability of a sub-Alfvénic plasma expansion is developed. The analysis is similar to those performed for the lower-hybrid-drift instability and the drift cyclotron instability. In addition to the diamagnetic drift (Vdi) that drives these instabilities, the gravitational drift (Vg) caused by the deceleration of the plasma shell, and the Pedersen drift (VP) caused by ion–neutral collisions and neutral gas flow, are included. The emphasis of the paper is on the instability driven by the gravitational drift. The theory is fully kinetic and includes finite-beta effects (i.e., electromagnetic coupling and electron ∇B drift-wave resonances), collisional effects (electron–ion, electron–neutral, and ion–neutral collisions), and neutral gas flow, effects that have not been considered to date. The analysis is carried out in a slab geometry although the applications are to spherical expansions. The main conclusions are as follows. In the strong drift limit (Vg>vi and Vdi∼vi, where vi is the ion thermal velocity) it is found that (1) finite-beta effects are stabilizing and reduce the wavelength of the maximum growth rate; (2) ion–neutral collisions are stabilizing and do not affect the wavelength of the maximum growth rate; (3) electron–neutral collisions are stabilizing and increase the wavelength of the maximum growth rate; (4) the gravitational drift driven mode maximizes the growth rate at longer wavelengths than the diamagnetic drift driven mode; (5) the Pedersen drift effectively reduces the gravitational drift, and is therefore a stabilizing influence; and (6) the instability splits into two modes for Te≫Ti in finite-beta plasmas: the lower-hybrid-drift instability at high frequencies and short wavelengths, and a gravitational mode at lower frequencies and longer wavelengths.

In the weak drift regime (Vg<vi and Vdi<vi) it is found that (1) finite-beta effects are stabilizing and increase the wavelength of the maximum growth rate; (2) ion–neutral collisions are destabilizing and decrease the wavelength of the maximum growth rate; and (3) electron–ion and electron–neutral collisions are stabilizing, and increase the wavelength of the maximum growth rate. When the growth rate becomes less than the ion cyclotron instability (γ<Ωi), the growth rate as a function of wave number ‘‘breaks up’’ into a discrete set of modes which is associated with the coupling of the drift waves to ion cyclotron waves. These results are applied to the AMPTE magnetotail release [J. Geophys. Res. 92, 5777 (1987)], the Naval Research Laboratory laser experiment [Phys. Rev. Lett. 59, 2299 (1987)], and the upcoming CRRES GTO releases [D. Reasoner (private communication, 1989)].
The effect of thin film variations and transverse curvature on the shape of fingers in a Hele–Shaw cell
Authors: Reinelt D. A.
Published: July 2002

The steady-state shape of a finger penetrating into a viscous fluid that fills the gap between two closely spaced parallel plates is examined. Boundary conditions that take into account variations in the thickness of the thin film and both transverse curvature (across the gap) and lateral curvature (along the interface edge) are applied at the leading edge of the interface. These interface conditions, derived from local solutions in the vicinity of the interface edge, depend on μUn/T, where μ is the viscosity of the original fluid, Un is the normal velocity of the interface edge, and T is the interfacial tension. They also depend on ε/R, where ε=b/a≪1 is the ratio of gap width to cell width and aR is the lateral radius of curvature. The problem is solved by conformally mapping the domain to a circle. By expanding the solution in terms of analytic functions and satisfying the boundary conditions, the shape of the interface edge and finger width λ are determined. The agreement between numerical and experimental results is good and an improvement over previous models. The relaxation of the film thickness is also discussed.
The anomalous behavior of the runup of cnoidal waves
Authors: Synolakis Costas Emmanuel , Deb Manas Kumar , Skjelbreia James Eric
Published: July 2002

A new solution to the linearized shallow-water wave equations is introduced for the case of cnoidal waves climbing up a plane beach. The solution is used to calculate the maximum runup. It is shown that the maximum relative runup of cnoidal waves is significantly larger than the runup of monochromatic waves with the same wave height and wavelength far from the shore. It is also shown that the maximum relative runup of cnoidal waves is not a monotonically varying function of the normalized wavelength.
Magnetohydrodynamic flow in a curved pipe
Authors: Issacci F. , Ghoniem N. M. , Catton I.
Published: July 2002

The flow of conductive fluids in highly conductive curved pipes is studied analytically in this paper. The flow is assumed to be steady state, laminar, and fully developed. Coupled continuity, Navier–Stokes, and appropriate Maxwell equations are solved in toroidal coordinates. The dimensionless parameters of the problem are Dean number K and Hartmann number Ha. For low Hartmann numbers [Ha2∼θ(1)], the solution is expanded in a power series of K and Ha2. For intermediate Hartmann numbers [Ha2∼θ(1000)], the solution is expressed as a power series of K. The axial velocity contours are shown to be shifted towards the outer wall. For low Ha, these contours are nearly circular. The effect of a strong transverse magnetic field is to enhance the compression of fluid towards the outer wall. The secondary flow field comprises a symmetric pair of counter-rotating vortices. A strong magnetic field is found to confine the secondary flow streamlines to a thin layer near the tube wall. The secondary flow rate in the near-wall boundary layer is increased by the magnetic field. This increase in flow rate raises the possibility of efficient convective cooling of curved first wall tubes in magnetic confinement fusion reactors (MFCR).
A collisional model of the plasma presheath
Authors: Scheuer J. T. , Emmert G. A.
Published: July 2002

The problem of a collisional plasma flowing into a perfectly absorbing wall has been investigated using a kinetic approach. The plasma is assumed to have a nonzero ion temperature and a Boltzmann distribution of electrons. Ion collisions are included in the analysis through a Bhatnagar–Gross–Krook (BGK) collision term. An equation describing the electrostatic potential variation in the presheath region is derived. This equation is solved numerically for a range of collisionalities. In addition to the potential variation in the presheath, the ion distribution function, the wall potential, and the ion particle and energy fluxes into the sheath are also calculated. The calculation is repeated for three different cases. In the first case ion–neutral collisions are modeled by conserving only particles in the BGK operator. Ion–ion collisions are modeled by conserving particles and momentum in the second case, and by conserving particles, momentum, and energy in the third case. These results give insight into the role of collision conservation laws in describing the plasma flow.
Viscous dissipation rate in concentrated suspensions
Authors: Seifu B. , Nir A. , Semiat R.
Published: July 2002

The constitutive equation proposed by Phillips et al. [Phys. Fluids A 4, 30 (1992)] for shear induced particle migration in viscous flows of concentrated suspensions is used to calculate the change in viscous dissipation rate occurring when the particle distribution changes from a homogeneous state to the steady state. Four cases of simple unidirectional flows are considered. Two of these cases were discussed by Phillips et al. and are revisited here. In all cases, the expected decrease in the dissipation rate is found to be considerable. The degree of reduction in dissipation rate is influenced by whether the shear-induced migration is parallel or normal to the velocity gradient.