bluuebunny/crossref_metadata_2025 huggingface dataset:
A combined experimental-theoretical study of the vibrational predissociation and product rotational distributions for high vibrational levels of He79Br2
Authors: Rohrbacher Andreas , Ruchti Thomas , Janda Kenneth C. , Buchachenko Alexei A. , Hernández Marta I. , González-Lezana Tomás , Villarreal Pablo , Delgado-Barrio G.
Published: July 2002

Pump-probe spectra of HeBr2 in vibrational states v′=10 and 39 through 48 of the B electronic state are reported and the fragment rotational distributions from vibrational predissociation of the cluster are extracted from the measured E(0g+)←B(3Π0u+) spectra of Br2. The experimental results are compared to theoretical calculations on the B←X spectra using atom-atom model potentials and performing a thermal average over transitions that contribute to the net excitation. Very good agreement between experiment and theory is obtained, except in the region of v′=44, where the Δv=−1 channel closes, and in the region of v′=48 where the Δv=−2 channel closes. For v′=43, and v′=44, the agreement is less satisfactory because the dynamics are extremely sensitive to details of the potential energy surface due to threshold effects associated with the Δv=−1 channel closing. Similar sensitivity to the potential due to the Δv=−2 channel closing impairs the agreement between experiment and theory for v′=48. Below v′=43, the rotational distributions for Δv=−1 and Δv=−2 are quite similar. Above v′=43 the peaks of the rotational distributions for Δv=−2 move to higher values of j. These results are compatible with the theoretical conclusion that dissociation shifts from a direct mechanism to one involving intramolecular vibrational distribution in the region of the closing of the Δv=−1 channel. Although the simple additive potential model used in this work succeeds in reproducing most of the experimental data for this system, further improvements in the potential energy surface will be required to achieve precise agreement between experiment and theory for large Br-Br separations.
What causes the vibrational lifetime plateau in supercritical fluids?
Authors: Goodyear Grant , Tucker Susan C.
Published: July 2002

Using molecular dynamics simulation, we show that the vibrational relaxation lifetime of a diatomic in a two-dimensional supercritical rare-gas fluid exhibits the same unexpected plateau behavior as was observed experimentally for W(CO)6 in supercritical CO2 by Fayer and co-workers, and we link this behavior to average local solvent density enhancements arising from the solvent’s near-critical density fluctuations.
Ab initio calculation of the rotation–vibration energy levels of H3+ and its isotopomers to spectroscopic accuracy
Authors: Polyansky Oleg L. , Tennyson Jonathan
Published: July 2002

Surfaces are fitted to the Born–Oppenheimer potential energy, electronic relativistic correction and adiabatic correction data calculated ab initio by Cencek et al. [J. Chem. Phys. 108, 2831 (1998)]. These surfaces are used in calculations of the rotation–vibration energy levels of H3+, H2D+, D2H+, and D3+. Nonadiabatic corrections to the Born–Oppenheimer approximation are introduced following models developed for diatomics which involve the use of isotopomer independent scaled vibrational reduced masses. It is shown that for triatomics this approach leads to an extra term in the nuclear motion Hamiltonian. Our final calculations reproduce the known spectroscopic data for H3+ and its isotopomers to within a few hundredths of a cm−1.
Nuclear magnetic shielding of noble gases in liquid crystals
Authors: Ylihautala Mika , Lounila Juhani , Jokisaari Jukka
Published: July 2002

A theoretical model for nuclear magnetic shielding of noble gas atoms soluted in liquid crystal solvents is developed. It is found that the solvent effect on the shielding can be represented as a linear combination of products of the liquid crystal orientational order parameters of varying rank. In a special case of pairwise additive shielding perturbations, most of the coefficients vanish and the shielding reduces to a sum of two terms, the isotropic and anisotropic parts. Both contributions are directly proportional to the density of the liquid crystal, and the anisotropic part is also directly proportional to the second rank orientational order parameter of the liquid crystal. The developed model is used to account for the behavior of the 129Xe shielding in the nematic liquid crystal 4-ethoxybenzylidene-2,6-dideutero-4′-n-butylaniline (d2-EBBA). The pairwise additivity approximation of the shielding perturbations is found to explain the observed temperature dependence of the 129Xe shielding satisfactorily. In particular, the temperature dependence of the isotropic part is mostly due to the change in the liquid crystal density, whereas the anisotropic part is mainly controlled by the temperature dependence of the Xe–liquid crystal molecule pair correlation function and the second rank orientational order parameter of the liquid crystal. This result differs from the results of the phenomenological theory of Lounila et al. [J. Chem. Phys. 97, 8977 (1992)], where only the density and the orientational order parameter were assumed to be significantly temperature dependent.
Variation of the resonance width of HOCl(6νOH) with total angular momentum: Comparison between ab initio theory and experiment
Authors: Skokov Sergei , Bowman Joel M.
Published: July 2002

Complex L2 calculations of the variation of (very narrow) resonance widths of the 6νOH state of HOCl with total angular momentum are reported, using a recently developed, accurate ab initio potential energy surface [S. Skokov, J. M. Bowman, and K. A. Peterson, J. Chem. Phys. 109, 2662 (1998)]. The calculations are carried out within the adiabatic rotation approximation for the overall rotation and a truncation/recoupling method for the vibrational states. Comparisons with recent double-resonance experiments of the Rizzo and Sinha groups are made. The variation of resonance width with J for K=0 is shown to be due to rotation-induced coupling of the 6νOH state with a dense set of states with large excitation in the dissociative coordinate.
Sum rules and the photoabsorption cross sections of C60
Authors: Berkowitz J.
Published: July 2002

The absolute photoabsorption spectrum of C60 is constructed from experimental data, by linking relative measurements to some recent absolute determinations. Sum rule analysis supports these recent determinations over earlier ones, but substantially better agreement is achieved with ∼20% reduction in the cross-sections. Attention is focused on the 11–40 eV region, where discrepancies exist in both pseudophotoabsorption and photoionization data. Some inferences are drawn regarding the propensity of large molecules such as C60 toward multiple ionization, rather than photodissociative ionization. Problems encountered with prior application of quasi-equilibrium theory to the dissociative ionization of C60 are discussed.
Photodissociation of the vinyl radical (C2H3) via the first excited state: The C2H2(X̃1Σg+)+H channel
Authors: Xu Kesheng , Zhang Jingsong
Published: July 2002

Photodissociation of C2H3 via its first excited Ã2A″ state is studied at 327.4 and 366.2 nm using high-n Rydberg-atom time-of-flight technique. C2H2(X̃1Σg+)+H product channel is identified. Product translational energy distributions reveal two highly-inverted vibrational progressions of C2H2(X̃1Σg+) (most likely C≡C stretch and its combination band with C–H bend). Anisotropic H-atom angular distributions indicate a short Ã2A″ state lifetime with respect to dissociation. D0(C2H2–H)=33.0±0.5 kcal/mol is obtained.
Symmetric diblock copolymers in thin films. I. Phase stability in self-consistent field calculations and Monte Carlo simulations
Authors: Geisinger T. , Müller M. , Binder K.
Published: July 2002

We investigate the phase behavior of symmetric AB diblock copolymers confined into a thin film. The film boundaries are parallel, impenetrable and attract the A component of the diblock copolymer. Using a self-consistent field technique [M. W. Matsen, J. Chem. Phys. 106, 7781 (1997)], we study the ordered phases as a function of incompatibility χ and film thickness in the framework of the Gaussian chain model. For large film thickness and small incompatibility, we find first order transitions between phases with different number of lamellae which are parallel oriented to the film boundaries. At high incompatibility or small film thickness, transitions between parallel oriented and perpendicular oriented lamellae occur. We compare the self-consistent field calculations to Monte Carlo simulations of the bond fluctuation model for chain length N=32. In the simulations we quench several systems from χN=0 to χN=30 and monitor the morphology into which the diblock copolymers assemble. Three film thicknesses are investigated, corresponding to parallel oriented lamellae with 2 and 4 interfaces and a perpendicular oriented morphology. Good agreement between self-consistent field calculations and Monte Carlo simulations is found.
Melittin at a membrane/water interface: Effects on water orientation and water penetration
Authors: Bachar Michal , Becker Oren M.
Published: July 2002

Melittin, a small peptide found in bee venom, is known to induce membrane lysis. A molecular dynamics simulation of melittin embedded in a hydrated dipalmitoylphosphatidylcholine bilayer is analyzed in order to study the peptide’s effect on water molecules at the membrane/water interface. The peptide, with a protonated N-terminus, was embedded in a trans-bilayer orientation. The simulation highlights the microscopic mechanism by which melittin induces the formation of transmembrane water “pores,” leading to membrane lysis. It was found that melittin has a profound effect on the behavior of the water molecules at the membrane/water interface. It modifies the orientation of the water dipoles and induces water penetration into the bilayer. In fact, melittin’s residue Lys-7 and its protonated N-terminus facilitate the formation of transmembrane water pores by steering water penetration from both sides of the bilayer. The initial step towards pore formation takes about 200 ps, and the process relays on melittin’s bent conformation and tilted orientation. A large body of experimental observations supports the simulation results and the suggested microscopic mechanism.
Molecular simulation of hydrogen adsorption in charged single-walled carbon nanotubes
Authors: Simonyan Vahan V. , Diep Phong , Johnson J. Karl
Published: July 2002

The adsorption of molecular hydrogen gas onto charged single-walled carbon nanotubes (SWNTs) is studied by grand canonical Monte Carlo (GCMC) computer simulation. The quadrupole moment and induced dipole interaction of hydrogen with “realistically” charged (0.1 e/C) nanotubes leads to an increase in adsorption relative to the uncharged tubes of ∼10%–20% for T=298 K and 15%–30% for 77 K. Long-range electrostatic interactions makes second layer (exohedral) adsorption significantly higher. Hydrogen orientation-ordering effects and adsorption anisotropy in the electrostatic field of the nanotube were observed. The geometry of nanotube arrays was optimized at fixed values of charge, temperature, and pressure. In general, negatively charged nanotubes lead to more adsorption because the quadrupole moment of hydrogen is positive. Calculated isotherms indicate that even charged nanotube arrays are not suitable sorbents for achieving the DOE target for hydrogen transportation and storage at normal temperatures, unless the charges on the nanotubes are unrealistically large.
Solvation in highly nonideal solutions: A study of aqueous 1-propanol using the coumarin 153 probe
Authors: Shirota Hideaki , Castner Edward W.
Published: July 2002

We have investigated the anomalous behavior of aqueous 1-propanol binary solutions using a typical fluorescence probe molecule, coumarin 153. We present data on the fluorescence lifetimes, fluorescence anisotropies, and solvent reorganization dynamics, as well as the steady-state absorption and emission spectra of coumarin 153 in the binary solutions. The rotational diffusion and solvation time constants depend strongly on the content of 1-propanol, especially at low 1-propanol mole fractions. Spectroscopic results presented here are consistent with prior light scattering [G. H. Großmann and K. H. Ebert, Ber. Bunsenges. Phys. Chem. 85, 1026 (1981)], small angle x-ray scattering [H. Hayashi, K. Nishikawa, and T. Iijima, J. Phys. Chem. 94, 8334 (1990)], and dielectric relaxation [S. Mashimo, T. Umehara, and H. Redlin, J. Chem. Phys. 95, 6257 (1991)] data. The anomalous dynamics features likely arise from the effect of the preferential solvation due to the 1-propanol clustering.
Composition dependence of chi from neutron scattering, compressibility, and a purely interaction chi
Authors: Gujrati P. D.
Published: July 2002

We demonstrate that the concept of a bare chi parameter as exchange energy is meaningful only within the context of a lattice theory. We introduce a simple ensemble to describe a compressible system. The ensemble shares many features present in the ensemble describing an incompressible system. This allows us to express the intensity in terms of fluctuations in only one species, a feature also present in the incompressible model. We demonstrate that the perplexing features seen experimentally and theoretically in the wings of small-angle-neutron-scattering (SANS) measured χSANS are spurious and unrelated to the energetics, and result from a definition that leaves behind some nonenergetic contribution, which dominates the behavior in the wings and controls the sign of the curvature. It is easy to identify an appropriate χscatt that properly characterizes the interactions without any superfluous composition dependence. We use our recently developed lattice theory, which gives rise to genuine composition dependence in χscatt due to nonrandomness. For a symmetric blend, χscatt depends only weakly on compressibility. This is not true of an asymmetric blend, where compressibility effects can be strong. In particular, we demonstrate that a linear χscatt results from the asymmetry in the model and not from the compressibility.
Accurate wave packet propagation for large molecular systems: The multiconfiguration time-dependent Hartree (MCTDH) method with selected configurations
Authors: Worth G. A.
Published: July 2002

The multiconfiguration time-dependent Hartree (MCTDH) method is a general, accurate algorithm for wave packet propagation calculations. Its efficiency is due to the use of an optimally small time-dependent basis set which evolves with the wave packet. The method however suffers from an exponential scaling of the required effort with system size, though with a much lower base than the exponential scaling of the standard propagation scheme. Here, we present a method to reduce the computational resources required for MCTDH calculations on large systems by selecting and propagating only the most important configurations for the representation of the wave function. At the same time the properties of the MCTDH method, such as convergence against numerically exact solutions, are retained.
An infinite hierarchy of conservation laws and nonlinear superposition principles for self-dual Einstein spaces
Authors: Boyer Charles P. , Plebański Jerzy F.
Published: July 2002

Self-dual Einstein spaces are shown to admit an infinite hierarchy of conservation laws, and this hierarchy is then used to derive a formal version of Penrose’s twistor construction. The set of formal holomorphic bundles of fiber dimension 2 over the Riemann sphere P1 is shown to form a formal infinite group which is used to derive nonlinear superposition principles. As an example of our methods a new self-dual Einstein space is obtained as the result of a ‘‘collision’’ of complex pp-waves ‘‘traveling in opposite directions.’’
Symmetry reduction for the Kadomtsev–Petviashvili equation using a loop algebra
Authors: David D. , Kamran N. , Levi D. , Winternitz P.
Published: July 2002

The Kadomtsev–Petviashvili (KP) equation (ut+3uux/2+ 1/4 uxxx)x +3σuyy/4=0 allows an infinite-dimensional Lie group of symmetries, i.e., a group transforming solutions amongst each other. The Lie algebra of this symmetry group depends on three arbitrary functions of time ‘‘t’’ and is shown to be related to a subalgebra of the loop algebra A(1)4. Low-dimensional subalgebras of the symmetry algebra are identified, specifically all those of dimension n≤3, and also a physically important six-dimensional Lie algebra containing translations, dilations, Galilei transformations, and ‘‘quasirotations.’’ New solutions of the KP equation are obtained by symmetry reduction, using the one-dimensional subalgebras of the symmetry algebra. These solutions contain up to three arbitrary functions of t.
Coulomb Green’s functions, in an n-dimensional Euclidean space
Authors: Chetouani L. , Hammann T. F.
Published: July 2002

The H-atom Green’s function is calculated in an n-dimensional Euclidean space, following the Feynman Lagrangian formulation. The use of generalized polar coordinates allows the expansion of the propagator into partial propagators, and the separation of the angular and radial variables. The angular part is shown to be a generalized Legendre polynomial while the radial part may be transformed in that of the harmonic oscillator. The H-atom spectrum is given by the poles of the Green’s function.
Parastatistics and the Clifford algebra unitary group approach to the many-electron correlation problem
Authors: Gould M. D. , Paldus J.
Published: July 2002

It is shown that the Clifford algebra unitary group approach, which is based on the subgroup chain U(2n)⊇SO(2n+1)⊇SO(2n)⊇U(n), may be described in terms of the para-Fermi algebra. Applications to the development of efficient algorithms for the evaluation of matrix elements of U(n) generators and of their products are also briefly discussed.
The Ricci curvature of Diff S1/SL(2, R)
Authors: Bowick M. J. , Lahiri A.
Published: July 2002

Previous calculations of the Ricci curvature for the manifold Diff Diff(S1)/S1 are extended to Diff(S1)/SL(2↛). These manifolds are distinguished by being coadjoint orbits of Diff(S1) which admit compatible symphectic and complex structures, making them Kähler manifolds.
τ functions and zero curvature equations of Toda–AKNS type
Authors: Bergvelt M. J. , ten Kroode A. P. E.
Published: July 2002

The connection between τ functions and zero curvature equations for the homogeneous construction of the basic module L(Λ0) over the simplest affine Kac–Moody algebra A(1)1 is studied.
Exact solutions for wave equations of two-layered media with smooth transition
Authors: Bluman George , Kumei Sukeyuki
Published: July 2002

The wave equation c2(x)uxx−utt=0 is solved for wave speeds c(x) corresponding to two-layered media with smooth transition from layer to layer. The wave speed c(x) has four free parameters to fit a given medium. Solutions are constructed from invariant solutions of a related system of first-order partial differential equations that admit a four-parameter symmetry group. These solutions are superposed to solve general initial value problems for data with compact support; the computation of the superposition coefficients uses elementary Fourier analysis. Solutions are illustrated for various initial conditions.
On the infinite-dimensional symmetry group of the Davey–Stewartson equations
Authors: Champagne B. , Winternitz P.
Published: July 2002

The Lie algebra of the group of point transformations, leaving the Davey–Stewartson equations (DSE’s) invariant, is obtained. The general element of this algebra depends on four arbitrary functions of time. The algebra is shown to have a loop structure, a property shared by the symmetry algebras of all known (2+1)-dimensional integrable nonlinear equations. Subalgebras of the symmetry algebra are classified and used to reduce the DSE’s to various equations involving only two independent variables.
The constraints of potentials and the finite-dimensional integrable systems
Authors: Zeng Yunbo , Li Yishen
Published: July 2002

Restricting potential to the space spanned by the eigenvectors of the recursion operator leads to a natural constraint of potential and a finite-dimensional integrable Hamiltonian system. The general method for proving the consistency of the two systems stemming from the Lax pair and obtaining the constants of the motion for the Hamiltonian system is illustrated by the classical Boussinesq and AKNS hierarchies. By using gauge transformation, similar results for the Jaulent–Miodek and Kaup–Newell hierarchies are presented.
The concept of a time-of-sojourn operator and spreading of wave packets
Authors: Jaworski W.
Published: July 2002

The concept of sojourn time and a sojourn time operator, aimed at describing the length of time spent by a quantum mechanical system in a given subspace of states, is investigated. A general rigorous definition to the sojourn time operator is given and some of its properties are studied. In particular, it is shown that the usual Born’s probability interpretation of the associated spectral measure yields strange, if not paradoxical, results, resembling the well-known quantum mechanical Zeno paradox. Also a specific example of a free nonrelativistic particle is considered. Here it is proven that the probability Pt(Ω) of the particle being present in a volume Ω at time t cannot vanish on a set of t having nonzero measure. This implies that the sojourn time in Ω never vanishes, and that zero is never an eigenvalue of the sojourn time operator. It is also shown that for a very general class of sets Ω, including all bounded sets, the sojourn time turns out to be bounded with a bound independent of the initial state of the particle. Correspondingly, the sojourn time operator turns out to be a bounded one.
Cayley–Klein parameters and evolution of two- and three-level systems and squeezed states
Authors: Dattoli G. , Torre A.
Published: July 2002

In this paper the time behavior of quantum states ruled by Hamiltonians linear in the SU(2), SU(1,1), and SU(3) generators in terms of the Cayley–Klein parameters, originally introduced in classical mechanics is analyzed. Also pointed out is the link between the Cayley–Klein parameters and the Wei–Norman ordering functions, exploited in the context of the Schrödinger representation.
Painlevé analysis and Lie group symmetries of the regularized long-wave equation
Authors: Rollins David K.
Published: July 2002

The Painlevé formulation is given for the regularized long-wave equation, which has been used to describe shallow water waves and drift waves in a plasma. The Lie group symmetries of the equation is then studied and it is shown that the only symmetries are due to the three conserved quantities.
E(2)-symmetric two-mode sheared states
Authors: Kim Y. S. , Yeh Leehwa
Published: July 2002

It is noted that the symmetry of two-mode squeezed states of light is governed by the group Sp(4) that is locally isomorphic to O(3,2). This group has subgroups that are locally isomorphic to the two-dimensional Euclidean group. Two-mode states having the E(2) symmetry are constructed. The translation-like transformations of this symmetry group shear the Wigner distribution function defined over the four-dimensional phase space consisting of two pairs of canonical variables. Sheared states are constructed in the Schrödinger picture of quantum mechanics and in the Fock space for photon numbers. It is shown that the Wigner phase-space picture is a convenient representation of quantum mechanics for calculating measurable quantities of the sheared states.
Finite Lorentz transformations, automorphisms, and division algebras
Authors: Manogue Corinne A. , Schray Jörg
Published: July 2002

An explicit algebraic description of finite Lorentz transformations of vectors in ten-dimensional Minkowski space is given by means of a parametrization in terms of the octonions. The possible utility of these results for superstring theory is mentioned. Along the way automorphisms of the two highest dimensional normed division algebras, namely, the quaternions and the octonions, are described in terms of conjugation maps. Similar techniques are used to define SO(3) and SO(7) via conjugation, SO(4) via symmetric multiplication, and SO(8) via both symmetric multiplication and one-sided multiplication. The noncommutativity and nonassociativity of these division algebras plays a crucial role in our constructions.
q-Deformation of the Coulomb problem
Authors: Chan F. L. , Finkelstein R. J.
Published: July 2002

The hydrogenic Schrödinger equation may be transformed into an integral equation on the group space of SO(3). The solutions of this integral equation are the Wigner functions Djmn, the matrix elements of the irreducible representations of SO(3). In this article we examine a q-deformation of the Coulomb problem for which the new wave functions are the matrix elements of the irreducible representations of the quantum group SUq(2). The new integral equation is formulated in terms of the Woronowicz integral. The eigenvalues are given by a modified Balmer formula which lifts the Coulomb degeneracy and replaces n by [n].
Levinson’s theorem, zero-energy resonances, and time delay in one-dimensional scattering systems
Authors: Sassoli de Bianchi M.
Published: July 2002

The one-dimensional Levinson’s theorem is derived and used to study zero-energy resonances in a double-potential system. The low energy behavior of time delay is also investigated. In particular, it is shown that the quantum mechanical time delay admits a classical lower bound, in the low energy limit, if the potential has no bound-state solutions.
Becchi–Rouet–Stora–Tyutin structure of polynomial Poisson algebras
Authors: Dresse Alain , Henneaux Marc
Published: July 2002

The Becchi–Rouet–Stora–Tyutin (BRST) structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide nontrivial models where the full BRST recursive procedure is needed. Quadratic Poisson algebras may already be of arbitrarily high rank. Explicit examples are provided, for which the first terms of the BRST generator are given. The calculations are cumbersome but purely algorithmic, and have been treated by means of the computer algebra system reduce. Our analysis is classical (=nonquantum) throughout.
Hamiltonian structures for the n-dimensional Lotka–Volterra equations
Authors: Plank Manfred
Published: July 2002

Under what algebraic conditions n-dimensional Lotka–Volterra equations are Hamiltonian for a suitable Poisson structure is investigated herein.
Lie symmetries and invariants of the Lotka–Volterra system
Authors: Almeida M. A. , Magalhães M. E. , Moreira I. C.
Published: July 2002

In this paper we use the Lie symmetry method for finding rational and transcendental symmetry transformations and invariants for the 3D Lotka–Volterra system.
Einstein’s equations in the presence of signature change
Authors: Dray Tevian
Published: July 2002

We discuss Einstein’s field equations in the presence of signature change using variational methods, obtaining a generalization of the Lanczos equation relating the distributional term in the stress tensor to the discontinuity of the extrinsic curvature. In particular, there is no distributional term in the stress tensor, and hence no surface layer, precisely when the extrinsic curvature is continuous, in agreement with the standard result for constant signature.
The algebra of q-pseudodifferential symbols and the q-WKP(n) algebra
Authors: Mas Javier , Seco Marcos
Published: July 2002

In this paper we continue with the program to explore the topography of the space of W-type algebras. In the present case, the starting point is the work of Khesin, Lyubashenko, and Roger on the algebra of q-deformed pseudodifferential symbols and their associated integrable hierarchies. The analysis goes on by studying the associated Hamiltonian structures for which compact expressions are found. The fundamental Poisson brackets yield q-deformations of WKP and related W-type algebras which, in specific cases, coincide with the ones constructed by Frenkel and Reshetikhin. The construction underlies a continuous correspondence between the Hamiltonian structures of the Toda lattice and the KP hierarchies.
Bounds on Schrödinger eigenvalues for polynomial potentials in N dimensions
Authors: Hall Richard L. , Saad Nasser
Published: July 2002

If a single particle obeys nonrelativistic QM in RN and has the Hamiltonian H=−Δ+∑q>0 a(q)rq, a(q)⩾0, then the lowest eigenvalue E is given approximately by the semiclassical expression E=minr>0{(1/r2)+∑q>0 a(q)(P(q,N)r)q}. It is proved that this formula yields a lower bound when P(q,N)=(Ne/2)1/2(N/qe)1/q[Γ(1+N/2)/Γ(1+N/q)]1/N and an upper bound when P(q,N)=(N/2)1/2[Γ((N+q)/2)/Γ(N/2)]1/q. An extension is made to allow for a Coulomb term when N>1. The general formula is applied to the examples V(r)=r+r2+r3 and V(r)=r2+r4+r6 in dimensions 1 to 10, and the results are compared to accurate eigenvalues obtained numerically.
Extended double Riemann–Hilbert problem and multiple representations of the infinite-dimensional symmetric group for the stationary axisymmetric vacuum field equations
Authors: Gao Ya-Jun , Zhong Zai-Zhe , Gui Yuan-Xing
Published: July 2002

The double-complex function method suggested in previous papers is extended and the extended method is used to establish two mutually dual extended double Hauser–Ernst equations and related Riemann–Hilbert problems, then quadruple representations of the semidirect product of the Kac–Moody and Virasoro groups are given. These show that, for the stationary axisymmetric vacuum space–times, there are more and richer symmetry structures than previously expected. The multiple forms of some well-known transformations can be obtained as some special cases.
On the Born–Oppenheimer approximation of diatomic wave operators. II. Singular potentials
Authors: Klein Markus , Martinez André , Wang Xue Ping
Published: July 2002

This paper is a continuation of an earlier paper [Commun. Math. Phys. 152, 73–95 (1993)]. Its purpose is to extend the quantitative estimates given previously for regular potentials to the case of potentials admitting some Coulomb-type singularities. More precisely, considering the two-cluster wave operators in diatomic-scattering, we approximate them by so-called “adiabatic’’ wave operators as the mass of the nuclei tends to infinity.
A histories approach to quantum mechanics
Authors: Gudder Stanley
Published: July 2002

A histories approach to quantum mechanics is formulated without the consistency requirement. Plausible, physically motivated axioms for a history structure are presented. In this structure, the consistency requirement is unnecessary because the joint sequential distributions are already probability measures. It is shown that the logic of a history structure is a temporal effect algebra and conversely, any temporal effect algebra is isomorphic to the logic of a history structure. When this general framework is specialized to a Hilbert space context, it reduces to a previously studied formalism.
The nonlinear Schrödinger equation on the half line
Authors: Gattobigio Mario , Liguori Antonio , Mintchev Mihail
Published: July 2002

The nonlinear Schrödinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is constructed. The construction is based on a new algebraic structure, which is called in what follows boundary algebra and which substitutes, in the presence of boundaries, the familiar Zamolodchikov–Faddeev algebra. The fundamental quantum field theory properties of the solution are established and discussed in detail. The relative scattering operator is derived in the Haag–Ruelle framework, suitably generalized to the case of broken translation invariance in space.
Pseudo-orthogonal groups and integrable dynamical systems in two dimensions
Authors: Calzada Juan A. , del Olmo Mariano A. , Rodrı́guez Miguel A.
Published: July 2002

Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are determined. Widely applied models in Physics are shown to appear as particular cases of the method.
Spherically symmetric solutions of the SU(N) Skyrme models
Authors: Ioannidou T. , Piette B. , Zakrzewski W. J.
Published: July 2002

Recently we have presented an ansatz which allows us to construct skyrmion fields from the harmonic maps of S2 to CPN−1. In this paper we examine this construction in detail and use it to construct, in an explicit form, new static spherically symmetric solutions of the SU(N) Skyrme models. We also discuss some properties of these solutions.
Integrable and superintegrable Hamiltonian systems in magnetic fields
Authors: McSween Eric , Winternitz Pavel
Published: July 2002

In this article we are devoted to the construction of integrable and superintegrable two-dimensional Hamiltonian systems with scalar and vector potentials. All integrable systems with a quadratic polar coordinate type integral of motion are found. Classical trajectories are calculated in integrable cases and compared with those for a system that is not integrable.
Formation and growth dynamics of domains under phase transitions in an external field
Authors: Stefanovich L. I.
Published: July 2002

The formation and the growth dynamics of 180°-domains in ferroelectrics in external field are investigated with the use of the statistical approach within the Ginzburg–Landau model. It is shown that despite the polarizing role of an external field the formation of an intermediate polydomain structure is found to be more preferable than immediate transfer to the monodomain ordering state.
Low-frequency dynamics of cubic crystals with next-nearest neighbor interaction
Authors: Manzheliı̆ E. V. , Syrkin E. S.
Published: July 2002

The influence of next-nearest neighbor interaction on the dispersion characteristics of simple cubic, bcc, and fcc lattices is studied. It is shown that the next-nearest neighbor interaction affects significantly the dynamic characteristics of the above systems. In the scalar model describing the one-magnon excitations in magnetically ordered Heisenberg systems, the inclusion of the second coordination sphere can lead to the emergence of a minimum and an additional peak on the dispersion curves inside the Brillouin zone and to the disappearance of divergence of the density of states. In some cubic lattice models, the inclusion of next-nearest neighbor interaction may lead to a significant variation of the “anisotropy parameter:” in the longwave limit, two transverse branches may coincide or differ sharply from each other, depending on the relation between the force constants characterizing the interaction between the nearest and next-nearest neighbors.
On the evolution of instabilities in the near field of a plane jet
Authors: Hsiao Fei-Bin , Huang Jiann-Min
Published: July 2002

The dynamic behaviors of coherent structures in the near field of a plane jet are extensively studied by hot-wire measurements. The instability evolution for both streamwise and transverse velocity fluctuations are investigated simultaneously. The shear stresses contributed by the individual instabilities are detected by using the cross-spectrum technique. Experimental results show that the jet spreading is governed by the vortex interaction mechanism, and the evolution of the instabilities for the two velocity components is found to perform distinct patterns. The characteristics for the instability evolution cannot be adequately identified from only streamwise velocity fluctuations. The vortex formation and merging locations should be determined from the saturation condition of the transverse velocity fluctuations v′( f ). Results also indicate that the instabilities cannot only absorb energy from the mean flow, but also transfer their energy to the subharmonics, or even back to the mean flow. The variations of these instability shear stresses are associated with the resulting formation and merging processes of the coherent structures. The subharmonic evolution model proposed by Ho [in Proceedings of the Symposium on Numerical and Physical Aspects of Aerodynamic Flow, edited by T. Cebeci (Springer, New York, 1982), p. 521] is then further demonstrated and extended from the energy transfer characteristics between the instability waves. Finally, the near-field acoustic properties are investigated to verify that the interaction processes of the coherent structures are the dominant mechanism for the production of sound.
Mixed convection flow in a heated curved pipe with core
Authors: Karahalios G. T.
Published: July 2002

Mixed convection flow in a heated pipe with a heated inner core is examined. Analytic solutions are derived in power series of the Dean number and the product of Reynolds and Rayleigh numbers. The results are compared with flows in the absence of an axial core. The core modifies the flow and the fluid temperature distribution.
Effect of convective Mach number on mixing of coaxial circular and rectangular jets
Authors: Gutmark E. , Schadow K. C. , Wilson K. J.
Published: July 2002

Rectangular supersonic free and coaxial jets were used to enhance mixing relative to a circular jet in a convective Mach number range of 0.5 to 2.2. The different convective Mach numbers were obtained by changing the central jet gas composition, the temperatures of the inner and outer flows, and the velocity of the coaxial flow. The experimental techniques used were schlieren photography, total pressure, and gas-sampling measurements. For all test conditions the rectangular jets showed substantial improved mixing relative to a circular jet. The free jets showed high mixing in the circumferential region of the jet while the coaxial jet had a high mixing rate inside the central jet.
The motion of long bubbles in tubes of square cross section*
Authors: Kolb W. Blake , Cerro Ramon L.
Published: July 2002

The flow of a long bubble in an otherwise liquid-filled tube is a hydrodynamics problem with interesting practical applications in enhanced oil recovery, the coating of monolithic structures, and more recently the design and operation of three-phase monolithic reactors. For intermediate to large capillary numbers the ‘‘bubble’’ is axisymmetric and the theoretical approach of Bretherton [J. Fluid Mech. 10, 166 (1961)] can be applied if the velocity profile of the fluid flowing between the bubble and the square tube wall is known. The velocity profile can be computed using an infinite series expansion of harmonic polynomials. A film evolution equation—which includes all the terms that are important throughout the entire bubble profile—is integrated using a parametric representation as a function of arclength and free-surface angle. The flow is analyzed and complete bubble profiles are generated. The results are shown to be in good agreement with experiment.
Self-organization in sheared drift-wave turbulence
Authors: Scott Bruce D. , Biglari H. , Terry P. W. , Diamond P. H.
Published: July 2002

Turbulent drift-wave dynamics in a sheared magnetic field are studied using direct numerical simulations. Self-consistent nonadiabatic electron and parallel ion dynamics are both retained in a 2-D sheared-slab model. Magnetic shear causes division of the system into two physically distinct regions with differing cascade dynamics. In a hydrodynamic layer centered upon the mode resonant surface, linear coupling between the density and potential is weak, and the density gradient acts to force spontaneous nonlinear alignment of density fluctuations with the turbulent flows. Further away, shear-induced collisional dissipation constrains the density fluctuations to respond adiabatically, so that the density cannot vary on flow streamlines. The dynamics of the interregion spatial energy flow leads to strong phase coherence between modes at scales larger than the hydrodynamic layer width. Concurrently, the alignment between flows and density fluctuations at scales comparable to the layer width becomes even stronger, increasing the energy input at those scales. This self-organizing tendency is sufficiently robust as to survive competition with a linear external drive. Because of its greater structural freedom, the full nonadiabatic system is much more likely than an adiabatic model with a linear density response to support saturated turbulence below the threshhold for linear instability.
Interaction of bootstrap-current-driven magnetic islands
Authors: Hegna C. C. , Callen J. D.
Published: July 2002

The formation and interaction of fluctuating neoclassical pressure-gradient-driven magnetic islands is examined. The interaction of magnetic islands produces a stochastic region around the separatrices of the islands. This interaction causes the island pressure profile to be broadened, reducing the island bootstrap current and drive for the magnetic island. A model is presented that describes the magnetic topology as a bath of interacting magnetic islands with low to medium poloidal mode number (m≂3–30). The islands grow by the bootstrap current effect and damp due to the interaction of the magnetic islands. The effect of this sporadic growth and decay of the islands (‘‘magnetic bubbling’’) is not normally addressed in theories of plasma transport due to magnetic fluctuations. The nature of the transport differs from statistical approaches to magnetic turbulence since the transfer of particles and heat occur as discrete, abrupt events, not as a random walk process. This model suggests that tokamak experiments have relatively short-lived, coherent, long-wavelength magnetic oscillations present in the steep pressure-gradient regions of the plasma.
Driven magnetic reconnection in the COMPASS-C tokamak
Authors: Morris A. W. , Carolan P. G. , Fitzpatrick R. , Hender T. C. , Todd T. N.
Published: July 2002

The question of the influence of nonaxisymmetric field perturbations on tokamaks is investigated. Recent experiments in the COMPASS-C tokamak [in Proceedings of the 15th Symposium on Fusion Technology, Utrecht (North-Holland, Amsterdam, 1989), Vol. 1, p. 361] with externally applied helical fields reveal that magnetic islands do not appear until the applied field exceeds a certain value, when plasma rotation and confinement are affected. A new resistive magnetohydrodynamic model including plasma rotation now provides an explanation of this threshold, and is quantitatively consistent with experimental results in Ohmic plasmas. The results indicate the tolerable error fields in future tokamaks. The effects of perturbations with various poloidal and toroidal mode numbers have been studied.
Physics optimization of stellarators
Authors: Grieger G. , Lotz W. , Merkel P. , Nührenberg J. , Sapper J. , Strumberger E. , Wobig H. , Burhenn R. , Erckmann V. , Gasparino U. , Giannone L. , Hartfuss H. J. , Jaenicke R. , Kühner G. , Ringler H. , Weller A. , Wagner F. ,   the W7-X Team,   the W7-AS Team
Published: July 2002

The theoretical and experimental development of stellarators has removed some of the specific deficiencies of this configuration, viz., the limitations in β, the high neoclassical transport, and the low collisionless confinement of α particles. These optimized stellarators can best be realized with a modular coil system. The W7-AS experiment [Plasma Phys. Controlled Fusion 31, 1579 (1989)] has successfully demonstrated two aspects of advanced stellarators, the improved equilibrium and the modular coil concept. Stellarator optimization will much more viably be demonstrated by W7-X [Plasma Physics and Controlled Fusion Research, Proceedings of the 12th International Conference, Nice, 1988 (IAEA, Vienna, 1989), Vol. 2, p. 369], the successor experiment presently under design. Optimized stellarators seem to offer an independent reactor option. In addition, they supplement, in a unique form, the toroidal confinement fusion program, e.g., energy transport is anomalous in stellarators too, but possibly more easily understandable in the frame of existing theoretical concepts than in tokamaks.
Ion cyclotron range of frequencies stabilization of sawteeth on Tokamak Fusion Test Reactor
Authors: Phillips C. K. , Hosea J. , Marmar E. , Phillips M. W. , Snipes J. , Stevens J. , Terry J. , Wilson J. R. , Bell M. , Bitter M. , Boivin R. , Bush C. , Cheng C. Z. , Darrow D. , Fredrickson E. , Goldfinger R. , Hammett G. W. , Hill K. , Hoffman D. , Houlberg W. , Hsuan H. , Hughes M. , Jassby D. , McCune D. , McGuire K. , Nagayama Y. , Owens D. K. , Park H. , Ramsey A. , Schilling G. , Schivell J. , Smithe D. N. , Stratton B. , Synakowski E. , Taylor G. , Towner H. , White R. , Zweben S. ,   the TFTR Group
Published: July 2002

Results obtained from experiments utilizing high-power ion cyclotron range of frequencies (ICRF) heating to stabilize sawtooth oscillations on Tokamak Fusion Test Reactor (TFTR) [Hawryluk et al., Plasma Phys. Controlled Fusion 33, 1509 (1991)] are reviewed. The key observations include existence of a minimum ICRF power required to achieve stabilization, a dependence of the stabilization threshold on the relative size of the ICRF power deposition profile to the q=1 volume, and a peaking of the equilibrium pressure and current profiles during sawtooth-free phases of the discharges. In addition, preliminary measurements of the poloidal magnetic field profile indicate that q on axis decreases to a value of 0.55±0.15 after a sawtooth-stabilized period of ∼0.5 sec has transpired. The results are discussed in the context of theory, which suggests that the fast ions produced by the ICRF heating suppress sawteeth by stabilizing the m=1 magnetohydrodynamic (MHD) instabilities believed to be the trigger for the sawtooth oscillations. Though qualitative agreement is found between the observations and the theory, further refinement of the theory coupled with more accurate measurements of experimental profiles will be required in order to complete quantitative comparisons.
Very high confinement discharges in DIII-D after boronization
Authors: Jackson G. L. , Winter J. , Taylor T. S. , Greenfield C. M. , Burrell K. H. , Carlstrom T. N. , DeBoo J. C. , Doyle E. J. , Groebner R. J. , Lao L. L. , Rettig C. , Schissel D. P. , Strait E. J. ,   the DIII-D Research Team
Published: July 2002

A regime of very high confinement (VH mode) has recently been observed in DIII-D with global energy confinement times up to a factor of 3.5 above the ITER89-P L-mode scaling [Nucl. Fusion 30, 1999 (1990)] and 1.5 to 2 times greater than the DIII-D/JET edge-localized-mode-free H-mode scaling relation [Nucl. Fusion 31, 73 (1991)]. These discharges were obtained after boronization in DIII-D and are characterized by low radiated power and Zeff, increasing confinement time during the VH phase of the discharge and low Ohmic target density. The low radiated power and Zeff are a consequence of the boronization. During the VH phase these discharges exhibit an inward shift in the region of highest electric field shear and a large calculated edge bootstrap current. The outer region (ρ≳0.85) is calculated to be in the second stable regime to ideal ballooning modes.
The nonlinear saturation of beam-driven instabilities: Theory and experiment
Authors: Heidbrink W. W. , Duong H. H. , Manson J. , Wilfrid E. , Oberman C. , Strait E. J.
Published: July 2002

Intense fast-ion populations created by neutral-beam injection into a tokamak can destabilize toroidicity-induced Alfvén eigenmodes (TAE modes) or internal kink modes. Experimentally, these modes stabilize when fast ions are ejected from the plasma, producing a cycle of relaxation oscillations about the marginal stability point. A pair of coupled differential equations describes this cycle. This simple theoretical formalism successfully describes the cycles observed during TAE experiments in DIII-D [Plasma Physics Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159].