bluuebunny/crossref_metadata_2025 huggingface dataset:
Phase space structure of triatomic molecules
Authors: Lu Zi-Min , Kellman Michael E.
Published: July 2002

The bifurcation structure is investigated for a Hamiltonian for the three coupled nonlinear vibrations of a highly excited triatomic molecule. The starting point is a quantum Hamiltonian used to fit experimental spectra. This Hamiltonian includes 1:1 Darling–Dennison resonance coupling between the stretches, and 2:1 Fermi resonance coupling between the stretches and bend. A classical Hamiltonian is obtained using the Heisenberg correspondence principle. Surfaces of section show a pronounced degree of chaos at high energies, with a mixture of chaotic and regular dynamics. The large-scale bifurcation structure is found semianalytically, without recourse to numerical solution of Hamilton’s equations, by taking advantage of the fact that the spectroscopic Hamiltonian has a conserved polyad quantum number, corresponding to an approximate constant of the motion of the molecule. Bifurcation diagrams are analyzed for a number of molecules including H2O, D2O, NO2, ClO2, O3, and H2S.
Relaxation without spin diffusion in fractal systems: Polymers in glassy solutions
Authors: Tabti T. , Goldman M. , Jacquinot J.-F. , Fermon C. , Le Goff G.
Published: July 2002

We describe the nuclear relaxation of protons by paramagnetic centers in glassy solutions of polymers. Both the protons and the paramagnetic radicals are on the polymers, and the solvent is fully deuterated. Two cases have been analyzed, that when the relaxing centers are randomly distributed, and that when each polymer has a single center grafted at one end. The analysis was made for dilute and semi-dilute solutions of polymers. Experiments performed on poly-2 vinyl pyridine (P2VP) and on polystyrene yield results in agreement with theory, both as regards the NMR and the polymer models.
The oxygen vacancy at the surface and in bulk MgO: An embedded-cluster study
Authors: Scorza Erminia , Birkenheuer Uwe , Pisani Cesare
Published: July 2002

The oxygen vacancy in bulk MgO and at its (001) surface have been studied by means of the EMBED program which adopts an embedded-cluster approach in the frame of the Hartree–Fock (HF) approximation [Comp. Phys. Comm. 82, 139 (1994); 96, 152 (1996)]: A spin restricted (RHF) or unrestricted (UHF) method has been used according to whether the vacancy contains an even number (F and F2+ centers) or an odd number (F+ center) of electrons. The semi-infinite crystal has been simulated with a three-layer slab. Particular attention has been given to the optimization of the basis functions which serve to describe the trapped electron(s) in the vacancy. The correlation energy was estimated using second order Mo/ller–Plesset theory. The three electronic configurations have been studied by allowing for relaxation of all neighboring ions. For the paramagnetic center, spin density data are provided and discussed with reference to results from EPR experiments and molecular cluster calculations.
Simulation of the hard-sphere crystal–melt interface
Authors: Davidchack Ruslan L. , Laird Brian B.
Published: July 2002

In this work, we examine in detail the structure and dynamics of the face-centered cubic (100) and (111) crystal–melt interfaces for systems consisting of approximately 104 hard spheres using molecular dynamics simulation. A detailed analysis of the data is performed to calculate density, pressure, and stress profiles (on both fine and coarse scales), as well as profiles for the diffusion and orientational ordering. The strong dependence of the coarse-grained profiles on the averaging procedure is discussed. Calculations of 2-D density contours in the planes perpendicular to the interface show that the transition from crystal to fluid occurs over a relatively narrow region (over only 2–3 crystal planes) and that these interfacial planes consist of coexisting crystal- and fluidlike domains that are quite mobile on the time scale of the simulation. We also observe the creation and propagation of vacancies into the bulk crystal.
On the adiabatic to diabatic states transformation in the presence of a conical intersection: A most diabatic basis from the solution to a Poisson’s equation. I
Authors: Sadygov Rovshan G. , Yarkony David R.
Published: July 2002

We report the first determination of a “most” diabatic basis for a triatomic molecule based exclusively on ab initio derivative couplings that takes careful account of the limitations imposed by the nonremovable part of those couplings. Baer [Chem. Phys. Lett. 35, 112 (1975)] showed that an orthogonal transformation from adiabatic states to diabatic states cannot remove all the derivative coupling unless the curl of the derivative coupling vanishes. Subsequently, Mead and Truhlar [J. Chem. Phys. 77, 6090 (1982)] observed that this curl does not, in general, vanish so that some of the derivative coupling is nonremovable. This observation and the historical lack of efficient algorithms for the evaluation of the derivative coupling led to a variety of methods for determining approximate diabatic bases that avoid computation of the derivative couplings. These methods neglect an indeterminate portion of the derivative coupling. Mead and Truhlar also observed that near an avoided crossing of two states the rotation angle to a most diabatic basis, i.e., the basis in which the removable part of the derivative coupling has been transformed away, could be obtained from the solution of a Poisson’s equation requiring only knowledge of the derivative couplings. Here a generalization of this result to the case of a conical intersection is used to determine a most diabatic basis for a section of the 1 1A′ and 2 1A′ potential energy surfaces of HeH2 that includes the minimum energy point on the seam of conical intersection.
Pressure calculation in polar and charged systems using Ewald summation: Results for the extended simple point charge model of water
Authors: Hummer Gerhard , Gro/nbech-Jensen Niels , Neumann Martin
Published: July 2002

Ewald summation and physically equivalent methods such as particle-mesh Ewald, kubic-harmonic expansions, or Lekner sums are commonly used to calculate long-range electrostatic interactions in computer simulations of polar and charged substances. The calculation of pressures in such systems is investigated. We find that the virial and thermodynamic pressures differ because of the explicit volume dependence of the effective, resummed Ewald potential. The thermodynamic pressure, obtained from the volume derivative of the Helmholtz free energy, can be expressed easily for both ionic and rigid molecular systems. For a system of rigid molecules, the electrostatic energy and the forces at the atom positions are required, both of which are readily available in molecular dynamics codes. We then calculate the virial and thermodynamic pressures for the extended simple point charge (SPC/E) water model at standard conditions. We find that the thermodynamic pressure exhibits considerably less system size dependence than the virial pressure. From an analysis of the cross correlation between the virial and thermodynamic pressure, we conclude that the thermodynamic pressure should be used to drive volume fluctuations in constant-pressure simulations.
An ab initio path integral molecular dynamics study of double proton transfer in the formic acid dimer
Authors: Miura Shinichi , Tuckerman Mark E. , Klein Michael L.
Published: July 2002

Double proton transfer in the formic acid dimer has been investigated with Car–Parrinello ab initio molecular dynamics calculations. The electronic structure of the dimer has been obtained using gradient-corrected density functional theory based on the B-LYP (Becke exchange [Phys. Rev. A 38, 3098 (1988)] and Lee–Yang–Parr correlation [Phys. Rev. B 37, 785 (1988)] functional. The optimized equilibrium and saddle-point geometries, obtained by simulated annealing, are in good agreement with previous ab initio quantum chemical predictions and experiment. Thermal and quantum fluctuations of nuclei along the double proton transfer reaction path have also been investigated at T=300 K. Thermal fluctuations give a broad distribution of nuclei around the minimum energy path on the potential energy surface. Quantum fluctuations, investigated using ab initio path integral molecular dynamics, make the distribution even broader around the equilibrium structure, and cause the distribution to deviate appreciably from the minimum energy path on approaching the reaction barrier. In particular, the system passes through higher energy regions than the geometrical saddle point by tunneling; an observation which is consistent with the conventional understanding of heavy–light–heavy mass combination reactions. While there is asynchronous movement of the two protons around the equilibrium structure, synchronous movement becomes relevant on approaching the reaction barrier.
Electronic absorption spectra of C2nH−, C2n−1N− (n=4–7), and C2n−1N (n=3–7) chains in neon matrices
Authors: Grutter Michel , Wyss Muriel , Maier John P.
Published: July 2002

The Σ+1←XΣ+1 electronic transition of the C2nH− and C2n−1N− (n=4–7) anion chains has been observed following mass selection and codeposition with excess neon at 6 K. Photodetachment of the electron resulted in the detection of a band system due to the neutral C2n−1N radical. The spectra suggest that C7N, like C5N, has a Σ2 ground state. The B 2Π←X 2Π transition is detected for the larger C2n−1N (n=5–7) chains. These appear at slightly higher energies than those of the isoelectronic C2nH radicals and show similar spectral features. Several infrared transitions of the anions have also been observed.
A path integral centroid molecular dynamics study of nonsuperfluid liquid helium-4
Authors: Miura Shinichi , Okazaki Susumu , Kinugawa Kenichi
Published: July 2002

Path integral centroid molecular dynamics (CMD) calculation for normal liquid 4He has been performed. Dynamical behavior of the liquid at 4 K, which can not be reproduced by classical approximation, was well described by the CMD formalism. The calculated self-diffusion coefficient was found to be 5.06±0.04×10−5 cm2/s, which is in the same order of magnitude as that of ordinary liquids. Relaxation function of density fluctuation has also been calculated within the CMD approximation. Detailed comparison between the static susceptibility function χ̂(k) and the static structure factor of the centroid density Ŝ(c)(k) has been made. These correspond to the initial value of the exact and the centroid relaxation functions, respectively. For small k (⩽1.0 Å−1), χ̂(k) is well approximated by Ŝ(c)(k). For larger k, both the correlation functions have identical peak position. However, the intensity of Ŝ(c)(k) is systematically larger than that of χ̂(k). The calculated dynamic structure factor has been compared with the spectrum obtained from neutron scattering experiment. The agreement is satisfactory for 0.2<k<2.2 Å−1. The calculated peak frequency as a function of k, i.e., the dispersion relation, has a minimum around 1.9 Å−1, where the static correlation function shows maximum intensity. This behavior has also been experimentally observed for the dispersion relation for superfluid 4He. The peak continuously loses collective character and shows single-particle behavior with increasing k around the minimum. This behavior gives rise to the minimum in the dispersion relation for normal liquid 4He. The spectrum becomes narrow as the peak approaches the minimum, showing that the single-particle contribution becomes dominant in the dynamic structure factor. This narrowing is widely found among classical liquid; but is not observed in the spectrum of the superfluid 4He, indicating that the excitation around the minimum for the superfluid may have a different molecular origin than that for normal liquid 4He.
Ultrafast exciton and excited-exciton dynamics in
J
-aggregates of three-level porphyrin molecules
Authors: Misawa Kazuhiko , Kobayashi Takayoshi
Published: July 2002

We observed the ultrafast response of exciton (S1-exciton) and excited-exciton (S2-exciton) in one-dimensional J-aggregates of three-level porphyrin molecules by femtosecond pump–probe spectroscopy. The decay profiles of the nonlinear response can be fitted to a sum of instantaneous response and two exponential decay components with time constants of 1.3±0.1 and 40±1 ps. The former and latter were found to correspond to the lifetimes of S2- and S1-excitons, respectively. The origins of the nonlinearity were attributed to the following three contributions: (1) coherent effects between the pump and probe via one-photon virtual S1-exciton, (2) induced absorption of real S2-excitons generated by two photons, and (3) induced absorption of real S1-exciton.
The aurophilic attraction as interpreted by local correlation methods
Authors: Runeberg Nino , Schütz Martin , Werner Hans-Joachim
Published: July 2002

The nature of the aurophilic interaction is studied by applying local second-order Mo/ller–Plesset perturbation theory (LMP2) on model dimers of [X–Au–PH3]2 (X=H, Cl) type. The possibility to decompose the correlation contribution of the interaction energy in the dimer (A–B) into different excitation classes reveals that the dispersion contribution (A→A′,B→B′) is accompanied by an almost equally important ionic component (A→A′,B→A′), at shorter distances. Double excitations where at least one electron originates from the gold 5d orbitals account for almost 90% of the attraction. Relativistic effects amount to 28% of the binding energy and can be traced to arise almost exclusively from the relativistic expansion of gold d-shells.
NMR study of InP quantum dots: Surface structure and size effects
Authors: Tomaselli M. , Yarger J. L. , Bruchez M. , Havlin R. H. , deGraw D. , Pines A. , Alivisatos A. P.
Published: July 2002

We report the results of P31 NMR measurements on trioctylphosphine oxide (TOPO) passivated InP quantum dots. The spectra show distinct surface-capping sites, implying a manifold of crystal–ligand bonding configurations. Two In 31P surface components are resolved and related to different electronic surroundings. With decreasing particle size the In 31P core resonance reveals an increasing upfield chemical shift related to the overall size dependence of the InP electronic structure.
The correlation, relativistic, and vibrational contributions to the dipole moments, polarizabilities, and first and second hyperpolarizabilities of ZnS, CdS, and HgS
Authors: Raptis S. G. , Papadopoulos M. G. , Sadlej A. J.
Published: July 2002

The dipole moments, dipole polarizabilities, and the first and second hyperpolarizabilities of the Group IIb sulfides have been calculated by using different high-level-correlated methods and including both the relativistic and vibrational contributions. The electron correlation effects have been studied at the levels of the second-order Møller–Plesset perturbation theory and the coupled-cluster methods. The relativistic contributions and the interference relativistic-correlation effects have been accounted for by using the spin-averaged Douglas–Kroll approximation. The vibrational properties (pure vibrational contributions and the zero-point vibrational averaging corrections) have been computed using CCSD(T) theory with and without relativistic corrections. The present pure electronic nonrelativistic results exhibit essentially the same pattern as that observed for similar molecules studied earlier. Most of the relativistic effects on dipole moments and dipole polarizabilities is accounted for at the level of the SCF approximation and rapidly increases with the nuclear charge of the heavy atom. The contribution of the relativistic-correlation interference terms has been found to be quite significant for axial components of the first and second dipole hyperpolarizabilities. All the properties reported here are static. This is the first study which reports on the relativistic contributions to hyperpolarizabilities as well as on vibrational effects upon both polarizabilities and hyperpolarizabilities of heavy metal (Group IIb) involving compounds. Thus the reported results add to the knowledge and understanding of the importance of the electron correlation, relativistic, and vibrational effects on electric properties of heavy molecules and extend the corresponding data beyond the linear response approximation. The reliability of the computed data is discussed in terms of the underlying approximations and limitations of methods used in this study.
On phase factors and geometric phases in isotopes of H3: A line integral study
Authors: Xu ZongRong , Baer Michael , Varandas António J. C.
Published: July 2002

In this work we apply the line-integral technique to study possible geometric phase effects in the 2×2 diabatic double many-body expansion (DMBE) potential energy surface of three hydrogenic systems, namely, H3, DH2, and HD2. First, we show that the phase obtained by employing the line-integral method is identical (up to a constant) to the ordinary diabatic angle of the orthogonal transformation that diagonalizes the diabatic potential matrix. Next this angle is studied numerically along the line formed by fixing the two hyperspherical coordinates ρ and θ and letting φ change along the interval [0, 2π]. We find that in the H3 system, where this line always encircles the seam, the corresponding line integral always produces the value π for the geometric (Berry) phase. In the cases of the two isotopic systems we usually find the same results, but we also verify that for substantial regions in configuration space these lines do not encircle the seam and that, therefore, the line integrals produce the value of zero for the geometric phase. Analyzing the results, we establish that the Longuet-Higgins phase, which is usually assumed to be equal to φ/2, is in general significantly different from this value for all studied mass combinations.
The binding of CO to nickel clusters. I. Determination of saturation coverages
Authors: Parks E. K. , Kerns K. P. , Riley S. J.
Published: July 2002

The reactions of small nickel clusters Nin (n=3–60) with carbon monoxide are studied in a gas-phase flow-tube reactor. Cluster coverage is determined as a function of CO pressure at temperatures between −160 and 20 °C. The reactions are kinetically controlled under these conditions, but the CO uptake is characterized by a transition from a fast kinetics to a slow kinetics process. Sticking probabilities in the fast kinetics region are near unity at low temperature. The coverage at the transition is consistent with random filling of the cluster surface with van der Waals CO molecules in a standing up configuration with the carbon end toward the metal. Higher coverages in most cases are a consequence of changes in nickel cluster structure to more open ones having larger surface areas.
Computer simulation studies of anisotropic systems. XXXII. Field-induction of a smectic A phase in a Gay–Berne mesogen
Authors: Luckhurst G. R. , Saielli G.
Published: July 2002

Molecular field theory predicts the induction of a smectic A phase by the application of a field, either magnetic or electric, to a nematic phase. This intriguing behavior results from an enhancement of the orientational order which is coupled to the translational order and so shifts the smectic A-nematic transition. To test this prediction we have investigated a system of Gay–Berne mesogenic molecules subject to an applied field of second rank using isothermal–isobaric Monte Carlo simulations. The results of our calculations are compared with the Kventsel–Luckhurst–Zewdie molecular field theory of smectogens, modified to include the effect of an external field. We have also used the simulations to explore the possibility of inducing more ordered smectic phases with stronger fields.
Semiclassical study of the isomerization states of HCP
Authors: Joyeux Marc , Sugny Dominique , Tyng Vivian , Kellman Michael E. , Ishikawa Haruki , Field Robert W. , Beck Christian , Schinke Reinhard
Published: July 2002

The vibrational spectrum of HCP (phosphaethyne) is studied and analyzed in terms of a 1:2 resonance effective Hamiltonian. The parameters of the model Hamiltonian are determined by fitting 361 out of the first 370 energy levels obtained from diagonalization of the full Hamiltonian, which is based on a newly calculated potential-energy surface with near spectroscopic accuracy. It is demonstrated that all features characteristic of the approach to the HCP↔CPH isomerization, such as the strong mixing between the bending and CP-stretching motions, the appearance of “isomerization states” (large amplitude bending motion) at intermediate energies, and the diagnostically significant appearance of a zig–zag pattern in the energy spacings between neighboring levels within each polyad, are quantitatively reproduced by the effective Hamiltonian. The semiclassical analysis of the model Hamiltonian for specific combinations of the HC-stretch and polyad quantum numbers explains all of the observed features of the full Hamiltonian in terms of stable and unstable periodic orbits. In particular, the birth of the isomerization states is found to be related to a saddle-node bifurcation of the classical phase space. The connection with the “polyad phase sphere” representation of quantum polyads is also discussed.
Singularities in the behavior of density functionals in predictions of singlet biradicals: The 1,2-dichalcogenins
Authors: Orlova Galina , Goddard John D.
Published: July 2002

The performance of conventional exchange-correlation functionals for the description of singlet biradicals which possess a small admixture of an auxiliary electronic state was examined using a broken symmetry spin unrestricted density functional approach. A pure density functional, BLYP, and the hybrid B3LYP and BHandHLYP exchange-correlation functionals were employed to study the thermal ring opening of 1,2-dichalcogenins and the subsequent formation of the bicyclic products. A stepwise mechanism was predicted for the reaction of the 1,2-dithiin and 2-selenathiin rings and no biradical structures were located. For 1,2-diselenin, the biradical stepwise mechanism competes energetically with a concerted reaction which is slightly favored. For 1,2-ditellurin, a high-energy open intermediate with considerable biradical character was located. The hybrid functionals show an increase in biradical character with an increase in the percentage of Hartree–Fock exchange incorporated into the exchange functional. The instability of the restricted Kohn–Sham solutions was used to indicate the existence of biradical structures with lower energy. Interesting incorrect behavior of certain of the hybrid functionals was noted. The instability of the restricted BHandHLYP solution results from too large a contribution of Hartree–Fock exchange. An unexpected stability of the restricted B3LYP solution was found and attributed to cancellation of two different sources of instability: one from the pure density functional and the other from the inclusion of Hartree–Fock exchange.
Symmetry transformations, isovectors, and conservation laws
Authors: Caviglia Giacomo
Published: July 2002

A system of second-order partial differential equations is considered. It is shown that a conservation law may be associated with any pair consisting of (i) a symmetry transformation, (ii) a symmetry transformation if the system is self-adjoint, a solution to the adjoint of the equations of variation otherwise. Such conservation laws continue to hold when symmetry transformations are replaced by isovectors. It is also proved that isovectors identify additional conservation laws by deformation of a given one, whence it follows that there exists a natural conserved current associated with every isovector. Also an application is made to find conserved currents for the Navier–Stokes equations.
A metric space construction for the boundary of space-time
Authors: Meyer David A.
Published: July 2002

A distance function between points in space-time is defined and used to consider the manifold as a topological metric space. The properties of the distance function are investigated: conditions under which the metric and manifold topologies agree, the relationship with the causal structure of the space-time and with the maximum lifetime function of Wald and Yip, and in terms of the space of causal curves. The space-time is then completed as a topological metric space; the resultant boundary is compared with the causal boundary and is also calculated for some pertinent examples.
The structure of the Clifford algebra
Authors: Wilmot G. P.
Published: July 2002

The properties of the Clifford algebra are concisely summarized in four identities that extend the usual Lie algebra to the entire algebra. This formulation may be used to analyze the general structure of the Clifford algebra, but it is found that the symmetry properties are not consistent with the geometrical content. The extension of the graded Lie algebra to the entire algebra generates a geometrical algebra which simplifies the analysis of the structure of the Clifford algebra. This produces a direct proof of the fundamental theorem that relates the Clifford and Grassmann algebras via the Pfaffian.
Isometric embedding of the spherically symmetric Stephani universe: Some explicit examples
Authors: Da̧browski Mariusz P.
Published: July 2002

Some general properties of the local isometric embedding of the spherically symmetric Stephani universe are examined. A representative set of the explicit embeddings is found. It is composed of the embeddings of the Stephani–de Sitter universe (the de Sitter universe with unusual foliation) and the embeddings of the really inhomogeneous (though still spherically symmetric) Stephani universe. In order to investigate the structure of infinity and the light propagation in space-time each embedding is accompanied by a suitable Penrose diagram. It is realized that apart from both the density and pressure big-bang-type singularities, also the finite-density singularities of pressure appear in the model. The latter singularities are carefully discussed because they exist in the general, not even spherically symmetric Stephani universe. Under some conditions these singularities can be avoided.
Structured spaces and their application to relativistic physics
Authors: Heller Michael , Sasin Wieslaw
Published: July 2002

A sheaf of functions on a topological space is called a differential structure if it satisfies an axiom of a closure with respect to composition with the Euclidean functions. A differential structure on a nonempty set is called a structured space. It is a generalization of the smooth manifold concept and of an earlier concept of differential space. Differential geometry on structured spaces is developed (tangent space, vector fields, differential forms, exterior algebra, linear connection, curvature, and torsion). Some of its techniques are applied to the classical singularity problem in general relativity. It turns out that Einstein’s equations can be defined on space–times with singularities. This can have important consequences for the search of the quantum theory of gravity.
The functional–analytic versus the functional–integral approach to quantum Hamiltonians: The one-dimensional hydrogen atoma)
Authors: Fischer Werner , Leschke Hajo , Müller Peter
Published: July 2002

The capabilities of the functional–analytic and of the functional–integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics. Differences are worked out by taking the one-dimensional hydrogen atom as an example, that is, a point mass on the Euclidean line subjected to the inverse–distance potential. This particular choice is made with the intent to clarify a long-lasting discussion about its spectral properties. In fact, for the four-parameter family of possible Hamiltonians the corresponding energy-dependent Green functions are derived in closed form. The multiplicity of Hamiltonians should be kept in mind when modeling certain experimental situations as, for instance, in quantum wires.
Lie symmetries of finite-difference equations
Authors: Floreanini Roberto , Vinet Luc
Published: July 2002

Discretizations of the Helmholtz, heat, and wave equations on uniform lattices are considered in various space–time dimensions. The symmetry properties of these finite-difference equations are determined and it is found that they retain the same Lie symmetry algebras as their continuum limits. Solutions with definite transformation properties are obtained; identities and formulas for these functions are then derived using the symmetry algebra.
Quantization of diffeomorphism invariant theories of connections with local degrees of freedom
Authors: Ashtekar Abhay , Lewandowski Jerzy , Marolf Donald , Mourão José , Thiemann Thomas
Published: July 2002

Quantization of diffeomorphism invariant theories of connections is studied and the quantum diffeomorphism constraint is solved. The space of solutions is equipped with an inner product that is shown to satisfy the physical reality conditions. This provides, in particular, a quantization of the Husain–Kuchař model. The main results also pave the way to quantization of other diffeomorphism invariant theories such as general relativity. In the Riemannian case (i.e., signature ++++), the approach appears to contain all the necessary ingredients already. In the Lorentzian case, it will have to be combined in an appropriate fashion with a coherent state transform to incorporate complex connections.
On tractability of path integration
Authors: Wasilkowski Grzegorz W. , Woźniakowski Henryk
Published: July 2002

Many applications require approximate values of path integrals. A typical approach is to approximate the path integral by a high dimensional integral and apply a Monte Carlo (randomized) algorithm. However, Monte Carlo algorithm requires roughly ε−2 integrand evaluations to provide an ε approximation. Moreover, the error bound of ε is guaranteed only in a stochastic sense. Do we really need to use randomized algorithms for path integrals? Perhaps, we can find a deterministic algorithm that is more effective even in the worst case setting. To answer this question, we study the worst case complexity of path integration, which, roughly speaking, is defined as the minimal number of the integrand evaluations needed to compute an approximation with error at most ε. We consider path integration with respect to a Gaussian measure, and for various classes of integrands. Tractability of path integration means that the complexity depends polynomially on 1/ε. We show that for the class of r times Frechet differentiable integrands, tractability of path integration holds iff the covariance operator of the Gaussian measure has finite rank. Hence, if the Gaussian measure is supported on an infinite dimensional space then path integration is intractable.

In this case, there exists no effective deterministic algorithm, and the use of randomized algorithms is justified. In fact, for this class of integrands, the classical Monte Carlo algorithm is (almost) optimal and the complexity in the randomized setting is proportional to ε−2. On the other hand, for a particular class of entire integrands, the worst case complexity of path integration is at most of order ε−p with p depending on the Gaussian measure. Hence, path integration is now tractable. Furthermore, for any Gaussian measure, the exponent p is less than or equal to 2. For the Wiener measure, p=2/3. For this class, we provide effective deterministic algorithms which solve the path integration problem with (worst case) cost that is usually much less than the (randomized) cost of the classical Monte Carlo algorithm.
Prepotential of N=2 SU(2) Yang–Mills gauge theory coupled with a massive matter multiplet
Authors: Ohta Yűji
Published: July 2002

We discuss the N=2 SU(2) Yang–Mills theory coupled with a massive matter in the weak coupling. In particular, we obtain the instanton expansion of its prepotential. Instanton contributions in the mass-less limit are completely reproduced. We study also the double scaling limit of this massive theory and find that the prepotential with instanton corrections in the double scaling limit coincides with that of N=2 SU(2) Yang–Mills theory without matter.
Universal and integrable nonlinear evolution systems of equations in 2+1 dimensions
Authors: Maccari Attilio
Published: July 2002

Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio–temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a “universal” character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part.
The Maxwell–Vlasov equations in Euler–Poincaré form
Authors: Cendra Hernán , Holm Darryl D. , Hoyle Mark J. W. , Marsden Jerrold E.
Published: July 2002

Low’s well-known action principle for the Maxwell–Vlasov equations of ideal plasma dynamics was originally expressed in terms of a mixture of Eulerian and Lagrangian variables. By imposing suitable constraints on the variations and analyzing invariance properties of the Lagrangian, as one does for the Euler equations for the rigid body and ideal fluids, we first transform this action principle into purely Eulerian variables. Hamilton’s principle for the Eulerian description of Low’s action principle then casts the Maxwell–Vlasov equations into Euler–Poincaré form for right invariant motion on the diffeomorphism group of position-velocity phase space, R6. Legendre transforming the Eulerian form of Low’s action principle produces the Hamiltonian formulation of these equations in the Eulerian description. Since it arises from Euler–Poincaré equations, this Hamiltonian formulation can be written in terms of a Poisson structure that contains the Lie–Poisson bracket on the dual of a semidirect product Lie algebra. Because of degeneracies in the Lagrangian, the Legendre transform is dealt with using the Dirac theory of constraints. Another Maxwell–Vlasov Poisson structure is known, whose ingredients are the Lie–Poisson bracket on the dual of the Lie algebra of symplectomorphisms of phase space and the Born–Infeld brackets for the Maxwell field. We discuss the relationship between these two Hamiltonian formulations. We also discuss the general Kelvin–Noether theorem for Euler–Poincaré equations and its meaning in the plasma context.
A new integrable Davey–Stewartson-type equation
Authors: Maccari Attilio
Published: July 2002

A new integrable nonlinear partial differential equation (PDE) in 2+1 dimensions is derived starting from the Konopelchenko–Dubrovsky equation. We use an asymptotically exact reduction method based on Fourier expansion and spatio-temporal rescaling and obtain a new integrable Davey–Stewartson-type equation. In order to demonstrate the integrability of the new equation by the inverse scattering method, we apply the reduction technique to the Lax pair of the Konopelchenko–Dubrovsky equation and find the corresponding Lax pair of the new equation. The new equation reduces to the Davey–Stewartson or the nonlinear Schrodinger equation by appropriate limits.
Quantum groups and noncommutative geometry
Authors: Majid Shahn
Published: July 2002

Quantum groups emerged in the latter quarter of the 20th century as, on the one hand, a deep and natural generalization of symmetry groups for certain integrable systems, and on the other as part of a generalization of geometry itself powerful enough to make sense in the quantum domain. Just as the last century saw the birth of classical geometry, so the present century sees at its end the birth of this quantum or noncommutative geometry, both as an elegant mathematical reality and in the form of the first theoretical predictions for Planck-scale physics via ongoing astronomical measurements. Noncommutativity of space–time, in particular, amounts to a postulated new force or physical effect called cogravity.
An improved algebraic Reynolds stress model and corresponding nonlinear stress model
Authors: Taulbee Dale B.
Published: July 2002

An improved algebraic Reynolds stress model is developed from the modeled dynamic equations for the Reynolds stress. The improved model more closely represents the original Reynolds stress model equation than the standard algebraic Reynolds stress model over the range of time scales for the turbulence and mean flow strain field. Quasi-non-local convective effects are also included in the formulation. Explicit solutions to the algebraic Reynolds stress model equation set, in the form of nonlinear stress-strain models, are presented for two and three dimensions.
Generalized Smagorinsky model for anisotropic grids
Authors: Scotti Alberto , Meneveau Charles , Lilly Douglas K.
Published: July 2002

The Smagorinsky subgrid model is revised to properly account for grid anisotropy, using energy equilibrium considerations in isotropic turbulence. For moderate resolution anisotropies, Deardorff’s estimate involving an equivalent grid scale Δeq=(Δ1Δ2Δ3)1/3 is given a rigorous basis. For more general grid anisotropies, the Smagorinsky eddy viscosity is recast as νT=[csΔeqf(a1, a2)]2‖S̃‖, where f(a1,a2) is a function of the grid aspect ratios a1 and a2, and ‖S̃‖ is the resolved strain rate magnitude. The asymptotic behavior of νT at several limits of the aspect ratios are examined. Approximation formulas are developed so that f(a1,a2) can easily be evaluated in practice, for arbitrary values of a1 and a2. It is argued that these results should be used in conjunction with the dynamic model of Germano et al. whenever the anisotropy of the test-filter differs significantly from that of the basic grid.
Nozzle flows of dense gases
Authors: Cramer M. S. , Fry R. N.
Published: July 2002

Numerical solutions for steady inviscid flows in conventional converging–diverging nozzles are obtained. The fluids considered are Bethe–Zel’dovich–Thompson fluids, i.e., those having specific heats so large that the fundamental derivative of gas dynamics is negative over a finite range of pressures and temperatures. Three general classes of flow are delineated which include two nonclassical types in addition to the usual classical flows; the latter are qualitatively similar to those of perfect gases. The nonclassical flows are characterized by isentropes containing as many as three sonic points. Numerical solutions depicting finite-strength expansion shocks, steady flows with shock waves standing upstream of the nozzle throat, and steady flows containing as many as three shock waves are presented. Flows having arbitrarily large-exit Mach numbers are found to be possible only if a sonic expansion shock is formed in the nozzle. This observation contrasts with prediction based on the perfect gas theory which states that the occurrence of shock waves always results in a subsonic exit flow.
Electric field profile of a Compact Helical System Heliotron/Torsatron plasma with tangential neutral beam injection
Authors: Ida K. , Yamada H. , Iguchi H. , Hidekuma S. , Sanuki H. , Yamazaki K. ,   the CHS Group
Published: July 2002

The radial electric field profiles derived from poloidal rotation velocity are compared with neoclassical estimates for a plateau regime plasma heated by a tangentially injected neutral beam in the Compact Helical System Heliotron/Torsatron device [Plasma Physics and Controlled Nuclear Fusion Research 1988 (IAEA, Vienna, 1989), Vol. 2, p. 411]. The measured electric field (Er) is more negative than the neoclassical prediction, especially near the plasma periphery. A gradient of radial electric field (∂Er/∂r) in this region is found to be more negative in the plasma with higher electron density. Although the corresponding poloidal rotation velocity is too small to trigger the L/H transition, these negative Er and ∂Er/∂r are associated with a reduction of thermal electron conductivity.
JT-60U latest results and future prospects
Authors: Ninomiya H. ,   the JT-60 Team
Published: July 2002

Experimental results achieved in the initial operation of JT-60U [Plasma Devices Operat. 1, 43 (1990)] are described in this paper. Experiments of JT-60U were initiated in March and deuterium experiments started in the middle of July. Multivariable noninteracting control was adopted to allow independent control despite the strong mutual coupling between the Ohmic heating coils and the vertical field coils. Well-controlled divertor discharges were successfully obtained using this method and discharges with plasma current up to 5 MA were achieved. In neutral beam heating experiments with PNBI≲22 MW, plasma stored energies Wdia of up to 4.8 MJ were obtained for 4 MA discharges. The high-βp regime with hot ions and enhanced confinement was investigated. The maximum βp reached 2.3, the maximum Ti of 20 keV was achieved and τE was improved to about 2.7 times as large as that of ITER89-P scaling [Nucl. Fusion 30, 1999 (1990)]. The maximum neutron rate of 1.3×1016 n/sec was also obtained in the highest-βp discharge. The corresponding QDD and the equivalent QDT were 8.9×10−4 and ∼0.20, respectively. Localized heat load in both toroidal and poloidal directions was clearly identified as ripple loss, and this was the first measurement of heat load mainly due to ripple trapped loss consistent with calculated results. Divertor plasma profiles measured with Langmuir probes show significant in–out asymmetry.
Joint European Torus results with both fast and lower-hybrid wave consequences for future devices
Authors: Jacquinot J. , Bures M. ,   the JET Team
Published: July 2002

Heating and current drive studies were performed during the JET [Phys Fluids B 3, 2209 (1991)] 1990/91 operation using two large systems capable of generating either fast waves in the ion cyclotron range of frequencies (ICRF) or slow waves at a frequency above the lower-hybrid resonance (LH). The maximum wave power coupled to the torus reached 22 MW for ICRH and 2.4 MW for LH. The results obtained in plasma heating experiments qualify ICRH as a prime candidate for heating reactor grade plasmas. A centrally localized deposition profile in the cyclotron damping regime was demonstrated in a wide range of plasma density resulting in (i) record value nd τE Ti0 ≂ 7.8 × 1020 m−3 sec keV in ‘‘thermal’’ conditions Ti = Te ≂ 11 keV at high central densities generated by pellet injection; (ii) large normalized confinement 2.5 ≤ τE/τGoldston≤4. The large values of τE/τGoldston are reached in H-mode discharges (I≤1.5 MA) with large bootstrap current fraction IBS/I ≤ 0.7 ± 0.2; (iii) the highest to date D–3He fusion power (140 kW) generated with 10–14 MW of ICRH in the L-mode regime at the 3He cyclotron frequency. All specific impurity generations have been reduced to negligible levels by proper antenna design and the generic difficulty of wave–plasma coupling has been greatly reduced using feedback loops controlling in real time the antenna circuits and the plasma position.

Current drive efficiencies γ=ICD〈ne〉R/P ≂ 0.4 × 1020 m−2 A/W have been reached in 1.5 MA L-mode plasma with zero loop voltage by combining LHCD and ICRH. Fast electrons are driven by LHCD alone to tail temperatures of up to 70 keV. The fast electron density is peaked in the plasma center at lower densities (ne0 ≤ 2.6 × 1019 m−3) and high field (Bφ ∼ 3.1 T). In these conditions, the fast electrons are further accelerated (even at zero loop voltage) to tail temperatures above 150 keV by heating the plasma with ICRF in monopole phasing. Direct electron damping of the fast wave on the fast electrons created by LH appears to be the driving mechanism of this synergism which produces fast wave current drive even without phasing the ICRH antennas. Finally, the first results obtained in the minority current drive regime are reported. The sawtooth instability is considerably modified when the resonance is located near the q=1 resonance. The effect is reversed from stabilization to destabilization when the phase of the ICRH antennas is reversed from +90° to −90°.
Stability of high-energy particle plasmas to magnetohydrodynamic-like modes
Authors: Berk H. L. , Wong H. V.
Published: July 2002

The stability of symmetric mirror systems, such as tandem mirrors and multiple mirrors (or equivalently, bumpy tori of large aspect ratio), is investigated when stabilization is attempted with high-energy particles. The analysis is derived from a zero Larmor radius variational form, and the stability criteria for eikonal and long wavelength layer modes are obtained. For eikonal modes it is shown that line bending can stabilize the low l-number modes and together with finite Larmor radius effects discussed elsewhere, complete stabilization is possible. For disk-shaped plasma pressure profiles it is shown that currents induced by conducting walls can stabilize the l=1 layer mode, while the higher-l layer modes require finite Larmor radius effects for stabilization. For thin, ring-like pressure profiles, wall stabilization of the l=1 mode cannot be achieved, although the line bending term reduces the core beta limit and the growth rate of low l-number layer modes. The coupling of the precessional mode of a plasma ring to the surface Alfvén wave in a multiple mirror plasma is also discussed.
Lifetime measurements of electron-cyclotron-resonance-heated electrons
Authors: Boehmer H. , Goede H. , Talmadge S.
Published: July 2002

The lifetime of energetic electrons generated via second harmonic electron-cyclotron-resonance heating in a symmetric magnetic mirror configuration is investigated experimentally. The decay time is observed to be as much as a factor of 4 shorter than the value calculated for the most rapid classical loss mechanism, Coulomb drag. The nonclassical loss component is shown to be induced by the microwave power available for electron heating. The microwave power required to sustain the temperature and density of the energetic electrons is calculated from the observed lifetimes and stored energy. It is found to be only a few percent of the total injected power which, in this experiment, is equal to or less than 1 kW.
Simulation model for lower hybrid current drive
Authors: Bonoli Paul T. , Englade Ronald C.
Published: July 2002

A simulation model for steady-state, lower hybrid current drive is described which incorporates a relativistic, one-dimensional Fokker–Planck calculation and a toroidal ray tracing code. Two-dimensional (v⊥) effects are included in the Fokker–Planck analysis in the form of a large perpendicular electron temperature that results from pitch angle scattering. An increase in the parallel refractive index of the lower hybrid waves, arising from toroidal geometry effects, is proposed as a physical mechanism whereby injected rf waves at high phase velocity (ve≪v∥ ≲c) can interact via the Landau resonance with electrons at low phase velocity (v∥ ≲3ve). Numerical results relevant to the Alcator C [Phys. Rev. Lett. 53, 450 (1984)] and PLT [Phys. Rev. Lett. 49, 1255 (1982)] experiments are presented which demonstrate the dependency of the current drive efficiency on various plasma parameters.
Axial plasma injection and shock formation in multiple mirrors
Authors: Bravenec R. V. , Lichtenberg A. J. , Lieberman M. A.
Published: July 2002

The axial expansion of a high-beta collisional plasma from a source into a multiple-mirror device and its subsequent trapping is examined both experimentally and with an ideal-fluid simulation code. The studies are performed on the Berkeley multiple-mirror device MMX [Phys. Fluids 28, 392 (1985)] using a conical theta-pinch plasma source. Studies of injection into a uniform solenoidal field reveal that increasing the theta-pinch energy does not dramatically increase the thermal energy density of the plasma in the solenoid region unless the solenoid field is comparably increased. Injection into sufficiently strong mirrors results in shocks which form sequentially in the mirror throats, beginning in the upstream mirror. The timing of these shocks is studied as a function of Rm and is related to the trapping efficiency.