bluuebunny/crossref_metadata_2025 huggingface dataset:
Discrete singular convolution for the solution of the Fokker–Planck equation
Authors: Wei G. W.
Published: July 2002

This paper introduces a discrete singular convolution algorithm for solving the Fokker–Planck equation. Singular kernels of the Hilbert-type and the delta type are presented for numerical computations. Various sequences of approximations to the singular kernels are discussed. A numerical algorithm is proposed to incorporate the approximation kernels for physical applications. Three standard problems, the Lorentz Fokker–Planck equation, the bistable model and the Henon–Heiles system, are utilized to test the accuracy, reliability, and speed of convergency of the present approach. All results are in excellent agreement with those of previous methods in the field.
Regularity in chaotic reaction paths. I. Ar6
Authors: Komatsuzaki Tamiki , Berry R. Stephen
Published: July 2002

We scrutinize the saddle crossings of a simple cluster of six atoms to show (a) that it is possible to choose a coordinate system in which the transmission coefficient for the classical reaction path is unity at all energies up to a moderately high energy, above which the transition state is chaotic; (b) that at energies just more than sufficient to allow passage across the saddle, all or almost all the degrees of freedom of the system are essentially regular in the region of the transition state; and (c) that the degree of freedom associated with the reaction coordinate remains essentially regular through the region of the transition state, even to moderately high energies. Microcanonical molecular dynamics simulation of Ar6 bound by pairwise Lennard-Jones potentials reveals the mechanics of passage. We use Lie canonical perturbation theory to construct the nonlinear transformation to a hyperbolic coordinate system which reveals these regularities. This transform “rotates away” the recrossings and nonregular behavior, especially of the motion along the reaction coordinate, leaving a coordinate and a corresponding dividing surface in phase space which minimize recrossings and mode–mode mixing in the transition state region. The action associated with the reactive mode tends to be an approximate invariant of motion through the saddle crossings throughout a relatively wide range of energy. Only at very low energies just above the saddle could any other approximate invariants of motion be found for the other, nonreactive modes. No such local invariants appeared at energies at which the modes are all chaotic and coupled to one another.
Intermolecular vibrations of naphthalene trimer by ionization-detected stimulated Raman spectroscopy
Authors: Kim Wousik , Schaeffer Mark W. , Lee Soohyun , Chung James S. , Felker Peter M.
Published: July 2002

We present nonlinear Raman spectra of intermolecular vibrational transitions in four naphthalene trimer isotopomers. The spectra, measured at 0.03 cm−1 by mass-selective ionization-loss stimulated Raman spectroscopy, reveal distinctly shaped pendular band contours, which, upon comparison to simulated pendular contours, lead to ready assignments for almost all of the observed bands. The results show clearly that the trimer has C3h (or very nearly C3h) symmetry with the naphthalenes arranged such that their long axes are parallel to one another. Comparison of the experimental results to the results of calculations of naphthalene-trimer intermolecular spectra performed by assuming harmonic intermolecular modes and by taking the intermolecular potential energy surface to be a pair-wise additive one reveals significant qualitative agreement. This agreement strongly suggests a relatively rigid cluster with no large amplitude intermolecular motions within 100 cm−1 of the zero-point level. Finally, the results highlight the dominance of librational motions in giving rise to scattering intensity in the intermolecular portion of the cluster’s Raman spectrum.
Flow of zero-point energy and exploration of phase space in classical simulations of quantum relaxation dynamics. II. Application to nonadiabatic processes
Authors: Müller Uwe , Stock Gerhard
Published: July 2002

The unphysical flow of zero-point energy (ZPE) in classical trajectory calculations is a consequence of the fact that the classical phase-space distribution may enter regions of phase space that correspond to a violation of the uncertainty principle. To restrict the classically accessible phase space, we employ a reduced ZPE γεZP, whereby the quantum correction γ accounts for the fraction of ZPE included. This ansatz is based on the theoretical framework given in Paper I [G. Stock and U. Müller, J. Chem. Phys. 111, 65 (1999), preceding paper], which provides a general connection between the level density of a system and its relaxation behavior. In particular, the theory establishes various criteria which allows us to explicitly calculate the quantum correction γ. By construction, this strategy assures that the classical calculation attains the correct long-time values and, as a special case thereof, that the ZPE is treated properly. As a stringent test of this concept, a recently introduced classical description of nonadiabatic quantum dynamics is adopted [G. Stock and M. Thoss, Phys. Rev. Lett. 78, 578 (1997)], which facilitates a classical treatment of discrete quantum degrees of freedom through a mapping of discrete onto continuous variables. Resulting in negative population probabilities, the quasiclassical implementation of this theory significantly suffers from spurious flow of ZPE. Employing various molecular model systems including multimode models with conically intersecting potential-energy surfaces as well as several spin-boson-type models with an Ohmic bath, detailed numerical studies are presented. In particular, it is shown, that the ZPE problem indeed vanishes, if the quantum correction γ is chosen according to the criteria established in Paper I. Moreover, the complete time evolution of the classical simulations is found to be in good agreement with exact quantum-mechanical calculations. Based on these studies, the general applicability of the method, the performance of the classical description of nonadiabatic quantum dynamics, as well as various issues concerning classical and quantum ergodicity are discussed.
The electronic structure of MoC and WC by anion photoelectron spectroscopy
Authors: Li Xi , Liu Sherry S. , Chen Wenwu , Wang Lai-Sheng
Published: July 2002

Photoelectron spectra of MoC− and WC− are reported at two detachment energies, 532 and 355 nm. The electron affinities of MoC and WC were measured to be 1.358 (0.010) and 1.022 (0.010) eV, respectively. Seven low-lying electronic states were observed for MoC within 2 eV above its ground state whereas six were observed for WC within 2.4 eV above its ground state. The bonding and spectroscopy of MoC and WC were found to be different and were attributed to their different atomic configurations due to the strong relativistic effects in W. The current study reports the first spectroscopic information on WC.
Ab initio calculations on the ground and excited states of BeOH and MgOH
Authors: Theodorakopoulos Giannoula , Petsalakis Ioannis D. , Hamilton Ian P.
Published: July 2002

Ab initio configuration interaction calculations have been carried out on the ground and excited electronic states of the BeOH and MgOH molecules as well as of the cations BeOH+ and MgOH+, for linear and bent geometries. The excited states of the above molecules have not previously been calculated and experimental information exists only for the A–X system in MgOH and MgOD. The present results show that in the excited states the molecules MgOH and BeOH have similar M–O (M=Mg,Be) stretching and bending potentials. In general, the stretching potentials are rather complicated, showing a number of avoided crossings. Furthermore, most of the excited states show minima at R near Rmin of the corresponding cations BeOH+ and MgOH+, indicating Rydberg contributions to the molecular excited states. The first excited state in both BeOH and MgOH is 2 2A′, which along with 1 2A″, forms the 1 2Π state of linear geometries and which in both systems has minimum energy at a bent geometry with bond angle near 115°. In MgOH, the 2 2A′ state is the A state of the observed A–X spectra and the theoretical transition energy and the barrier to linearity are in good agreement with the corresponding experimental quantities. Analogous spectra for BeOH, not reported as yet, would be expected on the basis of the present calculations at higher energies than the MgOH spectra by 0.6 eV. The results on the molecular ground-state potentials are similar to those of previous calculations, showing a linear minimum geometry for MgOH but with a very shallow bending potential, and for BeOH a bent minimum but with only a 50 cm−1 barrier to linearity.
A two-dimensional model of water: Theory and computer simulations
Authors: Urbič T. , Vlachy V. , Kalyuzhnyi Yu. V. , Southall N. T. , Dill K. A.
Published: July 2002

We develop an analytical theory for a simple model of liquid water. We apply Wertheim’s thermodynamic perturbation theory (TPT) and integral equation theory (IET) for associative liquids to the MB model, which is among the simplest models of water. Water molecules are modeled as 2-dimensional Lennard-Jones disks with three hydrogen bonding arms arranged symmetrically, resembling the Mercedes-Benz (MB) logo. The MB model qualitatively predicts both the anomalous properties of pure water and the anomalous solvation thermodynamics of nonpolar molecules. IET is based on the orientationally averaged version of the Ornstein-Zernike equation. This is one of the main approximations in the present work. IET correctly predicts the pair correlation function of the model water at high temperatures. Both TPT and IET are in semi-quantitative agreement with the Monte Carlo values of the molar volume, isothermal compressibility, thermal expansion coefficient, and heat capacity. A major advantage of these theories is that they require orders of magnitude less computer time than the Monte Carlo simulations.
Molecular dynamics of folding of secondary structures in Go-type models of proteins
Authors: Hoang Trinh Xuan , Cieplak Marek
Published: July 2002

We consider six different secondary structures of proteins and construct two types of Go-type off-lattice models: with the steric constraints and without. The basic amino acid–amino acid potential is Lennard–Jones for the native contacts and a soft repulsion for the non-native contacts. The interactions are chosen to make the target secondary structure be the native state of the system. We provide a thorough equilibrium and kinetic characterization of the sequences through the molecular dynamics simulations with the Langevin noise. Models with the steric constraints are found to be better folders and to be more stable, especially in the case of the β structures. Phononic spectra for vibrations around the native states have low frequency gaps that correlate with the thermodynamic stability. Folding of the secondary structures proceeds through a well-defined sequence of events. For instance, α helices fold from the ends first. The closer to the native state, the faster establishment of the contacts. Increasing the system size deteriorates the folding characteristics. We study the folding times as a function of viscous friction and find a regime of moderate friction with the linear dependence. We also consider folding when one end of a structure is pinned which imitates instantaneous conditions when a protein is being synthesized. We find that, under such circumstances, folding of helices is faster and that of the β sequences slower.
A first principles study of CH3 dehydrogenation on Ni(111)
Authors: Michaelides A. , Hu P.
Published: July 2002

Density functional theory with gradient corrections and spin polarization has been used to study the dehydrogenation of CH3 on Ni(111), a crucial step in many important catalytic reactions. The reaction, CH3(ads)→CH2(ads)+H(ads), is about 0.5 eV endothermic with an activation energy of more than 1 eV. The overall reaction pathway is rather intriguing. The C moiety translates from a hcp to a fcc site during the course of the reaction. The transition state of the reaction has been identified. The CH3 species is highly distorted, and both C and the active H are centered nearly on top of a row of Ni atoms with a long C–H bond length of 1.80 Å. The local density of states coupled with examination of the real space distribution of individual quantum states has been used to analyze the reaction pathway.
An estimate for the Gibbs energy of amorphous solid waters and differences between the low-density amorph and glassy water
Authors: Johari G. P.
Published: July 2002

Molar volume and compressibility of the high density amorph (HDA) and of hexagonal ice (ice Ih) were measured at 77 K and high pressures, and the Gibbs energy, G, of HDA and of the low density amorph (LDA) calculated from their volume–pressure integrals. The relative magnitudes of their G predict that a step increase from ∼3 to ∼7 kbar will transform LDA at 77 K to ice Ih, not to HDA. The excess G of LDA over ice Ih is 1.6±0.1 kJ mol−1, which is higher than the experimentally determined value of 1.1±0.1 kJ mol−1 for amorphous solid water [J. Chem. Phys. 105, 240 (1996)]. A path for the volume in the pressure plane needed to satisfy the requirement of 1.1±0.1 kJ mol−1 was not found. These suggest that LDA is different from the amorphous solid or glassy water, which is consistent with the findings by other methods, thus calling into question the inferences [Nature (London) 392, 164 (1998)] based on a thermodynamic continuity between LDA and supercooled water.
Analysis of plastic deformation in atomic force microscopy: Application to ice
Authors: Butt Hans-Jürgen , Döppenschmidt Astrid , Hüttl Gritt , Müller Eberhard , Vinogradova Olga I.
Published: July 2002

In force measurements with the atomic force microscope (AFM) often nonelastic deformations of the sample are observed. This is especially the case for AFM experiments on ice. In this paper two theoretical approaches are used to calculate the indentation of the tip. First, in an extended plastic indentation model we assume that the pressure exerted by the tip plastifies the sample material once the pressure exceeds three times the yield stress. The rate of plastification limits the indentation speed. With two parameters this model adequately describes measured force curves on ice in a temperature range of −4°C to −20°C and for driving speeds of 0.8 to 110 μm/s. The calculation also shows that in general plastic deformation can lead to different force curves depending on the driving speed. For low driving speeds a jump-in and a linear force curve is expected. For fast driving speeds plastic deformation leads to curved force curves with gradually increasing slope. Second, in a hydrodynamic model we assume that the presence of the tip surface leads to an interfacial premelting of the ice. The flow of the liquidlike water out of the gap between tip and bulk ice is limiting the indentation speed of the tip. The hydrodynamic model does not fit measured force curves as good as the extended plastic indentation model and viscosities which are unrealistically high need to be assumed. Hence, we can exclude that a liquidlike layer of a thickness significantly larger than a monolayer exists in AFM experiments on ice.
An effective algorithm for obtaining polynomials for dimer statistics. Application of operator technique on the topological index to two- and three-dimensional rectangular and torus lattices
Authors: Hosoya Haruo , Motoyama Akiko
Published: July 2002

Recursion formulas on the numbers of ways for placing an arbitrary number of indistinguishable dumbbells on the various rectangular lattice spaces (3×n, 4×n) and torus spaces (2×n, 3×n, 2×2×n) were obtained by the use of the operator technique to the counting polynomial on the topological characteristics (e.g., nonadjacent number, Kekulé number, and topological index). Perfect matching numbers or Kekulé numbers were also obtained for larger lattices such as the 4×n torus and the 2×3×n lattice. By deriving these new results the utility of the proposed method for dimer statistics is demonstrated and some of their mathematical features are discussed.
Functional integrals for spin-Bose systems
Authors: Papadopoulos G. J.
Published: July 2002

The problem of obtaining the propagator of a spin-Bose system consisting of spins- 1/2 and several radiation modes in interaction is reduced to developing a bosonized Hamiltonian for the system from the propagator of which, by appropriate projection, the propagator relating to the original Hamiltonian is extracted. The analysis proceeds via functional integration involving the evaluation of two auxiliary propagators of Schrödinger equations whose Hamiltonians depend separately on radiation operators, and bosonized spin operators. These propagators are coupled through a complex field and the functional average of their product against a Gaussian measure of the field leads to the bosonized system’s propagator. The procedure is applied to the propagator for a single spin-Bose system which is obtained as a power series in the spin flipping energy. The analysis is also applied for an explicit evaluation in the case of a simplified spin-Bose Hamiltonian.
Comment on an aspect of a paper by G. Thompson
Authors: Leach P. G. L.
Published: July 2002

G. Thompson [J. Math. Phys. 25, 3474 (1984)], by way of example of a general method, examined the existence of integrals of the form I=(ypx−xpy)3+A(x,y) px +B(x,y)py, for the Hamiltonian H= 1/2  (p2x+p2y)+V(x,y). The treatment was not complete. A complete solution is given here as well as indications for further development to integrals of higher order in the momenta.
The connection of two-particle relativistic quantum mechanics with the Bethe–Salpeter equation
Authors: Sazdjian H.
Published: July 2002

The formal equivalence between the wave equations of two-particle relativistic quantum mechanics, based on the manifestly covariant Hamiltonian formalism with constraints, and the Bethe–Salpeter equation are shown. This is achieved by algebraically transforming the latter so as to separate it into two independent equations that match the equations of Hamiltonian relativistic quantum mechanics. The first equation determines the relative time evolution of the system, while the second one yields a three-dimensional eigenvalue equation. A connection is thus established between the Bethe–Salpeter wave function and its kernel on the one hand and the quantum mechanical wave function and interaction potential on the other. For the sector of solutions of the Bethe–Salpeter equation having nonrelativistic limits, this relationship can be evaluated in perturbation theory. A generalized form of the instantaneous approximation that simplifies the various expressions involved in the above relations is also devised. It also permits the evaluation of the normalization condition of the quantum mechanical wave function as a three-dimensional integral.
Gauge transformations for the quadratic bundle
Authors: Vaklev Y. S.
Published: July 2002

Gauge transformations constructed by means of the Jost solutions related to two similar cases of the quadratic bundle of general form are studied. Those transformations are taken at arbitrary fixed point λ=λ0 of the continuous spectrum of the problem. The entire class of gauge-equivalent nonlinear evolution equations (NLEE) and their Hamiltonian structures are obtained. An interesting case of reduction of the potential is examined. It was shown that the entire class of NLEE splits into three different (in terms of coefficient functions) subclasses of gauge-equivalent NLEE. The gauge equivalence between the derivative nonlinear Schrödinger equation and some modifications of the derivative Landau–Lifshitz equation (DLLE) is demonstrated. The simplest soliton solutions of the DLLE and its higher analogs are obtained.
BRST formulation of the Gupta–Bleuler quantization method
Authors: Hasiewicz Z. , Kowalski-Glikman J. , Lukierski J. , van Holten J. W.
Published: July 2002

In this paper it is shown how an algebra of mixed first- and second-class constraints can be transformed into an algebra of the Gupta–Bleuler type, consisting of holomorphic and antiholomorphic constraints. Its quantization is performed by BRST methods. A second-level BRST operator Ω is constructed by introducing a new ghost sector (the second-level ghosts), in addition to the ghosts of the standard BRST operator. An inner product in this ghost sector is found such that the operator Ω is Hermitean. The physical states, as defined by the non-Hermitean holomorphic constraints, are shown to be given in terms of the cohomology of this Hermitean BRST charge.
Ricci collineations of static spherically symmetric spacetimes
Authors: Amir M. Jamil , Bokhari Ashfaque H. , Qadir Asghar
Published: July 2002

The Ricci collineations of static spherically symmetric spacetimes are classified and their relationship with isometries is discussed. A general theorem about this relationship is stated and its extension to all spherically symmetric spacetimes is discussed.
Generalized intelligent states and squeezing
Authors: Trifonov D. A.
Published: July 2002

The Robertson–Schrödinger uncertainty relation for two observables A and B is shown to be minimized in the eigenstates of the operator λA+iB, λ being a complex number. Such states, called generalized intelligent states (GIS), can exhibit arbitrarily strong squeezing of A or B. The time evolution of GIS is stable for Hamiltonians which admit linear in A and B invariants. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the spin CS are a subset of SU(2) GIS. CS for an arbitrary semisimple Lie group can be considered as a GIS for the quadratures of the Weyl generators.
η-invariants and determinant lines
Authors: Dai Xianzhe , Freed Daniel S.
Published: July 2002

The η-invariant of an odd dimensional manifold with boundary is investigated. The natural boundary condition for this problem requires a trivialization of the kernel of the Dirac operator on the boundary. The dependence of the η-invariant on this trivialization is best encoded by the statement that the exponential of the η-invariant lives in the determinant line of the boundary. Our main results are a variational formula and a gluing law for this invariant. These results are applied to reprove the formula for the holonomy of the natural connection on the determinant line bundle of a family of Dirac operators, also known as the ‘‘global anomaly formula.’’ The ideas developed here fit naturally with recent work in topological quantum field theory, in which gluing (which is a characteristic formal property of the path integral and the classical action) is used to compute global invariants on closed manifolds from local invariants on manifolds with boundary.
Vector fields on a disk with mixed boundary conditions
Authors: Vassilevich D. V.
Published: July 2002

Vector fields on a disk satisfying two types of boundary conditions are studied. These boundary conditions are selected by BRST-invariance in electrodynamics. They also appear in the de Rham complex. The construction of the harmonic expansion is presented. The eigenfunctions of the vector Laplace operator are expressed in terms of fields satisfying pure Dirichlet or Robin boundary conditions. For the case of four-dimensional disk several first coefficients of the heat kernel expansion are computed. An error in the analytical expression by Branson and Gilkey is corrected.
A duality for endomorphisms of von Neumann algebras
Authors: Jorgensen Palle E. T.
Published: July 2002

We consider endomorphisms of von Neumann algebras: Let M be a von Neumann algebra, represented on a Hilbert space ℋ, and let M′ be the corresponding commutant. Let α∈End(M) be given, and suppose M has a cyclic vector in ℋ, such that the corresponding state leaves α invariant. Then there is a ‘‘dual’’ completely positive mapping β on M′ which we find and describe: Each of the two α and β has an associated spectral group, and we show that the group for β is contained in that for α. We consider the following three restrictions on α: i) α is a shift on M, ii) α is strongly ergodic, and iii) α is ergodic. We give spectral theoretic conditions on α (using the two groups described above) to fall into each of the three classes. We also show that the two groups are conjugacy invariants, and we discuss the case of cocycle conjugacy.
A q-deformation of the Coulomb problem
Authors: Feigenbaum James , Freund Peter G. O.
Published: July 2002

The algebra of observables of SOq(3)-symmetric quantum mechanics is extended to include the inverse 1/R of the radial coordinate and used to obtain eigenvalues and eigenfunctions of a q-deformed Coulomb Hamiltonian.
Generalized Pöschl–Teller, Toda, Morse potentials and SL(2,R) group
Authors: Sezgin M. , Verdiyev A. Y. , Verdiyev Y. A.
Published: July 2002

Quantum integrable systems related with SL(2,R) group manifold in various coordinate systems defined by the various decompositions: KHK, HAH, HKH, NHN, NHK of the group SL(2,R) on one parameter subgroups K,H,A,N are considered. The explicit expressions for waves functions, spectra, and S-matrices are given.
Phase space reduction and Poisson structure
Authors: Zaalani Nadhem
Published: July 2002

Let (P,π,B,G) be a G-principal fiber bundle. The action of G on the cotangent bundle T*P is free and Hamiltonian. By Liberman and Marle [Symplectic Geometry and Analytical Mechanics (Reidel, Dortrecht, 1987)] and Marsden and Ratiu [Lett. Math. Phys. 11, 161 (1981)] the quotient space T*P/G is a Poisson manifold. We will determine the Poisson bracket on the reduced Poisson manifold T*P/G, and its symplectic leaves.
Desingularization of Jacobi metrics and chaos in general relativity
Authors: Szydłowski Marek
Published: July 2002

It has been proposed by Wheeler and deWitt to look at the evolution of three-metrics as a geodesic flow on the superspace. Since then a lot of attention has been paid towards better understanding the geometric structure of the superspace. In particular it has been appreciated that the minisuperspace can in a natural way be equipped with the Jacobi metric. However the Jacobi metric is degenerate on certain codimension one hypersurfaces (boundary sets) leading to severe difficulties. The dynamics of minisuperspace models is a special case of dynamics of simple indefinite mechanical systems. It is proved that trajectories of an indefinite mechanical system (M,g,V), with the natural Lagrangian, are pregeodesics with respect to the Jacobi metric gE=2|E−V|g, where M is the configuration space, g the metric defined by the kinetic energy form, V a potential function, and E the total energy of the system. In this paper we also propose to use Eisenhart’s principle as an alternative geometrical construction on minisuperspace. Then the dynamics of general relativity is mapped onto a geodesic flow on a smooth manifold without boundary. Hence Eisenhart’s proposal seems to be the right way to desingularization of motion in the Jacobi metric which is nontractable in the Jacobi picture. Different methods of desingularizing of the Jacobi metric through the isometric embedding into a more dimensional flat space with the Lorentzian signature is also presented.
Anomalies and analytic torsion on hyperbolic manifolds
Authors: Bytsenko A. A. , Gonçalves A. E. , Simões M. , Williams F. L.
Published: July 2002

The global additive and multiplicative properties of the Laplacian on j-forms and related zeta functions are analyzed. The explicit form of zeta functions on a product of closed oriented hyperbolic manifolds Γ\Hd and of the multiplicative anomaly are derived. We also calculate in an explicit form the analytic torsion associated with a connected sum of such manifolds.
Extended gauge theories starting from the matter field Lagrangian
Authors: Amorim R. , Barcelos-Neto J.
Published: July 2002

We obtain an extended gauge theory by imposing that the matter field Lagrangian is invariant under a local gauge transformation that also contains a vector parameter besides the usual scalar one.
Three flavor neutrino oscillations in matter
Authors: Ohlsson Tommy , Snellman Håkan
Published: July 2002

We derive analytic expressions for three flavor neutrino oscillations in the presence of matter in the plane wave approximation using the Cayley–Hamilton formalism. Especially, we calculate the time evolution operator in both flavor and mass bases. Furthermore, we find the transition probabilities, matter mass squared differences, and matter mixing angles all expressed in terms of the vacuum mass squared differences, the vacuum mixing angles, and the matter density. The conditions for resonance in the presence of matter are also studied in some examples.
Asymptotic Massey products, induced currents and Borromean torus links
Authors: Laurence Peter , Stredulinsky Edward
Published: July 2002

We introduce a class of currents which allows a new and very explicit form for the Massey product of a third order link as a line integral. The explicit form permits the introduction of an asymptotic Massey product analogous to that introduced previously for Gauss’s integral by V. Arnold. The average third order asymptotic Massey product is shown to be equal to Berger’s third order helicity for divergence-free vector fields in linked tori.
Noncollinear spin configuration induced by a magnetic field in the surface gadolinium layer of multilayered Gd/Fe films
Authors: Gnatchenko S. L. , Chizhik A. B. , Merenkov D. N. , Eremenko V. V. , Szymczak H. , Szymczak R. , Fronc K. , Zuberek R.
Published: July 2002

A comparison of field dependences of the meridional Kerr effect and magnetization leads to the conclusion that a noncollinear inhomogeneous magnetic state is formed in the surface layer of gadolinium in multilayered Gd/Fe films in a magnetic field. Experimental results are described by using a theoretical model predicting the formation of a noncollinear spin configuration in the surface Gd layer as a result of a spin-reorientation phase transition induced by the magnetic field.
On turbulence in bores
Authors: Yeh Harry H. , Mok Kai-Meng
Published: July 2002

Turbulence generated in bores is found to be sporadic and three dimensional when the Froude number is less than approximately 2.0. The turbulence characteristics behind the front are strongly affected by the behavior of the surface roller; the turbulence is created by intermittent advection of the recirculating flow of the surface roller. Although the one-dimensional approximation of a bore motion is identical to that of a hydraulic jump in an inviscid fluid, there are fundamental differences in a real fluid environment. When the Froude number is less than approximately 1.7, the difference in the shear-flow field between a bore and hydraulic jump affects their turbulence spreading rates.
Scalar dissipation and mixing in turbulent reacting flows
Authors: Leonard Andy D. , Hill James C.
Published: July 2002

The mixing term that appears in probability density function-based formulations of the statistical behavior of turbulent reacting flows was studied with the use of direct numerical simulations of an irreversible, second-order, isothermal chemical reaction between initially segregated reactants in decaying, homogeneous turbulence. Three-dimensional, time-dependent pseudospectral calculations with 643 Fourier modes were made as well as were Monte Carlo simulations of the joint concentration pdf equations for coalescence–dispersion (C/D) models. It was found that the development of the scalar microscales depends largely on the initial concentration distributions (both isotropic and nonisotropic distributions were used) and is relatively independent of the reaction rate constant. Joint concentration probability density functions (pdf ’s) were compared to predictions of C/D models that make use of parameters evaluated from the nonreacting or inert system. Although the models predict proper variance decay when the microscales are specified, the shapes of the pdf ’s are not accurately predicted, in that the models predict too rapid a growth of probability near the mean value.
Dispersion and reaction in two-dimensional model porous media
Authors: Edwards David A. , Shapiro Michael , Brenner Howard
Published: July 2002

Darcy-scale convective–diffusive–reactive phenomenological coefficients characterizing the transport of a reactive solute through the interstices of a two-dimensional, spatially periodic, model porous medium (on whose surfaces the solute undergoes a first-order, irreversible chemical reaction) are herein determined numerically as functions of the microscale Péclet (Pe), Damköhler (Da), and Reynolds (Re) numbers. The role of bed porosity ε and (circular) cylindrical array configuration are also studied, the latter encompassing square, staggered, and hexagonal arrays. Calculations are effected via generalized Taylor dispersion theory. The Darcy-scale reactivity coefficient K̄* characterizing the effective (first-order, irreversible) volumetric reaction rate is found, inter alia, to be (approximately) inversely proportional to Pe, a conclusion confirmed by analytical results for the limiting case of small Da. Configurational properties of the porous medium are observed to significantly influence K̄*, especially for small porosities and large Da. Moreover, it is found that the mean interstitial velocity vector Ū* of the reactive solute generally differs (often dramatically) from the comparable velocity vector (1/ε)Ū of the (inert) solvent as a consequence of the chemical reaction occurring at the surfaces of the cylindrical bed particles. These data reveal that the mean solute speed ‖Ū*‖ through the interstices may be larger or smaller than the comparable solvent speed (1/ε)‖Ū‖, depending upon the existence and nature of a diffusive boundary layer adhering to the cylindrical bed-particle surfaces. Finally, the longitudinal and lateral components of the solute’s (transversely isotropic) dispersivity dyadic D̄*, parallel and perpendicular, respectively, to the direction of mean flow, are generally observed to decrease with increasing Da. This behavior stems from the fact that, in the diffusion boundary-layer limit, an increasing proportion of the total depletion of solute (via microscale reaction at the cylinder surfaces) arises from those interstitial zones characterized by the existence of large velocity gradients.
Rotating oscillatory flow past a cylinder
Authors: Xu Yunxiu , Boyer Don L. , Zhang Xiuzhang
Published: July 2002

The flow of a homogeneous, incompressible, rotating fluid past a vertical circular cylinder oscillating laterally in a uniform free stream is investigated experimentally. An a/D against λ/D flow regime diagram is developed under conditions of fixed Ekman number, E=3.6(10)−4 and cylinder aspect ratio H/D=1.0; here a is the amplitude of the cross-stream oscillation, D is the cylinder diameter, λ is the streamwise wavelength of the oscillation, and H is the fluid depth (cylinder height). Six distinct characteristic flow types are identified, including fully attached flow, eddy shedding for pure oscillatory motion (i.e., a zero free-stream current), double eddy structures, vortex shedding/merging, eddy chains, and irregular eddy shedding. For comparison purposes, experiments are also conducted in the same ranges of a/D and λ/D for nonrotating flows. The effects of rotation are found to be most important for the smaller values of a/D and λ/D. Rotation tends to induce rectified anticyclonic currents (i.e., in a direction opposite to the background rotation) near the cylinder boundary. Rotation also has the tendency to destroy the cross-streamwise centerline symmetry characteristic of nonrotating flows. Numerous flow observables are measured and, where possible, compared with scaling analyses.
A generalized hard-sphere model for Monte Carlo simulation
Authors: Hassan H. A. , Hash David B.
Published: July 2002

A new molecular model, called the generalized hard-sphere, or GHS model, is introduced. This model contains, as a special case, the variable hard-sphere (VHS) model of Bird [Rarefied Gas Dynamics, edited by S. S. Fisher (AIAA, New York, 1981), Part 1, p. 239] and is capable of reproducing all of the analytic viscosity coefficients available in the literature that are derived for a variety of interaction potentials incorporating attraction and repulsion. In addition, a new procedure for determining interaction potentials in a gas mixture is outlined. Expressions needed for implementing the new model in the direct simulation Monte Carlo (DSMC) methods are derived. This development makes it possible to employ interaction models that have the same level of complexity as used in Navier–Stokes calculations.
Two-layer flows past a semicircular obstruction
Authors: Sha Huyun , Vanden-Broeck J.-M.
Published: July 2002

The flow past a semicircular cylinder at the bottom of a channel is considered. The channel is of finite vertical extent and of infinite horizontal extent. The fluid consists of two layers of constant densities. Both viscosity and surface tension are neglected. It is assumed that the flow is symmetric with respect to a vertical line through the center of the circular cross section and uniform in each layer at infinity. An integrodifferential equation for the unknown shape of the interface is derived, discretized, and solved numerically using Newton’s method. It is shown that there are flows that are perturbations of uniform streams and others that are perturbations of solitary waves. Progression along the various branches of solutions produce two different types of limiting configurations. One is characterized by an infinite broadening in the horizontal direction and the other by overhanging interfacial profiles.
The magnetic pumping of plasmas with sawtooth waveforms
Authors: Borovsky Joseph E. , Hansen Paul J.
Published: July 2002

The pumping of plasmas by sawtooth-waveform magnetic induction variations is studied theoretically and by means of computer simulations. A sawtooth is a cyclic waveform that is characterized by a slow increase in the magnetic induction followed by a rapid drop in the induction. Two types of sawtooth pumping are analyzed, and the types classified as to whether or not the first adiabatic invariants of the plasma particles are conserved during the rapid drops in the magnetic induction. When the invariants are conserved, the sawtooth waveforms are found to be less efficient than square waves for pumping plasmas. When the adiabatic invariants are not conserved, the pumping efficiency is found to be a slight improvement over square waves. Both types of pumping are applied to a hypothetical tokamak plasma and it is concluded that neither type of sawtooth pumping is practical for heating magnetically confined fusion plasmas.
The observation of isolated long-lived current filaments in two-dimensional microtearing turbulence
Authors: Craddock G. G. , Diamond P. H. , Terry P. W.
Published: July 2002

Long-lived isolated current filaments are found to evolve from an initially random current distribution in a numerical simulation of 2-D microtearing, i.e., coupled electron density and flux evolution similar to two-dimensional magnetohydrodynamics (MHD). These filaments arise under the constraint of mean square flux conservation with negligible resistive dissipation and finite cross-field particle diffusivity. The kurtosis of current is found to be large (≫3) indicating strongly non-Gaussian or intermittent behavior. Isolated filaments appear to be force-free. Like sign filaments are observed to attract and merge.
Limiting current in a crossed-field gap
Authors: Lau Y. Y. , Christenson P. J. , Chernin David
Published: July 2002

An analytic theory is presented that yields the maximum transmittable current across an anode–cathode gap that is embedded in an arbitrary transverse magnetic field (B). The limiting current is found to be relatively insensitive to B for all B<BH, where BH is the Hull cutoff magnetic field required for magnetic insulation. The classical Child–Langmuir solution is recovered in the limit B→0.
On the solar and interplanetary causes of geomagnetic storms*
Authors: Tsurutani Bruce T. , Gonzalez Walter D.
Published: July 2002

This article reviews some of the physical properties of geomagnetic storms and the solar and interplanetary causes of these sporadic events. To give the reader an overview of the whole system, the focus will be on the primary plasma processes. References will be provided for those who wish to obtain further information.
Random walk models for particle displacements in inhomogeneous unsteady turbulent flows
Authors: van Dop H. , Nieuwstadt F. T. M. , Hunt J. C. R.
Published: July 2002

First a small time analysis is developed for the first and second moments of the velocity (W) and displacement (Z) in one direction of particles marked at a given point in an inhomogeneous unsteady turbulent flow, in terms of the local energy dissipation rate, and the local derivatives of the second and third moments of the vertical component of the velocity field, ∂∼(u23)/∂z and ∼(∂u33)/∂z. Then the appropriate form of a Langevin equation in inhomogeneous turbulence is suggested, namely, dW=(−W/TL+a1)dt+a1/22 dωt where a1, a2, and TL are functions of the particle position and time, and dωt is a random Gaussian velocity increment with ∼(dωt)=0 and ∼((dωt))2=dt. For simplicity, only one component of the particle motion, W(t), is considered. The functions a1 and a2 are determined by relating the random walk model to the Eulerian conservation equations for the mass of the contaminant and volume of the flow (i.e., the continuity equation), using the Fokker–Planck equation and the Eulerian equations for the moments of a vertical velocity. The coefficients a1 and a2 reduce to the same form as that obtained by the statistical analysis, namely a1=∂∼(u23)/∂z, (≊dW̄/dt, when t → 0) and a2=2∼(u23)/TL +d∼(u23)/dt (≊2∼(W′2)/TL+d∼(W′2)/dt, when t → 0).

It is shown that the random walk model has the correct behavior as t/TL → 0. The theory is shown to agree reasonably well with the measurements of mean height and mean vertical displacement of particles released in a convective boundary layer [Q. J. R. Meteorol. Soc. 102, 427 (1976)]. Yaglom’s [Isv. Atmos. Oceanic Phys. 8, 333 (1972)] surface similarity result is recovered as a special case. For t ≫ TL, and in a zero-skewness steady turbulence, the random walk model reduces to the familiar K-diffusion equation. Some examples are presented to show that mean and mean square particle displacements from the random walk model are virtually identical to those obtained from the analytical solution of the corresponding Eulerian moment equations. Careful analysis is still required when concentration distributions in turbulent flows near a boundary are evaluated using random walk models.
On the theory of pairwise coupling embedded in more general local dispersion relations
Authors: Fuchs V. , Bers A. , Harten L.
Published: July 2002

Earlier work on the mode conversion theory by Fuchs, Ko, and Bers is detailed and expanded upon, and its relation to energy conservation is discussed. Given a local dispersion relation, D(ω; k, z)=0, describing stable waves excited at an externally imposed frequency ω, a pairwise mode-coupling event embedded therein is extracted by expanding D(k, z) around a contour k=kc(z) given by ∂D/∂k=0. The branch points of D(k, z)=0 are the turning points of a second-order differential-equation representation. In obtaining the fraction of mode-converted energy, the connection formula and conservation of energy must be used together. Also, proper attention must be given to distinguish cases for which the coupling disappears or persists upon confluence of the branches, a property which is shown to depend on the forward (vgvph>0) or backward (vgvph<0) nature of the waves. Examples occurring in ion-cyclotron and lower-hybrid heating are presented, illustrating the use of the theory.
Analytical mode conversion calculations for the full wave equations at the ion second harmonics
Authors: Chiu S. C.
Published: July 2002

The wave equations for the second harmonic ion-cyclotron heating as derived from the Maxwell equations, rather than the model fourth-order equation, are solved analytically. With a better treatment of the wave field near the second harmonic resonance layer, the WKBJ solution can be improved to give results valid over a larger range of tunneling parameters than those derived in a previous work on a similar subject [J. Plasma Phys. 27, 327 (1982)]. Dissipation is also discussed and connection with the Budden model is shown.
Effective diffusion in laminar convective flows
Authors: Rosenbluth M. N. , Berk H. L. , Doxas I. , Horton W.
Published: July 2002

The effective diffusion coefficient D* of a passive component, such as test particles, dye, temperature, magnetic flux, etc., is derived for motion in periodic two-dimensional incompressible convective flow with characteristic velocity v and size d in the presence of an intrinsic local diffusivity D. Asymptotic solutions for effective diffusivity D*(P) in the large P limit, with P∼ vd/D, is shown to be of the form D*=cDP1/2 with c being a coefficient that is determined analytically. The constant c depends on the geometry of the convective cell and on an average of the flow speed along the separatrix. The asymptotic method of evaluation applies to both free boundary and rough boundary flow patterns and it is shown that the method can be extended to more complicated patterns such as the flows generated by rotating cylinders, as in the problem considered by Nadim, Cox, and Brenner [J. Fluid Mech. 164, 185 (1986)]. The diffusivity D* is readily calculated for small P, but the evaluation for arbitrary P requires numerical methods. Monte Carlo particle simulation codes are used to evaluate D* at arbitrary P, and thereby describe the transition for D* between the large and small P limits.
The spatial stability of compressible elliptic jets
Authors: Morris Philip J. , Bhat Thonse R. S.
Published: July 2002

This paper describes the spatial stability characteristics of compressible elliptic jets. Solutions are obtained to the compressible, inviscid, linearized equations of motion; the compressible Rayleigh equation. Separable forms of solution are obtained in the jet potential core and outside the jet in terms of series of Mathieu and modified Mathieu functions. These solutions are matched using a shooting method that integrates the Rayleigh equation through the region of nonuniform velocity and density. Four classes of instability modes are studied; modes that are odd or even about the jet’s major and minor axes. Their stability characteristics are documented for a range of jet aspect ratios, jet Mach numbers and temperatures, and azimuthal distributions of jet shear layer thickness. The growth rates of the modes are found to depend on their class and the jet thickness on the major and minor axes. The mode that ‘‘flaps’’ about the jet major axis is found to be the most unstable as the jet Mach number or aspect ratio increases.