bluuebunny/crossref_metadata_2025 huggingface dataset:
On eigenvalues in gaps for perturbed magnetic Schrödinger operators
Authors: Hempel Rainer , Levendorskiı̆ Serge Z.
Published: July 2002

We study Schrödinger operators H0 with a gap in the essential spectrum, perturbed by either a decreasing electric potential or a decreasing magnetic field; in both cases the strength of the perturbation is measured by a coupling constant λ⩾0. Here we are mainly interested in the asymptotic behavior (as λ→∞) of certain counting functions for the eigenvalues that are produced by the perturbation inside the spectral gap. The case where we perturb by a potential can be handled using current technology, even if H0 contains a fixed magnetic background. For perturbations by magnetic fields, however, we require rather strong assumptions—like exponential decay of the perturbations—to obtain a lower bound on the counting function. To gain some additional intuition, we use separation of variables in the closely related model of a Schrödinger operator with constant magnetic field in R2, perturbed by a rotationally symmetric magnetic field that decays at infinity.
Radiation principle for inhomogeneous media
Authors: Eidus D.
Published: July 2002

The classical Sommerfeld radiation principle, well known for stationary oscillations in homogeneous media, is extended to a more general case where a smooth density ρ=ρ(x), x∈RN, depends both on r=|x| and on angular coordinates of the point x. We assume that the density behaves like a power rm, m>−2, at infinity, and, moreover, that there exists a one-parameter family of closed asymptotic wave fronts. A Sommerfeld–Rellich-type radiation condition is obtained and a corresponding theorem of unique solvability of the stationary oscillation problem is proved under some conditions imposed on the asymptotic phase. Some examples are given which include the case of elliptic wave fronts.
Energy levels of a quantal particle enclosed in N identical, mirror symmetric wells of a periodic potential. Numerical test of phase-integral formulas
Authors: Fröman Per Olof , Larsson Kilian , Hökback Anders
Published: July 2002

An interesting structure prevails for the energy levels of a quantal particle in a periodic potential with N (⩾2) mirror symmetric wells separated by N−1 mirror symmetric barriers, when the logarithmic derivative of the wave function is given at corresponding (periodically and mirror symmetrically situated) points in the barrier to the left of the first well and in the barrier to the right of the Nth well. It is shown that the quantization conditions that one obtains for these energy levels by means of a careful and rigorous phase-integral treatment are capable of giving extremely accurate results. The accuracy obtainable is demonstrated for N=3 by comparison with numerically exact results, which were obtained by means of the extended version of the phase-amplitude method presented in an Appendix. In the concluding section we summarize the results and point out unexpected features of the energy spectrum and the wave functions. Two different boundary conditions, commonly used in the theory of crystals, and closely related to the present investigation, are also discussed there.
Gauge symmetries of the master action in the Batalin–Vilkovisky formalism
Authors: Grigoriev M. A. , Semikhatov A. M. , Tipunin I. Yu.
Published: July 2002

We study the geometry of the Lagrangian Batalin–Vilkovisky (BV) theory on an antisymplectic manifold. We show that gauge symmetries of the BV theory are essentially the symmetries of an even symplectic structure on the stationary surface of the master action.
On path integral localization and the Laplacian
Authors: Kärki Topi
Published: July 2002

We introduce a new localization principle, which is a generalized canonical transformation. It unifies BRST localization, the non-Abelian localization principle and a special case of the conformal Duistermaat–Heckman integration formula of Paniak, Semenoff, and Szabo. The heat kernel on compact Lie groups is localized in two ways. First, using a non-Abelian generalization of the derivative expansion localization of Palo and Niemi and second, using the BRST localization principle and a configuration space path integral. In addition, we present some new formulas on homogeneous spaces, which might be useful in a possible localization of Selberg’s trace formula on locally homogeneous spaces.
Geometry and representations of the quantum supergroup OSPq(1|2n)
Authors: Lee H. C. , Zhang R. B.
Published: July 2002

The quantum supergroup OSPq(1|2n) is studied systematically. A Haar functional is constructed, and an algebraic version of the Peter–Weyl theory is extended to this quantum supergroup. Quantum homogeneous superspaces and quantum homogeneous supervector bundles are defined following the strategy of Connes’ theory. Parabolic induction is developed by employing the quantum homogeneous supervector bundles. Quantum Frobenius reciprocity and a generalized Borel–Weil theorem are established for the induced representations.
A one-dimensional model for n-level atoms coupled to an electromagnetic field
Authors: Bassi Zorawar S. , LeClair André
Published: July 2002

A model for n-level atoms coupled to quantized electromagnetic fields in a fibrillar geometry is constructed. In the slowly varying envelope and rotating wave approximations, the equations of motion are shown to satisfy a zero curvature representation, implying integrability of the quantum system.
Conformal behavior of the Lorentz–Dirac equation and Machian particle dynamics
Authors: Sonego Sebastiano
Published: July 2002

It is shown that the self-interaction force on a pointlike electric charge in curved space-time has conformal weight −1. Motivated by this result, a conformally covariant version of the Lorentz–Dirac equation is presented, where the particle mass is treated as a position- and time-dependent quantity. This feature suggests that the underlying dynamics is Machian.
Geodesic completeness of orthogonally transitive cylindrical space–times
Authors: Fernández-Jambrina L.
Published: July 2002

In this paper a theorem is derived in order to provide a wide sufficient condition for an orthogonally transitive cylindrical space–time to be singularity free. The applicability of the theorem is tested on examples provided by the literature that are known to have regular curvature invariants.
Canonical angular supermomentum tensors in general relativity
Authors: Garecki Janusz
Published: July 2002

We introduce the canonical supermomentum tensors Siklm(P;vt) and Siklg(P;vt) for matter and gravitation, respectively. These tensors give kinds of the quasilocal quantities which have recently been considered in the framework of general relativity though usually constructed in some special cases and for the mass only. Our method to construct the quasilocal quantities (i.e., superenergy and supermomentum tensors) is very general and does not require introducing any supplementary elements into general relativity. It merely extracts covariant data from the suitable canonical objects which exist in the framework of the standard general relativity. Having given a constructive definition of the canonical supermomentum tensors for gravitation and matter, we apply the canonical gravitational supermomentum tensor Siklg(P;vt) for the local analysis of the plane and plane-fronted gravitational waves. Next, we apply the canonical supermomentum tensors Siklg(P;vt) and Siklm(P;vt), gravitation and matter, to local and global analysis of the Friedman, Schwarzschild, and Kerr space–times. We show that the canonical angular supermomentum tensors and integral angular supermomenta have better geometric and physical properties than the canonical objects which describe densities of the angular momenta and integral quantities determined by these densities.
Phase-space representation of quantum state vectors: The relative-state approach and the displacement-operator approach
Authors: Ban Masashi
Published: July 2002

Phase-space representation of quantum state vectors has been recently formulated by means of the relative-state method developed by the present author [J. Math. Phys. 39, 1744 (1998)]. It is, however, pointed out by Mo/ller that the displacement-operator method provides another basis of phase-space representation of quantum state vectors [J. Math. Phys. (to appear)]. Hence the relation between the relative-state approach and the displacement-operator approach is discussed, both of which yield equivalent phase-space representations.
Coulomb wave functions with complex values of the variable and the parameters
Authors: Dzieciol Aleksander , Yngve Staffan , Fröman Per Olof
Published: July 2002

The motivation for the present paper lies in the fact that the literature concerning the Coulomb wave functions FL(η,ρ) and GL(η,ρ) is a jungle in which it may be hard to find a safe way when one needs general formulas for the Coulomb wave functions with complex values of the variable ρ and the parameters L and η. For the Coulomb wave functions and certain linear combinations of these functions we discuss the connection with the Whittaker function, the Coulomb phase shift, Wronskians, reflection formulas (L→−L−1), integral representations, series expansions, circuital relations (ρ→ρe±iπ) and asymptotic formulas on a Riemann surface for the variable ρ. The parameters L and η are allowed to assume complex values.
The branch process of cosmic strings
Authors: Jiang Ying , Duan Yishi
Published: July 2002

In light of the φ-mapping method and the topological tensor current theory, the topological structure and the topological quantization of topological defects are obtained under the condition that Jacobian J(φ/v)≠0. When J(φ/v)=0, it is shown that there exists the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the generation, annihilation, and bifurcation of the linear defects are detailed in the neighborhoods of the limit points and bifurcation points of φ-mapping, respectively.
A superspace formulation of an “asymptotic” OSp(3,1|2) invariance of Yang–Mills theories
Authors: Joglekar Satish D. , Mandal Bhabani Prasad
Published: July 2002

We formulate a superspace field theory which is shown to be equivalent to the c−c̄ symmetric BRS/anti-BRS invariant Yang–Mills action. The theory uses a six-dimensional superspace and one OSp(3,1|2) vector multiplet of unconstrained superfields. We establish a superspace WT identity and show that the formulation has an asymptotic OSp(3,1|2) invariance as the gauge parameter goes to infinity. We give a physical interpretation of this asymptotic OSp(3,1|2) invariance as a symmetry transformation among the longitudinal/time like degrees of freedom of Aμ and the ghost degrees of freedom.
Dynamical system analysis for the Einstein–Yang–Mills equations
Authors: Zotov M. Yu.
Published: July 2002

Local solutions of the static, spherically symmetric Einstein–Yang–Mills (EYM) equations with SU(2) gauge group are studied using dynamical systems methods. This approach enables us to classify EYM solutions in a neighborhood of the origin, to prove the existence of solutions with an oscillating metric as well as the existence of local solutions for all known formal power series expansions, to study the extendibility of solutions, and to find some new local singular solutions.
Hyperfine-driven persistent currents in mesoscopic rings based on a 2D electron gas with Rashba spin-orbit interaction
Authors: Cherkaskiy V. A. , Shevchenko S. N. , Rozhavsky A. S. , Vagner I. D.
Published: July 2002

We present a detailed theory of induced persistent current (PC) produced by hyperfine interaction in mesoscopic rings based on a 2D-electron (hole) gas in the absence of external magnetic field. PC emerges due to combined action of the hyperfine interaction of charge carriers with polarized nuclei, spin-orbit interaction and Berry phase.
Dynamics of domain walls and solitons in easy-plane magnets with weak exchange interaction
Authors: Gvozdikova M. V. , Kovalev A. S.
Published: July 2002

Internal spin dynamics of collinear domain walls and collinear soliton-like localized states in easy plane magnets is investigated. The dependence of internal mode frequencies of these excitations on the exchange interaction is determined using the essentially discrete Takeno–Homma model for low values of this interaction.
The propagation of long waves over an undulating bed
Authors: Davies A. G. , Guazzelli E. , Belzons M.
Published: July 2002

The propagation of long surface water waves over an undulating bed is governed by a Mathieu equation. Instabilities of solutions of this equation indicate resonant interactions associated with the strong reflection of the surface waves by the bedforms. The strongest interaction occurs when the bed wavenumber (l) is approximately twice the surface wavenumber (k). This interaction is known in solid-state physics as Bragg reflection. In this paper the interaction of incident surface waves with a patch of ripples on an otherwise flat bed is considered. For the general nonresonant case (l≠2k), a perturbation solution of the Mathieu equation is obtained. This solution indicates that the reflection coefficient R, defined as the ratio of the magnitudes of the reflected and incident waves, is both oscillatory in the ratio of the overall length of the ripple patch to the surface wavelength and also resonant in the vicinity of l=2k. The condition of exact resonance (l=2k) is studied separately and the solution obtained predicts that R tends uniformly to unity as the number of ripples (having l=2k) is increased. The present approach is simpler and more readily applicable than the use of previous more complicated methods based on potential theory. It also provides some insight into the higher-order resonant interactions between waves on a free surface and an undulating bed. The results are particularly important in oceanography, in connection with the reflection of incident surface waves by sandbars off beaches.
‘‘Echo’’ tracer dispersion in porous media
Authors: Hulin J. P. , Plona T. J.
Published: July 2002

The reversibility of tracer dispersion in porous media is investigated experimentally using a ‘‘dispersion echo’’ technique in which tracer is injected into the sample and then pumped back. In homogeneous materials, the ‘‘echo’’ dispersion coefficient is the same as for ‘‘transmission’’ measurements at all Peclet numbers, and the dispersion is fully irreversible. In heterogeneous materials (giving non-Gaussian transmission curves), the dispersion is partly reversible; ‘‘echo’’ dispersion curves are Gaussian with a dispersion coefficient lower than in transmission experiments. It is shown that the dispersion irreversibility corresponds to the combined effects of geometrical disorder in the flow field and of molecular diffusion.
The oscillations of a small floating bubble
Authors: Lu N. Q. , Oguz H. N. , Prosperetti A.
Published: July 2002

A simple model of a small bubble floating at the surface of a liquid before bursting is considered. The oscillations of this system are studied by means of a Lagrangian method. It is found that two fundamentally different modes exist. The surface mode has low frequency and does not change appreciably the volume of the immersed part of the bubble: As a consequence, its efficiency as a source of sound in the water is very limited. The volume mode has a much higher frequency and is a more efficient radiator in the water, although it may be hard to excite. Both modes behave as monopole sources in the air. It is therefore predicted that an oscillating floating bubble is a much more intense source of sound in the air than in the liquid. This conclusion seems to be supported by experimental observations.
Transport of gas bubbles in capillaries
Authors: Ratulowski John , Chang Hsueh-Chia
Published: July 2002

The pressure drop and wetting film thickness for isolated bubbles and bubble trains moving in circular and square capillaries are computed. An arclength-angle formulation of a composite lubrication equation allows for the numerical matching of the lubrication solution of the transition region to the static profiles away from the channel wall. This technique is shown to extend the classical matched asymptotic analysis of Bretherton for circular capillaries to higher capillary numbers Ca. More importantly, it allows the study of finite bubbles, which are shown to resemble infinitely long bubbles in film thickness and pressure drop if their lengths exceed the channel width. The numerical study of bubble trains, verified by a matched asymptotic analysis, shows a surprising result that the pressure drop across one member bubble is identical to that of an isolated bubble at low capillary numbers. This analysis of square capillaries neglects azimuthal flow and is only valid for Ca>3.0×10−3. Nevertheless the film radius and pressure drop of a bubble traveling in a square capillary above this capillary number are computed. These results are conveniently summarized in a correlation for the apparent viscosity of bubbles as a function of foam texture and capillary geometry and dimension.
A general classification of three-dimensional flow fields
Authors: Chong M. S. , Perry A. E. , Cantwell B. J.
Published: July 2002

The geometry of solution trajectories for three first-order coupled linear differential equations can be related and classified using three matrix invariants. This provides a generalized approach to the classification of elementary three-dimensional flow patterns defined by instantaneous streamlines for flow at and away from no-slip boundaries for both compressible and incompressible flow. Although the attention of this paper is on the velocity field and its associated deformation tensor, the results are valid for any smooth three-dimensional vector field. For example, there may be situations where it is appropriate to work in terms of the vorticity field or pressure gradient field. In any case, it is expected that the results presented here will be of use in the interpretation of complex flow field data.
Fluctuating flow with mass transfer induced by a rotating disk electrode with a superimposed time-periodic modulation
Authors: Schwartz Daniel T. , Rehg Timothy J. , Stroeve Pieter , Higgins Brian G.
Published: July 2002

Fluctuating flow with mass transfer induced by a rotating disk electrode with a time-periodic angular velocity Ω0[1+α cos(pτ)]b is analyzed by solving numerically the time-dependent von Kármán self-similar form of the Navier–Stokes and convective diffusion equations when the electrochemical reaction at the disk electrode is mass transfer limited. Results are presented for the full frequency range for several values of the waveform parameter b and α<1. At the intermediate frequency p=1.24 (with α=0.9, b=1), the time-periodic flow undergoes a transition from a quasisteady von Kármán flow to a double boundary layer structure. The transition, which is characterized by an abrupt shift from phase lead (p<1.24) to phase lag (p>1.24) in the far-field angular velocity, is discussed in terms of a viscous wave confined to the Stokes layer by axial inflow. The numerical results for b=1 are compared to the low- and high-frequency asymptotic theories of Chawla and Verma [Proc. R. Soc. London Ser. A 386, 163 (1983)], and it is shown that terms of O(p−5/2) neglected by Chawla and Verma are required in the high-frequency expansion to describe the flow in the far field. Electrochemical measurements of the fluctuating mass transfer limited flux induced by the modulating disk electrode are in excellent agreement with the numerical results. The low-frequency calculations show that a judicious choice of b results in the cancellation of all harmonics other than the fundamental near the disk surface for certain field variables. The implications for electrochemical studies are discussed.
Breakup of a liquid jet in a swirling gas
Authors: Lian Z. W. , Lin S. P.
Published: July 2002

The convective instability of a viscous liquid jet emanating into a inviscid gas with a swirl is investigated. Contrary to the known case of a swirling liquid jet in a quiescent gas, the swirl in the ambient gas is shown to have a stabilizing effect. The inertia force in the gas is shown to play dual roles of both stabilization and destabilization. The gas inertia associated with the swirl has a stabilizing influence, but that associated with the interfacial pressure fluctuation has a destabilizing effect. A physical explanation of the mechanism of stabilization by the gas swirl is given.
Dispersion of suspended particles in turbulent flow
Authors: Noh Y. , Fernando H. J. S.
Published: July 2002

The upward dispersion of heavy particles in suspension in turbulent flow was studied using a numerical model. The interaction between the turbulence and the particle diffusion leads to the formation of a horizontal front (or a ‘‘lutocline’’), across which the diffusion of particles and the propagation of turbulent energy are inhibited. However, as the settling velocity of the particles becomes larger, or as the particle concentration becomes smaller, the interaction weakens, thus suppressing the front formation. One-dimensional model equations for the problem are solved numerically to calculate the evolution of the particle concentration. A criterion for the formation of the front is proposed and the steady depth of the suspension layer is determined.
Subgrid-scale backscatter in turbulent and transitional flows
Authors: Piomelli Ugo , Cabot William H. , Moin Parviz , Lee Sangsan
Published: July 2002

Most subgrid-scale (SGS) models for large-eddy simulations (LES) are absolutely dissipative (that is, they remove energy from the large scales at each point in the physical space). The actual SGS stresses, however, may transfer energy to the large scales (backscatter) at a given location. Recent work on the LES of transitional flows [Piomelli et al., Phys. Fluids A 2, 257 (1990)] has shown that failure to account for this phenomenon can cause inaccurate prediction of the growth of the perturbations. Direct numerical simulations of transitional and turbulent channel flow and compressible isotropic turbulence are used to study the backscatter phenomenon. In all flows considered roughly 50% of the grid points were experiencing backscatter when a Fourier cutoff filter was used. The backscatter fraction was less with a Gaussian filter, and intermediate with a box filter in physical space. Moreover, the backscatter and forward scatter contributions to the SGS dissipation were comparable, and each was often much larger than the total SGS dissipation. The SGS dissipation (normalized by total dissipation) increased with filter width almost independently of filter type. The amount of backscatter showed an increasing trend with Reynolds number. In the near-wall region of the channel, events characterized by strong Reynolds shear stress correlated fairly well with areas of high SGS dissipation (both forward and backward). In compressible isotropic turbulence similar results were obtained, independent of fluctuation Mach number.
The response of isotropic turbulence to isotropic and anisotropic forcing at the large scales
Authors: Yeung P. K. , Brasseur James G.
Published: July 2002

The nonlinear interscale couplings in a turbulent flow are studied through direct numerical simulations of the response of isotropic turbulence to isotropic and anisotropic forcing applied at the large scales. Specifically, forcing is applied to the energy-containing wave-number range for about two eddy turnover times to fully developed isotropic turbulence at Taylor-scale Reynolds number 32 on an 1283 grid. When forced isotropically, the initially isotropic turbulence remains isotropic at all wave numbers. However, anisotropic forcing applied through an array of counter-rotating rectilinear vortices induces high levels of anisotropy at the small scales. At low wave numbers the force term feeds energy directly into two velocity components in the plane of the forced vortices. In contrast, at high wave numbers the third (spanwise) component receives the most energy, producing small-scale anisotropy very different from that at the large scales. Detailed analysis shows that the development of small-scale anisotropy is caused primarily by nonlocal wave-vector triads with one leg in the forced low-wave-number range. This latter result is particularly significant because asymptotic analysis of the Fourier-transformed Navier–Stokes equations shows that distant triadic interactions coupling the energy-containing and dissipative scales persist at asymptotically high Reynolds numbers, suggesting that the structural couplings between large and small scales in these moderate Reynolds number simulations would also exist in high Reynolds number forced turbulence. The results therefore imply a departure from the classical hypothesis of statistical independence between large- and small-scale structure and local isotropy.
Weakly decaying turbulence in an equivalent-barotropic fluid
Authors: Larichev Vitaly D. , McWilliams James C.
Published: July 2002

Numerical solutions are analyzed for the evolution of turbulent flow in an equivalent-barotropic fluid (i.e., a shallow water layer in the limit of strong rotation) from random, narrow-band initial conditions with small viscosity. Particular attention is given to the regime of small deformation radius: the solutions are weakly dissipative of both energy and potential enstrophy; after a brief initial interval of broadening in wave number, the shapes of the energy and potential enstrophy spectra are nearly invariant in time but their centroids move toward larger scales, and coherent vortex structures spontaneously develop with a preferred shape of axisymmetric potential vorticity monopoles. An asymptotic model is derived for small deformation radius, and its behavior exhibits the essential features of the equivalent-barotropic model. Solutions are analyzed for increasing deformation radii, ranging from small to infinite (i.e., nondivergent, two-dimensional flow). In this sequence, both the dynamical evolution rates (e.g., dissipation) and the degree of non-Gaussianity (intermittency) increase substantially. In particular, the spatial sparseness of the coherent vortices increases with deformation radius.
An investigation of chaotic Kolmogorov flows
Authors: Platt N. , Sirovich L. , Fitzmaurice N.
Published: July 2002

A two-dimensional flow governed by the incompressible Navier–Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number Re varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow have been observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of periodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with nonunique chaotic attractors. Spatially disordered, but temporally steady states have been discovered in the large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincaré sections and, where possible, Lyapunov exponents and Lyapunov dimension.
Long wave and lubrication theories for core-annular flow
Authors: Chen Kang Ping , Joseph Daniel D.
Published: July 2002

Different nonlinear amplitude equations for long waves in core-annular flow are compared. Each equation has its own limits of validity that can be critically assessed by comparing the linearization of approximate and exact theories. Long wave theory gets the dispersion relation for the longest waves correctly but cannot accommodate cases like capillary instability, in which the most dangerous wave is not surpassingly long. Small gap lubrication based theories accommodate shorter waves of the size of the core when various extra conditions are satisfied, but various stabilizing mechanisms associated with inertia may not be well represented. One theory in which lubrication theory is used in the water film but not in the core captures the shear stabilization of inertia when the gap is small enough. The criterion for small enough is not uniform in the viscosity ratio and surpassingly small films are required for validity when the oil viscosity is large. The results of lubrication theory are not robust with respect to changes to larger gaps outside the regime of asymptotic validity; for example, the stabilizing effects of the inertia of the core and annulus may reverse for larger, but still small thicknesses.
Observations of axisymmetric tracer particle orientation during flow through a dilute fixed bed of fibers
Authors: Frattini Paul L. , Shaqfeh Eric S. G. , Levy Jeffrey L. , Koch Donald L.
Published: July 2002

Direct microstructural evidence for net tracer particle orientation induced solely by hydrodynamic interactions in a dilute, disordered, fibrous media is reported. A dilute fixed bed of randomly placed fibers was constructed and glycerol/water suspensions of either synthetic akaganeite (βFeOOH, average aspect ratio 6.3) or hematite (αFe2O3, average aspect ratio 1.6) tracer particles were made to flow axially through the bed at prescribed flow rates. Conservative linear dichroism, a noninvasive light scattering technique, was employed to provide a direct measure of the orientational order parameter for the tracer particle population at the end of the bed. The effect of Brownian motion on the hydrodynamically induced order in the suspensions was studied over three orders of magnitude in scaled rotary Peclet number, 5<P<2000. The steady degree of particle alignment exhibited by each suspension as it exited the fiber bed was found to be in good quantitative agreement with theory [Phys. Fluids 31, 728 (1988); ibid. 31, 2769 (1988)]. Time scales characterizing the development of net order induced in the tracer populations were investigated and compared qualitatively to theoretically derived bounds.
Suppression of turbulence in wall-bounded flows by high-frequency spanwise oscillations
Authors: Jung W. J. , Mangiavacchi N. , Akhavan R.
Published: July 2002

The response of wall-flow turbulence to high-frequency spanwise oscillations was investigated by direct numerical simulations of a planar channel flow subjected either to an oscillatory spanwise cross-flow or to the spanwise oscillatory motion of a channel wall. Periods of oscillation, Tosc+=Toscuτ2/ν, ranging from 25 to 500 were studied. For 25≤Tosc+≤200 the turbulent bursting process was suppressed, leading to sustained reductions of 10% to 40% in the turbulent drag and comparable attenuations in all three components of turbulence intensities as well as the turbulent Reynolds shear stress. Oscillations at Tosc+=100 produced the most effective suppression of turbulence. The results were independent of whether the oscillations were generated by a cross-flow or by the motion of a channel wall. In the latter case, suppression of turbulence was restricted to the oscillating wall while the flow at the other wall remained fully turbulent. Spanwise oscillations may provide a simple and effective method for control of turbulence in wall-bounded flows.
Particle force and heat transfer in a dusty gas sustaining an acoustic wave
Authors: Temkin S.
Published: July 2002

This work considers the effects of finite mass concentrations on the force and the heat transfer rate for a small particle in a dusty gas. The particular flow studied is a plane, monochromatic sound wave, where the particle velocity and temperature slips are very small. Assuming that the fluid’s temperature and velocity near a test particle are changed by amounts which depend on the mass loading and on the respective slips, it is shown that the heat transfer rate to a sphere in the suspension changes from the pure conduction limit q̇k0, applicable to an isolated sphere, to q̇k0(1+Cmcpp/cpf), where Cm is the mass loading, cpp is the specific heat of the particle material, and cpf is the constant pressure specific heat of the gas. Another but less significant effect is to change the corresponding viscous force from the Stokes value, Fν0, to Fν0γm/γf, where γm and γf are the specific heat ratios for the suspension and for the dust-free gas, respectively.
Optimal excitation of three-dimensional perturbations in viscous constant shear flow
Authors: Farrell Brian F. , Ioannou Petros J.
Published: July 2002

The three-dimensional perturbations to viscous constant shear flow that increase maximally in energy over a chosen time interval are obtained by optimizing over the complete set of analytic solutions. These optimal perturbations are intrinsically three dimensional, of restricted morphology, and exhibit large energy growth on the advective time scale, despite the absence of exponential normal modal instability in constant shear flow. The optimal structures can be interpreted as combinations of two fundamental types of motion associated with two distinguishable growth mechanisms: streamwise vortices growing by advection of mean streamwise velocity to form streamwise streaks, and upstream tilting waves growing by the down gradient Reynolds stress mechanism of two-dimensional shear instability. The optimal excitation over a chosen interval of time comprises a combination of these two mechanisms, characteristically giving rise to tilted roll vortices with greatly amplified perturbation energy. It is suggested that these disturbances provide the initial growth leading to transition to turbulence, in addition to providing an explanation for coherent structures in a wide variety of turbulent shear flows.
Effect of bulk viscosity on Couette flow
Authors: Gonzalez H. , Emanuel G.
Published: July 2002

The effect of bulk viscosity on a compressible Couette flow between two porous parallel walls is considered. A Stokes’ hypothesis solution is contrasted with one where μb/μ=2000 (μ is shear viscosity, μb is bulk viscosity), where the later value characterizes CO2. A new way of measuring μb is suggested, since the two cases differ significantly for the moving wall skin friction coefficient.
NMR velocity phase encoded measurements of fibrous suspensions
Authors: Seymour J. D. , Maneval J. E. , McCarthy K. L. , McCarthy M. J. , Powell R. L.
Published: July 2002

Nuclear magnetic resonance (NMR) imaging is a noninvasive technique that allows velocity measurement in systems where classical techniques are not suitable due either to opacity or the presence of a solid phase. NMR velocity phase encode measurements for the flow of fiber suspensions yield quantitative data for the average flow field in the suspensions and qualitative information on the microscopic nature of the flow. Bulk translational motion causes modulation of the phase of the sample magnetization which provides information on the average velocity field within the sample. Motions on spatial and time scales that are small relative to the measurement scales cause damping of the magnetization, as reflected by signal attenuation.
Three-dimensional oscillatory convection in a gravitationally modulated fluid layer
Authors: Clever R. , Schubert G. , Busse F. H.
Published: July 2002

The equations for three-dimensional, time-dependent convection in a gravitationally modulated fluid layer heated from below are solved numerically using the Galerkin method in space and a Crank–Nicolson scheme in time. Nonlinear solutions are obtained for the Prandtl number of air (0.71) and for two Rayleigh numbers above the value for onset of oscillatory convection. Multiples of the fundamental frequency of oscillatory convection were chosen in order to study the effects of possible resonances of the frequency of gravitational modulation. Modulation causes a transition from traveling wave convection, which persists in the unmodulated case, to standing wave convection and phase locking occurs for moderate values of the amplitude of the dimensionless gravitational modulation (scaled with the standard acceleration of gravity) in the range 0 to 3. For larger values of the modulation amplitude, frequency locking breaks down and chaotic time dependence occurs.
The random uniform shear layer: An explicit example of turbulent diffusion with broad tail probability distributions
Authors: Majda Andrew J.
Published: July 2002

Recent experimental and computational observations demonstrate the occurrence of large-scale intermittency for diffusing passive scalars, as manifested by broader than Gaussian probability distribution functions. Here, a family of explicit exactly solvable examples is developed which demonstrates these effects of large-scale intermittency at any positive time through simple formulas for the higher flatness factors without any phenomenological approximations. The exact solutions involve advection–diffusion with velocity fields involving a uniform shear flow perturbed by a random fluctuating uniform shear flow. Through an exact quantum mechanical analogy, the higher-order statistics for the scalar in these models are solved exactly by formulas for the quantum-harmonic oscillator. These explicit formulas also demonstrate that the large time asymptotic limiting probability distribution function for the normalized scalar can be either broader than Gaussian or Gaussian depending on the relative strength of the mean flow and the fluctuating velocity field.
Dynamics of decaying two-dimensional magnetohydrodynamic turbulence
Authors: Biskamp D. , Welter H.
Published: July 2002

High-resolution numerical studies of decaying two-dimensional magnetohydrodynamic turbulence were performed with up to 10242 collocation points in general periodic systems using various initial states, but restricting consideration to weak velocity-magnetic field correlation ρ. The global evolution is self-similar with constant kinetic to magnetic energy ratio EV/EM, macro- and microscale Reynolds numbers, and correlation ρ, while the total energy decays as E(t)∝(t+t0)−1. As in three dimensions, dissipative small-scale turbulence adjusts in such a way as to make the energy dissipation rate ε independent of the collisional dissipation coefficients. Normalized energy spectra are also invariant. The spectral index in the inertial range is, in general, close to 3/2 in agreement with Kraichnan’s Alfvén wave argument Ek =DB1/2ε1/2k−3/2, B=(EM)1/2, D≂1.8±0.2, but may be close to 5/3 in transient states, in which turbulence is concentrated in regions of weak magnetic field. In the dissipation range, intermittency gives rise to a modified dissipation scale leff =(l2λ)1/3, with l=Kolmogorov scale and λ=Taylor microscale. This reflects the intermittency of the dissipation process, which is consistent with the picture of current microsheets of thickness l and width and spacing λ.
Evolution of the Orszag–Tang vortex system in a compressible medium. I. Initial average subsonic flow
Authors: Dahlburg R. B. , Picone J. M.
Published: July 2002

In this paper the results of fully compressible, Fourier collocation, numerical simulations of the Orszag–Tang vortex system are presented. The initial conditions for this system consist of a nonrandom, periodic field in which the magnetic and velocity field contain X points but differ in modal structure along one spatial direction. The velocity field is initially solenoidal, with the total initial pressure field consisting of the superposition of the appropriate incompressible pressure distribution upon a flat pressure field corresponding to the initial, average Mach number of the flow. In these numerical simulations, this initial Mach number is varied from 0.2–0.6. These values correspond to average plasma beta values ranging from 30.0 to 3.3, respectively. It is found that compressible effects develop within one or two Alfvén transit times, as manifested in the spectra of compressible quantities such as the mass density and the nonsolenoidal flow field. These effects include (1) a retardation of growth of correlation between the magnetic field and the velocity field, (2) the emergence of compressible small-scale structure such as massive jets, and (3) bifurcation of eddies in the compressible flow field. Differences between the incompressible and compressible results tend to increase with increasing initial average Mach number.
The effect of trapped particles on the linear stability of long wavelength resistive modes
Authors: Fitzpatrick R.
Published: July 2002

The set of semicollisional layer equations derived by Fitzpatrick [Phys. Fluids B 1, 2381 (1989)] is used to investigate the effect of trapped particles on the linear stability of long wavelength resistive modes in a large-aspect-ratio tokamak. At O(1) shear, destabilization by trapped particles is found to significantly modify previous cylindrical results for the drift-tearing mode. At low shear, a fairly weak trapped particle-driven interchange (g mode) instability is found, in addition to the usual drift-tearing mode instability, which, in this limit, is virtually unaffected by trapped particles.
rf stabilization of external kink modes in the presence of a resistive wall
Authors: Goedbloed J. P. , D’Ippolito D. A.
Published: July 2002

The problem of controlling external kink instabilities that arise on the slow time scale characteristic of magnetic field diffusion through a conducting wall with finite resistivity is considered. An expression for the growth rate of these ‘‘resistive wall’’ kink modes is derived in a low-beta cylindrical tokamak model assuming a thin wall and small resistivity, including the additional stabilizing effect of a spatially localized, externally applied surface force. It is shown that the marginal stability condition is identical to that of the ideal kink in the absence of a conducting wall. The model is applied to ponderomotive stabilization arising from the near field of an ion-Bernstein-wave (IBW) antenna system. It is found that radio-frequency (rf) fields below the marginal stability threshold can significantly reduce the growth rate of the m=2 instability. The required rf fields can be attained using present IBW antennas with Ωi≲ω<2Ωi in tokamaks with relatively low magnetic fields and may therefore be useful for high-beta and second-stability studies.
Properties of dc helicity injected tokamak plasmas
Authors: Darrow D. S. , Ono M. , Forest C. B. , Greene G. J. , Hwang Y. S. , Park H. K. , Taylor R. J. , Pribyl P. A. , Evans J. D. , Lai K. F. , Liberati J. R.
Published: July 2002

Several dc helicity injection experiments using an electron beam technique have been conducted on the Current Drive Experiment (CDX) [Phys. Rev. Lett. 59, 2165 (1987)] and the Continuous Current Tokamak (CCT) [Phys. Rev. Lett. 63, 2365 (1989)]. The data strongly suggest that tokamak plasmas are being formed and maintained by this method. The largest currents driven to date are 1 kA in CDX (qa =5) and 6 kA in CCT (qa =3.5). An initial comparison of discharge properties with helicity theory indicates rough agreement. Current drive energy efficiencies are 9% and 23% of Ohmic efficiency in two cases analyzed. Strong radial electric fields are observed in these plasmas that cause poloidal rotation and, possibly, improved confinement.
Compact, high-current accelerators and their prospective applications
Authors: Kapetanakos C. A. , Len L. K. , Smith T. , Dialetis D. , Marsh S. J. , Loschialpo P. , Golden J. , Mathew J. , Chang J. H.
Published: July 2002

This paper briefly surveys the three compact, high-current accelerators that are presently under development in the United States in support of a national program. In addition, it reports recent experimental results from the Naval Research Laboratory (NRL) modified betatron [Phys. Rev. Lett. 64, 2374 (1990)] with emphasis on the electron-cyclotron resonance that presently limits the energy of the beam to approximately 18 MeV. Finally, it briefly addresses selective existing and prospective applications of accelerators.
Density and temperature profiles in strongly absorbing plasma with distributed absorption
Authors: De Groot J. S. , Cameron S. M. , Mizuno K. , Estabrook K. G. , Drake R. P. , Kruer W. L. , Young P. E.
Published: July 2002

A model is presented of the spatial structure of a laser-heated, strongly absorbing, planar plasma. Inverse bremsstrahlung is very strong so that laser light absorption is not localized. Absorption is distributed over densities from well below critical to the critical density. It is shown that the spatial structure of the plasma is self-consistent with laser energy deposition and heat transport so measurement of the plasma structure can be used as diagnostic of absorption and transport. Nonphysical discontinuities in density and temperature at the critical surface that are predicted by previous local absorption models for strongly flux-limited heat transport are reduced. These jumps persist in the present model. It is shown that an improved flux-limited heat transport model, strongly limited in the underdense plasma and weakly limited in the overdense plasma, results in continuous density and temperature profiles.
Negative viscosity and generation of dissipative solitons and zonal dissipative structures by drift waves
Authors: Tur A. V. , Chechkin A. V. , Yanovsky V. V.
Published: July 2002

In this paper the stability of a drift wave in a plasma with dissipation due to ion viscosity is examined. If the wave amplitude exceeds a threshold value, determined by ion–ion collisions, large-scale perturbations (i.e., with scales much greater than the drift wavelength) grow. Maximum growth rate belongs to perturbations that are periodical along plasma inhomogeneity and constant in transverse directions, i.e., azimuthal direction in cylindrical geometry (zonal dissipative structures). The analysis of nonlinear stage of large-scale instability shows that the solitonlike large-scale structures of the electric field and vorticity are possible (dissipative solitons).
Equilibrium statistical constraints and the guiding-center plasma
Authors: Krommes John A.
Published: July 2002

A pedagogical calculation based on the thermal-equilibrium guiding-center plasma model is used to illustrate deep consistency relations that the nonlinear dielectric response must obey. It is shown that these are satisfied by both the direct-interaction approximation and a related Markovian statistical closure.
Modulational instabilities in strongly pumped systems
Authors: Héron A. , Adam J. C.
Published: July 2002

In this paper, results of a set of numerical simulations applicable to the problem of particle acceleration by the beating of high-energy laser waves are presented. The simulations have periodic or open-ended boundary conditions. The growth rates of the parametric instabilities that are present in both situations are identical. In all cases they yield a destruction of the large amplitude plasma wave in a very short time. The amplitude of the saturation level is shown to be strongly dependent on initial conditions. Finally, some results in the term of the evolution of the distribution function of the background plasma in the context of strong turbulence are shown.