bluuebunny/crossref_metadata_2025 huggingface dataset:
Constant solutions of reflection equations and quantum groups
Authors: Kulish P. P. , Sasaki R. , Schwiebert C.
Published: July 2002

To the Yang–Baxter equation an additional relation can be added. This is the reflection equation that appears in various places, with or without spectral parameter, e.g., in factorizable scattering on a half-line, integrable lattice models with nonperiodic boundary conditions, noncommutative differential geometry on quantum groups, etc. Two forms of spectral-parameter-independent reflection equations are studied, chosen by the requirement that their solutions be comodules with respect to the quantum group coaction leaving invariant the reflection equations. For a variety of known solutions of the Yang–Baxter equation the constant solutions of the reflection equations are given. Various quadratic algebras defined by the reflection equations are also given explicitly.
Algebraic structure of the gradient-holonomic algorithm for Lax integrable nonlinear dynamical systems. I
Authors: Prykarpatsky A. K. , Samoilenko V. Hr. , Andrushkiw R. I. , Mitropolsky Yu. O. , Prytula M. M.
Published: July 2002

The algebraic structure of the gradient-holonomic algorithm for Lax integrable dynamical systems is discussed. A generalization of the ℛ-structure approach for the case of operator-valued affine Lie algebras is used to prove the bi-Hamiltonian formulation of nonlinear integrable dynamical systems in multidimensions. The monodromy transfer matrix is constructed to describe the operator manifold in relation to canonical Lie–Poisson bracket on initial affine Lie algebra with gauge central extension. As an illustration, the two-dimensional operator Benney–Kaup integrable hierarchy is considered and their bi-Hamiltonicity is proved.
Topological interpretations of quantum Hall conductance
Authors: Thouless D. J.
Published: July 2002

The high precision of the quantum Hall effect is cited as evidence that the Hall conductance is a topological quantum number invariant under reasonably small perturbations. In this article a survey is made of the Hall conductance as a topological quantum number, of relations between the various interpretations of the integer quantum Hall effect, and of their generalization to the fractional quantum Hall effect.
Knowledge about noncommuting quantum observables by means of Einstein–Podolsky–Rosen correlations
Authors: Nisticò Giuseppe , Romania Maria Concetta
Published: July 2002

It is well known that quantum physics forbids the simultaneous measurement of two noncommuting projection operators. However, sometimes there exists a third projection (mirror projection) which may be measured together with the second one and whose outcomes are completely correlated, in the Einstein–Podolsky–Rosen sense, with the outcomes of the first projection. In this article the states for which such a mirror projection exists are characterized and a procedure for constructing the mirror is given. In particular, it is shown that for two noncommuting projections there are always states for which the mirror projection exists, but also states for which it does not exist.
Spherically symmetric random walks in noninteger dimension
Authors: Bender Carl M. , Boettcher Stefan , Moshe Moshe
Published: July 2002

A previous article proposed a new kind of random walk on a spherically symmetric lattice in arbitrary noninteger dimension D. Such a lattice avoids the problems associated with a hypercubic lattice in noninteger dimension. This article examines the nature of spherically symmetric random walks in detail. A large-time asymptotic analysis of these random walks is performed and the results are used to determine the Hausdorff dimension of the process. Exact results are obtained in terms of Hurwitz functions (incomplete zeta functions) for the probability of a walker going from one region of the spherical lattice to another. Finally, it is shown that the probability that the paths of K independent random walkers will intersect vanishes in the continuum limit if D≳2K/(K−1).
A nodal theorem for coupled systems of Schrödinger equations and the number of bound states
Authors: Amann Herbert , Quittner Pavol
Published: July 2002

It is shown that the number of bound states of coupled systems of radial Schrödinger equations can be found by computing the number of zeros of a suitable determinant. This is related to the concept of conjugate points from Morse theory and is the basis for a numerically efficient method.
A solvable Hamiltonian system
Authors: Calogero F.
Published: July 2002

The initial-value problem for the dynamical system characterized by the Hamiltonian H=λn∑nj=1 pj+μ∑nj,k=1 (pjpk)1/2 cos[ν(qj−qk)] is solved in completely explicit form, for arbitrary n. A set of matrices is introduced, whose remarkable properties are related to this problem, and also present an interest of their own.
Generalized fermions and Lie superalgebras spl(m/n)
Authors: Debergh N.
Published: July 2002

Different statistics generalizing the Fermi–Dirac one, i.e., statistics associated with parafermions of order p, orthofermions, deformed parafermions, and genons, are studied in connection with Lie superalgebras. The class spl(m/n) appears as the fundamental one in this context. A specific relation between parafermions and orthofermions is also pointed out.
Cabled Wilson loops in BF theories
Authors: Cattaneo Alberto S.
Published: July 2002

A generating function for cabled Wilson loops in three-dimensional BF theories is defined, and a careful study of its behavior for vanishing cosmological constant is performed. This allows an exhaustive description of the unframed knot invariants coming from the pure BF theory based on SU(2), and, in particular, it proves a conjecture relating them to the Alexander–Conway polynomial.
Rigged Hilbert spaces for chaotic dynamical systems
Authors: Suchanecki Z. , Antoniou I. , Tasaki S. , Bandtlow O. F.
Published: July 2002

We consider the problem of rigging for the Koopman operators of the Renyi and the baker maps. We show that the rigged Hilbert space for the Renyi maps has some of the properties of a strict inductive limit and give a detailed description of the rigged Hilbert space for the baker maps.
Transmission of conduction electrons through a symmetric pair of delta-barriers or delta-wells embedded in a semiconductor or a metal
Authors: Bezák V.
Published: July 2002

The transmission coefficient T(k0) is calculated for conduction electrons incident with a wave vector k0 upon a double barrier (double well) formed of two equal delta-barriers (of two equal delta-wells) embedded in a one-dimensional (1-D) semiconductor or in a 1-D metal. The stationary Schrödinger–Wannier equation E(−i∂/∂x)ψ+V(x)ψ=ℰψ is solved for V(x)=γ[δ(x+a/2)+δ(x−a/2)] (with real and time-independent parameters γ, a) and ℰ=E(k0)>0. (The interband transitions are neglected.) The operator E(−i∂/∂x) corresponds to a given (possibly nonquadratic) dispersion function E(k) of the conduction electrons [E(0)=0]. It is shown that T(k0) is an oscillating function reaching the maximum value [T(k0)→1] on an infinite set {K(j)} of values of k0. The shape of T(k0) depends on the shape of the dispersion function E(k) in a simple way: T(k0)=Tpar(mv(k0)/ℏ)) where Tpar(k0) means the transmission coefficient in the special case when the dispersion function is quadratic, Epar(k)=ℏ2k2/2m, and v(k)=(1/ℏ)∂E(k)/∂k is the group velocity due to E(k). [Here E(k) is taken as an increasing function.]
A note on fractional KdV hierarchies
Authors: Casati Paolo , Falqui Gregorio , Magri Franco , Pedroni Marco
Published: July 2002

One of the cornerstones of the theory of integrable systems of KdV type has been the remark that the n-GD (Gel’fand–Dickey) equations are reductions of the full Kadomtsev–Petviashvilij (KP) theory. In this paper we address the analogous problem for the fractional KdV theories, by suggesting candidates of the “KP theories” lying behind them. These equations are called “KP(m) hierarchies,” and are obtained as reductions of a bigger dynamical system, which we call the “central system.” The procedure allowing passage from the central system to the KP(m) equations, and then to the fractional KdVnm equations, is discussed in detail in the paper. The case of KdV32 is given as a paradigmatic example.
Frequency domain wave-splitting techniques for plane stratified bianisotropic media
Authors: Borzdov George N.
Published: July 2002

A plane harmonic electromagnetic wave obliquely incident on a plane stratified bianisotropic medium with multiple discontinuities in the parameters is considered. A covariant wave-splitting approach, based on the use of the formula of integration by parts for multiplicative integrals and the impedance concept, is presented. It encompasses various types of decomposition of the total internal field into two waves propagating in opposite directions, including the physical and vacuum wave splittings treated earlier in the literature, and provides a convenient means for both analytical investigation and numerical calculation of evolution operators (Green’s functions) and impedance tensors of split waves as well as characteristic matrices and reflection and transmission tensors of stratified bianisotropic media. The potentialities of the approach are illustrated by its application to the problems of reflection, transmission, and guided propagation, and by generalizing the method of multiple reflections to the case of stratified bianisotropic media.
Hamiltonian time-dependent mechanics
Authors: Sardanashvily Gennadi A.
Published: July 2002

The usual formulation of time-dependent mechanics implies a given splitting Y=R×M of an event space Y. This splitting, however, is broken by any time-dependent transformation, including transformations between inertial frames. The goal is the frame-covariant formulation of time-dependent mechanics on a bundle Y→R, whose fibration Y→M is not fixed. Its phase space is the vertical cotangent bundle V*Y, provided with the canonical 3-form and the corresponding canonical Poisson structure. An event space of relativistic mechanics is a manifold Z whose fibration Z→R is not fixed.
Complementary group resolution of the SU(n) outer multiplicity problem. II. Recoupling approach for SU(3)⊃U(2) reduced Wigner coefficients
Authors: Pan Feng , Draayer J. P.
Published: July 2002

A general procedure for the derivation of SU(3)⊃U(2) reduced Wigner coefficients (RWCs) for the coupling (λ1μ1)×(λ2μ2)↓(λμ)η, where η is the outer multiplicity label required in the decomposition, is proposed based on a recoupling approach that follows the complementary group technique for a resolution of the outer multiplicity of SU(n) introduced in Part (I) of this series. RWCs of SU(n) are not unique under a canonical resolution of the outer multiplicity; the transformation from one set to another are elements of SO(m), where m is the number of occurrences of the (λμ) irrep in the decomposition (λ1μ1)×(λ2μ2)↓(λμ). A special resolution of the multiplicity is identified that leads to a recursive procedure for the determination of RWCs. New features of these special RWCs and differences from those obtained with other choices are discussed. The method can be applied to the derivation of general SU(n) Wigner or RWCs. Algebraic expressions for another kind of RWCs, the so-called reduced auxiliary Wigner coefficients for SU(3)⊃U(2), are also obtained.
Branching rules for restriction of the Weil representations of Sp(n,R) to its maximal parabolic subgroup CM(n)
Authors: Rowe D. J. , Repka J.
Published: July 2002

The symplectic group Sp(n,R) is the group of linear canonical transformations of a real 2n-dimensional phase space and CM(n)⊂Sp(n,R) is a maximal parabolic subgroup. The symplectic groups are the fundamental dynamical groups of classical and quantal Hamiltonian mechanics. In particular, Sp(3,R) is the dynamical group of the spherical harmonic oscillator and its Weil (harmonic series) representations are important for the microscopic (shell model) description of the collective motions of many-particle systems. The subgroup CM(3)⊂Sp(3,R) also appears in the microscopic theory of nuclear collective motion as the dynamical group of a hydrodynamic model of quadrupole vibrations and rotations of a nucleus. Thus, the Sp(3,R)→CM(3) branching rules are needed in finding the embedding of the hydrodynamic collective model in the microscopic shell model. Some new developments are made in the vector-coherent-state theory of induced representations.
Asymptotic behavior in polarized T2-symmetric vacuum space–times
Authors: Isenberg James , Kichenassamy Satyanad
Published: July 2002

We use the Fuchsian algorithm to study the behavior near the singularity of a class of solutions of Einstein’s vacuum equations. These solutions admit two commuting spacelike Killing fields like the Gowdy space–times, but their twist does not vanish. The space–times are also polarized in the sense that one of the “gravitational degrees of freedom” is turned off. Examining an analytic family of solutions with the maximum number of arbitrary functions, we find that they are all asymptotically velocity-term dominated as one approaches the singularity.
A note on the Morse index theorem for geodesics between submanifolds in semi-Riemannian geometry
Authors: Piccione Paolo , Tausk Daniel V.
Published: July 2002

The computation of the index of the Hessian of the action functional in semi-Riemannian geometry at geodesics with two variable endpoints is reduced to the case of a fixed final endpoint. Using this observation, we give an elementary proof of the Morse index theorem for Riemannian geodesics with two variable endpoints, in the spirit of the original Morse proof. This approach reduces substantially the effort required in the proofs of the theorem given previously [Ann. Math. 73(1), 49–86 (1961); J. Diff. Geom 12, 567–581 (1977); Trans. Am. Math. Soc. 308(1), 341–348 (1988)]. Exactly the same argument works also in the case of timelike geodesics between two submanifolds of a Lorentzian manifold. For the extension to the lightlike Lorentzian case, just minor changes are required and one obtains easily a proof of the focal index theorem previously presented [J. Geom. Phys. 6(4), 657–670 (1989)].
Mixing properties of the Swendsen–Wang process on the complete graph and narrow grids
Authors: Cooper Colin , Dyer Martin E. , Frieze Alan M. , Rue Rachel
Published: July 2002

We consider the mixing properties of the Swendsen–Wang process for the two-state Potts model or Ising model, on the complete n vertex graph Kn and for the Q-state model on an a×n grid where a is bounded as n→∞.
The origin of chiral anomaly and the noncommutative geometry
Authors: Prešnajder P.
Published: July 2002

We describe scalar and spinor fields on a noncommutative sphere starting from canonical realizations of the enveloping algebra A=U(u(2)). The gauge extension of a free spinor model, the Schwinger model on a noncommutative sphere, is defined and the model is quantized. The noncommutative version of the model contains only a finite number of dynamical modes and is nonperturbatively UV regular. An exact expression for the chiral anomaly is found. In the commutative limit the standard formula is recovered.
Electron structure of diborides of 3d metals
Authors: Grechnev G. E. , Ushakova N. V. , Kervalishvili P. D. , Kvachantiradze G. G. , Kharebov K. S.
Published: July 2002

The electron energy spectra of diborides of 3d-metals ScB2, TiB2, VB2, CrB2, and MnB2 are calculated ab initio. Thermodynamic properties and stability of these compounds are investigated at low temperatures. An analysis of the low-temperature heat capacity and magnetic properties of diborides has made it possible to establish a number of parameters of many-particle interactions.
On the large-eddy simulation of transitional wall-bounded flows
Authors: Piomelli Ugo , Zang Thomas A. , Speziale Charles G. , Hussaini M. Yousuff
Published: July 2002

The structure of the subgrid-scale fields in plane channel flow has been studied at various stages of the transition process to turbulence. The residual stress and subgrid-scale dissipation calculated using velocity fields generated by direct numerical simulations of the Navier–Stokes equations are significantly different from their counterparts in turbulent flows. The subgrid scale dissipation changes sign over extended areas of the channel, indicating energy flow from the small scales to the large scales. This reversed energy cascade becomes less pronounced at the later stages of transition. Standard residual stress models of the Smagorinsky type are excessively dissipative. Rescaling the model constant improves the prediction of the total (integrated) subgrid scale dissipation, but not that of the local one. Despite the somewhat excessive dissipation of the rescaled Smagorinsky model, the results of a large-eddy simulation of transition on a flat-plate boundary layer compare quite well with those of a direct simulation, and require only a small fraction of the computational effort.
Local shear stress measurements on an axisymmetric body in a microbubble modified flow field
Authors: Deutsch S. , Pal S.
Published: July 2002

An array of flush-mounted hot film probes has been used to measure the local shear stress reduction as a result of microbubble injection over an axisymmetric body at the four discrete, free-stream speeds of 4.6, 10.7, 13.2, and 16.8 m/sec. Visualization of the bubble flow pattern supplement these results at intermediate free-stream speeds. At speeds of 10.7 m/sec and above, a circumferential gradient in skin friction, with skin friction reduction larger at the top than at the bottom of the model occurs at some distance downstream of injection. For these speeds, the gradient is stronger at the lower speeds and higher gas injection conditions. Higher speeds tend to drive the axial location of the gradient farther from the injection location. At speeds below 10.7 m/sec, the flow is dominated by a double vortex structure that entrains the bubbles at the bottom and sides of the model and transports them to the top. At sufficiently high gas flow rates a cavity, large enough to be observed visually, is formed just upstream of the vortices, centered near the body midline. The axial position of the cavity is roughly independent of flow speed and gas flow conditions. The transport of bubbles by the vortices, to the top of the body, is the cause of the poor skin friction reduction performance of microbubble injection at low speeds on an axisymmetric shape. Integration of the current local skin friction results gives good agreement with earlier drag balance measurements. The persistence of the drag reduction phenomenon with axial distance as well as the statistics of the shear stress fluctuations are quite similar to what was observed earlier on flat plates.
Characteristics-based methods applied to infinite Prandtl number thermal convection in the hard turbulent regime
Authors: Malevsky A. V. , Yuen D. A.
Published: July 2002

The use of characteristics-based methods for the advection-dominated regimes in thermal convection is investigated. An operator-splitting method applied to the advection–diffusion equation for the very large Péclet (Pe) number regime is presented. In this approach two partial differential equations representing both the purely hyperbolic and the parabolic components must be solved simultaneously. This method has been compared with (1) the Galerkin approximation, (2) the streamwise upwinding Petrov–Galerkin method, and (3) the characteristics-based method using the Lagrangian formulation for the time-derivative operator of the advection–diffusion equation. Solution accuracy of the operator-splitting method improves with larger Pe, while the accuracy of other methods deteriorates with Pe. For the nonlinear problem of two-dimensional thermal convection the Lagrangian method is found to be most computationally efficient. With this Lagrangian method, time-dependent, thermal convection solutions of extremely high Rayleigh number (Ra), up to 3×109, for infinite Prandtl number are obtained. For an aspect ratio of 1.8 the exponent in the scaling of the Nusselt number (Nu) with Ra in time-dependent convection is determined to be 0.301 in the hard turbulent regime and is smaller than in the soft turbulent regime. The behavior of this exponent as a consequence of the transition to hard turbulence agrees with experimental findings. Horizontal Fourier spectra of the thermal fields outside the boundary layers reveal a transition in the high wave-number domain from 1/k to 1/k2 in the transition from soft to hard turbulent regimes. Analysis of the kinetic energy spectra E(k) shows an asymptotic decay of E(k) close to k−2, for large k, spanning over two decades in wave number for strongly time-dependent convection.
Green’s law and the evolution of solitary waves
Authors: Synolakis Costas Emmanuel
Published: July 2002

An exact solution to the linear shallow-water wave equation is presented for solitary waves first evolving over constant depth and then over a sloping beach. An asymptotic expansion for the evolution of the maximum amplitude of the wave is shown to reduce to Green’s law. This appears to be the first derivation of Green’s law specifically for solitary waves and including reflection.
A transition from Kelvin–Helmholtz instabilities to propagating wave instabilities
Authors: Lott François , Kelder Hennie , Teitelbaum Hector
Published: July 2002

The object of this paper is to study the linear stability of an unbounded stably stratified shear layer in an inviscid, Boussinesq fluid. The flow is modeled by the velocity and buoyancy frequency profiles: U=U0 tanh(z/d) and N2=N12+N22 ‖tanh(z/d)‖α, where α≳0. It represents a shear layer which has already been mixed, to a certain extent, since the stratification is smaller inside the shear layer than outside. This flow can generate propagating wave instabilities if the layer of less static stability is sufficiently broad (i.e., α sufficiently large) as compared to the layer of large velocity shear: when α<2, the flow only generates Kelvin–Helmholtz instabilities; when α≳2, the flow generates both Kelvin–Helmholtz and propagating wave instabilities. In three specific cases (α=0,2,4), the neutral modes are derived systematically using an analytical transform of the Taylor–Goldstein equation into the hypergeometric equation. Furthermore, the neutral modes, associated to propagating wave instabilities, correspond to gravity waves with infinite critical level reflection and transmission (i.e., resonant overreflection). It is to be noted that resonant overreflection is possible in the present model as long as the minimum Richardson number of the flow is smaller than 0.25. In the conclusion, the importance of the results obtained is discussed, in relation with the spontaneous generation of gravity waves in a stratified shear layer.
The effect of hydrodynamic interactions on the average properties of a bidisperse suspension of high Reynolds number, low Weber number bubbles
Authors: Kumaran V. , Koch Donald L.
Published: July 2002

The hydrodynamic interaction between a pair of nondeformable bubbles (low Weber number limit) in potential flow (high Reynolds number limit) was analyzed. The velocity potential was determined using twin spherical expansions, and the equations of motion were calculated by enforcing the zero net force condition on the surface of the bubbles. The acceleration due to the interaction is expressed in a perturbation series in the parameter (ai/R), where ai is the radius of bubble i, R is the distance between the bubbles, and the leading-order acceleration was found to decrease as (ai/R)4. The effect of potential flow interactions on the trajectory of a pair of bubbles of different sizes (size ratio greater than 1.07 at a Reynolds number of 200) rising due to gravity was studied. A salient feature of the trajectories is that the surfaces of the bubble do not come into contact during the interaction, except when the smaller bubble radius is less than 0.233 times the larger bubble radius when the Reynolds number based on the larger bubble is 200. In the latter case, however, the Reynolds number based on the radius of the smaller bubble is not large enough to justify the potential flow approximation. For interactions where collisions do not occur, the mean-square fluctuating velocity in a uniform suspension and the hydrodynamic diffusivities in a nonuniform suspension were calculated by performing an ensemble average over pair interactions. The pair averaging procedure is valid for dilute suspensions (V≪18/Re, where V is the volume fraction of the bubbles and Re is the Reynolds number based on the bubble radius and its terminal velocity).
Hydrodynamic diffusion in dilute sedimenting suspensions at moderate Reynolds numbers
Authors: Koch Donald L.
Published: July 2002

The hydrodynamic diffusion of particles or bubbles sedimenting in a liquid is considered for moderate particle Reynolds numbers, Re∼O(1), and small particle volume fractions, φ≪1. Here, Re≡ρUta/μ, Ut is the mean terminal velocity of the particles, a is their mean radius, and ρ and μ are the density and viscosity of the fluid. The interactions that control the diffusion occur when one particle is in the wake of another particle with a separation that is large compared with the particle radius a. The conditionally averaged velocity disturbance in the wake of a particle is screened at an O(aφ−1) distance behind the particle. Beyond this distance, the wake spreads more quickly because of a deficit of particles in the center and an excess at the periphery of the wake of a test particle. This structure is produced by lift forces, which tend to resist the advection of particles into the wake. Screening is required in order to obtain finite values of the variances of the vertical velocities of the particles and fluid. The particle diffusion is anomalous even at wavelengths larger than the screening length; the mean-square displacements of the particles in the vertical and horizontal directions grow in proportion to t3/2 and t ln2 t, respectively. The calculations are carried out for a suspension with a small degree of polydispersity.
The influence of linear mechanisms during the adjustment of sheared turbulence to flow curvature
Authors: Holloway A. G. L. , Gupta R.
Published: July 2002

Recent experimental studies on homogeneous curved shear flow have shown that the imposition of strong mean flow curvature can cause a reversal of the turbulent shear stress, giving it the same sign as the gradient of mean velocity. Measurements of the coherence spectrum for these flows has revealed that this reversal is not uniform across all scales, and that eddies of different sizes can have opposite orientations and transport momentum in opposite directions. To evaluate the influence of linear mechanisms in the shear stress reversal a ‘‘rapid distortion’’ type of model was applied to those flows which demonstrated this phenomenon. The model predicts that flow curvature causes a periodic modulation of the structure of sheared turbulence, and that the sign of the shear stress reverses because of these oscillations. The period of the modulation, in terms of the total strain, was found to decrease as the turning rate increases relative to the shearing rate. For those flows which showed a reversal of the shear stress, the range of experimental observation was only a fraction of the predicted period, but interpreting the observed development as a portion of an oscillation the measurements were found to be qualitatively similar to the predictions of the linear theory. In cases of stronger turbulence a self-preserving structure developed, before the shear stress could reverse, and the measurements deviated significantly from the predictions.
Self-similarity and multifractals in turbulence
Authors: Borgas Michael S.
Published: July 2002

A simple argument based on self-similarity is used to derive a relationship between pointwise energy-dissipation-rate moments, 〈εq〉, and inertial-range volume-averaged moments, 〈εqr〉, in homogeneous, isotropic and stationary turbulence. These results support the multifractal description of energy dissipation. The moment relationship implies that pointwise and inertial-range volume-averaged energy-dissipation rates cannot both be lognormally distributed. Some pointwise moments may not even exist if the volume-average counterpart is lognormal. The Schwartz inequalities for moments satisfying the self-similar relationship are examined and support the realizability of such processes.
Nonlinear depletion of ultrashort and relativistically strong laser pulses in an underdense plasma
Authors: Bulanov S. V. , Inovenkov I. N. , Kirsanov V. I. , Naumova N. M. , Sakharov A. S.
Published: July 2002

The depletion of a relativistically strong laser pulse in the course of interaction with underdense plasmas is considered. The driving mechanisms of distortion and fast depletion of the pulse due to the nonlinear plasma wake excitation are discussed. The role of the backward stimulated Raman scattering in the process of the leading front steepening is traced. Electron acceleration and heating due to plasma wave breaking are demonstrated. The evidence that the final stage of the pulse depletion can be accompanied by the formation of relativistically strong solitonlike electromagnetic modes is presented.
Ionospheric plasma flow over large high-voltage space platforms. I: Ion-plasma–time scale interactions of a plate at zero angle of attack
Authors: Wang J. , Hastings D. E.
Published: July 2002

Theory and particle simulation results are presented for the ionospheric plasma flow over large, high-voltage space platforms. In this paper, dynamic interactions of a negatively biased plate at a zero angle of attack on the ion-plasma–time scale are emphasized. Results of the transient plasma response to a rapid surface potential change show that ion-acoustic disturbances are generated by the leading edge, and they evolve to form a Mach wedge expansion fan. The transient ion current exhibits a strong overshoot in the first few ion-plasma periods. It is shown that the current overshoot is due to the ions trapped within the initial sheath, and its magnitude is proportional to the plate dimension and the square root of the surface voltage. Simulations of time-dependent interactions of a plate connected to external circuits are also performed. A rapidly changing voltage source may cause a very complex transient current and surface voltage due to the coupling of the transient plasma and circuit properties. Interactions of a plate with electron beam emissions are also studied, and the beam effects on the sheath structure and ion current collection are discussed.
Effects of ion diamagnetic flow on shock formation in poloidally rotating tokamak plasmas
Authors: Shaing K. C. , Hsu C. T.
Published: July 2002

When the poloidal ion diamagnetic flow is of the order of the E×B drift velocity, it significantly affects the shock formation in a poloidally rotating tokamak plasma. (Here, E is the electric field and B is the magnetic field.) The poloidal density variation in both linear and shock regimes can be weakened if the poloidal ion diamagnetic flow tends to cancel the poloidal E×B flow. The magnitude of the density variation is not symmetric with respect to the direction of the E×B poloidal rotation. The resonant condition at which strong shock occurs is also modified dramatically by the diamagnetic flow. For some cases, the poloidal density variation inside the bifurcated electric field layer in the L–H transition [Phys. Rev. Lett. 42, 1408 (1982)] may not be large enough to significantly modify the plasma viscosity obtained by neglecting the compressibility effects.
Poloidal variation of viscous forces in the banana collisionality regime
Authors: Wang J. P. , Callen J. D.
Published: July 2002

The poloidal variation of the parallel viscous and heat viscous forces are determined for the first time using a rigorous Chapman–Enskog-like approach that has been developed recently. It is shown that the poloidal variation is, like the poloidal distribution of the trapped particles, concentrated on the outer edge (large major radius side) of the tokamak.
Lower-hybrid wave propagation in toroidal plasmas
Authors: Schuss J. J.
Published: July 2002

The electrostatic lower-hybrid wave equation is solved in toroidal geometry by expanding the wave potential as a sum of poloidal eigenmodes and calculating their mutual coupling to first order in ε=r/R. The resulting solutions are compared to toroidal ray tracing calculations. These solutions present a technique that can explicitly determine the evolution of the wave poloidal mode number spectrum over long trajectories that involve multiple passes of the plasma column.
Dissipative instabilities at the edge of reversed-field pinches driven by a combination of plasma gradients and a parallel current
Authors: Mondt J. P. , Goedert J.
Published: July 2002

Stability in the edge region of reversed-field pinches is analyzed within the context of a two-fluid model. Two major sources of instability are identified: in combination with a parallel electric field, either an electron temperature gradient and/or a density gradient leads to rapid growth (of several to many Ohmic heating rates) over a region of several millimeters around the mode-rational surfaces in the edge region. The basic signature of both instabilities is electrostatic. In the case of the density gradient mode, it relies on the effects of electron compressibility, whereas the temperature gradient mode can be identified as the current-convective instability by taking the limit of zero density gradient, thermal force, and electron compressibility. The possibility of enhanced particle loss and thermal convection as a nonlinear consequence of the instability is indicated. A criterion for the overlap of the linearly unstable regions in the edge of reversed-field pinches is obtained.
Resistive evolution of general plasma configurations
Authors: Miller Guthrie
Published: July 2002

The resistive evolution through equilibrium states of general plasma configurations with closed magnetic field lines is described. Cases where the magnetic field forms magnetic surfaces and where the magnetic field is ergodic are treated. In the former case a simple equation for the rate of change of rotational transform at fixed values of toroidal flux is obtained, as is already known. In the latter case the evolution of the equilibrium is naturally described in terms of the magnetic helicity, using the formalism of relaxed states introduced by J. B. Taylor [Phys. Rev. Lett. 133, 1139 (1974)]. The equation for rate of change of magnetic helicity is shown to be a general law of resistive evolution, implying the former equation for rotational transform in the case of magnetic surfaces. In principle, the resistive evolution model provides a complete description of global long-time-scale plasma behavior in the limit where the plasma density vanishes. In this limit, the magnetohydrodynamic description of a plasma is not practical because of the vanishing of the inertial time scale.
Driven, resistive, force-free plasmas and reversed-field-pinch physics revisited
Authors: Prager S. C. , Turner Leaf
Published: July 2002

Solutions of the coupled steady-state equations, Ohm’s law, and curl B=λ(r)B, are obtained in slab and cylindrical geometries with two ignorable coordinates. Aside from the stark feature of small toroidal-field reversal near the plasma edge, the numerically obtained field profiles in cylindrical geometry mimic the observed experimental reversed-field-pinch profiles; e.g., Bz is a monotonically decreasing function of radius and, if the parallel resistivity is spatially independent, then also λ (i.e., j/B) is a monotonically decreasing function of radius. It is also shown that toroidal-field reversal is impossible in a toroidally symmetric, force-free, steady-state, Ohmic plasma having nested flux surfaces. It is suggested that the more sophisticated dynamics required to sustain the observed field reversal may be able to be relegated to the outer annular region containing the reversal surface. Understanding of this dynamics then may be facilitated by the fact that only one field component, the poloidal one, is dominant throughout this region.
Current-driven instabilities in the fluid limit: Parallel kinetic effects in reversed field pinches
Authors: Cayton Thomas E.
Published: July 2002

In order to lay a foundation for understanding kinetic effects on waves and instabilities in reversed field pinches, three different plasma models are employed to study linear perturbations of uniformly magnetized, infinite, homogeneous, current-carrying plasmas. Two different types of instability emerge: configuration-space instabilities driven by the macroscopic current and velocity-space instabilities driven by the relative drift between electrons and ions parallel to B. The dispersion properties of waves and parallel current and drift-driven instabilities with frequencies below the ion gyrofrequency are used to establish the physics limitations of the asymptotic guiding center plasma model. This model is then used to investigate parallel drift-driven instabilities in fully self-consistent, cylindrically symmetric, radially inhomogeneous equilibria that manifest large parallel currents and strong magnetic shear, as in reversed field pinches. The results of the cylindrical guiding center plasma are compared with those of the current-carrying infinite plasma to illustrate the effects of the magnetic shear and curvature generated by the equilibrium current. Although quantitative differences appear, the same qualitative features are found in each case. The results illuminate the nature of current-carrying plasmas. The dispersion properties of shear Alfvén waves in such a plasma are very different from ω=k∥cA. Some of the modified shear Alfvén waves that propagate against the current are destabilized by resonant electrons.
Guiding center Hamiltonian theory of free-electron lasers
Authors: Grebogi Celso , Uhm Han S.
Published: July 2002

The relativistic guiding center ponderomotive Hamiltonian for free-electron lasers is derived. The ponderomotive Hamiltonian together with the Poisson structure gives the full dynamical description of the slow electron motion. The derivation takes into account arbitrary signal wave polarization and wiggler field geometry including guide field nonuniformities. In particular, it is allowed (i) for a tapered axial guide quasistatic magnetic field along its direction of propagation, (ii) for a realizable wiggler to be tapered both in amplitude and in period, and (iii) for the signal electromagnetic wave to be a growing modulated wave of arbitrary geometry propagating in the direction of the static magnetic field. The equations of motion are then derived including the guiding center perpendicular drifts and beam quasistatic self-fields.
Current-driven drift waves in reversed field pinches
Authors: Gladd N. T. , Krall N. A.
Published: July 2002

Stability properties of current-driven drift waves are examined in the parametric environment typical of the toroidal reversed field pinch. In particular, the effects of field-aligned current, plasma beta, collisionality, and magnetic shear are examined. Under conditions leading to instability, transport effects are calculated, and found to be dominated by the electromagnetic nature of this instability.
Helicity content and tokamak applications of helicity
Authors: Boozer Allen H.
Published: July 2002

Magnetic helicity is approximately conserved by the turbulence associated with resistive instabilities of plasmas. To generalize the application of the concept of helicity, the helicity content of an arbitrary bounded region of space will be defined. The definition has the virtues that both the helicity content and its time derivative have simple expressions in terms of the poloidal and toroidal magnetic fluxes, the average toroidal loop voltage and the electric potential on the bounding surface, and the volume integral of E⋅B. The application of the helicity concept to tokamak plasmas is illustrated by a discussion of so-called MHD (magnetohydrodynamic) current drive, an example of a stable tokamak q profile with q less than 1 in the center, and a discussion of the possibility of a natural steady-state tokamak due to the bootstrap current coupling of tearing instabilities.
Equilibrium studies of a poloidal divertor pinch with a reversed toroidal field
Authors: Sarff J. S. , Sprott J. C. , Turner L.
Published: July 2002

An analytic solution for the force-free magnetic field, ∇×B=λB, in the poloidal divertor configuration of the Tokapole II device [Nucl. Fusion 19, 1509 (1979)] is presented. Experiments conducted on Tokapole II which provide equilibrium magnetic field profile measurements using a magnetic probe are then described. Observations include a non-constant-λ profile and a large diamagnetic current near the magnetic separatrix.
Vortex dynamics and the existence of solutions to the Navier–Stokes equations
Authors: Pumir Alain , Siggia Eric D.
Published: July 2002

The Biot–Savart model for a vortex filament predicts a finite time singularity in which the maximum velocity diverges as (t*−t)−1/2 for the time t tending to t*. The filament pairs with itself, yet remains locally smooth even though the characteristic length scales as (t*−t)1/2. A multiscale perturbative treatment of the Euler equations is developed for solutions that are locally a two-dimensional vortex dipole centered on a slowly varying three-dimensional space curve. For short periods of time the Euler and Biot–Savart solutions agree. Provided this correspondence persists, a sufficiently small viscosity ν will not control the divergence in the maximum velocity until it is of order exp(cst/ν), where cst is a constant of order the filament circulation. Singularities in the Navier–Stokes equations cannot be easily dismissed. The most questionable step in the arguments presented occurs for ν=0, namely whether the Euler vortex dipole solutions break down when they self-stretch.
Laser anemometer measurements of Reynolds stress in a turbulent channel flow with drag reducing polymer additives
Authors: Willmarth W. W. , Wei T. , Lee C. O.
Published: July 2002

Turbulence measurements with a high resolution laser Doppler anemometer in a channel flow with injection of a concentrated polyethylene oxide solution are reported. With polymer injection sufficient to yield a well mixed concentration of 10 ppm the total drag is reduced by 38%, but the sum of the Reynolds stress and the conventional molecular shear stress is only (2)/(3) of the force produced by the streamwise pressure gradient. Thus, the injected polymer solution has a significant effect on the turbulence and causes an additional retarding force equal to approximately (1)/(3) of the total drag.
Stochasticity in numerical solutions of the nonlinear Schrödinger equation
Authors: Shen Mei-Mei , Nicholson D. R.
Published: July 2002

The cubically nonlinear Schrödinger equation is an important model of nonlinear phenomena in fluids and plasmas. Numerical solutions in a spatially periodic system commonly involve truncation to a finite number of Fourier modes. These solutions are found to be stochastic in the sense that the largest Lyapunov exponent is positive. As the number of modes is increased, the size of this exponent appears to converge to zero, in agreement with the recent demonstration of the integrability of the spatially periodic case.
Stability of the low-frequency hot-electron interchange mode for a bumpy torus simulation model
Authors: Ohsawa Y. , Dawson J. M. , Van Dam J. W.
Published: July 2002

The parametric dependence of the growth rate of the low-frequency hot-electron interchange mode is studied with a two-and-a-half-dimensional relativistic electromagnetic particle code that models the geometry of a bumpy torus. The simulation results are compared in detail with finite-Larmor-radius theory, as well as zero-Larmor-radius theory. For the long-wavelength modes, the growth rates measured in the simulations tend to agree with those predicted from zero-Larmor-radius theory. For short-wavelength modes, the stabilizing effects of finite Larmor radius are significant.
Microconvection effects at double-diffusive gradient zone boundaries
Authors: Hull John R. , Katti Yojana
Published: July 2002

Microconvection in double-diffusive gradient zones is predicted to occur near the zone boundaries because of effects of boundary undulation and temperature modulation caused by impinging thermals in adjacent convecting zones. The equations that govern convective motion in a double-diffusive horizontal slab are solved for boundary conditions that incorporate these effects. Solution of these equations predicts a weakened salinity gradient near the gradient zone boundary between the rising thermals. When the salinity gradient is too weak, instability occurs, taking the form of descending plumes, which are seen in experiments.
A kinetic analysis of unsteady evaporation and condensation with an Oseen-like approximation
Authors: Soga Takeo
Published: July 2002

A linearized kinetic model equation with an Oseen-like approximation was applied to study the moderately strong unsteady evaporation and condensation problems. Asymptotic solutions were obtained for the weak (linearized) evaporation and condensation problems, disjoining the fluid dynamic equation with the Oseen approximation from the Knudsen layer equation. The asymptotic solution yielded correct features of the flow due to evaporation or condensation. The kinetic model equation was further applied to study the moderately strong evaporation and condensation problems. The results showed good agreement with the previous results derived from the nonlinear treatments and confirmed that the conventional slip flow theory is applicable for studying the moderately strong evaporation and condensation problems.
Electron cyclotron absorption at downshifted frequencies in the presence of a current-carrying superthermal tail
Authors: Bornatici M. , Ruffina U.
Published: July 2002

The absorption of the extraordinary mode at frequencies downshifted with respect to either the fundamental or the second harmonic electron cyclotron resonance and such that the relevant resonance lies outside the plasma is evaluated for a Maxwellian distribution with a current-carrying superthermal tail. The contribution from the current-carrying electrons to the absorption is obtained by Lorentz-transforming the dielectric tensor from the comoving to the laboratory frame. The dielectric tensor accounts for the fully relativistic cyclotron resonance condition and the corresponding Hermitian part includes the relevant thermal effects. The spatial dependence of the drift momentum, the density, and the temperature of both the bulk and the superthermals is accounted for in the evaluation of the absorption profile. The relevance of the relativistic effects is discussed with respect to both the profile of the absorption and the overall absorption.
Kolmogorov-like spectra in decaying three-dimensional supersonic flows
Authors: Porter D. H. , Pouquet A. , Woodward P. R.
Published: July 2002

A numerical simulation of decaying supersonic turbulence using the piecewise parabolic method (PPM) algorithm on a computational mesh of 5123 zones indicates that, once the solenoidal part of the velocity field, representing vortical motions, is fully developed and has reached a self-similar regime, a velocity spectrum compatible with that predicted by the classical theory of Kolmogorov develops. It is followed by a domain with a shallower spectrum. A convergence study is presented to support these assertions. The formation, structure, and evolution of slip surfaces and vortex tubes are presented in terms of perspective volume renderings of fields in physical space.