bluuebunny/crossref_metadata_2025 huggingface dataset:
A non-Abelian square root of Abelian vertex operators
Authors: Frieler K. , Rehren K.-H.
Published: July 2002

The quantum field theoretical formulation of Kadanoff’s “correlations along a line” in the critical two-dimensional Ising model is given in terms of p-products of Wightman fields. It provides a quadratic factorization, in the sense of operator-valued distributions, of Abelian chiral vertex operators into non-Abelian exchange fields. This basic result implies p-polynomial relations between fields from various conformal models in two dimensions; notably the two-dimensional local fields with chiral SU(2) symmetry at level 2 are shown to share the nontrivial peculiarities of the Ising model order and disorder fields. These examples have interesting implications for the properties of p-products in general.
Maxwell equations and the optical geometry
Authors: Sonego Sebastiano , Abramowicz Marek A.
Published: July 2002

We show that, in conformally static spacetimes, Maxwell equations take their simplest form when written in terms of the so-called “optical metric.”
Free energy and correlations of the number-theoretical spin chain
Authors: Guerra Francesco , Knauf Andreas
Published: July 2002

We analyze the number-theoretical spin chain with partition function Z(β) =ζ(β−1)/ζ(β) using the polymer model technique. The finite (grand) canonical chains give bounds for the limit free energy and internal energy. The correlation functions for inverse temperature β=−1 are products of two-point functions. A combinatorial result for general interval graphs is derived.
An application of Lax’s formalism to a class of curvilinear axially symmetric coordinates in three-dimensional space
Authors: Cerkaski Marcin
Published: July 2002

Solutions of a nonlinear system of differential partial equations in two-dimensional space are studied. We prove that the considered system is fully integrable and that its solutions determine an infinite class of mappings of the space of curvilinear axially symmetric coordinates onto the space of cylindric coordinates. The corresponding family of reverse transformations is found in a closed form. An infinite number of the first integrals of the nonlinear system is obtained. Symmetries of a class of electrostatic systems associated with the considered family of curvilinear coordinates are discussed.
Yang–Mills flow and uniformization theorems
Authors: Braham S. P. , Gegenberg J.
Published: July 2002

We consider a paraboliclike system of differential equations involving geometrical quantities to examine uniformization theorems for two- and three-dimensional closed orientable manifolds. We find that in the two-dimensional case there is a simple gauge theoretic flow for a connection built from a Riemannian structure, and that the convergence of the flow to the fixed points is consistent with the Poincare Uniformization Theorem. We construct a similar system for the three-dimensional case. Here the connection is built from a Riemannian geometry, an SO(3) connection and two other 1-form fields which take their values in the SO(3) algebra. The flat connections include the eight homogeneous geometries relevant to the three-dimensional uniformization theorem conjectured by Thurston. The fixed points of the flow include, besides the flat connections (and their local deformations), nonflat solutions of the Yang–Mills equations. These latter “instanton” configurations may be relevant to the fact that generic 3-manifolds do not admit one of the homogeneous geometries, but may be decomposed into “simple 3-manifolds” which do.
Wavelets and quantum algebras
Authors: Ludu A. , Greiner M. , Draayer J. P.
Published: July 2002

Wavelets, known to be useful in nonlinear multiscale processes and in multiresolution analysis, are shown to have a q-deformed algebraic structure. The translation and dilation operators associate to any scaling equation a nonlinear, two parameter algebra. This structure can be mapped onto the quantum group slq(2) in one limit, and approaches a Fourier series generating algebra, in another limit. A duality between any scaling function and its corresponding nonlinear algebra is obtained. Examples for the Haar and B-wavelets are worked out in detail.
On Lie algebras all nilpotent subalgebras of which are Abelian
Authors: Dallmer Elke
Published: July 2002

By Kirillov’s theorem, every non-Abelian nilpotent Lie algebra contains the three-dimensional Heisenberg algebra H(3) as a subalgebra. [R. Schimming, Arch. Math. 24, 65–74 (1988)]. Here we are interested in a sufficient condition for a non-nilpotent Lie algebra to contain a subalgebra isomorphic to H(3). Explicitly, we show: Every indecomposable non-nilpotent Lie algebra L of dimension dim L⩾3 with a nonvanishing center Z(L)≠{0} contains a non-Abelian nilpotent subalgebra and hence a copy of H(3).
Chiral limit of the two-dimensional fermionic determinant in a general magnetic field
Authors: Fry M. P.
Published: July 2002

We consider the effective action for massive two-dimensional QED in flat Euclidean space–time in the background of a general square-integrable magnetic field with finite range. It is shown that its small mass limit is controlled by the chiral anomaly. New results for the low-energy scattering of electrons in 2+1 dimensions in static, inhomogeneous magnetic fields are also presented.
Exceptional Lagrangians for spin-2 field: Standard variables
Authors: de Freitas Luciane R.
Published: July 2002

Exceptional Lagrangians for spin-2 field in terms of standard second order tensor φμν may be obtained using the method proposed some years ago by Lax. We found several nonlinear theories which can be used to describe the gravitational field. Among them, we discovered a particularly interesting one which has (in a strike analogy with Born model for spin one) an upper field value.
Dynamical symmetries, bi-Hamiltonian structures, and superintegrable n=2 systems
Authors: Rañada Manuel F.
Published: July 2002

The theory of dynamical but non-Cartan (or non-Noether) symmetries and the existence of bi-Hamiltonian structures is studied using the symplectic formalism approach. The results are applied to the study of superintegrable systems. It is shown that certain families of n=2 superintegrable systems related with the harmonic oscillator (as, e.g., the so-called Smorodinsky–Winternitz system) are bi-Hamiltonian systems endowed with dynamical symmetries of non-Cartan class.
A relation between anomaly coefficients and the group G2
Authors: Cutler R. W. , Kephart T. W.
Published: July 2002

We show that in 4D the anomaly coefficients for SU(3) irreps are equal to the dimensions of G2 irreps. This allows the direct calculation of 4D anomalies for any group in terms of the Weyl dimension formula for G2. We also give results for 6D and comment on the D>6 case.
Taylor vortex flow between eccentric coaxial rotating spheres
Authors: Bar-Yoseph P. , Solan A. , Hillen R. , Roesner K. G.
Published: July 2002

The rotationally symmetric, incompressible, spherical Couette flow between two spheres is examined, where the inner one rotates and the outer one is at rest. The investigation was done by means of a finite-element program that solves the axisymmetric Navier–Stokes equations. Both concentric and eccentric spherical gaps are considered for two different radii ratios of a medium sized gap. The emphasis is laid upon the development of Taylor vortices out of the basic laminar flow, the transition between flow modes and the effect of eccentricities of different magnitudes. In the concentric case, the transition from the basic flow to a flow with two pairs of Taylor vortices is investigated by a steady as well as a transient analysis. The transition from the basic flow to a flow with one pair of Taylor vortices is examined by a steady analysis using a mesh that is asymmetric about the equator and also by introducing a geometrical perturbation in the form of a small eccentricity. A hysteresis for this transition is found. As the eccentricity is increased, the magnitude of the hysteresis decreases until it disappears. Comparisons of the flow patterns with experimental results show good agreement.
A point vortex dipole model of an isolated modon
Authors: Hobson Dana D.
Published: July 2002

A point vortex dipole model for an isolated modon governed by the Charney–Hasegawa–Mima (CHM) equation is developed, building on the point vortex formulation of Zabusky and McWilliams [Phys. Fluids 25, 2175 (1982)]. The model dipole is compared to the exact modon solution in order to determine parameter values for which the model dipole matches the modon’s speed and far-field behavior. The model allows one to study nonuniform motions analytically. It predicts that right-moving modons in uniform motion should be stable in the sense that their paths exhibit small-amplitude oscillations in response to small perturbations of their initial orientation. It also predicts that left-moving modons in uniform motion should be unstable, being pushed into finite-amplitude motions by arbitrarily small perturbations. These predictions are confirmed by direct numerical simulation of modons evolving under the CHM equation. It is noted that although the distribution of vorticity within modons may be Lyapunov stable in nearly uniform motions, the paths of modons may be unstable to asymmetric perturbations.
Numerical investigation on the structure of a confined supersonic mixing layer
Authors: Lu P. J. , Wu K. C.
Published: July 2002

Direct numerical simulations using the high-resolution TVD scheme are performed for the study of two-dimensional confined spatially growing supersonic mixing layers. Numerical simulations, being forced by the linear instability wall modes, are justified by comparing the calculated results with both theoretical and experimental data. The numerically visualized downstream compression/expansion wave system explains the so-called ‘‘strange waves’’ observed in experiments and are found to be responsible for the rapid growth of the mixing layer in that region. The existence of shock waves would lead to mixing enhancement by accelerating the process of extracting turbulent kinetic energy from the mean stream. However, the phenomenon of shock-induced mixing improvement is found quite local around the shock impingement area, and often is followed by a saturation in turbulent energy absorption which impedes the further growth of the shear layer in the immediate downstream region. For the present cases considered, the subharmonic instability modes are not dominant, and the baroclinic-torque effect is comparatively less important for the vorticity development. These observations suggest that compressibility effects may behave in a considerably different manner as the underlying instability mechanism changes from the subsonic Kelvin–Helmholtz type to the present supersonic wall instability type.
Decomposition of the Boussinesq equations for shallow-water waves into a set of coupled Korteweg–de Vries equations
Authors: Mattioli F.
Published: July 2002

The Boussinesq equations for shallow-water waves are decomposed into a set of equations for waves propagating in two opposite directions. Such a decomposition is valid under the assumption of slowly varying depth, and includes a nonlinear interaction term neglected in the previous derivation by Kirby and Vengayil [J. Geophys. Res. 93, 10 782 (1988)]. It is shown, however, that the decomposition is not unique, because high-order terms can be dealt with in different manners.
Unity and diversity in mixing: Stretching, diffusion, breakup, and aggregation in chaotic flows
Authors: Ottino J. M.
Published: July 2002

Experiments and theory have produced a reasonably good qualitative understanding of the evolution of chaotic mixing of passive tracers, especially in two-dimensional time-periodic flow fields. Such an understanding forms a fabric for the evolution of breakup, aggregation, and diffusion-controlled reactions in more complex flows. These systems can be viewed as a population of ‘‘microstructures’’ whose behavior is dictated by iterations of a chaotic flow; microstructures break, diffuse, and aggregate, causing the population to evolve in space and time. This paper presents simple physical models for such processes. Self-similarity is common to all the problems; examples arise in the context of the distribution of stretchings within chaotic flows, in the asymptotic evolution of diffusion-reaction processes at striation thickness scales, in the equilibrium distribution of drop sizes generated upon mixing of immiscible fluids, in the equations describing mean-field kinetics of coagulation, in the sequence of actions necessary for the destruction of islands in two-dimensional flow, and in the fractal structure of clusters produced upon aggregation in chaotic flows.
The effect of walls on instability waves in supersonic shear layers
Authors: Morris P. J. , Giridharan M. G.
Published: July 2002

A spatial stability analysis is performed to determine the effect of wall placement on instability waves in confined supersonic shear layers. It is shown that the growth rates of Kelvin–Helmholtz instability waves are independent of wall height. However, supersonic instability waves are found to exhibit peaks and valleys in their growth rate curve as a result of the reinforcement and cancellation of the reflected Mach waves at the shear layer. Finally, it is shown how the instability growth rates in a ducted shear layer may be maximized by the proper choice of the duct width to height ratio.
Instabilities and bifurcations of interfacial water waves
Authors: Zhou C. P. , Lee J. H. W. , Cheung Y. K.
Published: July 2002

The fourth-order Zakharov equation for interfacial waves of two-layered fluids with finite depths is derived to include quintet interactions. Using this new equation the class I and class II instability and bifurcation of a two-dimensional Stokes interfacial wave into a three-dimensional steady wave is studied. Results are in good agreement with those by numerical calculations from the full unapproximated water wave and with experimental data.
A two-dimensional instability in a mixed convection flow with spatially periodic temperature boundary conditions
Authors: Tangborn Andrew
Published: July 2002

Two-dimensional numerical simulations of combined forced and natural convection have been carried out in a periodic channel with spatially periodic temperature boundary conditions at the lower wall and an insulated upper wall. The resulting flow separates from the lower wall just downstream of the hot section of the wall. At Re=45 and Ra=20 000 a weakly damped oscillatory flow is found in which the vortex periodically separates from the wall sending a plume of hot fluid to the center of the channel. After this periodic motion has died away, the upper half of the channel is at a uniform temperature and the vortex is again fixed to the wall. At Re=60 and Ra=100 000, self-sustained oscillations occur, but the plume motion is unable to reach the upper half of the channel. All of these flows show inflectional velocity profiles indicating that this is a Kelvin–Helmholtz type of instability.
Phase dynamics in the Taylor–Couette system
Authors: Wu Mingming , Andereck C. David
Published: July 2002

The phase dynamics of flows in the Taylor–Couette system have been studied by applying a forced modulation to the upper boundary of a large aspect ratio concentric cylinder system. In a one phase variable case, the Taylor vortex flow, the perturbations diffuse along the axial direction and the pattern’s response is well described by a simple diffusion model. In a two phase variable case, the wavy vortex flow, the perturbations either propagate as traveling waves or diffuse, depending on the coupling between the axial and azimuthal phase variables. In the turbulent Taylor vortex flow, where spatial coherence coexists with the turbulent flow, the phase dynamics of the coherent structure are described by a diffusion model with a diffusion coefficient an order of magnitude larger than for the laminar Taylor vortex flow.
A constitutive equation for concentrated suspensions that accounts for shear-induced particle migration
Authors: Phillips Ronald J. , Armstrong Robert C. , Brown Robert A. , Graham Alan L. , Abbott James R.
Published: July 2002

A constitutive equation for computing particle concentration and velocity fields in concentrated monomodal suspensions is proposed that consists of two parts: a Newtonian constitutive equation in which the viscosity depends on the local particle volume fraction and a diffusion equation that accounts for shear-induced particle migration. Particle flux expressions used to obtain the diffusion equation are derived by simple scaling arguments. Predictions are made for the particle volume fraction and velocity fields for steady Couette and Poiseuille flow, and for transient start-up of steady shear flow in a Couette apparatus. Particle concentrations for a monomodal suspension of polymethyl methacrylate spheres in a Newtonian solvent are measured by nuclear magnetic resonance (NMR) imaging in the Couette geometry for two particle sizes and volume fractions. The predictions agree remarkably well with the measurements for both transient and steady-state experiments as well as for different particle sizes.
Droplet migration, deformation, and orientation in the presence of a plane wall: A numerical study compared with analytical theories
Authors: Uijttewaal Wim S. J. , Nijhof Evert-Jan , Heethaar Robert M.
Published: July 2002

The motion of a deformable drop in linear unidirectional shear flow close to a fixed wall is considered using a boundary integral technique for Stokes flow. This problem is solved numerically to circumvent the limitations of existing analytical models, especially in the region near the wall. The lateral and longitudinal disturbance velocities of the particle were calculated and compared with analytical approximations. Although analytical theories give reasonable predictions, large deviations occur at small wall distances and large particle deformations. This is mainly due to the fact that the altered orientation and deformation of the particle, arising from the presence of a wall, is disregarded in all analytical models.
Two- and three-dimensional models for flow through a junction
Authors: Ranger K. B.
Published: July 2002

Two- and three-dimensional models of the fluid motion through a junction are described for Stokes flow. It is found that for both models separation of the streamlines can occur on the branch of the outer channel wall with smaller flow rate. The relevance of the results for flow at higher Reynolds numbers is also described.
A steady breaking wave
Authors: Dias Frédéric , Tuck E. O.
Published: July 2002

The problem of a supercritical uniform stream meeting a stagnant mass of water is considered. The whole oncoming flow is forced to overturn and to fall back and down forever like a waterfall into a bottomless chasm. The interaction between this waterfall and the oncoming flow is neglected. It is shown that the solution occurs only at a unique Froude number equal to 2.994.
Droplet patterns from capillary stream breakup
Authors: Orme Melissa , Willis Keeney , Nguyen Tuong-Van
Published: July 2002

Droplet patterns have been generated in a vacuum environment by capillary stream breakup initiated by a new form of applied disturbances. The method of producing droplet streams with flexibly controllable patterns is presented. The patterns are periodic sequences of droplets, characterized by specific drop-to-drop separations and diameters. The pattern repeats until the disturbance to the capillary stream is removed or altered. An important feature of this work is that the patterns are deterministic given knowledge of the characteristics of the disturbance waveform. A model has been developed that is based on conservation of momentum and linear theory, and predicts droplet stream configurations with excellent agreement with experiment. Use of spectral analysis demonstrates long-term periodicity and stability of the droplet patterns as well as the excellent agreement between the predicted droplet patterns and those experimentally obtained.
Wave interactions in the far wake of a body
Authors: Williamson C. H. K. , Prasad A.
Published: July 2002

There has been some question recently as to whether the far-wake structure of a bluff body is dependent on, or ‘‘connected’’ with, the precise details of the near-wake structure. Indeed, it has previously been assumed that there is no direct connection in scale or frequency. In the present work, observations are shown of a honeycomb-like 3-D pattern in the far wake, which is caused by an interaction between the decaying oblique shedding waves from upstream and large-scale 2-D waves in the far wake. A clear ‘‘connection’’ between the 3-D scales of the near and far wakes is thereby demonstrated. The symmetry and spanwise wavelength of Cimbala et al.’s [J. Fluid Mech. 190, 265 (1988)] 3-D pattern are precisely consistent with such wave interactions. In the presence of parallel shedding, the lack of a honeycomb pattern shows that the pattern is clearly dependent on oblique vortex shedding. It also follows that for oblique shedding, the far-wake 2-D waves cannot possibly be the result of vortex pairing.
Rotation invariance for steady Hele–Shaw flows
Authors: Tian Fei Ran , Vasconcelos Giovani L.
Published: July 2002

A new rotation symmetry for steady Hele–Shaw flows is reported. In the case when surface tension is neglected, it is shown that if a curve 𝒞 moving with constant velocity U is a solution to the Hele–Shaw problem, then the curve 𝒞̃ obtained from a rotation of 𝒞 about its center by an arbitrary angle is also a solution with the same velocity U. Similar results hold for the case with surface tension if and only if the Schwarz function of the curve 𝒞 is regular in the fluid region and at most a linear function at infinity. Several examples in which this principle is used to generate new solutions to the problem are also discussed.
The design and optimization of recombination extreme-ultraviolet lasers
Authors: Epstein R.
Published: July 2002

Recent evidence for amplification of the Balmer-alpha line of hydrogenlike carbon in a recombining plasma [Opt. Commun. 54, 289 (1985)] raises the question of the relative importance of radiative cooling in this experiment and of the role of radiative cooling in optimizing future experiments. This paper approaches this question using results from hydrodynamic and atomic-kinetic simulations of this experiment and some hypothetical variations. A new feature of these simulations is the use of an explicit nonlocal treatment of the Doppler-enhanced escape probability of resonance radiation to take into account opacity effects that are an important limitation of this and many other extreme-ultraviolet and x-ray laser schemes. It is shown that short-pulse (∼100 psec) illumination and cylindrical expansion are very important. Mixing is required for effective cooling of the carbon by a radiative coolant, but the resulting dilution of the lasant reduces the gain coefficient. It is found that amplification cannot be obtained with the prolonged heating caused by long (600 psec) pulses, even with radiative cooling. Gain results comparable to those of other workers have been obtained in simulations of hypothetical cases.
Coherent structures in the planar magnetron
Authors: Kaup D. J.
Published: July 2002

An analysis of the initial value problem for the planar magnetron reveals that a coherent structure (convective cell) can be created from arbitrary initial conditions and that these structures will grow linearly in time. This is proposed as the explanation of the origin of the convective cell formation seen in recent numerical simulations.
Strong radiation guiding in a Raman free-electron laser under space-charge neutralization
Authors: Tripathi V. K. , Liu C. S.
Published: July 2002

A high-current relativistic electron beam propagating through a plasma causes local depression in plasma electron density to attain charge neutralization. The plasma duct thus formed guides and localizes high-frequency radiation when the beam current Ib≳mc3/e≊17 K A. This scheme of plasma guiding of a free-electron laser leads to strong localization of the radiation wave, and to a much higher growth rate for free-electron lasers.
Imploding neon puff-gas plasmas. II
Authors: Clark R. W. , Davis J.
Published: July 2002

The influence of atomic and radiation modeling on the dynamics and energetics of imploding neon gas-puff plasmas is investigated using a one-dimensional nonlocal thermodynamic equilibrium radiation hydrodynamic model. Results using a simplified description of the atomic physics and radiation transport are contrasted with those from a detailed description. Two configurations are considered: an imploding hollow cylindrical gas puff, both with and without a low density central core plasma. It is found that, in both cases, the expanded atomic model simulations predict a larger fraction of the total energy lost to radiation; the radiative efficiency is greater both because of the enhanced L-shell structure and because of greater compressions obtained as a consequence of the enhanced cooling. For each case, the energy history of the implosion and representative emission spectra are presented.
Candidate mode for electron thermal energy transport in multi-keV plasmas
Authors: Coppi B. , Migliuolo S. , Pu Y-K.
Published: July 2002

The linear and quasilinear theory of the collisionless trapped electron mode (also called the ‘‘ubiquitous’’ mode) is analyzed, in order to illustrate its possible role in the electron thermal energy transport observed in magnetically confined plasmas. This instability is driven by the combined effects of the plasma pressure gradient (which includes the contributions from the temperature gradients of ions and electrons) and of the local magnetic curvature drift of trapped electrons and of circulating and trapped ions. Depending on the value of its wavelength across the magnetic field, this mode can connect with a branch of the ion temperature gradient instability, provided the ion temperature gradient is sufficiently strong. Also, under certain conditions, it can be driven unstable solely by a combination of electron temperature gradient and Landau damping by trapped electrons. The relevant modes are found to be robust against variation of parameters such as the electron collisionality, and to be consistent candidates in order to explain the experimentally observed rate of electron thermal energy transport from the center of the plasma column.
Microinstability threshold of an axially focused neutralized ion beam
Authors: Ågren O. , Berk H. L. , Wong H. V.
Published: July 2002

The response to electrostatic perturbations, φ=φ̂(r,z)ei(lθ−ωt), is investigated for the Migma Exyder, a proposed disk-shaped device where ions are trapped in the periphery and focused towards the axis [Nucl. Instrum. Methods A 271, 214 (1988)]. The ions are modeled as a relativistic monoenergetic distribution with a small spread in the impact parameter (the distance of closest approach to the axis) and with the axial extent ΔZ much shorter than the radial extent R0. It is found that odd l modes do not give rise to a low-frequency response. For l=0, an energy principle for low frequency ion–ion interactions is formulated, and it is shown that the extremizing perturbation is located in a narrow region surrounding the axis. The threshold is proportional to the total number of stored particles, N=4ε0(π−2)γ(γ2−1) ×mic2R0/q2i, where γ is the usual relativistic factor, and this stability condition therefore allows for a high density on axis in highly focused systems. Compared to a cylindrical shape, a disk-shaped plasma gives an improvement in the density by the factor R0/ΔZ. The threshold in particle number for the relativistic ion–ion two-stream instability scales as γ3 and thus with relativistic effects the instability is further suppressed. Inclusion of the electron response increases the threshold even further. Preliminary investigations indicate that finite frequency l=0 modes can give a lower threshold than the zero frequency case, at least for nonrelativistic beam energies. These finite frequency instabilities can arise from coupling between positive and negative energy modes. Finite l modes arise if electrons are magnetized at the axis of the device. A balance between the electron field energy and the cross field electron convection establishes discrete modes. When these modes resonate with the ion bounce motion or azimuthal drift motion, bands of instability arise with relatively low density thresholds compared to the l=0 case.
Magnetic neutral point stretching and coalescence in tearing-generated magnetohydrodynamic structures
Authors: Malara F. , Veltri P. , Carbone V.
Published: July 2002

The time evolution of the instability of a sheet pinch is numerically studied using a sufficiently high ratio of system length to width in order to allow the simultaneous growth of several unstable wavelengths. This numerical simulation provides new insights into the nonlinear development of the tearing instability. Before the instability saturates, the nonlinear interactions among the unstable modes produce local coalescence phenomena that destroy the weaker current pinches and reduce the number of magnetic islands. In contrast with the usual picture, this coalescence is not due to the attraction between the current maxima, but is due to the stretching of the X-neutral points associated with the most intense current pinches. The global perturbation growth rate remains essentially unchanged in time, being of the order of the resistive instability growth rate.
Self-consistent theory for ion gyroresonance
Authors: Ye Huanchun , Kaufman Allan N.
Published: July 2002

For describing ion gyroresonance processes, a complete set of self-consistent Vlasov–Maxwell equations is derived by systematically transforming a self-consistent action principle from particle coordinates to guiding-center/oscillation-center coordinates. They include the oscillation-center Vlasov equation; the equations for wave–particle resonant interactions; and Maxwell equations for the background electromagnetic fields. These equations satisfy local conservation laws for energy, momentum, and angular momentum, constructed by using the Noether algorithm. A heuristic interpretation based on the theory of linear mode conversion in ray phase space is also presented for ion gyroresonance processes, which suggests a method for obtaining analytic solutions in general geometry.
Plasma corners. I: Constant toroidal current density
Authors: Kaiser R. , Lortz D. , Spies G. O.
Published: July 2002

If a toroidal plasma–vacuum interface has a corner, then it contains a stagnation point of the poloidal magnetic field, thus being part of a separatrix. Plasma corners are studied in magnetohydrostatic equilibria with plane symmetry (the large-aspect-ratio limit of axially symmetric ones) and constant axial current density. Their structure depends only on the multiplicity n of the stagnation point (defined such that the separatrix divides a neighborhood into 2n sectors) and on the relative orientation of the axial current density and the poloidal magnetic field nearby (termed ‘‘ordinary’’ or ‘‘extraordinary,’’ depending on whether the latter can be viewed as being generated by the former): Simple (i.e., n=2) ordinary corners resemble simple X points in vacuum fields in that all four sectors are right angled, but differ in that, for small distances r from the X point, the poloidal magnetic field is O(r log r−1) rather than O(r), and in that the curvature of the separatrix is O(r−1) rather than O(1). Degenerate (i.e., n≥3) ordinary corners have a vanishing angle (plasma cusps), and all extraordinary corners have a straight angle (smooth plasma–vacuum interfaces).
Virial equation for the two-dimensional pure electron plasma
Authors: Corngold Noel R.
Published: July 2002

The virial for a system of very long, parallel, charged rods is particularly simple. The virial equation (‘‘theorem’’) relates that quantity to the wall virial and to random and organized internal energies of the system. In the case of a long cylinder of pure-electron plasma, the virial equation contains, as a special case, an equation derived recently by Davidson and Lund on the basis of mean-field theory. The virial equation may be used to control the computation of thermodynamic functions for the plasma. It also gives insight into the more complicated motions which occur when the central axis of the column moves in a closed orbit.
Particle and energy confinement bifurcation in tokamaks
Authors: Hinton F. L. , Staebler G. M.
Published: July 2002

A bifurcation in the particle and energy confinement properties of a tokamak plasma, with properties similar to the experimentally observed L-mode to H-mode transition, is shown to follow from a simple model for the transport. The basic assumptions are that the edge turbulence is suppressed by sheared E×B flow, and the radial ion pressure gradient is approximately balanced by the radial electric field. The particle and thermal diffusivities are assumed to be given by simple nonlinear functions of the radial electric field shear, which is related to the density and pressure gradients. The steady-state density and pressure profiles are found to have large gradient regions near the plasma edge when the product of edge energy flux and particle flux exceeds a threshold value, which corresponds to the H-mode threshold. The particle and energy confinement times are significantly larger when this threshold is exceeded. The confinement times exhibit hysteresis, corresponding to a dependence of quasiequilibrium states on the time history. The width of the edge layer where the gradients are large is determined mainly by the particle source profile, which is assumed to be concentrated near the plasma edge. This edge layer width increases slowly with increasing edge heat flux or heating power, as observed experimentally.
The thick, turbulent boundary layer on a cylinder: Mean and fluctuating velocities
Authors: Lueptow Richard M. , Leehey Patrick , Stellinger Thomas
Published: July 2002

The mean and fluctuating velocities in a turbulent boundary layer on a cylinder have been experimentally characterized for the case where the boundary layer is thick compared to the radius of transverse curvature. The mean velocity measurements suggest a mixed scaling for the ‘‘log law of the wall’’ using the wall coordinate yUτ/ν and the ratio of the local boundary layer thickness to the radius of the cylinder δ/a. A relation for the slope and intercept of the log law of the wall as functions of δ/a based on empirical results and simple analysis is presented. Measurements of the Reynolds stress for δ/a of order 10 show that the Reynolds stress drops off much more quickly with distance from the wall than for a turbulent boundary layer on a flat plate. Both the Reynolds stress data and the turbulent intensity in the mean flow direction data are functions of the inverse radial distance from the center of the cylinder.
Spectrum of resistivity-gradient-driven turbulence
Authors: Terry P. W. , Diamond P. H. , Shaing K. C. , Garcia L. , Carreras B. A.
Published: July 2002

The resistivity fluctuation correlation function and electrostatic potential spectrum of resistivity-gradient-driven turbulence are calculated analytically and compared to the results of three-dimensional numerical calculations. Resistivity-gradient-driven turbulence is characterized by effective Reynolds’ numbers of order unity. Steady-state solution of the renormalized spectrum equation yields an electrostatic potential spectrum 〈φ̂2〉ky ∼k−3.25y . Agreement of the analytically calculated potential spectrum and mean-square radial velocity with the results of multiple helicity numerical calculations is good. This comparison constitutes a quantitative test of the analytical turbulence theory used. The spectrum of magnetic fluctuations is also calculated and agrees well with that obtained from the numerical computations.
Instability mechanisms in dynamic thermocapillary liquid layers
Authors: Smith Marc K.
Published: July 2002

The physical mechanisms for the hydrothermal wave instability found in dynamic thermocapillary liquid layers by Smith and Davis [J. Fluid Mech. 132, 119 (1983)] are described.
The asymptotic velocity of fast ions in expanding plasmas
Authors: Sack Ch. , Schamel H. , Schmalz R.
Published: July 2002

The front of an expanding plasma generally exposed to charge separation is shown to acquire asymptotically a speed given by self-similar theory.
Numerical experiments on the stability of unsteady circular Couette flow with random forcing
Authors: Chen J.-C. , Neitzel G. P. , Jankowski D. F.
Published: July 2002

The stability of unsteady circular Couette flow generated by monotonically increasing the angular speed of the inner cylinder is examined through a series of numerical experiments. Random disturbances are imposed continually on the basic state by the inclusion of random forcing terms in the axisymmetric Navier–Stokes equations. Results of the calculations are compared with previous theoretical and experimental results.
The decay of kinetic energy and temperature variance in three-dimensional isotropic turbulence
Authors: Lesieur Marcel , Montmory Colette , Chollet Jean-Pierre
Published: July 2002

With the aid of the eddy-damped quasinormal Markovian statistical theory (EDQNM) developed by Orszag [J. Fluid Mech. 41, 363 (1970)], the dynamics of a passive scalar (such as the temperature in a slightly heated flow) in three-dimensional isotropic turbulence is studied. Starting initially with kinetic energy and temperature spectra exponentially decreasing above a wavenumber ki, it is shown that in the limit of zero viscosity (ν→0) and conductivity (κ→0) the temperature gradient variance diverges at a finite critical time tc, together with the enstrophy. After tc, the kinetic energy and temperature variance are dissipated at finite rates that are independent of ν and κ if both are small. Afterward, the decay laws of the temperature variance and the wavenumber kθ characteristic of the temperature spectrum maximum are determined analytically when the temperature is initially injected at kθ≫ki. First, a Richardson law for the temperature integral scale is demonstrated without any assumption on the low k behavior of the temperature spectrum. Second, it is shown that kθ(t) rapidly catches up with ki(t), which explains some ‘‘anomalous’’ temperature decay behavior, as observed experimentally by Warhaft and Lumley [J. Fluid Mech. 88, 659 (1978)]. The analytical analysis of the latter phenomenon generalizes, for an arbitrary infrared temperature spectrum, an earlier study of Nelkin and Kerr [Phys. Fluids 24, 1754 (1981)].
Stabilization of laminar boundary layers by compliant membranes
Authors: Domaradzki J. Andrzej , Metcalfe Ralph W.
Published: July 2002

Direct numerical simulations have been performed to study boundary layer flow over a compliant membrane. While coupling directly to the fluid dynamics code through the wall boundary condition, this membrane model displays many of the important features of other compliant coatings. While membrane parameters are identified that increase the critical Reynolds number by a factor of 2 compared with the rigid wall, this is mitigated by a significant increase in the growth rates in the unstable region. A detailed analysis of the temporal evolution and spatial structure of the terms in the kinetic energy balance equation shows significant differences in the behavior of two different classes of modes of the system: class A waves, which are destabilized by increased dissipation in the membrane, and class B waves, which are stabilized by membrane dissipation. For class A waves, the dominant dissipative mechanism is viscous damping in the fluid augmented by negative energy production, the principal stabilization mechanism seen in the ‘‘smart wall’’ algorithm simulations. For class B waves, direct transfer of energy to, and dissipation by, the membrane dominates stabilization of the flow. For class A waves, the membrane stabilizes the flow not by dissipating energy, but by modifying the flow to decrease energy production and enhance viscous dissipation in the fluid.
Solutal convection during directional solidification of a binary alloy: Influence of side walls
Authors: Guérin R. Z. , Billia B. , Haldenwang P. , Roux B.
Published: July 2002

In this study the effect of rigid side walls on the onset of solutal convection in the melt is investigated for upward solidification of a binary alloy. The physics is described by the Navier–Stokes equations in the Boussinesq approximation and by the balance of solute, which is coupled with the appropriate boundary conditions. By using a Tau–Chebyshev spectral method the numerical resolution of the perturbed system has been carried out for two alloys: lead–tin, which is the reference in the literature, and lead–thallium, which is currently under study. For both cases the lateral confinement has a stabilizing effect for all the aspect ratios that have been considered.
Observations of enhanced Thomson scattering
Authors: Batha S. H. , Bahr R. , Goldman L. M. , Seka W. , Simon A.
Published: July 2002

The optical spectrum of scattered laser radiation from laser-produced plasmas has been measured between half and twice the incident laser frequency ω0. Three spectral bands have been found, two of which straddle the 3ω0/2 spectrum. The third band is located near ω0/2. These observations can be successfully interpreted in terms of a model in which there is enhanced Thomson scattering into the ‘‘electron line.’’ This enhancement is due to fast electrons creating a local bump-on-tail instability [Phys. Rev. Lett. 53, 1912 (1984)]. An alternative interpretation in terms of the conventional stimulated Raman scattering and associated anti-Stokes radiation is inconsistent with our observations.
Inelastic collision model for vibrational–translational and vibrational–vibrational energy transfer in the direct simulation Monte Carlo method
Authors: Abe Takashi
Published: July 2002

The new model for molecular vibrational energy transfer is proposed for an application to the direct simulation Monte Carlo (DSMC) method. The model is based on the inelastic collision cross section with the detailed balance relation at equilibrium, and can treat not only the translational–vibrational energy transfer but also the vibrational–vibrational energy transfer. The vibrational energy is treated as a collection of discrete levels. The performance of the present model was demonstrated through an application to the relaxation problem. The simulation results by means of the DSMC incorporated with the present model show a good agreement with the results obtained by means of the master equation.
A plane mixing layer with cross-shear
Authors: Atsavapranee P. , Gharib M.
Published: July 2002

The effect of cross-shear on a nominally two-dimensional plane mixing layer is investigated. A temporal mixing layer is generated with a stratified tilting tank similar to that used by Thorpe [J. Fluid Mech. 32, 693 (1968)], and cross-shear is introduced to this mixing layer to simulate situations the authors believe are widespread in industrial and natural flows. A new type of ‘‘co-rotating’’ streamwise vortices arises from the introduction of cross-shear, and the mixing rate is found to be greatly enhanced.
Interfacial flow over a step
Authors: Moni J. N. , King A. C.
Published: July 2002

Steady, supercritical flow of a two fluid system, over a semiinfinite step at the bottom of a channel that is bounded above by a rigid horizontal plane, is considered. Both fluids are assumed to be inviscid and incompressible and to flow irrotationally, but to have different densities. A transformation technique is used to reformulate the problem as a system of nonlinear integrodifferential equations, for the interfacial angle θ, and a connection equation for the jump of the potential across the interface. A linearized theory, based upon a small-step height, is presented and indicates that the nature of the interface formed depends on whether the upstream flow is subcritical or supercritical. Numerical solutions for the system are presented showing their dependence on the step height, density, speed, and depth ratios, respectively, and also on the Froude number of the lower fluid.
Imposing a magnetic field across a nonaxisymmetric shear layer in a rotating spherical shell
Authors: Hollerbach Rainer
Published: July 2002

In the context of the generation of the Earth’s magnetic field, nonaxisymmetric solutions of the forced momentum equation in a rotating spherical shell are considered in the inertia-less, inviscid limit. It has previously been pointed out that, in general, such solutions are singular, with all three flow components discontinuous across the cylinder tangent to the inner core and parallel to the axis of rotation. An integral constraint on the forcing was derived, which must be satisfied if the inviscid solution is to be nonsingular, and it was suggested that in the presence of a magnetic field the Lorentz force would adjust to satisfy this constraint, thereby eliminating the need for the viscous shear layer, which otherwise resolves the singularity. In this work an axisymmetric field is imposed across this shear layer, and it is demonstrated that for a sufficiently strong field this adjustment does indeed occur.
Modification of the Euler equations for ‘‘vorticity confinement’’: Application to the computation of interacting vortex rings
Authors: Steinhoff John , Underhill David
Published: July 2002

A new ‘‘vorticity confinement’’ method is described which involves adding a term to the momentum conservation equations of fluid dynamics. This term depends only on local variables and is zero outside vortical regions. The partial differential equations with this extra term admit solutions that consist of Lagrangian-like confined vortical regions, or covons, in the shape of two-dimensional (2-D) vortex ‘‘blobs’’ and three-dimensional (3-D) vortex filaments, which convect in a constant external velocity field with a fixed internal structure, without spreading, even if the equations contain diffusive terms. Solutions of the discretized equations on a fixed Eulerian grid show the same behavior, in spite of numerical diffusion. Effectively, the new term, together with diffusive terms, constitute a new type of regularization of the inviscid equations which appears to be very useful in the numerical solution of flow problems involving thin vortical regions. The discretized Euler equations with the extra term can be solved on fairly coarse, Eulerian computational grids with simple low-order (first- or second-) accurate numerical methods, but will still yield concentrated vortices which convect without spreading due to numerical diffusion. Since only a fixed grid is used with local variables, the vorticity confinement method is quite general and can automatically accommodate changes in vortex topology, such as merging. Applications are presented for incompressible flow in 3D, where pairs of thin vortex rings interact and, in some cases, merge.
Capillary–gravity periodic and solitary waves
Authors: Dias Frédéric
Published: July 2002

It is now well-known that capillary–gravity waves of solitary type exist in deep water. These waves bifurcate from a train of trivial periodic waves when the wave number corresponds to the minimum of the dispersion curve. Such solitary waves are characterized by decaying oscillations in their tail. In this Letter, it is shown how these recently discovered waves can be obtained as the limit of periodic waves as the wavelength is continuously increased. Moreover, the existence of new branches of solitary waves is conjectured.