bluuebunny/crossref_metadata_2025 huggingface dataset:
A gauge condition for orthonormal three-frames
Authors: Nester James M.
Published: July 2002

A set of natural gauge conditions for an orthonormal frame on a three-dimensional Riemannian manifold is discussed. The conditions determine a teleparallel geometry. They may be regarded as a nonlinear elliptic system for a rotation. Existence and uniqueness of solutions are discussed using the linearized system. Applications to Einstein gravity are noted.
The Clifford algebra of an infinite-dimensional space
Authors: Wene G. P.
Published: July 2002

The Clifford algebra of a real infinite-dimensional vector space is constructed. This algebra contains all finite- and infinite-dimensional Clifford algebras over the real and complex numbers. Some of the mathematical properties of these algebras are discussed; the automorphisms and involutions are specifically addressed. The special case with metric gνμ=δνμ, ν, μ=1,2,..., follows as a corollary to the more general results.
Multivariable Meixner, Krawtchouk, and Meixner–Pollaczek polynomials
Authors: Tratnik M. V.
Published: July 2002

A multivariable biorthogonal generalization of the Meixner, Krawtchouk, and Meixner–Pollaczek polynomials is presented. It is shown that these are orthogonal with respect to subspaces of lower degree and biorthogonal within a given subspace. The weight function associated with the Krawtchouk polynomials is the multivariate binomial distribution.
All SL(3,R) ladder representations
Authors: Šijački Dj.
Published: July 2002

All unitary and nonunitary ladder (multiplicity free with respect to the ∼(SO)(3) maximal compact subgroup) representations of the double covering group ∼(SL) (3,R) of the SL(3,R) group are cataloged and presented explicitly. The list of nonunitary representations is corrected and completed, and a new insight concerning the Δj=2 ladder representation starting with j= (3)/(2) is obtained.
On Hamiltonian systems in two degrees of freedom with invariants quartic in the momenta of form p21p22⋅⋅⋅
Authors: Evans N. W.
Published: July 2002

A search is made for autonomous Hamiltonian systems in two degrees of freedom which admit a second invariant quartic in the momenta with leading term p21p22/ 2. A sufficient condition for the resulting functional equation to possess solutions is deduced and a family of integrable systems is identified, which under the equivalence class of linear transformations reduce to a simpler integrable system found originally by Bozis. The method of Lax pairs is used to find further solutions to the functional equation and give new classes of integrable but nonseparable Hamiltonians.
Two-body resonance scattering and annihilation of composite charged particles
Authors: Kuperin Yu. A. , Melnikov Yu. B.
Published: July 2002

A model of two-body scattering including interaction between the external (Coulomb) and internal (e.g., quark) channels is constructed and investigated. A mathematically strict description is based on extensions theory for symmetric operators. Extra (internal) channel simulates complicated structure of charged particles and generates energy-dependent effective interaction in the external channel. The main effects of this short-range energy-dependent interaction in the system of charged particles (Zel’dovich effect, appearance of resonances, relative shift formula, and so on) are studied. Both for models of zero–range and nonzero–range energy-dependent interaction stationary scattering theory is constructed. In the frames of the same method a model of a system with extra (annihilation) scattering channel is considered.
On the evaluation of the U(3) content of the matrix elements of one- and two-body operators
Authors: Vanagas V. , Castilho Alcarás J. A.
Published: July 2002

An expression for the U(3) content of the matrix elements of one- and two-body operators in Elliott’s basis is obtained. Three alternative ways of evaluating this content with increasing performance in computing time are presented. All of them allow an exact representation of that content in terms of integers, avoiding rounding errors in the computer codes. The role of dual bases in dealing with nonorthogonal bases is also clarified.
On polynomial solutions of differential equations
Authors: Turbiner A.
Published: July 2002

A general method of obtaining linear differential equations having polynomial solutions is proposed. The method is based on an equivalence of the spectral problem for an element of the universal enveloping algebra of some Lie algebra in the ‘‘projectivized’’ representation possessing an invariant subspace and the spectral problem for a certain linear differential operator with variable coefficients. It is shown in general that polynomial solutions of partial differential equations occur; in the case of Lie superalgebras there are polynomial solutions of some matrix differential equations, quantum algebras give rise to polynomial solutions of finite-difference equations. Particularly, known classical orthogonal polynomials will appear when considering SL(2, R) acting on RP1. As examples, some polynomials connected to projectivized representations of sl2(R), sl2(R)q, osp(2,2), and so3 are briefly discussed.
Spinors and the Dirac operator on hypersurfaces. I. General theory
Authors: Trautman Andrzej
Published: July 2002

It is shown that a hypersurface immersed isometrically into the Euclidean space Rn+1, where n=2ν or 2ν+1, has a pin structure such that the associated bundle of 2ν-component spinors is trivial. This is used to derive a new formula for the Dirac operator on hypersurfaces. The Dirac operator is slightly modified to be compatible with the twisted adjoint representation of the pin group. When Rn+1 is foliated by hypersurfaces, then the Dirac operator in Rn+1 splits into a radial and a tangential part with respect to the foliation. There is a corresponding new formula for the Laplacian.
Nondiagonal double seed solutions and double soliton solution family of the Einstein equations
Authors: Gao Ya-Jun , Zhong Zai-Zhe
Published: July 2002

By using the double inverse scattering method, the problem of how to find new soliton solutions of the stationary axisymmetric vacuum field equation is studied. It is found that, for some kinds of seed solutions, the scattering wave functions can be directly obtained. Some examples of application are given. Similar results in the cylindrically symmetric case are also discussed.
A gauge theoretical formulation of a frustrated Ising system
Authors: Basu B.
Published: July 2002

The gauge theoretical formulation of a frustrated Ising model is studied here. In this formulation the Chern–Simons term has played the key role. The inherent anisotropic feature of the system is associated with the order parameter which violates the commutativity of translation.
Yang–Baxter deformations of semisimple Lie algebras
Authors: Lüdde Mirko
Published: July 2002

To every solution of the unparametrized Yang–Baxter equation there is associated a bialgebra, which is generated by an analog of the Chevalley generators of semisimple Lie algebras. The q-deformed algebras Uq(g) are recovered as special cases, the algebra of Faddeev–Reshetikhin–Takhtadzhyan is contained as a subalgebra. A geometrical interpretation of the algebra is given, which hints at some connection to Dotsenko–Fateev models of two-dimensional conformal quantum fields and perturbations thereof.
Canonical commutation relations, the Weierstrass Zeta function, and infinite dimensional Hilbert space representations of the quantum group U
q(𝔰𝔩2)
Authors: Arai Asao
Published: July 2002

A two-dimensional quantum system of a charged particle interacting with a vector potential determined by the Weierstrass Zeta function is considered. The position and the physical momentum operators give a representation of the canonical commutation relations with two degrees of freedom. If the charge of the particle is not an integer (the case corresponding to the Aharonov–Bohm effect), then the representation is inequivalent to the Schrödinger representation. It is shown that the inequivalent representation induces infinite-dimensional Hilbert space representations of the quantum group Uq(𝔰𝔩). Some properties of these representations of Uq(𝔰𝔩) are investigated.
Nonrelativistic conformal groups. II. Further developments and physical applications
Authors: Negro J. , del Olmo M. A. , Rodrı́guez-Marco A.
Published: July 2002

The finite-dimensional conformal groups associated with the Galilei and (oscillating or expanding) Newton–Hooke space–time manifolds was characterized by the present authors in a recent work. Three isomorphic group families, one for each nonrelativistic kinematics, were obtained, whose members are labeled by a half-integer number l. Since the action of these groups on their corresponding space–time manifolds is only local, a linearization is introduced here such that the corresponding action is well defined everywhere. In particular, the (l=1)-conformal cases that can be obtained by contraction from the well-known Minkowskian conformal group are treated in more detail. As an application of physical interest, the conformal invariance of the Galilean electromagnetism is studied. In order to achieve it, the pertinent local representations of the Galilean conformal algebras are derived.
Energy conditions for a spherically symmetric kink space–time
Authors: Dunn K. A. , Harriott Tina A. , Williams J. G.
Published: July 2002

The tetrad formalism is used to study a broad class of spherically symmetric kink space–times whose Einstein tensor is computed and then diagonalized. A simple example of such a space–time is shown to satisfy the weak energy condition and to be extendible to a space–time that is geodesically complete.
Uncertainty principle for proper time and mass
Authors: Kudaka Shoju , Matsumoto Shuichi
Published: July 2002

We review Bohr’s reasoning in the Bohr–Einstein debate on the photon box experiment. The essential point of his reasoning leads us to an uncertainty relation between the proper time and the rest mass of the clock. It is shown that this uncertainty relation can be derived if only we take the fundamental point of view that the proper time should be included as a dynamic variable in the Lagrangian describing the system of the clock. Some problems and some positive aspects of our approach are then discussed.
Spin–lattice relaxation in phase-separated He3–4He solid solution
Authors: Mikhin N. P. , Polev A. V. , Rudavskii È. Ya. , Shvarts V. A.
Published: July 2002

The spin–lattice relaxation time in a He3–4He solid solution with the initial concentration 3.18%3He is measured during phase separation by using the pulsed NMR technique. The relaxation time in a concentrated bbc phase formed as a result of phase separation is found to be independent of temperature over the entire range of its existence and is determined by the Zeeman-exchange interaction mechanism. In the dilute hcp daughter phase, the spin–lattice relaxation time increases on cooling according to the law T1∼x−n, where n=0.88±0.12, and x is the He3 concentration. The values of T1 in this phase coincide with the values corresponding to a homogeneous (nonseparated) solution of the same concentration.
Melting of He3 in a phase-separated solid He3–4He mixture
Authors: Haley R. P. , Adams E. D.
Published: July 2002

The melting pressure of the He3-rich phase, which is formed after phase separation of a mixture of 0.6% He3 in He4, has been studied in the temperature range 1–150 mK, below the phase-separation temperature Tps, at pressures between 2.78 and 3.56 MPa. Measurements were made with the mixture confined in a silver sinter, and also in an open volume for comparison. An elevation of the melting pressure relative to pure He3 of up to 60 kPa in the sinter cell and 20 kPa in the open-volume cell was observed. Hysteresis between the freezing and melting temperatures was found for both cells, similar to that observed for pure He3 in small pores. The results of Schrenk et al. for heat capacity measurements on a similar system are discussed.
A new variational method in the problem of the spectrum of elementary excitations in an edge-dislocation crystal
Authors: Dubrovskii I. M.
Published: July 2002

A new method based on a combination of the direct variational method and perturbation theory is proposed to calculate approximately the eigenvalues and eigenfunctions of ground state and the states close to it. The new method is applicable to the Schrödinger equation with a potential proportional to the dilatation produced by an edge dislocation. The ground-state energy obtained in this case is lower than the theoretical values obtained in other works. The energy value is obtained for the lowest state for which the eigenfunction is odd in the azimuthal angle. It is assumed that the spectrum may be described only statistically near the condensation point.
Spectra of coupled magnetoelastic waves and peculiarities of phase transitions in easy-plane ferromagnets under mechanical boundary conditions
Authors: Mitsai Yu. N. , Fridman Yu. A. , Kozhemyako O. V. , Eingorn B. L.
Published: July 2002

Possible types of phase transitions as well as the spectra of coupled magnetoelastic waves are studied in an easy-plane ferromagnet with a rigidly fixed face. It is shown that the presence of such mechanical boundary conditions leads to a change in the type of phase transition. The dynamic properties of the system become most interesting at the point of absolute instability of the system rather than at the phase transition point.
Renormalization of acoustic phonon spectrum and space distribution of the induced charge in a double-layer quantum Hall system
Authors: Fil D. V.
Published: July 2002

The frequency renormalization of acoustic phonons interacting with a double-layer composite fermion system is calculated. The space distribution of the density of the charge induced by an external electrostatic potential in a double-layer composite fermion system is determined. It is shown that for a filling factor for which states with the interlayer statistical interaction and without it can be realized, the emergence of such an interaction causes a jump in the phase velocity of a finite-frequency acoustic phonon and changes the space distribution of the charge induced by the external potential. These effects can be used for observing a transition in a double-layer electron system under the conditions of the fractional quantum Hall effect to a new ground state upon a decrease in the separation between the layers.
Orientational effect in ultrasonic attenuation in metals under the conditions of magnetoacoustic resonance
Authors: Yeremenko A. V. , Kirichenko O. V. , Peschanskiı̆ V. G.
Published: July 2002

Ultrasonic absorption in metals (degenerate conductors) in a strong magnetic field is investigated theoretically. Peculiarities in the orientational magnetoacoustic resonance are discovered and compared with the known Reneker tilt effect. Special role of open Fermi surfaces is emphasized.
Effect of pressure on the Fermi surface and electronic structure of ErGa3
Authors: Pluzhnikov V. B. , Czopnik A. , Eriksson O. , Grechnev G. E. , Fomenko Yu. V.
Published: July 2002

The Fermi surface and cyclotron masses of the ErGa3 compound are studied by means of the de Haas–van Alphen technique under pressure. Concurrently, the electronic structure is calculated ab initio for the ferromagnetic phase of ErGa3. The experimental data have been analyzed on the basis of the calculated volume-dependent band structure and compared with available results for isostructural TmGa3 and LuGa3 compounds.
NMR of Fe57 in RFe1−xMnxO3 orthoferrites
Authors: Karnachev A. S. , Klechin Yu. I. , Prokhorov A. A. , Solov’ev E. E.
Published: July 2002

The spin echo method is used to investigate the NMR spectrum of the Fe57 nuclei in manganese-substituted Tm and Er orthoferrites. It is shown that the Jahn–Teller effect for the Mn3+ impurity ion is manifested in a proportional enhancement of the E-type deformation of the Fe3+–6O2− octahedron. In the region of the spin-reorientation transition a magnetic inequivalence of the sublattices is observed both for the Fe3+ ions and for the Mn3+ impurity ions.
Discrete scalar cascade models and magnetohydrodynamic turbulence
Authors: Carbone Vincenzo , Veltri Pierluigi
Published: July 2002

The role of discrete scalar models in modeling the magnetohydrodynamic (MHD) turbulence is discussed using the hypothesis that Alfvén wave propagation dominates in comparison to turbulent eddy effects. It is shown that standard statistical techniques (direct interaction closure, Markovian approximation, and random phase approximation) performed on discrete nonlinear cascade models give rise to a set of equations that can also be obtained independently. This is done by using either basic principles or introducing discrete shells in the wavenumber space into a statistical set derived directly from MHD equations. This result permits discussion of the role of discrete models in understanding the behavior of MHD turbulence.
The permeability of a random medium: Comparison of simulation with theory
Authors: Cancelliere Antonio , Chang Celeste , Foti Enrico , Rothman Daniel H. , Succi Sauro
Published: July 2002

The results of numerical simulations of the lattice-Boltzmann equation in three-dimensional porous geometries constructed by the random positioning of penetrable spheres of equal radii are presented. Numerical calculations of the permeability are compared with previously established rigorous variational upper bounds. The numerical calculations approach the variational bounds from below at low solid fractions and are always within one order of magnitude of the best upper bound at high solid fractions ranging up to 0.98. At solid fractions less than 0.2 the calculated permeabilities compare well with the predictions of Brinkman’s effective-medium theory, whereas at higher solid fractions a good fit is obtained with a Kozeny–Carman equation.
Onset and two-dimensional patterns of convection with strongly temperature-dependent viscosity
Authors: Bottaro Alessandro , Metzener Philippe , Matalon Moshe
Published: July 2002

The onset of two-dimensional convection with strongly temperature-dependent viscosity has been considered for a fluid obeying an Arrhenius law. The critical Rayleigh number Rc and the basic features of the flow field at criticality have been identified based on a linear stability analysis. Convective flow patterns near and beyond criticality have been determined based on a direct numerical simulation. It is shown that, as the Rayleigh number R increases beyond Rc, steady rolls first emerge supercritically and that at sufficiently large values of R there is a secondary Hopf bifurcation corresponding to pulsating cells; the peculiar structure of the flow field in each case has been described.
Some observations of bispectral behavior of large ensembles of exact solutions to the Burgers equation for random initial conditions
Authors: Zheng Weiguo , Reed X. B.
Published: July 2002

Accurate bispectra for the Burgers equation have been computed into the high wave-number domain. Although only the imaginary part ib(k,l) contributes to spectral transfer, new insights having implications for three-dimensional turbulence can be gained by incorporating the real part a(k,l). For fixed l, for instance, the modulus of the bispectrum of the Burgers equation manifests a power-law subrange corresponding to the inertial subrange of the energy spectrum and an exponential subrange corresponding to the viscous cutoff of the energy spectrum.
Two-dimensional jets falling from funnels and nozzles
Authors: Lee Jongwoo , Vanden-Broeck Jean-Marc
Published: July 2002

Two-dimensional flow in a domain bounded on one side by an infinite rigid wall and on the other by a semi-infinite rigid wall and a free surface is considered. Gravity is included in the free surface condition and surface tension is neglected. The flows are characterized by the parameters H=(Q2/gw3)1/3 and the angles α and β between the walls and the horizontal. Here, Q is the total flux, g the acceleration of the gravity and w the distance between the separation point (the point of intersection of the free surface with the semi-infinite wall) and the infinite wall. The configurations include, as particular cases, flows from nozzles and funnels, the Kirchhoff jet and the flow under a gate. Numerical solutions are computed by series truncation. It is shown that there are three distinct configurations at the separation point corresponding to contact angles 2π/3, π−α (horizontal free surface at the separation point), and π (free surface tangent to the rigid wall at the separation point). For given values of β and α≳π/3, there is a critical value Hc of the parameter H such that H=Hc for a contact angle of 2π/3, H≳Hc for a contact angle of π and H<Hc for a contact angle of π−α. On the other hand, for given values of β and α≤π/3, there is only one configuration with a contact angle of π. Free surface profiles are presented for various values of α, β, and H.
A quiver kinetic formulation and evaluation of fluxes in the long mean-free path limit
Authors: Catto Peter J. , Myra J. R.
Published: July 2002

Intense, applied radio frequency (rf) fields can cause one or more charged particle species to oscillate with a quiver speed comparable to its thermal speed. When collisional nonresonant wave particle processes dominate over collisionless resonant interactions, the quiver kinetic formalism [Phys. Fluids B 1, 1193 (1989)] may be employed. The intense wave fields in the edge plasma of an rf heated tokamak satisfy these criteria and are investigated in this paper. Previous work is extended to permit an evaluation of particle fluxes near the last closed flux surface in the long mean-free path limit. Two types of convective fluxes are found, one local to the region of intense fields and one nonlocal. The magnetization flux of electrons (which is local) is shown to be the dominant convective flux in a simple illustrative model for the case of fast wave ion cyclotron heating.
Analytic expressions for far fields and radiation fluxes caused by a moving source in some anisotropic dispersive media
Authors: Lai H. M. , Ng C. S.
Published: July 2002

A general method recently developed [Phys. Fluids 29, 1881 (1986)] is applied to calculate analytically the far field and the radiation flux caused by a current source moving in each of a uniaxial nondispersive medium, an isotropic cold plasma, and a cold plasma in an infinite magnetic field. Explicit expressions in terms of space and time are obtained, and particular attention is paid to the complex Doppler situation and the Čerenkov case with and without dispersion.
A model for determining relaxation electric fields in spheromaks
Authors: Mayo R. M. , Wysocki F. J. , Fernández J. C.
Published: July 2002

Past spheromak experiments have experienced poor confinement [Nucl. Fusion 28, 1555 (1988); Phys. Fluids B 2, 115 (1990)] as a result of edge-dominated helicity dissipation due to substantial field error and edge neutral inventory. Recent works have identified the importance of edge helicity loss and its effects on confinement [Phys. Fluids B 2, 115 (1990)]. Herein, the results of the edge helicity dissipation model [Phys. Fluids 30, 1177 (1987)] are applied to determine the relative magnitudes of electric fields during relaxation in spheromaks. This is achieved by quantifying the average electric field in the plasma edge region generated by (a) flux decay and (b) relaxation mechanism(s). It is shown that relaxation electric fields can be as much as three times the flux decay field in the edge. The model also correctly predicts no relaxation electric field when the spheromak is a cold, purely resistively decaying object. In addition, the model provides an estimate for the quantity of magnetic decay power from relaxation, which can be as much as 75% of the total decay power.
Absorption at the ion–ion hybrid resonance in the presence of incoherent density fluctuations
Authors: Romero H. , Morales G. J.
Published: July 2002

A numerical study is made of the effects caused by incoherent fluctuations in the minority density concentration on the absorption of fast Alfvén waves at the ion–ion hybrid resonance. This work extends to the incoherent regime of a previous study by Romero and Morales [Phys. Fluids B 2, 2007 (1990)], which surveyed in detail the effects of single-mode (coherent) fluctuations. The system is represented by a Budden equation that properly describes the resonance and cutoff structure arising from spatial variations of the equilibrium magnetic field. For wave incidence such that the cutoff is encountered before the resonance layer, the absorption coefficient increases monotonically as the fluctuation amplitude is increased. A specific case is presented in which the absorption changes from ∼0% to ∼70% for minority density fluctuations δn/n0∼60% that correspond to electron density variations of less than 5%. For wave incidence such that the resonance is encountered before the cutoff, the reflection coefficient increases for minority density fluctuations below 5% of the ambient value. For larger density fluctuations, the reflected energy saturates at ∼20% of the incident wave energy.
Stability of ion-temperature-gradient-driven modes in tokamaks with magnetic separatrix
Authors: Briguglio S.
Published: July 2002

The stability of the ion-temperature-gradient-driven modes is analyzed for a model equilibrium with a magnetic separatrix. In the flat-density-profile limit the separatrix turns out to be stabilizing, causing the ηi threshold to increase (ηi=d ln Ti/d ln n). In the steep-density-gradient limit the effect of the separatrix is destabilizing. Both these results are more pronounced for configurations with an outside X point.
Renormalization group in magnetohydrodynamic turbulence
Authors: Camargo S. J. , Tasso H.
Published: July 2002

The renormalization group (RNG) theory is applied to magnetohydrodynamic (MHD) equations written in Elsässer variables, as done by Yakhot and Orszag for Navier–Stokes equations. As a result, a system of coupled nonlinear differential equations for the ‘‘effective’’ or turbulent ‘‘viscosities’’ is obtained. Without solving this system, it is possible to prove their exponential behavior at the ‘‘fixed point’’ and also determine the effective viscosity and resistivity. Strictly speaking, the results do not allow negative effective viscosity or resistivity, but in certain cases the effective resistivity can be continued to negative values, but not the effective viscosity. In other cases, the system tends to zero effective viscosity or resistivity. The range of possible values of the turbulent Prandtl number is also determined; the system tends to different values of this number, depending on the initial values of the viscosity and resistivity and the way the system is excited.
An analytical and particle simulation study of localized semivacuum gas breakdown phenomena on high-voltage surfaces in low Earth orbit
Authors: Cho Mengu , Hastings Daniel E.
Published: July 2002

Gas breakdown phenomena occurring on a localized scale of less than 1 mm in a semivacuum environment p≤1(Torr) are studied analytically as well as numerically using a Monte Carlo–particle-in-cell (MC–PIC) code. The MC–PIC code is shown to reproduce real physical phenomena with quantitative accuracy. The breakdown of a gas in semivacuum conditions is attributed to field enhancement by positive ion space charges resulting in higher enhanced field electron emission from the cathode surface. The analytical expression for the breakdown condition is derived and very good agreement with the numerical and experimental results is obtained.
Connections between adiabatic and low-resistivity magnetohydrodynamics
Authors: Blank Albert A. , Kress Michael E.
Published: July 2002

A first step in the hierarchy of increasingly complex magnetohydrodynamic (MHD) models goes from the nondissipative Grad–Shafranov equilibrium model to the slow-evolution resistive Grad–Hogan model. In principle, as the resistivity tends to zero, the limit of solutions of a resistive problem might be a solution of the adiabatic equations, only in a generalized sense. Specifically, the adiabatic limit could exhibit discontinuities across singular surfaces where dissipation can occur, while the body of the fluid becomes truly adiabatic. For a suitable test case, a two-dimensional analog of an oscillating Doublet, behavior typical of such an approach to a singular adiabatic limit is presented. A boundary layer or sheath appears around the separatrix of this configuration. The sheath contains the bulk of the dissipative effects and its thickness decreases rapidly with resistivity. For example, flux transport is mainly confined to the sheath and current is nearly invariant outside it. The resistive equations are solved numerically by the alternating dimension (AD) technique devised by Grad. With decreasing resistivity, the run time of the algorithm grows rapidly to durations infeasible, even for a supercomputer. In contrast, the AD method for adiabatic codes has short run times and can be executed easily on a microcomputer. Thus, it is useful to approximate solutions of low-resistivity problems by solving appropriate singular adiabatic problems. It is shown how to obtain the given data of a suitable adiabatic problem from resistive data. The crucial connecting link between the two MHD models is the flux function μ(ψ), which appears as part of the given data in the adiabatic formulation. This is given directly by resistive information outside the sheath and, inside the sheath region, indirectly by extrapolation of the observed behavior of low-resistivity solutions of the Grad–Hogan equations.
Stagnation and interpenetration of laser-created colliding plasmas
Authors: Pollaine S. M. , Berger R. L. , Keane C. J.
Published: July 2002

An experiment that observed the collision of aluminum laser produced (Al) and magnesium (Mg) plasmas is described in an accompanying paper [Phys. Fluids B 4, ▪▪▪▪ (1992)]. Time- and space-resolved measurements were made of the electron density, Lyα and Heα lines of Al and Mg, and x-ray pinhole images. These measurements are interpreted with the use of a two ion fluid hydrodynamic model and a time-dependent atomic physics model. The qualitatively successful modeling of the line emission confirms that at early times, the Al interpenetrates the counterstreaming Mg plasma and deposits in the dense Mg region. At late times, the Al plasma stagnates against the Mg plasma, approximately halfway between the initial disk surfaces.
Linear and nonlinear analysis of the cyclotron two-stream instability
Authors: Chen Chiping , Bekefi George , Hu Wen
Published: July 2002

A two-dimensional, self-consistent, nonlinear model is used to determine the growth rate and saturation level of the cyclotron two-stream instability for two weakly relativistic electron beams copropagating along a uniform magnetic field with an inverted population in the perpendicular momentum. This instability has been proposed recently as the basis for a double-stream cyclotron maser. Good agreement is found between the dispersion analysis and computer simulations in the linear regime. The effect of axial momentum spread on the instability is investigated. It is shown that the cyclotron two-stream instability is primarily electrostatic, which calls for further exploration of an effective input and output coupling scheme for the maser.
A theoretical investigation of the plasma klystron amplifier
Authors: Uhm Han S.
Published: July 2002

The plasma klystron amplifier concept is investigated. The plasma klystron consists of a relativistic annular electron beam propagating through a space between a plasma column and drift tube wall. The annular electron beam, premodulated at the first cavity in the klystron, enters the space. An axial electric field accompanied by the modulated beam excites space charge waves in the plasma column, which acts like an inductive medium amplifying the electrostatic waves. The physical mechanism of self-amplification of the electrostatic waves is the two-stream instability, which is investigated in detail. Instability criteria indicate that the plasma should be opaque to sustain instability. A theoretical model to describe current modulation of the annular electron beam propagating through the space is developed. The electron beam current is modulated by the amplifying electric field fed by the plasma column. Saturation distance of the current modulation is a weakly dependent function of the initial energy modulation at the first cavity. Thus, a relatively low-power microwave input may well excite the two-stream instability and deliver a highly modulated beam to the extraction cavity. Due to a relatively large growth rate of the instability, required interaction length of the beam and plasma column is short for most applications.
Cascading process in the flute-mode turbulence of a plasma
Authors: González R. , Gómez D. , Ferro Fontán C. , Sicardi Schifino A. C. , Montagne R.
Published: July 2002

The cascades of ideal invariants in the flute-mode turbulence are analyzed by considering a statistics based on an elementary three-mode coupling process. The statistical dynamics of the system is investigated on the basis of the existence of the physically most important (PMI) triad. When finite ion Larmor radius effects are considered, the PMI triad describes the formation of zonal flows.
Magnetic topology of helical Ohmic steady states
Authors: Turner Leaf , Prager Stewart C.
Published: July 2002

Necessary analytic constraints for a force-free, single harmonic, single helicity, magnetic-field configuration to be an Ohmic equilibrium are derived. These conditions imply that the typical configuration possesses an m=1 helical structure and has only open magnetic flux surfaces. The conclusion is drawn that Taylor’s helical state is not a steady state in the presence of resistive dissipation, no matter how small. Nevertheless, the field configurations that commonly have been associated with Taylor’s minimum energy states retain significance because they may represent either the mean configuration of a temporally fluctuating state or the zero-resistivity limit of a (hypothetical) three-dimensional, Ohmic equilibrium. Examples of single harmonic, single helicity, reversed-field, Ohmic equilibria are presented.
Dynamics of runaway tails with time-dependent sub-Dreicer dc fields in magnetized plasmas
Authors: Moghaddam-Taaheri E. , Vlahos L.
Published: July 2002

The evolution of runaway tails driven by sub-Dreicer time-dependent dc fields in a magnetized plasma are studied numerically using a quasilinear code based on the Ritz–Galerkin method and finite elements. It is found that the runaway tail maintained a negative slope during the dc field increase. Depending on the values of the dc electric field at t=0 and the electron gyrofrequency to the plasma frequency ratio the runaway tail became unstable to the anomalous Doppler resonance or remained stable before the saturation of the dc field at some maximum value. The systems that remained stable during this stage became unstable to the anomalous Doppler or the Čerenkov resonances when the dc field was kept at the saturation level or decreased. Once the instability is triggered, the runaway tail is isotropized.
The effect of magnetized ions on the lower hybrid drift instability in field reversed configurations
Authors: Farengo R. , Guzdar P. N. , Lee Y. C.
Published: July 2002

The high beta regime of the lower hybrid drift instability is studied using a fully electromagnetic dispersion relation in the local approximation. The electrons are described using a kinetic model that includes the effect of finite beta orbit modifications and three different models (unmagnetized, magnetized without ∇B drifts, and magnetized with ∇B drifts) are used for the ions. It is found that when magnetized ions without ∇B drifts are considered, the modes remain unstable for larger values of beta and the spectrum is very different from the unmagnetized ion case. When ∇B drift effects are included, the results became very similar to the unmagnetized ion case and some arguments are provided to explain this behavior.
Transition prediction and control in subsonic flow over a hump
Authors: Masad Jamal A. , Iyer Venkit
Published: July 2002

The influence of a surface roughness element in the form of a two-dimensional hump on the transition location in a two-dimensional subsonic flow with a free-stream Mach number up to 0.8 is evaluated. Linear stability theory, coupled with the eN transition criterion, is used in the evaluation. The mean flow over the hump is calculated by solving the interacting boundary-layer equations; the viscous–inviscid coupling is taken into consideration, and the flow is solved within the separation bubble. The effects of hump height, length, location, and shape; unit Reynolds number; free-stream Mach number; continuous suction level; location of a suction strip; continuous cooling level; and location of a heating strip on the transition location are evaluated. The N-factor criterion predictions agree well with the experimental correlation of Fage (A. Fage, Br. Aero. Res. Council Report No. 2120, 1943); in addition, the N-factor criterion is more general and powerful than experimental correlations. The theoretically predicted effects of the hump’s parameters and flow conditions on transition location are consistent and in agreement with both wind-tunnel and flight observations.
Rates of thermal relaxation in direct simulation Monte Carlo methods
Authors: Haas Brian L. , Hash David B. , Bird Graeme A. , Lumpkin Forrest E. , Hassan H. A.
Published: July 2002

For internal energy relaxation in rarefied gas mixtures, exact relationships are derived between the selection probability P employed in direct simulation Monte Carlo (DSMC) methods and the macroscopic relaxation rates dictated by collision number Z in Jeans’ equation. These expressions apply to the Borgnakke–Larsen model for internal energy exchange mechanics and are not limited to the assumption of constant Z. Although Jeans’ equation leads to adiabatic relaxation curves, which coalesce to a single solution when plotted against the cumulative number of collisions, it is shown that the Borgnakke–Larsen selection probabilities depend upon the intermolecular potential, the number of internal degrees of freedom, and the DSMC selection methodology. Furthermore, simulation results show that the common assumption P=1/Z is invalid, in general, and leads to considerably slower relaxation than stipulated by Z in Jeans’ equation. Moreover, inconsistent definitions of collision rates appearing in the literature can lead to considerable errors in DSMC models. Finally, for general gas mixtures, Borgnakke–Larsen DSMC kinetics match Jeans’ behavior exactly only when using a selection methodology, which prohibits multiple relaxation events during a single collision.
Effect of three-dimensionality on the lift and drag of nominally two-dimensional cylinders
Authors: Mittal R. , Balachandar S.
Published: July 2002

It has been known for some time that two-dimensional numerical simulations of flow over nominally two-dimensional bluff bodies at Reynolds numbers for which the flow is intrinsically three dimensional, lead to inaccurate prediction of the lift and drag forces. In particular, for flow past a normal flat plate (International Symposium on Nonsteady Fluid Dynamics, edited by J. A. Miller and D. P. Telionis, 1990, pp. 455–464) and circular cylinders [J. Wind Eng. Indus. Aerodyn. 35, 275 (1990)], it has been noted that the drag coefficient computed from two-dimensional simulations is significantly higher than what is obtained from experiments. Furthermore, it has been found that three-dimensional simulations of flows lead to accurate prediction of drag [J. Wind Eng. Indus. Aerodyn. 35, 275 (1990)]. The underlying cause for this discrepancy is that the surface pressure distribution obtained from two-dimensional simulations does not match up with that obtained from experiments and three-dimensional simulations and a number of reasons have been put forward to explain this discrepancy. However, the details of the physical mechanisms that ultimately lead to the inaccurate prediction of surface pressure and consequently the lift and drag, are still not clear. In the present study, results of two-dimensional and three-dimensional simulations of flow past elliptic and circular cylinders have been systematically compared in an effort to pinpoint the exact cause for the inaccurate prediction of the lift and drag by two-dimensional simulations. The overprediction of mean drag force in two-dimensional simulations is directly traced to higher Reynolds stresses in the wake. It is also found that the discrepancy in the drag between two-dimensional and three-dimensional simulations is more pronounced for bluffer cylinders. Finally, the current study also provides a detailed view of how the fluctuation, which are associated with the Kármán vortex shedding in the wake, affect the mean pressure distribution and the aerodynamic forces on the body.
Predicting failure of the continuum fluid equations in transitional hypersonic flows
Authors: Boyd Iain D. , Chen Gang , Candler Graham V.
Published: July 2002

The manner in which the Navier–Stokes equations of fluid mechanics break down under conditions of low-density, hypersonic flow is investigated numerically. This is performed through careful and detailed comparisons of solutions obtained with continuum and Monte Carlo simulation techniques. The objective of the study is to predict conditions under which the continuum approach may be expected to fail. Both normal shock waves and bow shocks formed by flow over a sphere are considered for argon and nitrogen. It is found that a Knudsen number based on local flow conditions and gradients is a convenient and accurate criterion for indicating breakdown of the continuum flow equations. Failure of the Navier–Stokes equations in hypersonic transitional flows occurs both in the shock front and in the region immediately adjacent to the body surface.
Mean-velocity scaling in and around a mild, turbulent separation bubble
Authors: Alving Amy E. , Fernholz H. H.
Published: July 2002

This paper examines the question of the scaling of mean-velocity profiles in adverse-pressure-gradient flows. In these flows, the mean velocity scaling must be different than in zero-pressure-gradient flows, because the friction velocity used in the latter case can become vanishingly small in the former. Two decades ago, Perry and Schofield [Phys. Fluids 16, 2068 (1973)] proposed a new outer-region scaling law to be used when the boundary layer approaches separation. Since that time, a number of sets of experimental data close to separation have been shown to fall on a universal curve when the profiles are plotted in Perry–Schofield coordinates, and the profile shape was given by Dengel and Fernholz [J. Fluid Mech. 212, 615 (1990)]. Recently, however, a new set of scaling laws has been proposed by Durbin and Belcher [J. Fluid Mech. 238, 699 (1992)] as a result of their asymptotic analysis, in which they assumed the appropriate near-wall velocity scale to be based on the local strength of the pressure gradient. The resulting scaling laws are different than Perry and Schofield’s scaling and, in fact, predict a three-layered rather than a two-layered boundary-layer structure. Here, experimental results are shown for an adverse-pressure-gradient boundary layer which separates from and then reattaches to a smooth surface. These data provide a wide range of flow conditions for comparing the conflicting scaling laws mentioned above, under conditions of both decreasing and increasing skin friction, with and without instantaneous reverse flow.

It is found that the Perry–Schofield coordinates provide better collapse, over a wider range of streamwise positions and over a larger fraction of the boundary layer, than the scaling laws of Durbin and Belcher. Other proposed scaling laws are also evaluated. Yaglom’s half-power law is shown to hold for a subset of the profiles which fall on Dengel and Fernholz’s universal profile. And the data provide a test of the range of validity of the (zero-pressure-gradient) logarithmic law of the wall. The law is violated here when instantaneous reverse flow exists in the boundary layer and/or when the local pressure gradient is strong enough, as is consistent with earlier work. However, after reattachment these criteria are insufficient to indicate the return to the log law, and several bubble lengths are required after reattachment before the universal log law is satisfied. The wake region responds to reattachment more slowly and does not appear fully recovered six bubble lengths (twenty boundary-layer thicknesses) after reattachment.
Stability of Newtonian and viscoelastic dynamic contact lines
Authors: Spaid M. A. , Homsy G. M.
Published: July 2002

The stability of the moving contact line is examined for both Newtonian and viscoelastic fluids. Two methods for relieving the contact line singularity are chosen: matching the free surface profile to a precursor film of thickness b, and introducing slip at the solid substrate. The linear stability of the Newtonian capillary ridge with the precursor film model was first examined by Troian et al. [Europhys. Lett. 10, 25 (1989)]. Using energy analysis, we show that in this case the stability of the advancing capillary ridge is governed by rearrangement of fluid in the flow direction, whereby thicker regions develop that advance more rapidly under the influence of a body force. In addition, we solve the Newtonian linear stability problem for the slip model and obtain results very similar to those from the precursor film model. Interestingly, stability results for the two models compare quantitatively when the precursor film thickness b is numerically equal to the slip parameter α. With the slip model, it is possible to examine the effect of contact angle on the stability of the advancing front, which, for small contact angles, was found to be independent of the contact angle. The stability of an Oldroyd-B fluid was examined via perturbation theory in Weissenberg number. It is found that elastic effects tend to stabilize the capillary ridge for the precursor film model, and this effect is more pronounced as the precursor film thickness is reduced. The perturbation result was examined in detail, indicating that viscoelastic stabilization arises primarily due to changes of momentum transfer in the flow direction, while elasticity has little effect on the response of the fluid to flow in the spanwise direction.
On boundary conditions in lattice Boltzmann methods
Authors: Chen Shiyi , Martínez Daniel , Mei Renwei
Published: July 2002

A lattice Boltzmann boundary condition for simulation of fluid flow using simple extrapolation is proposed. Numerical simulations, including two-dimensional Poiseuille flow, unsteady Couette flow, lid-driven square cavity flow, and flow over a column of cylinders for a range of Reynolds numbers, are carried out, showing that this scheme is of second order accuracy in space discretization. Applications of the method to other boundary conditions, including pressure condition and flux condition are discussed.
Evolution of large eddies in compressible shear layers
Authors: Papamoschou Dimitri , Bunyajitradulya Asi
Published: July 2002

The evolution of large turbulent eddies has been investigated in seven supersonic shear layers with average convective Mach numbers Mc¯ ranging from 0.22 to 0.86 and with large variation in density and velocity ratios. A two-laser, single-detector planar laser-induced fluorescence technique was used to visualize the flow and its evolution. Two-dimensional pattern matching yielded the convective velocity of the eddies. For Mc¯>0.3, fast and slow modes of eddy propagation were detected in supersonic–subsonic and supersonic–supersonic combinations, respectively. An empirical model for the convective velocity is proposed. Plan views reveal coexistence of two- and three-dimensional disturbances. Interaction among eddies appears significantly suppressed. The findings have direct impact on supersonic jet noise and are very relevant to supersonic combustion.