bluuebunny/crossref_metadata_2025 huggingface dataset:
Poincaré algebra in ordinary and Grassmann space and supersymmetry
Authors: Mankoč Borštnik Norma
Published: July 2002

In this theory scalars, spinors, and vectors are described as particles living in a d-dimensional ordinary and a d-dimensional Grassmann space, with d≥5. Operators of translations and the Lorentz transformations in both spaces form the super-Poincaré algebra. It is the super-Pauli–Ljubanski vector of an odd Grassmann character, which generates spinors. The theory offers a new insight into quantum theory of particles and their supersymmetric nature.
Parametric manifolds. I. Extrinsic approach
Authors: Boersma Stuart , Dray Tevian
Published: July 2002

A parametric manifold can be viewed as the manifold of orbits of a (regular) foliation of a manifold by means of a family of curves. If the foliation is hypersurface orthogonal, the parametric manifold is equivalent to the one-parameter family of hypersurfaces orthogonal to the curves, each of which inherits a metric and connection from the original manifold via orthogonal projections; this is the well-known Gauss–Codazzi formalism. This formalism is generalized to the case where the foliation is not hypersurface orthogonal. Crucial to this generalization is the notion of deficiency, which measures the failure of the orthogonal tangent spaces to be surface forming, and which behaves very much like torsion. Some applications to initial value problems in general relativity will be briefly discussed.
Structure of the chiral scalar superfield in ten dimensions
Authors: Kwon P. S. , Villasante M.
Published: July 2002

We describe the tensors and spinor-tensors included in the θ-expansion of the ten-dimensional chiral scalar superfield. The product decompositions of all the irreducible structures with θ and the θ2 tensor are provided as a first step toward the obtention of a full tensor calculus for the superfield.
Projective representations of the 1+1-dimensional Poincaré group
Authors: Bose S. K.
Published: July 2002

The unitary irreducible representations of the central extension of the Poincaré group in 1+1 dimensions are constructed by an application of the Kirillov theory. These are then lifted to projective unitary irreducible representations of the Poincaré group. The 1+1 Galilean group is treated separately in an appendix.
Computation of Lie transformations from a power series: Bounds and optimum truncation
Authors: Gjaja Ivan
Published: July 2002

The problem considered is the computation of an infinite product (composition) of Lie transformations generated by homogeneous polynomials of increasing order from a given asymptotic power series. Bounds are computed for the infinitesimal form of the Lie transformations and for the domain of analyticity of the first n of them. Even when the power series is convergent, the estimates exhibit a factorial-type growth, and thus do not guarantee convergence of the product. The optimum truncation is determined by minimizing the remainder after the first n Lie transformations have been applied.
(α,β)-derivations on quantum function algebras
Authors: Swank L. J.
Published: July 2002

(α,β)-derivations, introduced by Cohn, are defined on several noncommutative function algebras including the Hopf function algebras of the quantum groups SLq(n), n=2,3, where their interpretation is most apparent. In analogy with algebraic groups, left-invariant (α,β)-derivations on the Hopf function algebra of SLq(n), n=2,3, generate its quantum universal enveloping algebra Uq(sl(n)). Derivations and their algebras are also found on the non-Hopf, function algebras of two noncommutative varieties, which are constructed similarly to SLq(2) and SLq(3). General (α,β) derivations (analogs of arbitrary vector fields) are found for SLq(2) and the quantum plane. The analog of the tangent bundle TSLq(2) is defined, and its relation to derivations is discussed. Some examples of (α,β) derivations on commutative algebras are also given. Generalities about (α,β) derivations and their algebras are discussed.
Solvable quantum version of an integrable Hamiltonian system
Authors: Calogero F. , van Diejen J. F.
Published: July 2002

Solvable quantum versions of the classical dynamical system characterized by the Hamiltonian H=∑nj,k=1 pjpk[λ+μ cos(qj−qk) ] are presented. The eigenvalues of the quantum Hamiltonians are exhibited, as well as the corresponding eigenfunctions.
Non-Abelian Berry’s phase in a slowly rotating electric field
Authors: Choi Ho-Meoyng , Ji Chueng-Ryong , Lee Hyun Kyu
Published: July 2002

We observe that the non-Abelian Berry’s potential can appear in the atomic system under the slowly rotating electric field (Stark effect). We calculate Berry’s phase using the perturbation theory in the weak external electric field. To elaborate the nature of non-Abelian character, we demonstrate the change of states during the adiabatic transportation for a particular set of paths.
Multibody operator matrix elements and subduction coefficients in U(n): II
Authors: Kent Robert D. , Schlesinger Mordechay
Published: July 2002

Matrix elements of multibody operators in Gel’fand and similar bases of irreducible representations of U(n) are evaluated algebraically to arbitrary order. It is shown that in all cases the matrix element expressions consist of products of terms, each a matrix factor associated only with subgroup labels at step U(k)⊃U(k−1) in the group chain U(n)⊃⋯⊃U(k)⊃⋯⊃U(1). Further, the matrices at step k occurring in the product are diagonalizable according to the irreps of SN, which signifies also for N the number of one-body operators contained in the multibody operator at the level. The results extend previous work that was directed at special cases of multibody operators. Attention has been focused recently on such operators in connection with spin-dependent and higher-order multipole spin-independent interactions as arise in the unitary group approach. Explicit phase relations are incorporated throughout the treatment.
Invariant imbedding and hyperbolic heat waves
Authors: Wall David J. N. , Olsson Peter
Published: July 2002

In this paper we build up a general wave splitting and imbedding theory for the solution of both direct and inverse problems associated with thermal processes. It is done by using a full representation of the thermal phenomenon by virtue of Cattaneo’s law. This law by ensuring finite thermal propagation speeds, enables an imbedding equation to be utilised to layer strip the medium; so allowing the solution to the inverse problem of determination of a spatially varying diffusivity. Theoretical results and numerical algorithms are developed and numerical experiments are used to illustrate the effectiveness of the latter.
Perturbation theory and the classical limit of quantum mechanics
Authors: McRae S. M. , Vrscay E. R.
Published: July 2002

We consider the classical limit of quantum mechanics from the viewpoint of perturbation theory. The main focus is time dependent perturbation theory, in particular, the time evolution of a harmonic oscillator coherent state in an anharmonic potential. We explore in detail a perturbation method introduced by Bhaumik and Dutta-Roy [J. Math. Phys. 16, 1131 (1975)] and resolve several complications that arise when this method is extended to second order. A classical limit for coherent states used by the above authors is then applied to the quantum perturbation expansions and, to second order, the classical Poincaré–Lindstedt series is retrieved. We conclude with an investigation of the connection between the classical limits of time dependent and time independent perturbation theories, respectively.
A q-oscillator Green’s function
Authors: Ahmedov H. , Duru I. H.
Published: July 2002

By using the generating function formula for the product of two q-Hermite polynomials, q-deformation of the Feynman Green’s function for the harmonic oscillator is obtained.
Semiclassical determinants of Schrödinger operators on bundles with curvature of low rank
Authors: Simon David S.
Published: July 2002

The semiclassical (k→∞) limit of a Schrödinger operator Δk acting on the kth tensor power of a line bundle is studied. An inductive argument is given to show that a previously derived infinite series representation for the leading term in the large k expansion of ln det Δk reduces under certain circumstances to simple expressions involving the Riemann zeta function. These results hold when the curvature of the bundle is confined to a single plane at each point.
Can a quantum process be oblivious to observation?
Authors: Kanter Marek
Published: July 2002

In this paper time is indexed by a “time group” G that may be either the real line or the integers. A quantum process is a homomorphic representation of G via unitary operators on a Hilbert space L, with the usual continuity restrictions if time is indexed by the reals. Consider a quantum process subject to nonselective observation at all points in time via an observation operator with purely discrete eigenvalues and corresponding simple eigenvectors. Suppose that the process evolves in such a way that the results of observation at a given time are the same, whether or not there have been previous observations. Suppose further that L is spanned by the set of vectors invariant modulo phase under the quantum evolution. If the time group is the integers, then the process is observed to evolve in a classical manner. If the time group is the real line, then the process is never observed to undergo a change of state. The results of this paper are essentially a corollary of von Neumann’s mean ergodic theorem.
A relativistic supersymmetry and some algebraic consequences
Authors: Cotăescu Ion I.
Published: July 2002

We analyze the supersymmetry and the shape invariance of the potentials which appear in the Klein–Gordon equations of the (1+1) relativistic Pöschl–Teller oscillators we have recently proposed. We point out how the main operators depend on the value of the unique parameter involved in the shape invariance of the supersymmetric partner potentials, and we propose a unitary transformation that changes its value.
Gauge-invariant variationally trivial problems on
T *M
Authors: López M. Castrillón , Masqué J. Muñoz
Published: July 2002

A classification of variationally trivial Lagrangians on T*M which are invariant under the Lie algebra of infinitesimal gauge transformations of the principal bundle π:M×U(1)→M, is given. A characterization of Lagrangian densities on T*M which are invariant under the Lie algebra of all infinitesimal automorphisms of M×U(1) is also obtained.
A recursive method for the construction of irreducible representations of the orthogonal group O(n)
Authors: Barnea Nir
Published: July 2002

An algorithm for the construction of O(n) Gel’fand–Zetlin states in an invariant vector space is developed. The states are calculated recursively using a new type of coefficient of fractional parentage. These coefficients are the eigenvectors of the Gel’fand invariants. It is shown that the calculation of the Gel’fand invariants' matrix elements can be reduced to the evaluation of a single generator at each step. This algorithm provides a new approach to the calculation of the Clebsh–Gordon coefficients and isoscalar factors for the orthogonal group and can be applied to construct a basis function with well-defined orthogonal symmetry for physical systems where separation between collective motions and intrinsic motions, associated with the group O(n), is of interest.
The Eikonal equation in asymptotically flat space–times
Authors: Frittelli Simonetta , Newman Ezra T. , Silva-Ortigoza Gilberto
Published: July 2002

In an arbitrary Lorentzian manifold we provide a description for the construction of null surfaces and their associated singularities, via solutions of the Eikonal equation. In particular, we study the singularities of the past light-cones from points on null infinity, the future light-cones from arbitrary interior points and the intersection of these with null infinity and unifying relationships between the different singularities. The starting point for this work is the assumption of a known family of solutions to the Eikonal equation. The work is based on the standard theory of singularities of smooth maps by Arnold and his colleagues. Though the work is intended to stand on its own, it can be thought of as being closely related to the recently developed null surface reformulation of GR.
On the spectral gap of Kawasaki dynamics under a mixing condition revisited
Authors: Cancrini N. , Martinelli F.
Published: July 2002

We consider a conservative stochastic spin exchange dynamics which is reversible with respect to the canonical Gibbs measure of a lattice gas model. We assume that the corresponding grand canonical measure satisfies a suitable strong mixing condition. We give an alternative and quite natural, from the physical point of view, proof of the famous Lu–Yau result which states that the relaxation time in a box of side L scales like L2. We then show how to use such an estimate to prove a decay to equilibrium for local functions of the form 1/tα−ε, where ε is positive and arbitrarily small and α=12 for d=1, α=1 for d⩾2.
Thomas–Fermi screening of a moving surface charge
Authors: Kulik I. O.
Published: July 2002

The dynamical screening effects in the skin layer of a metal are investigated. The electric charge density near the metal surface induced by a moving charged body outside the metal is screened at the Thomas–Fermi length if the velocity parallel to the surface is smaller than the Fermi velocity. Crisis of screening is found at the velocity approaching the Fermi velocity, which results in the electric field penetration inside the metal at large distances, and in the distortion of the electric field distribution outside the metal. The energy dissipation from a moving charged body as a function of the velocity has a pronounced singularity near the Fermi velocity.
Determination of characteristic parameters of n-CdxHg1−xTe from quantum oscillations
Authors: Bashirov R. I. , Elyzarov V. A. , Mollaev A. Yu. , Bashirov R. R.
Published: July 2002

The longitudinal and transverse magnetoresistances are studied in solid solutions of n-CdxHg1−xTe with x=0.19 and 0.226 at hydrogen and helium temperatures. Effective masses at the bottom of the conduction band are determined from an analysis of oscillation amplitudes at helium temperatures. The values of g-factors are determined from the splitting of the first magnetoresistance peak.
The linear stability of steady circular Couette flow with a small radial temperature gradient
Authors: Chen Jyh-Chen , Kuo Jer-Yow
Published: July 2002

The linear stability of steady circular Couette flow with a small radial temperature gradient has been investigated. The outer cylinder is assumed stationary, while the inner cylinder is rotated with a constant angular speed. The interaction of the radial temperature gradient with both gravity and centrifugal potentials is taken into account in the formulation of the stability problem. The critical Reynolds number is found to be dependent on the ratio of the centrifugal and gravitational potentials, the Prandtl number, and the temperature difference between the cylinders. Unlike previous theoretical results, the present results agree qualitatively with those obtained experimentally.
The effect of boundary conditions and shear rate on streak formation and breakdown in turbulent channel flows
Authors: Rashidi M. , Banerjee S.
Published: July 2002

Experiments in a horizontal channel indicate that low-speed/high-speed streaks form in the region very close to the interface if shear is imposed on the liquid surface by the motion of a gas. They also form at the wall. Even though the boundary conditions at the wall and at the interface are different (no slip versus nearly free slip with regard to fluctuations), the main characteristics of the streaks appear similar. The spanwise spacing of the streaks when nondimensionalized using the local shear stress and kinematic viscosity is about 100 units whether the streaks are at the wall or at the liquid surface. The ejection and breakdown of the streaks also show qualitatively similar features. For example, the burst frequency appears to scale on local inner variables and the numerical values in nondimensionalized frequency units are about the same whether the bursts originate near the interface or the wall. A number of experiments have been done varying the shear rate at the interface to determine its role in streak formation and breakdown. From the present experiments it is concluded that the shear rate has the main influence on the phenomena and the effect of the boundary conditions is much less important.
Lagrangian model simulations of molecular mixing, including finite rate chemical reactions, in a temporally developing shear layer
Authors: Chang Chester H. H. , Dahm Werner J. A. , Tryggvason Grétar
Published: July 2002

A local integral model for approximate simulations of the molecular mixing and chemical reaction processes in turbulent reacting flows is presented. The model is based on recent experimental results, which show that essentially all of the molecular mixing in turbulent flows occurs in thin strained laminar diffusion layers, and that the internal structure within these layers is essentially self-similar. This motivates a local integral treatment of the mixing and reaction processes in these layers that removes the resolution requirements imposed on full simulations by the steep gradients within the molecular diffusion and chemical reaction scales of the flow. The resulting integral model is applied to predict the mixing and reaction progress in a temporally developing shear layer over a range of Reynolds and Damköhler numbers, and to make comparisons with results obtained from full finite difference simulations. The resulting reactant and product concentration fields, as well as the temperature and reaction rate fields obtained from the model, are in good agreement with the full simulations. The results indicate that the model is able to accurately follow even highly sensitive nonlinear measures of the mixing and reaction progress such as the local extinction phenomenon characteristic of large Zel’dovich number Arrhenius kinetics.
Mixing during vortex ring collision
Authors: Zawadzki Ireneusz , Aref Hassan
Published: July 2002

Using a vortex-in-cell method, the interactions of two identical rings moving on a collision course along parallel lines are studied. Evolution of a passive nondiffusing scalar carried initially with the vortices is visualized and analyzed. Diagnostics of mixing of the scalar particles demonstrate an improvement in mixing as the offset of the lines of propagation of the vortices is increased from zero to about a quarter of the ring diameter. With further increase of the offset the mixing is gradually reduced due apparently to a vortex reconnection process that limits the amount of stretching of the configuration.
Transient natural convection with density inversion from a horizontal cylinder
Authors: Wang P. , Kahawita R. , Nguyen D. L.
Published: July 2002

This paper is devoted to a numerical investigation of the free convection flow about a horizontal cylinder maintained at 0 °C in a water ambient close to the point of maximum density. Complete numerical solutions covering both the transient as well as steady state have been obtained. Principal results indicate that the proximity of the ambient temperature to the point of maximum density plays an important role in the type of convection pattern that may be obtained. When the ambient temperature is within 4.7 °C<Tamb<8 °C, a ‘‘dual flow’’ appears around the cylinder with both upward and downward flow occurring in proximity to the cylinder in two distinct recirculating zones, generally separated by the 4 °C isotherm when Tamb<5.7 °C. The dual flow behavior is significantly modified as the ambient temperature is altered, disappearing when the ambient temperature is above 8 °C, or below 4.7 °C. Furthermore, when the ambient temperature is within about 4.8 °C<Tamb<5.5 °C, a well-defined steady state is never attained. Within this same range, solutions with an initially quasiperiodic behavior which persist for a long time have been observed. Multiple solutions have been observed when the above range of ambient temperature is approached from either side. The results of the computations have been compared with published experimental and numerical data with satisfactory agreement being obtained.
Experiments on the stability of a liquid bridge in an axial electric field
Authors: Sankaran Subramanian , Saville D. A.
Published: July 2002

The behavior of a neutrally buoyant liquid bridge was studied in the presence of axial electric fields. Silicone oil and a castor-oil–eugenol mixture were used to form cylinders with slenderness ratios larger than π with strong, axial, dc electric fields. Below a certain field strength, a smooth transition to an axisymmetric, vaselike shape occurred. Circulation patterns were observed in these bridges. At lower field strengths, the bridge shape was more deformed and, at a well-defined field, pinch-off occurred. With ac fields, the field strength required to stabilize the bridge was higher and the collapse of the cylinder was much sharper. Upon interchanging the fluids, a steady axial field was found to destabilize cylinders with slenderness ratios less than 3. This behavior is consistent with that anticipated if the fluids behave as leaky dielectrics but not if they act as perfect dielectrics.
The stability of a compressible stratified shear layer
Authors: Wang Z. , Pritchett P. L.
Published: July 2002

The stability of a stratified shear layer is studied using the compressible magnetohydrodynamic (MHD) equations, including an effective gravity term to represent curvature effects of the flow and magnetic field line geometry. A general eigenvalue equation is derived for a two-dimensional MHD fluid. For the case of a hyperbolic tangent shear flow and exponential density profile, it is found that in the Boussinesq approximation the compressibility raises the critical Richardson number from (1)/(4) to as much as (1)/(2) , with the exact value depending on the value of the magnetic field at infinity. Under the approximation of a strong asymptotic magnetic field, but without invoking the Boussinesq approximation, it is shown both analytically and numerically that the density gradient terms cause the shear instability to be dispersive. In particular, the long-wavelength stability boundary for the case of Richardson number J=0 is characterized by a normalized phase velocity c=−1. This result implies that the solution for the stability boundary found by Satyanarayana, Lee, and Huba [Phys. Fluids 30, 81 (1987)], which required that c=−β/2 (where β is the ratio of the velocity and density gradient scale lengths), is not valid, in general.
Three-dimensional plasma equilibrium near a separatrix
Authors: Reiman A. H. , Pomphrey N. , Boozer A. H.
Published: July 2002

The limiting behavior of a general three-dimensional magnetohydrodynamic (MHD) equilibrium near a separatrix is calculated explicitly. No expansions in beta or assumptions about island widths are made. Implications of the results for the numerical calculation of such equilibria are discussed, as well as for issues concerning the existence of three-dimensional MHD equilibria.
Computer simulations of finite plasma streams convected across a magnetized vacuum
Authors: Galvez Miguel , Gisler Galen , Barnes Christopher
Published: July 2002

A two-dimensional electrostatic particle-in-cell code is used to simulate the convection of a finite stream of initially neutral plasma across a uniform magnetic field. The simulations show that the stream loses momentum with distance as a result of two erosion mechanisms that have greater effects for denser plasmas: (1) erosion of the charge layers at the sides of the stream as a result of velocity shear and (2) erosion of the head of the stream as a result of charge separation where ions travel ahead of the electrons. The electron charge layer exhibits a velocity shear that excites the diocotron instability. This instability occurs earlier for denser plasmas but it does not appear when the length of the stream is shorter than four wavelengths. The charge separation at the head of the stream causes the eroded plasma to drift with a sheared velocity. A flutelike instability develops at the head of the plasma stream for sufficiently dense plasmas. The simulations show that the plasma is eroded faster by the head erosion mechanism. Electric field fringe effects cause the plasma head to broaden and the tail of the plasma to narrow. The simulations show that although the plasma configuration is changed a great deal by erosion and fringe effects, the stream is convected across the magnetic field with a constant velocity for sufficiently dense plasmas and with a velocity that approaches the injection for denser plasmas. The simulations also show that the convection velocity for a partially and for a completely eroded plasma is the same.
Atomic hydrogen density measurements in the Tara tandem mirror experiment
Authors: Guss W. C. , Yao X. Z. , Pócs L. , Mahon R. , Casey J. , Horne S. , Lane B. , Post R. S. , Torti R. P.
Published: July 2002

Neutral and plasma density have been measured in the north well of the central cell of the Tara tandem mirror [Nucl. Fusion 22, 549 (1982)]. The electron plasma density and temperature on the magnetic axis were measured by Thomson scattering to be about 3×1012 cm−3 and 70 eV, respectively. The corresponding axial neutral hydrogen density was found to be 1 ×109 cm−3, while near the plasma edge at r=15 cm it reached 1×1010 cm−3. The fill gas density at r≥22.5 cm was ≊1011 cm−3. Additional information from secondary electron detectors was used to estimate the radial ion temperature distribution, which was found to have about the same width, 12 cm, as the plasma density. The resulting ion pressure profile is peaked compared to the electron pressure profile. Charge exchange losses in the well are found to have a maximum at a radius equal to half the e-folding distance of the plasma density and ion temperature distributions.
Mass-loading at interplanetary shocks
Authors: Zank G. P.
Published: July 2002

The interaction of the solar wind with the atmospheres of nonmagnetized and weakly magnetized bodies, such as found at comets and the planets Venus and Mars, is currently an area of great interest in space plasma physics. Photoionization of the atmospheric coma surrounding a comet or a weakly magnetized planet leads to ‘‘mass-loading’’ of the impinging solar wind. A common velocity for the different plasma components is established rapidly via pitch-angle scattering, so ensuring that the bulk plasma flow is described adequately at the hydrodynamic level. On the basis of magnetohydrodynamic (MHD) models, two outstanding problems can be addressed. The first concerns the existence, strength, and properties of shocks in a mass-loading environment, and the second concerns the location of the bow shock. This paper concentrates on the former issue. A general theoretical description of mass-loading shocks in the heliosphere is presented and the differences between mass-loading shocks and classical nonreacting MHD shocks elucidated. In a formal sense, mass-loading shocks are qualitatively similar to combustion shocks, except that mass-loading induces the flow to shear. Mass-loading fronts represent a notably new and interesting class of shocks, which, although found frequently in the solar system, both at the head of comets and, under suitable conditions, upstream of weakly and nonmagnetized planets, has not yet been investigated in great detail.
Alfvén waves in inhomogeneous magnetic fields: An integrodifferential equation formulation
Authors: Uberoi C. , Sedlaček Z.
Published: July 2002

An integrodifferential formulation for the equation governing the Alfvén waves in inhomogeneous magnetic fields is shown to be similar to the polyvibrating equation of Mangeron. Exploiting this similarity, a time-dependent solution for smooth initial conditions is constructed. The important feature of this solution is that it separates the parts giving the Alfvén wave oscillations of each layer of plasma and the interaction of these oscillations representing the phase mixing.
Two-dimensional analytic theory for toroidal Alfvén eigenmodes
Authors: Ye Huanchun , Sedlacek Z. , Mahajan S. M.
Published: July 2002

A two-dimensional analysis of the toroidal Alfvén eigenmodes (TAE) is presented, based on an integrodifferential equation describing the shear Alfvén perturbation of a toroidal plasma equilibrium in terms of coupling among the toroidal Alfvén continua with the usual gap structure. Using a method similar to the Van Kampen–Case analysis for the Vlasov equation, exact analytic expressions are derived for the dispersion function and the two-dimensional eigenmode structure. The dispersion function is expressed in terms of Cauchy-type integrals, which explicitly expresses the global character of TAE modes and facilitates the calculation of their damping. The continuum-damped TAE modes are shown to be, in general, not true eigenmodes of the toroidal plasma equilibrium, but rather resonances corresponding to zeros of the analytic continuation of the dispersion function onto unphysical sheets of its Riemann surface. Approximate but explicit expressions for the dispersion relation and the eigenfunction are also obtained in the limit of vanishing inverse aspect ratio.
The stability of solutions of the classical unsteady boundary-layer equation
Authors: Cowley S. J. , Hocking L. M. , Tutty D. R.
Published: July 2002

An aspect of the stability of boundary-layer profiles containing a point of zero shear away from the wall is examined. Analysis of a viscous critical layer at the point of zero shear shows that the classical unsteady boundary-layer equation contains a short-wavelength unstable solution. The presence of this instability has consequences for the numerical solution of the classical boundary-layer equation, and may be connected with the initiation process of Van Dommelen and Shen’s nonlinear unsteady separation singularity.
Perturbation analysis of steady and oscillatory onset in a Bénard problem with two similar liquids
Authors: Renardy Yuriko , Renardy Michael
Published: July 2002

In a recent paper, Renardy and Joseph [Phys. Fluids 28, 788 (1985)] studied the Bénard problem for two layers of different fluids lying on top of each other and bounded by walls. Their study shows that, in contrast to the Bénard problem for one fluid, the onset of instability can be oscillatory. The number of parameters involved in the problem is large, and there is as yet no comprehensive picture of when the instability is oscillatory and when it is not. The study of limiting cases, accessible by perturbation methods, may be helpful in this respect. In this paper, an analysis is given for the case when the properties of the two fluids are nearly equal and the fluids are allowed to slip at the boundaries.
Upconversion of lower-hybrid waves by gyrating ion beams in a plasma
Authors: Sharma O. P. , Patel V. L.
Published: July 2002

A gyrating ion beam, with ring shape distribution in velocity space, supports negative energy modes near the harmonics of beam gyrofrequency. An investigation of the nonlinear interaction of high-frequency lower-hybrid waves with the negative energy beam cyclotron mode is made. A nonlinear dispersion relation is derived for the coupled modes. It is shown that a gyrating ion beam frequency upconverts the lower-hybrid waves separated by harmonics of the beam gyrofrequency. This process of upconversion may thus provide a tool for the diagnostics of the gyrating ion beams. The process may also be important in the saturation of lower-hybrid waves observed in the auroral zone S3-3 satellite data.
Solution to the piecewise linear continuous random initial value problem for Burgers’ equation
Authors: Shih Yin-Chin , Reed X B
Published: July 2002

A closed form solution to Burgers’ equation on an infinite domain has been obtained for ‘‘random sawtooth’’ continuous initial conditions defined on a finite domain. The ‘‘turbulent’’ solution is than used to compute statistical measures such as skewness and flatness factors, energy decay rates, and the temporal evolution of velocity autocorrelations and energy spectra.
High wavenumber spectrum of a passive scalar in isotropic turbulence
Authors: Bennett A. F.
Published: July 2002

The time-dependent solution is found for Kraichnan’s random-straining model [J. Fluid Mech. 64, 737 (1974)] of the viscous-diffusive subrange. Temporal decay increases very rapidly with increasing spatial dimension. The Batchelor spectrum is recovered as the conditional variance of spectral amplitudes in excess of a threshold value. A by-product of the analysis is a trivial derivation of the inversion theorem for the Kontorovich–Lebedev transform.
Effect of convective damping on the growth rate of magnetohydrodynamic ballooning modes
Authors: Andersson P. , Weiland J.
Published: July 2002

A new type of frequency dependence caused by an outgoing boundary condition has been found in the dispersion relation for ballooning modes. The new, simple dispersion relation has been found for the first time to give growth rates in excellent agreement with numerical results for small values of shear. The analytical stability condition has been improved.
Plasma potential enhancement by rf heating near the ion-cyclotron frequency
Authors: Smith D. K. , Brau K. , Goodrich P. , Irby J. , Mauel M. E. , McVey B. D. , Post R. S. , Sevillano E. , Sullivan J.
Published: July 2002

The observation of enhanced plasma potentials, i.e., potentials greater than the Boltzmann values, in a mirror device is reported. The potential structure is driven by strong radio frequency heating near the ion-cyclotron resonance and near the local electron bounce frequency. The potentials and their effect on losses from the central cell of a tandem mirror are discussed.
Diffusion with varying drag: The runaway problem. I
Authors: Corngold Noel , Rollins David
Published: July 2002

Diffusive phenomena characterized by variable coefficients of diffusion are important in several fields of physics. This paper is concerned with time-dependent diffusion in velocity space of one dimension, governed by a velocity-dependent diffusion coefficient D(v), which is nonzero in a finite interval v≤‖v0‖. The diffusing particles are driven by a uniform external electric field. When D(v) has linear, or quadratic behavior, exact solutions exist in terms of higher transcendental functions. In the general case, the saddle-point method yields runaway currents at short times and, when the field is large, for long times as well.
Transport in driven plasmas
Authors: Fisch N. J.
Published: July 2002

A plasma in contact with an external source of power, especially a source that interacts specifically with highvelocity electrons, exhibits transport properties, such as conductivity, different from those of an isolated plasma near thermal equilibrium. This is true even when the bulk of the particles in the driven plasma is near thermal equilibrium. To describe the driven plasma, we derive an adjoint equation to the inhomogeneous, linearized, dynamic Boltzmann equation. The Green’s functions for a variety of plasma responses can then be generated. It is possible to modify the Chapman–Enskog [Mathematical Theory of Nonuniform Gases, 3rd ed., (Cambridge U.P., Cambridge, MA, 1970)] expansion in order to incorporate the response functions derived here.
Wave structures in jets of arbitrary shape. II. Application of a generalized shooting method to linear instability analysis
Authors: Koshigoe Shozo , Tubis Arnold
Published: July 2002

The shooting method, used in the linear instability analysis of plane shear layers, is generalized so as to be applicable to the case of straight three-dimensional, inviscid, compressible jets of arbitrary mean flow profile. A jet is assumed to have a core region of constant flow W0 bounded by curve C, and an outer-flow boundary C̃ outside of which the flow is negligible. The instability eigenmodes are determined by using the Helmholtz surface integral relations between the incremental pressure and its normal derivative on C and C̃, together with finite difference approximate solutions of the Rayleigh differential equation in one region between C and C̃. Calculations typically require about 50 times less computer time than do equivalent integral-equation methods. Numerical results are presented for incompressible jets with circular and elliptic core regions and several azimuthal variations of momentum thickness.
A gyroviscous model of the magnetotail current layer and the substorm mechanism
Authors: Stasiewicz K.
Published: July 2002

An analytical model of the magnetotail current layer is constructed on the basis of fluid equations for collision-free plasmas with finite ion Larmor radius. The present model provides self-consistent solutions for the plasma flow vector, magnetic field, and electric currents in a one-dimensional current layer that are in agreement with measurements in the magnetosphere. It is shown that the gyroviscous stresses in the momentum equation, the Hall current term in the generalized Ohm’s law, and the cross-equatorial mass transport are essential for describing a dynamically stable configuration of the magnetotail current layer. It is found that a necessary condition for an equilibrium of a current layer with isotropic scalar pressure and finite ion Larmor radius is that the normal mass velocity across the layer is greater than the normal component of the Alfvén velocity; V2n>B2n/μ0 ρ. It is argued that magnetospheric substorms are associated with violation of the above condition in the tail current layer.
Generation of axial magnetic fields in a laser-produced plasma by a turbulent dynamo
Authors: Dragila R.
Published: July 2002

It is shown that axial magnetic fields earlier observed in laser-produced plasma experiments can be generated by the action of a turbulent dynamo in the presence of ion-acoustic turbulence in an underdense plasma.
Nonlinear Alfvén waves and the plasma vortices
Authors: Jovanović D.
Published: July 2002

A set of three coupled nonlinear differential equations describing low-frequency (∂/∂t≪Ωi, Ωi being the ion gyrofrequency), electromagnetic perturbations slowly varying (∂/∂z≪∇⊥) along the external magnetic field B0ez in a homogeneous plasma is derived using a two-fluid description. The equations are valid over a wide range of β (ratio of the electron thermal pressure and the magnetic pressure) and in proper limits reduce to the Hasegawa–Mima and convective cell equations, respectively. A general traveling solution for the full set of equations is described and studied in detail for the axially antisymmetric (dipole) case, when the only possible solution propagating with a finite velocity perpendicular to the external magnetic field has the form of a double vortex. There are two modes of vortices. The first one reduces to the Hasegawa–Mima modon in the limit vz =0, while the other in the limit vz=cA (Alfvén speed) has zero density perturbation and can be identified as a generalized convective cell.
Wave–plasma interaction near the second electron cyclotron harmonic
Authors: Pešić S.
Published: July 2002

The linear wave propagation and spatial damping near the second electron cyclotron harmonic in a weakly relativistic Maxwellian plasma for an arbitrary angle of wave incidence are investigated. It is found that mode interaction with linear conversion of the extraordinary mode into a quasilongitudinal mode occurs over a relatively large range of plasma parameters. The absorption properties of the extraordinary and ordinary modes and their scaling laws are examined. The noninductive current drive by electron cyclotron waves is also discussed. The results obtained indicate quite favorable features of the wave–plasma interaction near the second electron cyclotron harmonic for plasma heating, current drive, and diagnostics applications.
Magnetohydrodynamic clump instability
Authors: Tetreault D. J.
Published: July 2002

The theory of magnetohydrodynamic (MHD) clump instability in current driven plasma is presented. MHD clump fluctuations are current carrying bundles of correlated magnetic field lines. The instability occurs when turbulent mixing of the mean current density at island overlap produces clumps at a rate faster than their decay as a result of magnetic field line stochasticity. The renormalized dynamical equation describing MHD clump instability is derived from one-fluid MHD equations and conserves the dynamical invariants of the exact equations. The renormalized equation is a nonlinear, turbulent version of the Newcomb equation of linear MHD stability theory and can be cast into the form of a nonlinear MHD energy principle. MHD clump instability is a dynamical route to the Taylor state.
The dynamic sheath: Objects coupling to plasmas on electron-plasma-frequency time scales
Authors: Borovsky Joseph E.
Published: July 2002

The time-dependent interaction between solid objects and the unmagnetized plasmas in which they are immersed is investigated. To this end over 1900 high-resolution, one-dimensional particle-in-cell simulations of the plasmas surrounding cylindrical and planar objects are statistically analyzed. Numerical shot noise produces an electron-plasma-frequency ringing in the simulations, the amplitude of which is related to the plasma temperature and to the numerical system temperature. Whenever the potential of an object is rapidly biased, the surrounding plasma rings with a large amplitude at the electron-plasma frequency. During this ringing, a depletion layer forms around the object on ion-acoustic time scales. Positively charged objects discharge via plasma currents in about τpe /4 and negatively charged objects discharge in about τpi . Owing to charge separations in the plasmas, for the first few ion-plasma periods after a perturbation, the potential of an object is not directly related to the charge on it. The electron-plasma-frequency ringing drives large-amplitude Langmuir waves, which energize electrons and drive cavitation in the plasma. The fluxes of electrons reaching the objects are bursty at ωpe, and the energies of the ions striking the object slowly and systematically vary with time.
The influence of electron trapping on stationary Langmuir waves
Authors: Bergmann A. , Schnabl H.
Published: July 2002

The excitation of high-amplitude Langmuir waves in a warm plasma is investigated in the framework of the hydrodynamic model. An integral expression is found describing the maximum possible amplitude in the limit of stationary waves. The steep increase of compression energy in the density peaks is shown to be the reason for this limitation of amplitude. If electron trapping in the potential of the Langmuir wave is taken into consideration, two consequences occur: The limit for the density peaks in the stationary wave is lowered, and the dispersion relation is modified. Because of the trapped electrons, allowed frequency bands appear below the original plasma frequency. Thus plasma waves containing trapped electrons are able to propagate in the overdense region.
Modeling multiple reactive scalar mixing with the generalized IEM model
Authors: Tsai Kuochen , Fox Rodney O.
Published: July 2002

An outstanding feature of the amplitude mapping closure is its ability to relax an arbitrary initial probability density function (PDF) to a Gaussian PDF asymptotically. Due to the difficulties in computing either the analytical or numerical solution, the mapping closure has never been applied to multiple scalars with finite reaction rates. In this work, the generalized IEM (GIEM) model is combined with the mapping closure to model the molecular mixing terms in the PDF balance equation. The GIEM model assumes a linear relationship between the rates of change of the reactive scalars and an inert scalar (shadow scalar) during the mixing step. By applying the mapping closure for binary mixing to the shadow scalar, the GIEM model yields excellent agreement for both one- and two-step reactions with DNS data, the conditional moment closure (CMC) and reaction–diffusion in a random lamellar system for a wide range of initial volume ratios and reaction rates.
Application of optical flow techniques to flow velocimetry
Authors: Hitt Darren L. , Lowe Mary L. , Newcomer Ryan
Published: July 2002

Optical flow refers to an image processing technique originally developed for computer and robot vision applications. In this Letter, optical flow algorithms are utilized to obtain two-dimensional velocity fields corresponding to fluid flows. The performance of the algorithms with regard to three flows is discussed: computer-simulated suspension flow, bubble detachment from a submerged needle, and in vivo blood flow in a microvascular network. For small changes in successive images, the algorithms yield good quantitative and qualitative information about the flows.
Viscosity of periodic suspensions
Authors: Gondret P. , Petit L.
Published: July 2002

By submitting macroscopic (non-Brownian) monodisperse suspensions of solid spheres to an oscillating shear flow with a ‘‘rheo-optical’’ set-up, a quasi-periodic ordering of spheres has been observed during the shearing motion, and viscosity measurements have been performed simultaneously. The viscosity values corresponding to the ordered suspensions are significantly smaller than the values corresponding to the disordered suspensions; they are compared with viscosity calculations made by other authors in the case of periodic suspensions of particles.
Shear stabilization of a solidifying front: Weakly nonlinear analysis in a long-wave limit
Authors: Schulze T. P. , Davis S. H.
Published: July 2002

The manufacturing of single crystals of multi-component materials with uniform material properties is frequently hampered by the presence of morphological instabilities during the solidification. In this paper we extend into the nonlinear regime our previous work on the influence of shear flows on the linear stability of the solid/liquid interface during the directional solidification of binary alloys. The flows are generated by unidirectional or nonplanar harmonic oscillations of the crystal parallel to the mean interface position, and oscillations with physically realizable amplitudes and frequencies are found to be useful for stabilization purposes. A strongly nonlinear equation which governs the evolution of the interface in the limit of high surface energy, a weak flow and thermodynamic equilibrium is derived, and a weakly nonlinear analysis of this equation is performed. For the unidirectional case, it is found that oscillations with sufficiently large amplitude will change the initial bifurcation from super- to subcritical. For the nonplanar case, it is found that subcritical instability of roll, square and hexagonal cells is favored as the amplitude of the flow is increased. Thus, some of the stabilization due to the flow may be lost at finite amplitude, but substantial stabilization can be retained.
Boiling of superheated fluorocarbon drops in water. Effect of clathrate-hydrate shells encapsulating drops
Authors: Mori Yasuhiko H.
Published: July 2002

This communication briefly describes a high-speed videographic study on boiling of drops of a liquid fluorocarbon (HFC-134a; CF3CH2F) moderately superheated in a water pool. Each drop is either encapsulated by, or free from, a solid clathrate-hydrate phase, which can form at the fluorocarbon/water interface under particular thermodynamic conditions. The present study shows that such a hydrate phase over a drop causes multibubble nucleation in the drop, thereby making the succeeding boiling process far more vigorous than it would proceed in the absence of the hydrate phase.