bluuebunny/crossref_metadata_2025 huggingface dataset:
Spherically symmetric dyonic solutions for vacuum Einstein equations in 4+K dimensions
Authors: Lee S.-C. , Lou S.-L.
Published: July 2002

The general spherically symmetric dyonic solutions of vacuum Einstein equations compatible with a K-dimensional toroidal fiber structure in 4+K dimensions are found. Solutions with no electric and/or magnetic change can be obtained by suitable limiting procedures.
Markovian limit for a reduced operation-valued stochastic process
Authors: Barchielli Alberto
Published: July 2002

Operation-valued stochastic processes give a formalization of the concept of continuous (in time) measurements in quantum mechanics. In this article, a first stage M of a measuring apparatus coupled to the system S is explicitly introduced, and continuous measurement of some observables of M is considered (one can speak of an indirect continuous measurement on S). When the degrees of freedom of the measuring apparatus M are eliminated and the weak coupling limit is taken, it is shown that an operation-valued stochastic process describing a direct continuous observation of the system S is obtained.
Mass corrections to periodic solitons
Authors: Braden H. W.
Published: July 2002

The quantum mass corrections to static periodic solitons are considered and expressed in terms of a functional quantity, the discriminant of the Hill’s operator appearing. Several general expansions for this and hence the mass corrections are given. In particular, the connection with integrable systems and inverse scattering is clearly seen; this enables one to obtain simple expressions for these corrections.
On the excitonic-polaron theory in angular variables
Authors: Strinati G.
Published: July 2002

The model of an electron bound to an impurity (or to a core hole) and interacting with a boson field is analyzed in terms of bosonic variables symmetry adapted to the spherical symmetry about the impurity center. It is shown that the use of this appropriate set of variables considerably simplifies the solution of the variational problem based on a Lee–Low–Pines-type of ansatz for the ground-state variational wave function.
Maximum entropy summation of divergent perturbation series
Authors: Bender Carl M. , Mead Lawrence R. , Papanicolaou N.
Published: July 2002

In this paper the principle of maximum entropy is used to predict the sum of a divergent perturbation series from the first few expansion coefficients. The perturbation expansion for the ground-state energy E(g) of the octic oscillator defined by H=p2/2+x2/2+gx8 is a series of the form E(g)∼ 1/2 +∑(−1)n+1 Angn. This series is terribly divergent because for large n the perturbation coefficients An grow like (3n)!. This growth is so rapid that the solution to the moment problem is not unique and ordinary Padé summation of the divergent series fails. A completely different kind of procedure based on the principle of maximum entropy for reconstructing the function E(g) from its perturbation coefficients is presented. Very good numerical results are obtained.
Hamiltonization for singular and nonsingular mechanics
Authors: Espindola Maria L. , Teixeira Nelson L. , Espindola Oslim
Published: July 2002

A Hamiltonization procedure valid for both singular and nonsingular mechanics is proposed. A comparison with Dirac’s theory (for singular systems) is developed.
The Jacobi-matrix method in parabolic coordinates: Expansion of Coulomb functions in parabolic Sturmians
Authors: Ojha P. C.
Published: July 2002

Previous analysis of the Jacobi-matrix method based on the underlying SO(2,1) Lie algebra is extended to the Coulomb Hamiltonian in parabolic coordinates. The general solution of the generic SO(2,1) eigenvalue equation is constructed and special cases, which furnish expansions of the Coulomb functions ψ(±)k(r) in a complete set of parabolic Sturmians, are discussed.
Coherent angular momentum states for the two-dimensional oscillator
Authors: Bracken A. J. , McAnally D. S. , Òdúndún O. A.
Published: July 2002

Coherent angular momentum states are defined for the two-dimensional isotropic harmonic oscillator. They share many attractive properties with the familiar (Cartesian) coherent states, but are in general distinct from those states. The probabilities of obtaining particular values for the radial and angular momentum quantum numbers follow independent Poisson distributions in the new states, but not in the old. In a quasiclassical description of the oscillator, corresponding to a given classical trajectory, the uncertainty in the angular momentum of the system is smaller if the new states are used rather than the old. The new states are the natural analogs of the coherent angular momentum states introduced for the three-dimensional oscillator by Bracken and Leemon [A. J. Bracken and H. I. Leemon, J. Math. Phys. 22, 719 (1981)].
On infinite-dimensional variational principles with constraints
Authors: Schmid Rudolf , Simoni Alberto
Published: July 2002

The Lagrange multiplier theorem is generalized for constrained functions on dual pairs of Banach spaces. Then a variational principle for dual pairs of Banach spaces is proven for the case when the constraint set is given by a symmetry and it is generalized to Banach manifolds.
Eigenvalue equations for Krichever–Novikov algebras
Authors: Fairlie D. B. , Fletcher P. , Nuyts J.
Published: July 2002

Nontrivial examples of Krichever–Novikov algebras are constructed. The construction involves parameters that satisfy eigenvalue conditions. In the linear case, for an r-term algebra, the eigenvalues are 0,1,...,r−3.
A note on the triple sum series for the 9j coefficient
Authors: Rao K. Srinivasa , Rajeswari V.
Published: July 2002

It is shown that the triple sum series of Jucys and Bandzaitis [Angular Momentum Theory in Quantum Physics (Vilnius, Mokslas, 1977)] for the 9j coefficient can be identified with a formal triple hypergeometric series due to Lauricella–Saran–Srivastava [G. Lauricella, Rend. Circ. Mat. Palermo 7, 111 (1893); L. Saran, Ganita 5, 77 (1954); H. M. Srivastava, Ganita 5, 97 (1964)].
Frequency-dependent susceptibility of a free electron gas in D dimensions
Authors: Lee M. Howard , Nelson Jon T.
Published: July 2002

The real and imaginary parts of the dynamic susceptibility of a free electron gas at T=0 are obtained as a function of wave vector k, frequency ω, and space dimensionality D. The real part of the dynamic susceptibility is shown to be simply related to the static susceptibility. For odd-numbered dimensions there exists a general dimensional relationship for the dynamic susceptibility, originating from a similar relationship for the static susceptibility. For even-numbered dimensions there is no such general relationship, but instead a restricted one.
A novel approach to the synthesis of nondispersive wave packet solutions to the Klein–Gordon and Dirac equations
Authors: Shaarawi Amr M. , Besieris Ioannis M. , Ziolkowski Richard W.
Published: July 2002

A systematic approach to the derivation of exact nondispersive packet solutions to equations modeling relativistic massive particles is introduced. It is based on a novel bidirectional representation used to synthesize localized Brittingham-like solutions to the wave and Maxwell’s equations. The theory is applied first to the Klein–Gordon equation; the resulting nondispersive solutions can be used as de Broglie wave packets representing localized massive scalar particles. The resemblance of such solutions to previously reported nondispersive wave packets is discussed and certain subtle aspects of the latter, especially those arising in connection to the correct choice of dispersion relationships and the definition of group velocity, are clarified. The results obtained for the Klein–Gordon equation are also used to provide nondispersive solutions to the Dirac equation which models spin 1/2 massive fermions.
Shift operators for a Dirac oscillator
Authors: de Lange O. L.
Published: July 2002

Shift operators are obtained for a Dirac oscillator. These operators and other algebraic methods are used to determine energy eigenvalues and eigenkets, expectation values, matrix elements, and coordinate-space wave functions.
Cosmological models that describe particle creation in the early universe and evolve into the ‘‘present-day’’ universe
Authors: Ponce de Leon J.
Published: July 2002

The disappearance of the cosmological constant can be formally treated by means of similarity solutions of general relativity that evolve from a stage with conformal symmetry to a stage with homothetic symmetry. In this work it is assumed that in this transition the universe does not ‘‘lose its memory’’ completely, but it does ‘‘remember’’ some of its past characteristics. Specifically, it is assumed that the equation of state remains the same in both stages. Then, the most general, spherically symmetric, cosmological model compatible with this assumption is developed. It is shown that it can be used to describe, classically, the birth, near the center of a spherical domain (a ‘‘bubble’’) of positive density and pressure from an early universe with particle production. As a consequence of the difference of pressures, the bubble grows in size and mass and evolves into a present-day FLRW universe with p=nρ. The model, therefore, is of relevance to the description of phase changes typical of inflationary universe models.
A study of a 90° vortex–vortex scattering process
Authors: Burzlaff J. , McCarthy P.
Published: July 2002

Following Ruback, the evidence for scattering at right angle of two vortices in a head-on collision is discussed. The evidence is given in terms of the approximate solutions of the equations of motion. This makes it possible to extend the analysis to the case of a small net repulsive force between the corresponding static vortex configurations. The ordinary differential equations, which result from the ansatz for the approximate solutions, are solved by Taylor series at the origin and by asymptotic series at infinity.
Nondispersive solutions of the Dirac equation
Authors: Hillion Pierre
Published: July 2002

Nondipersive solutions of the Dirac equation, that is, solutions depending on an arbitrary function F(u), where u is itself a solution of the characteristic equation (∇u)2−(c−1∂tu)2=0, are discussed.
Note on the representation of many-particle dynamics as higher-order single-particle dynamics, with a means to relativistic elevation of Newtonian dynamics
Authors: Kerner Edward H.
Published: July 2002

It is shown how (first in Newtonian physics), by processes of repeated differentiation of equations of motion and of algebraic elimination, the dynamics of many particles may be brought to another equivalent representation, that of a single higher-order equation of motion for a single particle. Here a higher-order Lagrangian followed by an Ostrogradsky Hamiltonian may be brought into play. (This leads parenthetically to the construction of a considerable class of canonically inequivalent specifications of one basic set of equations of motion.) The higher-order one-particle representation translates simply and directly (but not uniquely) into relativistic generalization (because only a single world line is being described), in which the Poincaré group is canonically represented in an Ostrogradsky Hamiltonian formulation. The examples of the Kepler problem and the harmonic oscillator are elaborated in detail.
Stochastic lengths
Authors: Jaekel M. T.
Published: July 2002

The autocorrelations of the line element for the sample paths of diffusion processes are computed. Lengths are defined for the sample paths of diffusions which depend upon an arbitrary function f and reduce to the classical relativistic length for differentiable trajectories. Their mean values are computed for a general diffusion and provide a family of stochastic actions labeled by f. In a variational principle, these actions are extremized over the drift and probability density and the equations characterizing the critical diffusions are derived. The Klein–Gordon equation is obtained from the variation of arbitrary f-dependent stochastic extensions of the length of trajectories.
The algebras of inhibited parafermionic violation of the Pauli principle
Authors: Cougo-Pinto M. V.
Published: July 2002

The theory of the algebras of Ignat’ev and Kuz’min and of Greenberg and Mohapatra is developed. These are algebras of inhibited parafermionic oscillators that describe possible small violations of the Pauli exclusion principle. The cyclic modules of the algebras are constructed so as to exhibit the connection of their fundamental properties, as uniqueness and statistical signature, with the relations in the algebras. The formalism is presented in such a way suited for further mathematical and physical developments, and has a natural continuation in a forthcoming paper.
Quantum Z3-graded space
Authors: Chung Won-Sang
Published: July 2002

In this paper the quantum Z3-graded space is discussed and its differential calculus is investigated and the quantum matrices in quantum Z3-graded space are obtained.
On the regular Hilbert space representation of a Moyal quantization
Authors: Braunss G.
Published: July 2002

It is shown that in the regular viz. phase space representation of a Moyal quantization real polynomials in the phase space variables become essentially self-adjoint operators, and that functions in the positive cone of monomials of even power in the phase space variables yield positive operators. Conditions on the boundedness of Moyal operators are given. The classical limit of a Moyal operator is defined and used to relate classical with quantum entropy.
Multiplane gravitational lensing. II. Global geometry of caustics
Authors: Petters A. O.
Published: July 2002

The global geometry of caustics due to a general multiplane gravitational lens system is investigated. Cusp-counting formulas and total curvatures are determined for individual caustics as well as whole caustic networks. The notion of light path obstruction points is fundamental in these studies. Lower bounds are found for such points and are used to get upper bounds for the total curvature. Curvature functions of caustics are also treated. All theorems obtained do not rely on the detailed nature of any specific potential assumed as a gravitational lens model, but on the overall differential-topological properties of general potentials. The methods employed are based on the following: Morse theory, projectivized rotation numbers, the Fabricius–Bjerre–Halpern formula, Whitney’s rotation number formula, Seifert decompositions, and the Gauss–Bonnet theorem.
Fermionic matter coupled to higher derivative Chern–Simons theories. II
Authors: Foussats A. , Manavella E. , Repetto C. , Zandron O. P. , Zandron O. S.
Published: July 2002

The diagrammatic and the Feynman rules for the higher derivative Chern–Simons theories in (2+1) dimensions coupled to fermionic matter are constructed. This is done by starting from the path-integral quantization. Once the diagrammatic and the Feynman rules are given, the regularization and renormalization problem of this higher derivative model is analysed in the framework of the perturbation theory. The unitarity problem related with the possible appearance of ghost states with negative norm is also discussed. Finally, the BRST formalism for the model is constructed and some interesting differences with respect to the formalism applied to usual Chern–Simons models are presented.
Fermion pair production from an electric field varying in two dimensions
Authors: Seger J. E. , Balantekin A. B.
Published: July 2002

The Hamiltonian describing fermion pair production from an arbitrarily time-varying electric field in two dimensions is studied using a group-theoretic approach. We show that this Hamiltonian can be encompassed by two, commuting SU(2) algebras, and that the two-dimensional problem can therefore be reduced to two one-dimensional problems. We compare the group structure for the two-dimensional problem with that previously derived for the one-dimensional problem, and verify that the Schwinger result is obtained under the appropriate conditions.
Recursively minimally-deformed oscillators
Authors: Katriel J. , Quesne C.
Published: July 2002

A recursive deformation of the boson commutation relation is introduced. Each step consists of a minimal deformation of a commutator [a,a°]=fk(... ;n̂) into [a,a°]qk+1=fk(... ;n̂), where ... stands for the set of deformation parameters that fk depends on, followed by a transformation into the commutator [a,a°]=fk+1(... ,qk+1;n̂) to which the deformed commutator is equivalent within the Fock space. Starting from the harmonic oscillator commutation relation [a,a°]=1 we obtain the Arik–Coon and Macfarlane–Biedenharn oscillators at the first and second steps, respectively, followed by a sequence of multiparameter generalizations. Several other types of deformed commutation relations related to the treatment of integrable models and to parastatistics are also obtained. The ‘‘generic’’ form consists of a linear combination of exponentials of the number operator, and the various recursive families can be classified according to the number of free linear parameters involved, that depends on the form of the initial commutator.
Two-dimensional supersymmetric harmonic oscillator carrying a representation of the GL(2|1) graded Lie algebra
Authors: Das A. , Wotzasek C.
Published: July 2002

We study a supersymmetric two-dimensional harmonic oscillator which carries a representation of the general graded Lie algebra GL(2|1), formulate it on the superspace, and discuss its physical spectrum.
An affine string vertex operator construction at an arbitrary level
Authors: Gebert R. W. , Nicolai H.
Published: July 2002

An affine vertex operator construction at an arbitrary level is presented which is based on a completely compactified chiral bosonic string whose momentum lattice is taken to be the (Minkowskian) affine weight lattice. This construction is manifestly physical in the sense of string theory, i.e., the vertex operators are functions of Del Giudice–Di Vecchia–Fubini (DFF) “oscillators” and the Lorentz generators, both of which commute with the Virasoro constraints. We therefore obtain explicit representations of affine highest weight modules in terms of physical (DDF) string states. This opens new perspectives on the representation theory of affine Kac–Moody algebras, especially in view of the simultaneous treatment of infinitely many affine highest weight representations of arbitrary level within a single state space as required for the study of hyperbolic Kac–Moody algebras. A novel interpretation of the affine Weyl group as the “dimensional null reduction” of the corresponding hyperbolic Weyl group is given, which follows upon re-expression of the affine Weyl translations as Lorentz boosts.
Gauge conditions in modern Kaluza–Klein theory
Authors: Sajko William N. , Wesson Paul S. , Liu Hongya
Published: July 2002

In the modern version of 5-D general relativity where the fifth dimension induces matter in 4-D space–time, a choice of coordinates and its restrictions on the geometry (a gauge) dictates the physics of the gravitational, electromagnetic, and scalar fields (spin 2, 1, 0). We extend previous work by concentrating on two related problems. First, we use the lapse and shift formalism to carry out a (4+1) split of Kaluza–Klein theory valid in any gauge. Second, we use a conformal gauge to simplify the 5-D field equations, find a plane-wave solution, and identify the energy and momentum of the particle associated with it.
Rotating dust solutions of Einstein’s equations with 3-dimensional symmetry groups. I. Two Killing fields spanned on uα and wα
Authors: Krasiński Andrzej
Published: July 2002

For a rotating dust with a 3-dimensional symmetry group all possible metric forms can be classified and, within each class, explicitly written out. This is made possible by the formalism of Plebański based on the Darboux theorem. In the resulting coordinates, the Killing vector fields (if any exist) assume a special form. Each Killing vector field may be either spanned on the fields of velocity and rotation or linearly independent of them. By considering all such cases one arrives at the classification. With respect to the structures of the groups, this is just the Bianchi classification, but with all possible orientations of the orbits taken into account. In this paper, which is part 1 of a 3-part series, all solutions are considered for which two Killing fields are spanned on velocity and rotation. The solutions of Lanczos and Gödel are identified as special cases, and their new invariant definitions are provided. In addition, a new invariant definition is given of the Ozsvath class III solution.
Electron paramagnetic resonance measurements of static magnetic susceptibility
Authors: Cherkasov F. G. , Ovchinnikov I. V. , Turanov A. N. , L’vov S. G. , Goncharov V. A. , Vitols A. Ya.
Published: July 2002

It is shown that the total volume magnetic susceptibility of a substance can be measured in principle with the help of electron paramagnetic resonance (EPR). For this purpose, the conventional EPR technique can be used along with a known reference compound with a very narrow resonant absorption line. The accuracy of absolute susceptibility measurements is comparable to that of classical methods.
Light scattering in LiCoPO4 single crystal: analysis of the vibrational spectrum
Authors: Fomin V. I. , Gnezdilov V. P. , Kumosov V. S. , Peschanskii A. V. , Eremenko V. V. , Gentil S. , Rivera J.-P.
Published: July 2002

In a single crystal of LiCoPO4 Raman scattering has been studied in a wide temperature range. Thirty-two of the 36 Raman-active vibrational modes predicted by group-theory analysis were detected. The experimental lines are identified on the basis of their polarization rules, frequency position, and temperature behavior.
Weak localization of low-frequency sound in a quasi-one-dimensional crystal
Authors: Chulkin E. P. , Zhernov A. P. , Kulagina T. N.
Published: July 2002

A study is made of the damping coefficient for sound in a dielectric chain crystal containing isotopic impurities at low temperatures T⩽0.1ΘD (ΘD is the Debye temperature). It is shown that in the case of strong disorder, effects due to weak localization of the phonon modes have a substantial influence on the propagation of sound.
On the dynamics of strong temperature disturbances in the upper atmosphere of the Earth
Authors: Meerson B.
Published: July 2002

The dynamics of the cooling of a strongly heated spherically symmetric cavity produced by an explosion in the upper atmosphere is investigated, allowing for the gas motion during the heat conduction. Conditions for a self-similar cooling process are found, and the corresponding self-similar dynamics equations are solved. The characteristic cooling time of the heated cavity is determined as a function of the energy release and parameters of the neutral atmosphere at the height of explosion.
Rotation of a torus
Authors: Chwang Allen T. , Hwang Wei-Shien
Published: July 2002

In order to study the rotational motion of a vortex ring or the locomotion of bacteria, which propel their cells by rotating their long curved filaments called flagella, the low-Reynolds-number flow resulting from the rotation of a torus is studied. The velocity field is obtained by distributing uniform rotlets along a circle with the rotlet directions tangent to the circle. It is found that the effect of curvature of this ring distribution of uniform rotlets is to displace this rotlet ring from the center of the cross section toward the outside of the torus in the normal direction. The net force exerted on the surrounding fluid by the rotational torus is zero. The net torque acting on the fluid is also zero.
The hydrodynamic stress in a suspension of rods
Authors: Shaqfeh Eric S. G. , Fredrickson Glenn H.
Published: July 2002

A theory is presented to describe the momentum transport properties of suspensions containing randomly placed, slender fibers. The theory is based on a diagrammatic representation of the multiple scattering expansion for the averaged Green’s function as developed in the authors’ previous work on the heat and mass transfer properties of fiber dispersions [Phys. Fluids A 1, 3 (1989)]. The ‘‘best one-body approximation’’ is used to calculate the wavenumber-dependent, ensemble-averaged stress for both aligned and isotropically oriented fiber dispersions. Both the dilute and semidilute concentration regimes are considered. The effective viscosity is calculated as a limit unit of the previously obtained wavenumber-dependent properties. In the semidilute concentration regime the scaling form originally suggested by Batchelor [J. Fluid Mech. 46, 813 (1971)] is recovered for both orientation distributions and its relation to short range ‘‘screening’’ is discussed. Corrections to this result in a ‘‘semidilute expansion’’ for small volume fraction are calculated and the dependence of these corrections on orientation distribution and particle shape is demonstrated.
Does contour dynamics go singular?
Authors: Dritschel D. G. , McIntyre M. E.
Published: July 2002

It has recently been claimed that the ‘‘contour-dynamics’’ model of two-dimensional inviscid vortex dyanmics spontaneously develops tangent-slope discontinuities, implying infinite contour curvature, within a finite time. The claim was made on the basis of numerical experimentation on three examples of vortex-patch merging, for one of which details were presented. This note presents contrary numerical evidence for the same example, strongly suggesting that no such singularity develops in the time claimed. The results are generated using overwhelmingly high spatial and temporal resolution. Comparisons with coarser-resolution calculations verify that the effects of resolution have been reduced to an insignificant level at the locations in question. It appears likely that contour smoothness persists for all finite time.
Motion of particles with inertia in a compressible free shear layer
Authors: Samimy M. , Lele S. K.
Published: July 2002

The effects of inertia of a particle on its flow tracking accuracy and particle dispersion are studied using direct numerical simulations of two-dimensional compressible free shear layers in convective Mach number (Mc) range of 0.2 to 0.6. The results show that particle response is well characterized by τ, the ratio of particle response time to the flow time scale (Stokes’ number). The slip between particle and fluid imposes a fundamental limit on the accuracy of optical measurements such as LDV and PIV. The error is found to grow like τ up to τ=1 and taper off at higher τ. For τ=0.2 the error is about 2%. In the flow visualizations based on Mie scattering, particles with τ>0.05 are found to grossly misrepresent the flow features. These errors are quantified by calculating the dispersion of particles relative to the fluid. The trend in lateral dispersion of particles is similar to that of incompressible flows reported by previous investigators. Overall, the effect of compressibility does not seem to be significant on the motion of particles in the range of Mc considered here.
Vortex drift. I: Dynamic interpretation
Authors: Rott Nicholas , Cantwell Brian
Published: July 2002

Vortical flow, restricted to a finite domain (in three dimensions) in an unbounded incompressible viscous fluid that is at rest at infinity, is investigated by the consideration of the dynamics in the potential flow region that surrounds the vortical domain. The evolution equations are considered for a flow that is given at an initial time t. The potential change in the far field is connected to the pressure, which in turn is expressed as the solution of a Poisson equation with sources distributed over the whole flow field. The leading term of the pressure at infinity is a quadrupole, which is caused by a drifting dipole field with a constant strength that is given by the impulse. This ‘‘dynamic’’ value of the drift is then identified with the classical ‘‘kinematic’’ definition as the speed of the impulse centroid. The main new result obtained by this method is the solution of the asymptotic drift problem in three dimensions, complementing the corresponding solution of Cantwell and Rott [Phys. Fluids 31, 3213 (1988)] for plane flow. The connection to the solution of the classical drift problem for a vortex ring is also established.
Conditional scalar dissipation rates in turbulent wakes, jets, and boundary layers
Authors: Kailasnath P. , Sreenivasan K. R. , Saylor J. R.
Published: July 2002

The expected value Eχ≡E(χ,θ=θ0) of the dissipation rate χ of a passive scalar θ conditioned on the scalar value θ=θ0 has been measured in three varieties of turbulent shear flows: heated wakes, dyed liquid jets, and the atmospheric surface layer. The quantity Eχ depends fairly strongly on θ0 and on the flow. For the wake, Eχ exhibits two peaks—one on the low-temperature end and the other on the high-temperature end—and the peaks are separated by an approximately flat region. The relative strength of the two peaks varies with the spatial position. Measured in the turbulent part alone, Eχ tends to have only one peak on the hot side, but is still nonuniform. The related quantity, Eθ″≡(∇2θ,θ=θ0), which is the expected value of the Laplacian of the scalar conditioned on the scalar concentration, has also been measured on the wake centerline and shows a simpler dependence on θ0 than Eχ. For jets, Eχ has a single peak on the high-concentration side. This feature appears to be essentially independent of the use of Taylor’s hypothesis and on whether or not the dissipation rate χ is approximated by only one of its components. It is, however, sensitive to the resolution of measurement. For the temperature fluctuation in the atmospheric boundary layer, the peak in Eχ on the cold side is far weaker than that on the hot side. From this combination of experiments, it is argued that the different shapes of Eχ in different flows are related to differences in the nature of the scalar pdf itself and, for the high-Schmidt-number dyes in water flows, on whether or not the finest scales of the scalar are resolved.
Laminar flow in twisted ducts
Authors: Kheshgi Haroon S.
Published: July 2002

Fully developed flow of an incompressible Newtonian fluid through a duct in which the orientation of the cross section is twisted about an axis parallel to an imposed pressure gradient is analyzed here with the aid of the penalty/Galerkin/finite element method. When the axis of twist is located within the duct, flow approaches limits at low and high torsion, the spatial frequency τ by which the duct is twisted. For small torsion, flow is nearly rectilinear and solutions approach previous asymptotic results for an elliptical cross section. For large torsion, flow exhibits an internal layer structure: a rotating circular-cylinder core with a nearly parabolic axial velocity profile, an internal layer of thickness τ−1 along the perimeter of the largest circular cylinder that can be inscribed in the duct, and nearly quiescent flow outside of the circular cylinder. The maximum rate of swirl in the core of a square duct is found to be at moderate torsion. The primary effect of inertia is an increase in pressure with distance from the axis, due to centrifugal acceleration. When the duct is offset from the axis of twist, inertia leads to one, two, or three primary vortices without apparent bifurcation of steady states, although stability of steady flows is lost beyond detected Hopf points.
Analytic boundary for resistive ballooning stability in the tokamak second-stable regime
Authors: Fu G. Y. , Van Dam J. W. , Holland D. L. , Fried B. D. , Baños A.
Published: July 2002

Analytical expressions for the marginal stability boundary for resistive ballooning modes at high beta are obtained in the limits of both large and small global shear. These results confirm the recent numerical finding of Sykes et al. [Plasma Phys. Controlled Fusion 29, 719 (1987)] that resistive ballooning modes are stable throughout most of the regime corresponding to ideal ballooning ‘‘second stability’’ in high-beta tokamaks.
Kinetic equilibria of plasma shear layers
Authors: Cai D. , Storey L. R. O. , Neubert T.
Published: July 2002

The analysis of plasma beam and shear problems in magnetic fields is usually based on a hydromagnetic fluid model. In a low-density collisionless plasma, however, the kinetic effects of the plasma, such as finite Larmor radius effects, are not yet clearly understood. In this paper, the kinetic equilibria of plasma shears in a uniform and fixed magnetic field, with full ion motion, are discussed by solving the Vlasov equation with a given electric field and drift velocity. In this model, the ion density profile through the plasma shear layer is quite different from the one predicted by a hydromagnetic model. As a result of a complicated ion gyromotion through the shear layer, single- and double-humped ion density profiles are obtained. The dependence on the temperature and the strength of the shear will be discussed. The results show a significant difference between positive and negative shears.
Planar laser-driven ablation model for nonlocalized absorption
Authors: Dahmani Faiz , Kerdja Tahar
Published: July 2002

A model for planar laser-driven ablation is presented. Nonlocalized inverse bremsstrahlung absorption of laser energy at a density n1<nc is assumed. A steady-state solution in the conduction zone is joined to a rarefaction wave in the underdense plasma. The calculations relate all steady-state fluid quantities to only the material, absorbed intensity, and laser wavelength. The theory agrees well with results from a computer hydrodynamics code medusa [Comput. Phys. Commun. 7, 271 (1974)] and experiments.
Change of confinement properties and transition from absolute to non-normal mode microinstabilities
Authors: Basu B. , Coppi B.
Published: July 2002

The change in confinement properties that can be induced in experiments, where the plasma is heated by an external injection system, is considered to be related to the transition from a regime where ‘‘absolute’’ microinstabilities are excited at the edge of the plasma column to a regime where these microinstabilities can exist only as non-normal modes because of the effects of the local gradient of the E×B rotation frequency that is induced. Ion-temperature-gradient-driven modes are analyzed as an important example and the threshold conditions for their disappearances as normal modes are evaluated.
Effects of equilibrium flow on the resistive tearing mode
Authors: Paris R. B. , Wood A. D. , Stewart S.
Published: July 2002

The growth rate of the resistive tearing mode is investigated in the presence of a sub-Alfvénic equilibrium plasma shear flow along the confining magnetic field and fluid viscosity. The flow exerts a destabilizing influence and the well-known instability condition, Δ′≳0, is modified to yield the possibility of instability with Δ′≤0. The effects of viscosity on the marginal stability condition and the transition between the inviscid and viscous-dominated limits are considered in detail.
Magnetohydrodynamic stability studies of supershot plasmas
Authors: Hughes M. H. , Phillips M. W. , Fredrickson E. D.
Published: July 2002

Slowly growing magnetohydrodynamic (MHD) instabilities are usually detected experimentally in supershot plasmas in the Tokamak Fusion Test Reactor [in Plasma Physics and Controlled Nuclear Fusion Research 1986, Kyoto (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 75] (TFTR). These instabilities, when they occur, result in deterioration of the confinement and limit the attainable β. Using initial profile data from transport analysis of specific high β supershot plasmas, the predictions of the single fluid, linear MHD stability model are studied and compared with the experimental observations. It is shown that, in the highest β plasmas achieved, the pressure gradients in the interior are such that the absence of the 1/1 mode is difficult to reconcile with the single fluid MHD model if the safety factor, q<1. On the assumption that q exceeds unity everywhere, it is found that supershot plasmas are predicted to be unstable or near marginal to small toroidal mode number, pressure-driven instabilities of the ballooning variety. When finite plasma resistivity is included in the analysis the range of parameters over which these instabilities are excited is significantly extended.
Simulation study of the dynamo structure in the reversed-field pinch
Authors: Nagata A. , Sato K. I. , Ashida H. , Amano T.
Published: July 2002

The dynamo structure in the reversed-field pinch (RFP) is studied through the nonlinear dynamics of a single-helicity mode. Simulation is concentrated upon the physical structure of nonlinear interactions of the plasma flow and magnetic fluctuation. The result indicates that when the initial equilibrium profile is deformed by resistive diffusion, the radial flow is driven near the core of the plasma. As this flow forms a vortex structure and magnetic fluctuation grows radially, the dynamo electric field is helically induced just inside the reversal surface and then the toroidal flux is increased. This dynamo electric field correlates to the nonlinear evolution of the kinetic energy of the m=1 mode, and the increase of the toroidal flux originates in the growth process of the magnetic energy of this mode. Consequently, the RFP configuration can be sustained by the single-helicity evolution of the m=1 mode alone, and the electric field induced by the interactions of the toroidal velocity and the radial magnetic field is the most dominant source on the dynamo action.
Conservation relations and violation of the Manley–Rowe relation for plasma–maser instability
Authors: Nambu Mitsuhiro , Hada Tohru
Published: July 2002

The total momentum and energy conservation relations between particle kinetic energy and wave energy is satisfied for the plasma–maser instability. The Manley–Rowe relation for plasma waves is violated and as a result an efficient energy up-conversion from the low-frequency mode to the high-frequency mode is possible even for a normal unreversed electron population in plasma turbulence. The entropy production rate for plasma turbulence with plasma–maser instability is estimated. The plasma–maser instability always coexists with the quasilinear interaction, thus it has a potential importance to interpret numerous experiments in fusion and astrophysical plasmas.
Electron-temperature-gradient-driven instability in tokamak boundary plasma
Authors: Xu X. Q. , Rosenbluth M. N. , Diamond P. H.
Published: July 2002

A general method is developed for calculating boundary plasma fluctuations across a magnetic separatrix in a tokamak with a divertor or a limiter. The slab model, which assumes a periodic plasma in the edge reaching the divertor or limiter plate in the scrape-off layer (SOL), should provide a good estimate, if the radial extent of the fluctuation quantities across the separatrix to the edge is small compared to that given by finite particle banana orbit. The Laplace transform is used for solving the initial value problem. The electron-temperature-gradient (ETG)-driven instability is found to grow like t−1/2eγmt.
Brillouin scattering, two-plasmon decay, and self-focusing in underdense ultraviolet laser-produced plasmas
Authors: Tanaka K. , Boswell B. , Craxton R. S. , Goldman L. M. , Guglielmi F. , Seka W. , Short R. W. , Soures J. M.
Published: July 2002

Underdense foam targets were irradiated with a single UV laser beam at intensities up to 1015 W/cm2. The incident laser propagated into the foam a distance of 500–1000 μm, depending on the average target density. The backscattered Brillouin and 3ω0/2 radiation were observed to have the same dependence on the incident laser intensity, indicating a strong interrelation of these processes. A possible coupling mechanism is proposed.
Kinetic theory of stimulated Raman sidescattering from magnetized plasmas
Authors: Rankin R. , Boyd T. J. M.
Published: July 2002

A theory of stimulated Raman sidescattering in magnetized plasmas is presented based on a solution of the Vlasov–Maxwell equations. The incident laser light, in the form of extraordinary mode radiation, decays into light waves which propagate along the uniform magnetic field as right or left circularly polarized waves. The scattered plasma mode is an obliquely propagating electron-Bernstein wave. The possible relevance of the theory to experiments in which structure is observed in radiation at one-half of the laser frequency is discussed.
Some observations on the evolution of shear layer instabilities in laminar flow through axisymmetric sudden expansions
Authors: Latornell D. J. , Pollard A.
Published: July 2002

The laminar flow in an axisymmetric sudden expansion has been studied experimentally. Using a nominal diameter ratio of 0.5 and well-defined inlet velocity profile conditions, data are presented that, for the first time, demonstrate clearly that the onset of shear layer instabilities is dependent on the inlet velocity profile. The reattachment length of the shear layer (normalized by the expansion step height) as a function of the inlet Reynolds number is linear with slopes of 0.096 and 0.068 for upstream velocity profile conditions of Poiseuille and nominal plug flow, respectively.
Slip at the surface of a translating–rotating sphere bisected by a free surface bounding a semi-infinite viscous fluid: Removal of the contact-line singularity
Authors: O’Neill M. E. , Ranger K. B. , Brenner H.
Published: July 2002

A linear slip, Basset-type, boundary condition having an experimentally adjustable phenomenological slip coefficient is used to remove the contact-line singularity that would otherwise prevent the movement of a partially penetrating sphere normal to a planar free surface F bounding a semi-infinite viscous fluid. Stokes flow calculations are presented for the quasistatic hydrodynamic force and torque resistance matrix for a half-submerged sphere that is instantaneously translating and rotating with vector velocities that are arbitrarily oriented relative to the free-surface unit normal vector. The singular components of this material matrix (arising either during translational motion normal to F or rotational motion about an axis lying within F) are shown to be finite for finite slip coefficients β, and to become logarithmically infinite in the traditional nonslip limit β→∞. The relative weakness of this logarithmic singularity suggests that a degree of slip as small as, say, 0.01%—which would presumably be kinematically indistinguishable from the no-slip case—could easily masquerade as a conventional ‘‘wall effect’’ on the Stokes drag. A small degree of slip is thus hypothesized as a mechanism that would permit the observed transport of Brownian corpuscles across interfacial regions.
Measurements of drop size at the spray edge near the nozzle in atomizing liquid jets
Authors: Wu K-J. , Reitz R. D. , Bracco F. V.
Published: July 2002

The drop size distribution was measured from back-lighted spark photographs at the edge of steady sprays in the immediate vicinity of the nozzle exit. The conditions of these liquid-into-gas sprays were such that the outer surface of the liquid jets broke up into small drops at the nozzle exit. The objective was to elucidate the mechanism of breakup. At room temperature, n-hexane and n-tetradecane at pressures from 2.86 to 9.76 MPa were injected into gaseous nitrogen at 1.48 to 2.86 MPa through three straight cylindrical nozzles of different diameters, 127 and 335 μm, and length-to-diameter ratios, 4 and 10. In all cases, the drop sizes could be fitted satisfactorily with a chi-square distribution with degree of freedom equal to 28. The Sauter mean drop diameter and other average diameters were found to decrease with increasing injection velocity and decreasing liquid surface tension, to be insensitive to nozzle diameter and length, and to increase slightly with increasing gas density. The trends and magnitudes are in agreement with those predicted by the supplemented aerodynamic theory of surface breakup if it is assumed that between the jet surface where the drops are formed, that is not visible, and the edge of the spray, where the measurements were made, drops undergo collisions and coalescence. In this region of dense sprays, drop coalescence leads to a rapid increase in drop size, particularly in high gas densities.
Experiments on transition enhancement by distributed roughness
Authors: Corke T. C. , Bar-Sever A. , Morkovin M. V.
Published: July 2002

Distributed roughness with nominal height k in a boundary layer with displacement thickness δ* is known to lead to early non-Tollmien–Schlichting–Schubauer (TS) transition when k/δ* exceeds unity in nonaccelerated flows. But could commonly occurring milder random roughness enhance the regular phase-conditioned TS mechanisms and also lead to early transition? The new affirmative answer rests on extensive hot-wire explorations and smoke-wire visualization of flow over smooth and rough walls. The effects appear to be threefold. First, the low-inertia fluid in the valleys between the elements evidently respond more readily to free-stream disturbances. Second, once the TS fluctuations commence, they grow faster. Whether this is caused by continued input from free-stream disturbances along the path or to an increased destabilization of the system or both remains unclear. No inflected mean boundary-layer profiles were registered in careful measurements. Third, there is evidence of roughness-induced three-dimensionalization of the wave fronts which leads to earlier secondary subharmonic instabilities and, hence, to turbulence.
Toroidal field effects on the stability of a Heliotron configuration
Authors: Carreras B. A. , Garcia L. , Lynch V. E.
Published: July 2002

The addition of a small toroidal field to the Heliotron E configuration [Plasma Phys. 13, 243 (1981)] improves the stability of the n=1 mode and increases the value of the stability beta critical. Total stabilization of this mode can be achieved with added toroidal fields between 5% and 15% of the total field. In this situation, the plasma can have direct access to the second stability regime. For the Heliotron E configuration, the self-stabilization effect is due to the shear, not to the magnetic well. The toroidal field threshold value for stability depends strongly on the pressure profile and the aspect ratio of the plasma.
Collective effects on equilibria of trapped charged plasmas
Authors: Turner Leaf
Published: July 2002

A fluid model is used to study analytically the equilibria of charged plasma in traps. Several geometries are explored: a one-dimensional slab equilibrium of a finite-temperature plasma mechanically confined by two plates that are externally maintained at fixed potentials, and both spherical as well as spheroidal equilibria of a zero-temperature plasma confined in traps distorted from the standard Penning-trap configuration by virtue of the multipole moments of the trapped plasma. Although this study was motivated by the necessity of understanding possible collective effects in charged-plasma traps for the design and future diagnosis of the ambitious antiproton-gravity experiment being undertaken by the Los Alamos Collaboration [Proceedings of the Second Conference on the Intersections between Particle and Nuclear Physics (American Institute of Physics, New York, 1986), AIP Pub. No. 150, p. 436], this study is also relevant to current and future attempts at producing strongly coupled plasmas and ionic crystals.
A model magnetron distribution function: Analysis and scalings
Authors: Kaup D. J. , Thomas Gary E.
Published: July 2002

The distribution function f=N exp[−βyw−(βx−βy)p2 x/(2m) −(βz−βy)p2z/(2m)], where w is the single-particle energy, px is the single-particle canonical momentum parallel to the cathode and perpendicular to the magnetic field, and pz is the single-particle canonical momentum parallel to the magnetic field, has been proposed as a model of the distribution of electrons in a planar magnetron [Phys. Fluids 29, 1746 (1986)]. The scalings of this model and the resulting density of electrons are determined by means of a singular perturbation expansion, carried out to second order.