bluuebunny/crossref_metadata_2025 huggingface dataset:
Heat kernel for nonminimal operators on a Kähler manifold
Authors: Alexandrov Sergei , Vassilevich Dmitri
Published: July 2002

The heat kernel expansion for a general nonminimal operator on the spaces C∞(Λk) and C∞(Λp,q) is studied. The coefficients of the heat kernel asymptotics for this operator are expressed in terms of the Seeley coefficients for the Hodge–de Rham Laplacian.
Algebraic characterization of vector supersymmetry in topological field theories
Authors: Sorella S. P. , Vilar L. C. Q. , Ventura O. S. , Sasaki C. A. G.
Published: July 2002

A cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed. The existence of these linearly broken Ward identities lies in the BRST exactness of suitable antifield dependent cocycles with negative ghost number. This algebraic set up turns out to be related to the cohomological reformulation of the Noether theorem given by G. Barnich, F. Brandt, and M. Henneaux, Commun. Math. Phys. 174, 57, 93 (1995); M. Henneaux, J. Pure Appl. Algebra 100, 3 (1995).
Differential calculus on the h-superplane
Authors: Çelik Salih , Çelik Sultan A. , Arik Metin
Published: July 2002

A noncommutative differential calculus on the h-superplane is presented via a contraction of the q-superplane. An R-matrix which satisfies both ungraded and graded Yang–Baxter equations is obtained and a new deformation of the (1+1)-dimensional classical phase space (the super-Heisenberg algebra) is introduced.
Hopf algebra structure of Grq(1|1) related to GLq(1|1)
Authors: Çelik Salih
Published: July 2002

We show that the algebra of functions on the Grassmann supergroup Grq(1|1) has a (graded) Hopf algebra structure related to GLq(1|1).
Cauchy analysis of the linearized skew sector of the massive nonsymmetric gravitational theory
Authors: Baki P. , Malo J. O.
Published: July 2002

Cauchy analysis of the linearized field equations of the skew sector of the massive nonsymmetric gravitational theory shows that small perturbations give rise to bounded accelerations thereby ensuring good asymptotic behavior for the skew part of the fundamental tensor.
Reductive decompositions and Einstein–Yang–Mills equations associated to the oscillator group
Authors: Dı́az Raúl Durán , Gadea Pedro M. , Oubiña José A.
Published: July 2002

All of the homogeneous Lorentzian structures on the oscillator group equipped with a bi-invariant Lorentzian metric, and then the associated reductive pairs, are obtained. Some of them are solutions of the Einstein–Yang–Mills equations.
Comment on “Geometric phase, bundle classification, and group representation” [J. Math. Phys. 37, 1218 (1996)]
Authors: Azad H. , Qureshi M. N. , Ziad M.
Published: July 2002

This note is a comment on the mathematical aspects of the paper by Mostafazadeh [J. Math. Phys. 37, 1218 (1996)]. Its aim is to remove some of the ambiguities and mistakes of the paper by making more transparent the mathematics involved in the calculation of topological charges.
On the Batalin, Fradkin, Fradkina, and Tyutin quantization of first order systems
Authors: Amorim Ricardo , Thibes Ronaldo
Published: July 2002

By using the field–antifield formalism, we show that the method of Batalin, Fradkin, Fradkina, and Tyutin (BFFT) to convert Hamiltonian systems submitted to second class constraints introduces compensating fields which do not belong to the BRST cohomology at ghost number one. This assures that the gauge symmetries which arise from the BFFT procedure are not obstructed at quantum level. An example where massive electrodynamics is coupled to chiral fermions is considered. We solve the quantum master equation for the model and show that the respective counterterm has a decisive role in extracting anomalous expectation values associated with the divergence of the Noether chiral current.
Evaluation of multiloop diagrams via lightcone integration
Authors: Feng Y. J. , Lam C. S.
Published: July 2002

We present a systematic method to determine the dominant regions of internal momenta contributing to any two-body high-energy near-forward scattering diagram. Such a knowledge is used to evaluate leading high-energy dependences of loop diagrams. It also gives a good idea where dominant multiparticle cross sections occur.
A generalization of Wigner’s unitary–antiunitary theorem to Hilbert modules
Authors: Molnár Lajos
Published: July 2002

Let ℋ be a Hilbert C*-module over a matrix algebra A. It is proved that any function T:H→H which preserves the absolute value of the (generalized) inner product is of the form Tf=φ(f )Uf (f∈H), where φ is a phase-function and U is an A-linear isometry. The result gives a natural extension of Wigner’s classical unitary–antiunitary theorem for Hilbert modules.
Some finite dimensional indecomposable representations of E(2)
Authors: Repka Joe , de Guise Hubert
Published: July 2002

We describe the construction of some finite dimensional nonunitary representations of E(2), the Lie group of Euclidean transformations in the plane. Some properties of these representations are also discussed, with emphasis on indecomposable representations.
SU(N) skyrmions and harmonic maps
Authors: Ioannidou T. , Piette B. , Zakrzewski W. J.
Published: July 2002

Harmonic maps from S2 to CPN−1 are introduced to construct low-energy configurations of the SU(N) Skyrme model. We show that one of such maps gives an exact, topologically trivial, solution of the SU(3) model. We study various properties of these maps and show that, in general, their energies are only a little higher than the energies of the corresponding SU(2) embeddings. Moreover, we show that the baryon and energy densities of the SU(3) configurations with baryon number B=3−6 are more symmetrical than their SU(2) analogs, thus suggesting that there exist solutions of the model with these symmetries. We also show that any SU(2) solution embedded into the SU(4) Skyrme model becomes a topologically trivial solution of this model.
On the sign of the instantaneous spanwise vorticity component in the near-wall region of turbulent boundary layers
Authors: Klewicki J. C. , Gendrich C. P. , Foss J. F. , Falco R. E.
Published: July 2002

A geometric feature of the vorticity field in the near-wall region is educed from an analysis of time-resolved spanwise vorticity measurements. The results of this analysis indicate the existence of a region near the wall in which the instantaneous z component of the vorticity vector is virtually always in the direction indicated by the mean shear. In accordance with the solenoidal condition of the vorticity field, this observed physical feature represents a limitation on the spatial structure of the vorticity field in the near-wall region. The present results also reinforce the conclusion of Klewicki (Ph.D. dissertation, Michigan State University, 1989) that, for the momentum deficit thickness Reynolds number range 1010≤Rθ≤4850, the statistical properties of the spanwise vorticity component are invariant under an inner variable normalization for y+ less than about 40.
Nonlinear study of the flow in a long rectangular cavity subjected to thermocapillary effect
Authors: Laure P. , Roux B. , Ben Hadid H.
Published: July 2002

This paper is devoted to the theoretical study of motions of viscous fluids driven by a constant stress acting on an upper surface of a long rectangular cavity. This problem was originally addressed to the flow behavior of molten metals in open boats driven by thermocapillarity (Bridgman technique solidification). Computations of two-dimensional Navier–Stokes equations show two totally different end circulations. Considering the spatial disturbances of the core flow (e.g., Couette flow), and, using the local theory of bifurcations (center manifold, normal forms), the appearance of two kinds of disturbances corresponding to these end circulations is explained. Moreover, on one hand a condition for the observability of the fully developed Couette flow in terms of aspect ratio (length/height) and Reynolds–Marangoni number is given, and on the other hand the analytical expression of the space periodic flow occurring in the direction of the cold wall is given.
Lagrangian velocity autocorrelation and eddy viscosity in two-dimensional anisotropic turbulence
Authors: Gotoh Toshiyuki , Kaneda Yukio
Published: July 2002

A numerical study is made of the Lagrangian and Eulerian velocity autocorrelations RL and RE, and the eddy viscosity νeddy in two-dimensional anisotropic turbulence with or without mean flow of simple shearing motion. A short-time analysis is made of RL and RE in anisotropic turbulence, and also of νeddy in initially isotropic turbulence. The Lagrangian renormalized approximation is numerically integrated to compute RL and νeddy, and the results are compared with direct numerical simulations.
Two-dimensionality in low-magnetic Reynolds number magnetohydrodynamic turbulence subjected to a uniform external magnetic field and randomly stirred two-dimensional force
Authors: Nakauchi Norihiko , Oshima Hiroshi , Saito Yoshio
Published: July 2002

Evolution of low-magnetic Reynolds number magnetohydrodynamic (MHD) turbulence from an initially three-dimensional isotropic state to a nearly two-dimensional stationary state is studied, when the turbulence is subjected to a uniform magnetic field B0 and randomly stirred two-dimensional force. The study is made by using the energy spectrum equation that is closed by the eddy-damped quasinormal Markovian (EDQNM) approximation assuming that the turbulent field is homogeneous and axisymmetric. Each stage of the processes is examined through the evolutions of total energy of the turbulence, and Joule dissipation, molecular dissipation, and angular energy transfer rates as well. It is shown that the MHD turbulence approaches a quasi-two-dimensional stationary state whose anisotropy strength in two-dimensionality is specified by B0. Also, it is shown that no apparent difference in the evolution of the k−5/3 energy spectrum toward low wave numbers, caused by inverse energy cascade, appears between Reynolds numbers, while the range of the k−3 energy spectrum in larger Reynolds number turbulence is more extended toward high wave numbers.
Modeling of a von Kármán vortex street at low Reynolds numbers
Authors: Ohle Frank , Eckelmann Helmut
Published: July 2002

Time signals of transient von Kármán vortex streets are represented as trajectories in a two-dimensional state space for Reynolds numbers between 53 and 148. From this representation, a two-dimensional system of ordinary differential equations with ten coefficients is derived and used as a model for the description of the asymptotic dynamics. Most of these coefficients are only slightly dependent on the Reynolds number, and some of them also reflect the change in vortex shedding dynamics. With the obtained low-dimensional model, the response of the vortex street to external sinusoidal and square wave signals is predicted. Furthermore, it is shown that an excessively large excitation of the vortex street by sound can lead to a more complicated higher-dimensional dynamical state.
Extended inertial range phenomenology of magnetohydrodynamic turbulence
Authors: Matthaeus William H. , Zhou Ye
Published: July 2002

A phenomenological treatment of the inertial range of isotropic statistically steady magnetohydrodynamic turbulence is presented, extending the theory of Kraichnan [Phys. Fluids 8, 1385 (1965)]. The role of Alfvén wave propagation is treated on equal footing with nonlinear convection, leading to a simple generalization of the relations between the times characteristic of wave propagation, convection, energy transfer, and decay of triple correlations. The theory leads to a closed-form steady inertial range spectral law that reduces to the Kraichnan and Kolmogorov laws in appropriate limits. The Kraichnan constant is found to be related in a simple way to the Kolmogorov constant; for typical values of the latter constant, the former has values in the range 1.22–1.87. Estimates of the time scale associated with spectral transfer of energy also emerge from the new approach, generalizing previously presented ‘‘golden rules’’ for relating the spectral transfer time scale to the Alfvén and eddy-turnover time scales.
High-frequency, step tunable, cyclotron harmonic gyrotron
Authors: Idehara Toshitaka , Tatsukawa Toshiaki , Tanabe Hidehiko , Matsumoto Satoru , Kunieda Kohji , Hemmi Kazuhisa , Kanemaki Tomohiro
Published: July 2002

The performance of a high-frequency gyrotron that operates at the fundamental of the electron cyclotron frequency and its higher harmonics is described. The high frequency of 220 GHz (corresponding wavelength 1.35 mm) has been achieved at both the fundamental and second harmonic. The dependence of output power on magnetic field and beam parameters and the scaling law of output power with harmonic numbers are described. The results are compared with a computer simulation.
Nonlocal heat transport effects on the filamentation of light in plasmas
Authors: Epperlein E. M. , Short R. W.
Published: July 2002

The nonlocal nature of electron heat transport in hot coronal plasmas is investigated. Its effect on the linear theory of laser filamentation is reviewed. The nonlinear evolution of filaments is modeled with the two-dimensional Fokker–Planck code spark, for the conditions of recent filamentation experiments. Simulation results agree with experimental data and imply the dominance of thermal over ponderomotive filamentation. The increased importance of the thermal filamentation mechanism is attributed to heat flux inhibition arising from nonlocal electron transport. The potential implications of filamentation for inertial-confinement-fusion target designs are discussed.
Stimulated Brillouin scattering of electromagnetic waves in a dusty plasma
Authors: Salimullah M. , Sen A.
Published: July 2002

The stimulated scattering of electromagnetic waves off low-frequency modes in a homogeneous, unmagnetized, and collisionless dusty plasma has been investigated theoretically. The presence of the dust particles introduces a background inhomogeneous electric field that significantly influences the dispersive properties of the plasma. The usual Brillouin scattering at the ion-acoustic branch is found to be slightly modified by the charged dust grains. However, significant scattering is also found to occur at a frequency lower than the ion-acoustic frequency, off a new mode of the plasma arising from the oscillations of the ions in the static structure of the dust distribution.
Moment series expansions for a model kinetic equation
Authors: Stevens D. C. , Weitzner H. , Pfirsch D.
Published: July 2002

A steady-state, one-dimensional model kinetic equation with a simple external force and a Lorentz collision term is solved by the approximation methods of moment expansions, by a neoclassical type of asymptotic expansion, and by other simple expansions. The very high-order moment expansions are assumed to give the correct solution, and a comparison is given with low-order moment expansions, the neoclassical expansion, and a small external force expansion. All the calculations and expansions are given for the cases in which the three fundamental dimensional physical parameters that characterize the problem are small. These parameters are the collisionality, the mean velocity to which the system is driven, and the magnitude of the spatially varying external force. Each of the expansions has regions of applicability and utility. Even in the very low collisionality case, low-order moment expansions give the correct order of magnitude of the solution, the mean flow velocity within 30%, the temperature quite accurately, the average value of the heat flow poorly, but give the spatially varying part of the heat flow very well. For the neoclassical expansion to be accurate, not only must the collisionality be small, but it also must be sufficiently smaller than other small physical parameters in the system. For parameter values somewhat less than one moment expansions of order five are quite accurate. For large values of the collisionality, the Hilbert–Chapman–Enskog expansion is recovered.
Linear propagation and absorption of ion Bernstein waves in toroidal geometry
Authors: Cardinali Alessandro , Romanelli Francesco
Published: July 2002

The ion Bernstein wave (IBW) propagation is investigated in toroidal geometry with particular regard for the absorption mechanism of the power along the trajectory which shows a strong dependence on the value of the poloidal angle at the antenna. A large power fraction launched by poloidally wide antennas turns out to be absorbed in the very edge of the plasma by electron Landau damping and no penetration of the wave up to the plasma core is allowed except for rays starting at poloidal angles very close to the horizontal plane. This result could provide an explanation for the absence of efficient core heating in some of the IBW heating experiments.
Electromagnetic radiation and nonlinear energy flow in an electron beam-plasma system
Authors: Whelan D. A. , Stenzel R. L.
Published: July 2002

The mechanism by which unstable electron plasma waves are converted into electromagnetic waves in a uniform plasma is investigated. Electromagnetic radiation is generated upon injection of an electron beam (500 eV) into a collisionless quiescent magnetoplasma (ne ≲1012 cm−3, kTe ≊2 eV). The emission (ω0) is observed to peak near the plasma frequency (ωp) which is well above the cyclotron frequency (ωc ≪ωp≲ω0). It is shown that electromagnetic waves (ω0, k0) are produced by the scattering of electrostatic plasma waves (ωe, ke) off self-consistently produced ion-acoustic waves (ωi, ki). At low beam intensities the frequency and wave vector matching conditions are experimentally verified (ωe=ωi+ω0, ke=ki+k0≂ki). The emission is found to be polarized, negligible in intensity at ω0=2ωp, and its source is localized. The space-time evolution of the three-wave interaction is presented. Besides these nonlinear wave–wave interactions the wave–particle interactions are investigated. It is found that the strong Langmuir turbulence exhibits a three-dimensional character. Cross-correlation surfaces are measured, and their characteristic scale lengths are found to decrease with increasing wave intensity toward the Debye length (λD ≂20 μm) although the resolution is probe limited (Lmin ≂1 mm). The beam electrons are diagnosed using a novel directional velocity analyzer which is capable of resolving the true three-dimensional distribution function. After interacting with the intense Langmuir waves, the beam electrons are scattered in velocity space, both parallel and perpendicular to their injection velocity. The background electron distribution is observed to develop an energetic anisotropic tail (E≲50 eV, kTe ≂1 eV). The energization of the background electrons coincides with the strong damping of the Langmuir waves. The nonlinear damping is seen as an anomalous ac resistivity produced by large amplitude ion-density fluctuations (δni/ni ≂5%) in the electron beam region.
Relativistic Hartree condition for magnetrons: Theory and comparison with experiments
Authors: Lovelace R. V. , Young T. F. T.
Published: July 2002

The Hartree voltage UH is derived for a cylindrical magnetron in the relativistic limit with and without an axial current. This voltage corresponds to the breakdown voltage of the magnetron in the presence of a rotating perturbation field. In general, UH is less than the cutoff voltage UI for magnetic insulation in the absence of a perturbation field. Comparisons with a number of different experiments at zero axial current indicate that the maximum microwave power occurs for voltages slightly larger than UH, but well below UI. With axial current, two different Hartree voltages are derived, UHA and UHB<UHA, based on different assumptions. Recent experiments at Physics International show little microwave power for voltages less than UHB and high power for voltages at or slightly larger than UHA. The absence of large microwave power outputs at large axial currents may be caused by the finite axial length of the magnetron.
The x-ray emission, ablation pressure, and preheating for foils irradiated at 0.26 μm wavelength
Authors: Pépin H. , Fabbro R. , Faral B. , Amiranoff F. , Virmont J. , Cottet F. , Romain J. P.
Published: July 2002

The x-ray emission, ablation pressure, and preheating for foils irradiated with a 0.26 μm laser at intensities ∼1015 W cm−2 are studied. The foils are Al with various thicknesses, coated or uncoated with CH or Au. The x-ray emission and conversion efficiency are obtained with a multichannel x-ray diode spectrometer, the ablation pressures are deduced from shock transit times, and the rear temperatures are inferred from x-ray pyrometry. For thin foils (≪12 μm), the rear temperatures can be predicted reasonably well with the use of the front x-ray spectra. For thick foils shock preheating is dominant.
Anomalous thermal relaxation of a two-dimensional magnetized plasma
Authors: Jechart Inge , Katsouleas Thomas , Dawson John
Published: July 2002

The thermal relaxation of a two-dimensional (2-D) plasma in a uniform magnetic field is investigated. Previous workers [J. Plasma Phys. 12, 21 (1974)] observed that the relaxation process is anomalous in that the relaxation may occur more rapidly with a modest magnetic field than without. A simple model is presented which explains the anomalous behavior in terms of correlations between successive collisions. The model predicts the relaxation time to scale as (ωc/ωp)−1/2(nλ2D)1/2 ω−1p for modest magnetic fields (ωc/ωp<1). This scaling law is tested with 2-D electrostatic particle simulations. These simulations show the relaxation time to scale with (ωc/ωp)−1/2 as predicted by the correlated collision model. For very large magnetic fields (ωc≫ωp) the simulations show the relaxation time to increase with ωc because of finite size particle effects as the cyclotron radius becomes comparable to the particle size. The predicted (nλ2D)1/2 dependence of the relaxation time was observed at early times in the simulations; however, as the distribution approached a Maxwellian, the dependence shifted toward (nλ2D)1 as in an unmagnetized plasma.
Magnetohydrodynamic stability of plasmas with aligned mass flow
Authors: Tataronis J. A. , Mond M.
Published: July 2002

The linear magnetohydrodynamic stability of plasmas with sub-Alfvénic flows aligned parallel to the equilibrium magnetic field is treated. Subject to the constraints that the fluid is incompressible, inviscid, and perfectly conducting, it is demonstrated that stabilizing effects appear as the flow speed approaches the Alfvén speed. The screw pinch plasma is treated explicitly, but it is conjectured that the conclusions are applicable to other equilibrium configurations.
The homogeneous axisymmetric passive scalar in isotropic turbulence
Authors: Nakauchi Norihiko , Sega Setsuko
Published: July 2002

The anisotropy of scalar fluctuations induced by scalar flux and the return to isotropy of the anisotropic scalar field are investigated by using the modified zero-fourth-cumulant (MZFC) expansion. The spectral equations of axisymmetric scalar flux and variance in decaying isotropic turbulence are formulated by applying the MZFC expansion. Numerical calculation is made under the initial conditions for two different degrees of anisotropy: one is an isotropic state with a flux, and another is a two-dimensional state that is strongly anisotropic in the three dimensions. Results show that the scalar flux produces an anisotropy of the scalar distribution so that scalar concentration increases in the direction parallel to the symmetric axis and decreases in the direction transverse to it. The return to isotropy is rapid, except for large scale fluctuations, even in the strongly anisotropic case.
Exact solutions for sonic shocks in van der Waals gases
Authors: Cramer M. S. , Sen R.
Published: July 2002

Exact closed-form solutions for finite amplitude sonic shocks are presented for the case of a van der Waals gas having a constant specific heat. Solutions are provided for both single and double sonic shocks. Sample calculations are presented that include sonic shocks embedded in smooth inviscid flows.
Transition to turbulence on a rotating flat disk
Authors: Aubry Nadine , Chauve Marie-Pierre , Guyonnet Régis
Published: July 2002

Experimental data from one-point measurements obtained in a transitional flow on a rotating flat disk are presented and analyzed by using biorthogonal decomposition techniques. The analysis is performed at various Reynolds numbers from slightly above the onset of the first instability to the transition to turbulence. As Reynolds number increases, biorthogonal spectra become broader and the entropy characterizing the distribution of energy among the various biorthogonal modes increases. Details of this increase are studied by analyzing local entropy maxima corresponding to eigenvalue degeneracies. At these values of the Reynolds number, internal bifurcations, responsible for a lack of smoothness in the dependence of the flow with Reynolds number, are shown to occur.
Recovery of the Rayleigh capillary instability from slender 1-D inviscid and viscous models
Authors: Bechtel S. E. , Carlson C. D. , Forest M. G.
Published: July 2002

For either inviscid or viscous jets, Rayleigh proved cylindrical jets are linearly unstable due to surface tension of the interface, with instability precisely in all wavelengths greater than the jet circumference. As an alternative to linearized analysis, many past and present studies of surface tension-driven jet breakup are based on slender asymptotic 1-D models; here we clarify two issues regarding this approach. First, self-consistent, leading-order models of inviscid or viscous slender jets do not have a finite instability cutoff. Indeed, the inviscid 1-D equations exhibit unbounded exponential growth in the small scale limit, while the viscous counterparts bound the growth rate but remain unstable in all wavelengths. Second, one can recover a finite instability cutoff by extending the asymptotic analysis to higher order. The linearized growth rate corrections at each finite order arise as algebraic approximations to Rayleigh’s exact exponential rate. We explicitly match, at leading and subsequent order, the slender longwave expansion of the exact results with the linearized behavior of 1-D slender asymptotic equations.
Thermal diffusion in binary mixtures of smooth, nearly elastic spheres with and without gravity
Authors: Arnarson Birgir Ö. , Willits Jeffrey T.
Published: July 2002

A Revised Enskog theory, valid to second order in the Enskog approximation, is used to characterize the amount of thermal diffusion in a steady, fully developed flow of a binary mixture of hard, inelastic spheres. The dependence of the thermal diffusion factor on mixture volume fraction, mole fraction, radii ratio, and material density ratio is explored in the presence and absence of gravity.
A model for the decay of rotating homogeneous turbulence
Authors: Park Ju Yeop , Chung Myung Kyoon
Published: July 2002

In order to analyze the decay rate of rotating homogeneous turbulence, the model coefficient Cε2 in the dissipation rate equation is theoretically formulated in terms of the macroscale Rossby number Rol and the power exponent m in the energy spectrum function E(κ)∼κm of small wave number range. The proposed model satisfies the asymptotic decay rate of turbulent kinetic energy, which depends on the small wave number range energy spectrum, for both extremes of rotation rate. A number of test computations prove that the present model faithfully reproduces the available experimental as well as direct numerical simulation data of rotating homogeneous turbulence.
The nonlinear equation for curved flames applied to the problem of flames in cylindrical tubes
Authors: Bychkov Vitaliy , Kleev Andrey
Published: July 2002

The nonlinear equation for curved stationary flames of realistic expansion coefficients is solved numerically for the problem of flame propagation in cylindrical tubes. Two different configurations of a flame front corresponding to convex and concave flames are obtained. The convex and concave flames propagate with different velocities that depend on the tube radius and on the expansion coefficient of the burning matter. For tubes of a moderate radius the velocity amplification for convex flames exceeds the respective velocity amplification of two-dimensional flames almost twice. For tubes of a large radius unlimited increase of the curved flame velocity with increase of the tube width takes place. The obtained theoretical results are in good quantitative agreement with the results of numerical experiments on flame dynamics in cylindrical tubes.
Bifurcation study of flow through rotating curved ducts
Authors: Selmi M. , Nandakumar K.
Published: July 2002

The bifurcation structure of the two-dimensional pressure-driven flow through a curved rotating duct is studied. In this study we add to the rich literature that already exists on this problem [J. Fluid Mech. 262, 353 (1994)], revealing even more intricate details of the solution structure. The problem depends on the Reynolds number, Re=Ub/ν, the Rotation number, RΩ=bΩ/U, the aspect ratio, γ=b/h, and the radius ratio (or curvature ratio), η=ri/ro; here U is the velocity scale, b is the duct width in the spanwise direction, Ω is the rotational speed, (ri,ro) are the inner and outer radii of the duct, h=ro−ri and ν is the kinematic viscosity of the fluid. For a curvature ratio η=0.960 784, continuation on Re is used to trace the bifurcation diagram for zero rotation (RΩ=0). Then, for Re=800, continuation on RΩ is used from the solutions at zero rotation (RΩ=0) to generate bifurcation diagrams for positive and negative rotational number for the purpose of studying the effect of rotation. Extended systems are used to solve for limit points and symmetry breaking points. These points are then traced as functions of the Reynolds number. Eigenvalue systems are solved to determine the stability properties of the multiple solutions to two-dimensional perturbations. Bifurcation diagrams reveal more intricate solution structures than those found in earlier studies, raising the question whether it is ever possible to construct a complete bifurcation diagram. New solution branches are found even for the well-studied case of a system with no rotation.
Pipe-flow relaminarization by temporal acceleration
Authors: Greenblatt D. , Moss E. A.
Published: July 2002

An experimental and computational study was conducted in temporally accelerated pipe flows under initially turbulent conditions. Relaminarization was identified when the imposed pressure gradient was of the same order as that required for relaminarization under steady conditions. Unlike the steady case, integral development of the mean flow does not characterize relaminarization. Rather, mean-flow effects were confined to the near-wall region, with significant departures from fully turbulent flow only evident at Y+⩽50. Streamwise turbulence fluctuations in the near-wall region initially decreased and then increased, and in the pipe core region the turbulence fluctuations were effectively frozen.
The interdependence of friction, pressure gradient, and flow rate in unsteady laminar parallel flows
Authors: Brereton G. J.
Published: July 2002

Solutions to the Laplace-transformed Navier–Stokes equations are developed that describe transients in fully developed channel and pipe flow. The relative ease with which inverse Laplace transforms can be carried out numerically makes it straightforward to find the form of new expressions relating flow rate, pressure gradient, and wall friction, for flows of arbitrary unsteadiness in time. In particular, expressions for flow rates and cumulative throughflows are derived in terms of wall shear stress and pressure–gradient histories, together with a channel-flow counterpart to Zielke’s pipe-flow friction law [J. Basic Eng. 90, 109 (1968)] expressing wall shear stress as a functional of flow-rate history. It is shown how these results can be expressed as the unsteady counterparts to well-known steady-flow relationships. The relative importance of unsteady effects to quasisteady ones is determined by a dimensionless parameter of the form (1/U)(∂U/∂t)R2/ν, where R is the span of the duct. When departures from quasisteady forms of these relations exist, the memory of the Navier–Stokes equations of earlier transients, comparable in size to present ones, extends roughly 0.2 R2/ν seconds backward in time. The derived relationships are used to illustrate how path-dependent quantities such as flow work vary with different unsteady flow histories.
Vorticity constraints on a fluid/fluid interface
Authors: Dopazo Cesar , Lozano Antonio , Barreras Felix
Published: July 2002

General relations among the components of the strain rate tensors and those of the tangential vorticities on the two sides of a liquid/gas interface are derived; kinematic constraints as well as the tangential-stress balance at the interface are used. For small gas to liquid dynamic viscosity ratios compared to unity simple expressions relating the liquid tangential vorticity components to the tangential velocity component perpendicular to them, the interface curvatures and the normal velocity surface-gradient components are obtained. Starting from the customary Eulerian vorticity equation, a transport equation for the vortex sheet strength is obtained.
Surface topology of a buoyant turbulent nonpremixed flame
Authors: Zhong R. , Elghobashi S. E. , Boratav O. N.
Published: July 2002

The temporal evolution of the three-dimensional stoichiometric mixture fraction Fst isosurface is investigated using direct numerical simulations of a turbulent nonpremixed flame with and without buoyancy. After an initial transient, the surface area of the Fst isosurface increases monotonically in time. The rate of area increase of the buoyant flame is larger than that of the nonbuoyant flame. The stretch rate of the buoyant flame surface indicates that the tangential strain rate St is dominant and positive at the troughs, whereas the relative propagation velocity term, un∇⋅n, is dominant and negative at the crests of the Fst isosurface. Thus, the local surface area of the crests decreases in time while that of the troughs increases, leading to the steep ridge topology. The strain rate field generated by the oppositely signed vortices saddling the Fst isosurface is responsible for this topology. The reaction rate in the buoyant flame is largest at the troughs where the scalar dissipation is maximum.
Asymptotic solution for film flow on a rotating disk
Authors: Kitamura Akihiro
Published: July 2002

Unsteady liquid film flow of nonuniform thickness on a rotating disk is analyzed. Assuming small aspect ratio of the initial film thickness to the disk radius and applying Higgins’ asymptotic method [Phys. Fluids 29, 3522 (1986)], the long and short-time scale solutions for transient film thickness were obtained and these two solutions were matched to give a composite solution. The results reveal the effects of gravitational and surface tension forces as well as the effect of inertial force on the film thinning and planarization.
Monte Carlo approach to collisional transport
Authors: Tessarotto Massimo , White Roscoe B. , Zheng Lin-Jin
Published: July 2002

A linearized discretization approach is proposed for the numerical investigation of the gyrokinetic equation describing the dynamics of a strongly rotating plasma in a toroidally axisymmetric configuration. The discretization scheme allows the numerical evaluation of the neoclassical transport matrix in terms of a suitably discretized distribution function. A basic feature of the discretization scheme here developed is that it permits the introduction of Monte Carlo collision operators to advance in time the gyrokinetic state of a suitable set of test particles. Such operators, which apply to general non-normal gyrokinetic coordinates, are constructed in such a way as to conserve exactly the collisional invariants. A fundamental consequence is that the neoclassical transport coefficients determined in this way fulfill exactly both Onsager’s symmetry relations and the condition of strict ambipolarity for the particle-flux transport coefficients. Such properties are proven to be satisfied independently of the number of test particles used in the discretization scheme.
Effect of a static external magnetic perturbation on resistive mode stability in tokamaks
Authors: Fitzpatrick R. , Hender T. C.
Published: July 2002

The influence of a general static external magnetic perturbation on the stability of resistive modes in a tokamak plasma is examined. There are three main parts to this investigation. First, the vacuum perturbation is expanded as a set of well-behaved toroidal ring functions, and is, thereafter, specified by the coefficients of this expansion. Second, a dispersion relation is derived for resistive plasma instabilities in the presence of a general external perturbation, and finally, this dispersion relation is solved for the amplitudes of the tearing and twisting modes driven in the plasma by a specific perturbation. It is found that the amplitudes of driven tearing and twisting modes are negligible until a certain critical perturbation strength is exceeded. Only tearing modes are driven in low-β plasmas with εβp≪1. However, twisting modes may also be driven if εβp≳1. For error-field perturbations made up of a large number of different poloidal and toroidal harmonics the critical strength to drive locked modes has a ‘‘staircase’’ variation with edge-q, characterized by strong discontinuities as coupled rational surfaces enter or leave the plasma. For single harmonic perturbations, the variation with edge-q is far smoother. Both types of behavior have been observed experimentally. The critical perturbation strength is found to decrease strongly close to an ideal external kink stability boundary. This is also in agreement with experimental observations.
Simulation of dense recombining divertor plasmas with a Navier–Stokes neutral transport model
Authors: Knoll D. A. , McHugh P. R. , Krasheninnikov S. I. , Sigmar D. J.
Published: July 2002

A two-dimensional combined edge plasma Navier–Stokes neutral transport model is presented for the simulation of dense recombining divertor plasmas. This model includes ions, electrons, and neutral atoms which undergo Coulomb collisions, electron impact ionization, ion–neutral elastic collisions, three-body and radiative recombination, and neutral–neutral collisions. The advanced fully implicit solution algorithm is briefly described and a variety of results on a model geometry are presented. It is shown that interesting neutral flow patterns can exist and that these flows can convect significant energy. A solution that ignores neutral–neutral collisions is shown to be quantitatively different from one that includes neutral–neutral collisions. Solutions are also shown to be sensitive to the plasma opacity for Lyman α radiation.
Nonlinear expansion and heating of a nonneutral electron plasma due to elastic collisions with background neutral gas
Authors: Davidson Ronald C. , Chao Edward H.
Published: July 2002

This paper investigates theoretically the heating and nonlinear expansion of a nonneutral electron plasma due to elastic collisions with constant collision frequency νen between the plasma electrons and a background neutral gas. The model treats the electrons as a strongly magnetized fluid (ωpe2/ωce2≪1) immersed in a uniform magnetic field B0êz. The model also assumes an axisymmetric plasma column (∂/∂θ=0) with negligible axial variation (∂/∂z=0), and that the process of heat conduction is sufficiently fast that the electrons have relaxed through electron-electron collisions to a quasi-equilibrium state with scalar pressure P(r,t)=n(r,t)T, and isothermal temperature T. Assuming that the electrons undergo elastic collisions with infinitely massive background gas atoms, global energy conservation is used to calculate the electron heating rate, dT(t)/dt, as the plasma column expands on a time scale τdiff∼(ωpe2νen/ωce2 )−1, and the electrostatic potential energy decreases. Coupled dynamical equations that describe the nonlinear evolution of the mean-square column radius r20(t) and electron temperature T(t) are derived and solved numerically.
An interface current balance formulation of neutral atom transport theory in plasmas
Authors: Stacey W. M.
Published: July 2002

An interface current balance (ICB) method for neutral particle transport is presented and specialized to the calculation of neutral atom transport in background plasmas. A multigroup extension of the ICB methodology is presented which enables the direct calculation of neutral atom energy distributions and energy and momentum transport, as well as particle transport. Extension of the ICB methodology to multidimensions recovers the transmission/escape probability method.
Three-dimensional particle-in-cell simulations of ion-driven parametric instabilities
Authors: Vu H. X.
Published: July 2002

HERCULES, a massively parallel three-dimensional hybrid particle-in-cell (PIC) code, implemented on the CRAY-T3D, is presented. The code is based on a physical model, described in a previous report, where the electrons are modeled as an adiabatic fluid with an arbitrary ratio of specific heats γ, and the electromagnetic field model is based on a temporal WKB approximation. On a CRAY-T3D with 512 processors, the code requires about 0.6 μs/particle/time step. The largest test problem performed with this code consists of a computational mesh of 4096×64×64 (16 million) cells, and a total of 256 million particles, and corresponds to a plasma volume of 250 μm×62.5 μm×62.5 μm. This code is the first PIC code capable of simulating ion-driven parametric instabilities in a large plasma volume, and it offers a unique opportunity for examining issues that are potentially vital to inertial confinement fusion (ICF), e.g., nonlinear ion kinetic effects and their role in nonlinear saturation mechanisms. Applications of HERCULES in simulations of Gaussian f/4 diffraction-limited lasers with and without transverse plasma flows are presented. Simulation parameters are chosen to correspond to actual experimental conditions, and the simulations are performed over a substantial portion of the actual laser pulse. The simulations indicate that while the transmitted laser beam can be significantly deflected by transverse flows, the SBS-reflected beam does not necessarily exhibit the same behavior. Furthermore, the total SBS reflectivity appears to be insensitive to transverse flows. In the simulations, the late-time SBS reflectivity is 25%, which compares favorably to the 10%–20% range measured in actual experiments. The simulations in this paper are the first PIC simulations of ICF experiments in which both the temporal and spatial scales of the experiments are captured in their entireties.
Sensitivity of predictive tokamak plasma transport simulations
Authors: Redd Aaron J. , Kritz Arnold H. , Bateman Glenn , Kinsey Jon E.
Published: July 2002

The sensitivity of our time-dependent simulations of low confinement (L-mode) discharges to variations in initial profiles and time-dependent boundary conditions has been explored. These time-dependent tokamak plasma simulations were performed using a theory-based Multi-mode transport model that includes ion temperature gradient (ITG) and trapped electron modes (TEM), kinetic and resistive ballooning modes and neoclassical modes. The density and temperature profiles predicted in our simulations of L-mode discharges are found to be robust, even with significant variations in the initial or boundary conditions. Although transport associated with a single mode can be strongly affected by local changes in plasma parameters resulting from changes in the boundary conditions, the total transport remains largely unchanged because of compensation by other transport modes. The sensitivity of the predicted temperature and density profiles to a variation in the Multi-mode model is also examined. When the Dominguez-Waltz theory of transport driven by ITG and TEM modes is replaced in the Multi-mode model by the Weiland description, we find that the predictions of the Weiland model more closely match the experimental data.
Relativistic theory of classical collisional transport in a weakly coupled plasma: Solution of Fokker–Planck equation
Authors: Baral K. C. , Mohanty J. N.
Published: July 2002

A generalized Fokker–Planck equation is developed in the pattern of a well-known collision operator [Beliaev and Budker, Sov. Phys. Dokl. 1, 218 (1957)] and solved for a relativistic singly charged electron–ion plasma under the impact of crossed electric and magnetic fields. Using the differential form of the collision operator and the modified Rosenbluth potentials appropriate for the relativistic plasma various cross-field transport coefficients are derived analytically in the limit of nonrelativistic, moderately relativistic and ultrarelativistic temperatures.
Shear flow destabilization of a slowly rotating tokamak
Authors: Chu M. S.
Published: July 2002

The Kelvin–Helmholtz destabilizing effect of shear in toroidal rotation on ideal magnetohydrodynamic localized interchange is studied in a tokamak with a general geometry. The method of maximizing the growth rate given by Frieman and Rotenberg is utilized. An explicit stability criterion is given for a slowly rotating tokamak with a non-negligible shearing rate in its rotation profile. It is found that rotation shear can weaken the stabilizing effect of the magnetic field shear and also allow the coupling of the sound wave to the shear Alfvén wave which destabilizes the plasma.
Electron plasma profiles from a cathode with an r2 potential variation
Authors: Kriesel J. M. , Driscoll C. F.
Published: July 2002

A simple one-dimensional model of Maxwellian injection into a cylindrical Penning–Malmberg trap is presented. This model is used to predict the radial density profile of an electron column produced by a biased cathode with an r2 potential variation. The column density n(r) is assumed to depend upon the cathode potential voltage Vk(r) and the self-consistent space-charge potential φ(r) as n(r)∝exp{e[φ(r)−Vk(r)]/T}. A one-parameter family of theoretical solutions describes the radial density profiles. The model’s predictions agree well with electron density profiles resulting from a spiral tungsten filament measured over a wide range in cathode voltages.
Two-dimensional bounce-averaged collisional particle transport in a single species non-neutral plasma
Authors: Dubin Daniel H. E. , O’Neil T. M.
Published: July 2002

In this paper we describe a new theory of like particle collisional transport for a non-neutral plasma confined in a Penning trap. The theory is valid in the regime ωb>ωE, ωb>νc, and rc<λD where ωb is the axial bounce frequency, ωE is the E×B rotation frequency, νc is the collision frequency, rc is the cyclotron radius, and λD is the Debye length. In this regime each particle can be bounce averaged into a long rod and the transport understood as arising from the E×B drift motion of the rods due to long-range mutual interactions. This is a very different mechanism than is considered in the classical theory of transport, where a particle guiding center undergoes a step of order rc as a result of a velocity scattering collision. For the parameter range considered, the new theory predicts transport rates that are orders of magnitude larger than those predicted by classical theory and that scale with magnetic field strength like 1/B rather than 1/B4. The new theory differs from a previous analysis of transport due to E×B drift interactions of charged rods, in that the finite length of the rods is taken into account. This enables transport to occur even for the case of an E×B drift rotation frequency that is a monotonic decreasing function of radius (as was the case in recent experiments).