bluuebunny/crossref_metadata_2025 huggingface dataset:
On the diagonalization of quantum Birkhoff–Gustavson normal form
Authors: Nikolaev A. S.
Published: July 2002

An application to quantum mechanics of one of classical perturbation theory methods, the Birkhoff–Gustavson normal form (BGNF), is described. In the quantum case it results in the Van Vleck perturbation theory performed upon Wick normal ordered operators. Algebraic aspects of this procedure and formal construction of invariants (integrals of motion) for a perturbed system are considered. It turned out that a larger set of such operators existed in the quantum mechanics, rather than in the classical one. It is demonstrated that, according to general results of the quantum mechanical perturbation theory, the quantum BGNF may always be diagonalized, and two formal processes for such diagonalization are constructed. In the opposite case, the classical BGNF is, in general, nondiagonalizable. This reflects the fact that the classical perturbation theory cannot handle a system with two or more resonances. Possible reasons for such different behavior of two very close, in spirit, perturbation procedures are discussed. Results of the described procedure, entirely performed upon the Wick normal ordered operators, are equivalent to those of Rayleigh–Schrödinger perturbation expansion.
Multi-Hamiltonian structures for a class of degenerate completely integrable systems
Authors: Bueken Peter
Published: July 2002

In this paper, a class of degenerate (i.e., associated to a degenerate Poisson structure) completely integrable systems is studied which generalizes the so-called odd and even master systems introduced and studied by Mumford and by Vanhaecke. It is shown that all these completely integrable systems, called the generalized master systems, admit a multi-Hamiltonian formulation, and a systematic construction of this multi-Hamiltonian structure is described.
Harmonic maps and periodic Toda systems
Authors: Doliwa Adam
Published: July 2002

Harmonic maps from the point of view of periodic Toda systems are considered. The correspondence between certain harmonic immersions of surfaces and solutions to periodic Toda systems related to nonexceptional simple Lie algebras is constructed.
A solvable Hamiltonian system: Integrability and action-angle variables
Authors: Karimipour V.
Published: July 2002

We prove that the dynamical system characterized by the Hamiltonian H=λN∑jNpj+μ∑ j,kN(pjpk)1/2{cos[ν(qj−qk)]} proposed and studied by Calogero [J. Math. Phys. 36, 9 (1994)] and Calogero and van Diejen [Phys. Lett. A 205, 143 (1995)] is equivalent to a system of noninteracting harmonic oscillators both classically and quantum mechanically. We find the explicit form of the conserved currents that are in involution. We also find the action-angle variables and solve the initial value problem in a very simple form.
de Rham cohomology of SO(n) by supersymmetric quantum mechanics
Authors: Oshima Kazuto
Published: July 2002

We study supersymmetric quantum mechanics on SO(n) to examine Witten’s Morse theory concretely. We give a simple instanton picture of the de Rham cohomology of SO(n). We show how the reflection symmetries of the theory select the true vacuums. The number of selected vacuums agrees with the de Rham cohomology of SO(n), at least for n⩽5.
p
-adic stochastic hidden variable model
Authors: Khrennikov Andrew
Published: July 2002

We propose stochastic hidden variables model in which hidden variables have a p-adic probability distribution ρ(λ) and at the same time conditional probabilistic distributions P(U,λ), U=A,A′,B,B′, are ordinary probabilities defined on the basis of the Kolmogorov measure-theoretical axiomatics. A frequency definition of p-adic probability is quite similar to the ordinary frequency definition of probability. p-adic frequency probability is defined as the limit of relative frequencies νn but in the p-adic metric. We study a model with p-adic stochastics on the level of the hidden variables description. But, of course, responses of macroapparatuses have to be described by ordinary stochastics. Thus our model describes a mixture of p-adic stochastics of the microworld and ordinary stochastics of macroapparatuses. In this model probabilities for physical observables are the ordinary probabilities. At the same time Bell’s inequality is violated.
Finite-dimensional irreducible representations of twisted Yangians
Authors: Molev A. I.
Published: July 2002

We study quantized enveloping algebras called twisted Yangians. They are analogs of the Yangian Y(gl(N)) for the classical Lie algebras of B, C, and D series. The twisted Yangians are subalgebras in Y(gl(N)) and coideals with respect to the coproduct in Y(gl(N)). We give a complete description of their finite-dimensional irreducible representations. Every such representation is highest weight and we give necessary and sufficient conditions for an irreducible highest weight representation to be finite dimensional. The result is analogous to Drinfeld’s theorem for the ordinary Yangians. Its detailed proof for the A series is also reproduced. For the simplest twisted Yangians we construct an explicit realization for each finite-dimensional irreducible representation in tensor products of representations of the corresponding Lie algebras.
Gauge theories with graded differential Lie algebras
Authors: Wulkenhaar Raimar
Published: July 2002

We present a mathematical framework of gauge theories that is based upon a skew-adjoint Lie algebra and a generalized Dirac operator, both acting on a Hilbert space.
An evolutionary equation in thermoelasticity of dipolar bodies
Authors: Marin Marin
Published: July 2002

In this paper we apply the theory of semigroups of operators in order to obtain the existence and uniqueness of solutions for the mixed initial-boundary value problems in thermoelasticity of dipolar bodies. The continuous dependence of the solutions upon initial data and supply terms is also proved.
Ground states of a model in nonrelativistic quantum electrodynamics. II
Authors: Hiroshima Fumio
Published: July 2002

The system of N-nonrelativistic spineless particles minimally coupled to a massless quantized radiation field with an ultraviolet cutoff is considered. The Hamiltonian of the system is defined for arbitrary coupling constants in terms of functional integrals. It is proved that the ground state of the system with a class of external potentials, if they exist, is unique. Moreover an expression of the ground state energy is obtained and it is shown that the ground state energy is a monotonously increasing, concave, and continuous function with respect to the square of a coupling constant.
Schlesinger transformations for elliptic isomonodromic deformations
Authors: Korotkin D. , Manojlović N. , Samtleben H.
Published: July 2002

Schlesinger transformations are discrete monodromy-preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic deformations on genus one Riemann surfaces. Their action on the system’s tau-function is computed and we obtain an explicit expression for the ratio of the old and the transformed tau-function.
Experimental Data for the Viscosity and Thermal Conductivity of Water and Steam
Authors: Assael Marc J. , Bekou E. , Giakoumakis D. , Friend Daniel G. , Killeen M. A. , Millat J. , Nagashima Akira
Published: July 2002

As part of a joint project between the International Association for the Properties of Water and Steam and the Subcommittee on Transport Properties of the International Union of Pure and Applied Chemistry Commission I.2 on Thermodynamics, all available and reliable experimental data on the viscosity and thermal conductivity of ordinary water and steam have been collected and converted to the current temperature scale (ITS-90) and a common set of units. The data are grouped according to state into four regions: the liquid phase (excluding data near 0.101 325 MPa), the steam (vapor) phase, the supercritical region (T>Tc for any pressure), and liquid water at ambient pressure (near 0.101 325 MPa) between the triple-point temperature and the normal boiling-point temperature. For each point with measured temperature and pressure (or at specified saturation conditions), a density has been computed with the current scientific standard thermodynamic formulation (IAPWS-95), and each experimental datum has been compared with the viscosity or thermal conductivity calculated from the current standard formulations for these properties. The total data collection contains 4090 points for viscosity in the range of temperatures from 238 to 1346 K with pressures to 346 MPa and 5107 points for thermal conductivity in the range of temperatures from 256 to 1191 K with pressures to 785 MPa. The current standard IAPWS formulations for the transport properties of water are based on correlations adopted in 1984 which considered experimental data available through 1980. The present study considers all data available in the earlier work, data collected in bibliographic efforts within IAPWS and documented in unpublished reports through 1988, and additional data published subsequent to the earlier reports or, in some cases, older data which were not considered in the previous compilations. Thus, this study has identified new data which were not available for the previous reviews of the transport properties of water, has identified regions in which the current standard transport property formulations can now be improved, and is intended to facilitate the development of new, more accurate, international formulations for the viscosity and thermal conductivity of water and steam.
Emission Mössbauer study of CMR manganite La0.8Ca0.2MnO3. II. Step-by-step snapshots of the metal-insulator transition
Authors: Chechersky V. , Nomura K. , Nath A. , Ju H. , Greene R. L.
Published: July 2002

We follow the step-by-step progression of events while approaching the Curie temperature TC from below using Co57 substituent as a microprobe in an emission Mössbauer study combined with resistivity measurements. In the temperature range 0.33<T/TC⩽1, the material consists of a mixture of ferromagnetic and paramagnetic regions within the same matrix. An increase of the amount of paramagnetic fraction is accompanied by a decrease in electron delocalization in the ferromagnetic regions. At T⩾TC, the electrons are localized to neighboring Mn4+/Mn3+ pairs only, in about 46% of the paramagnetic species. The strength with which Mn atoms are bound to the neighbors also decreases progressively and rather steeply in the range 0.65⩽T/TC=1. Zero field resistivity, ρ0, follows linearly with the amount of the paramagnetic phase in the range 0.65⩽T/TC⩽1 and still shows metal-like behavior up to T/TC=1.03.
On the role of accelerating fluid particles in the generation of Reynolds stress
Authors: Handler Robert A. , Bernard Peter S. , Rovelstad Amy L. , Swearingen Jerry D.
Published: July 2002

The connection between Reynolds stress and the kinematical and dynamical processes associated with streamwise fluid particle accelerations in the near-wall region of a fully developed channel flow is investigated. Visualizations of the particle paths contributing most significantly to Reynolds stress via such accelerations show them to be linked with spiraling motions in the cores of vortical structures tilted in the streamwise direction. This contrasts with the action of vortices in sweep and ejection events in which transport occurs through the displacement of fluid particles. A conceptual model for Reynolds stress generation by acceleration transport is suggested and the relative importance of pressure and viscous forces is computed. It is found that viscous forces play the dominant role until y+≳40 at which point pressure forces become most significant.
Development of turbulence models for shear flows by a double expansion technique
Authors: Yakhot V. , Orszag S. A. , Thangam S. , Gatski T. B. , Speziale C. G.
Published: July 2002

Turbulence models are developed by supplementing the renormalization group (RNG) approach of Yakhot and Orszag [J. Sci. Comput. 1, 3 (1986)] with scale expansions for the Reynolds stress and production of dissipation terms. The additional expansion parameter (η≡SK̄/■̄) is the ratio of the turbulent to mean strain time scale. While low-order expansions appear to provide an adequate description for the Reynolds stress, no finite truncation of the expansion for the production of dissipation term in powers of η suffices−terms of all orders must be retained. Based on these ideas, a new two-equation model and Reynolds stress transport model are developed for turbulent shear flows. The models are tested for homogeneous shear flow and flow over a backward facing step. Comparisons between the model predictions and experimental data are excellent.
A finite Reynolds-number approach for the prediction of boundary-layer receptivity in localized regions
Authors: Choudhari Meelan , Streett Craig L.
Published: July 2002

Earlier theoretical work on the boundary-layer receptivity problem utilized the triple-deck framework, and typically produced only the leading-order asymptotic result. The applicability of these predictions was limited to the generation of Tollmien–Schlichting-type (viscosity-conditioned) instabilities and rather high values of an appropriate Reynolds number. Generalizing the concepts behind the asymptotic theory of Goldstein and Ruban, the classical Orr–Sommerfeld theory is utilized to predict the receptivity due to small-amplitude surface nonuniformities. This approach accounts for the finite Reynolds-number effects, and can also be extended easily to problems involving other types of instabilities. It is illustrated here for the case of the Tollmien–Schlichting wave generation in a Blasius boundary layer, due to the interaction of a free-stream acoustic wave with a region of short-scale variation in one of the surface boundary conditions. The type of surface disturbances examined include regions of short-scale variations in wall suction, wall admittance, and wall geometry (roughness). Results from the finite Reynolds-number approach are compared in detail with previous asymptotic predictions, as well as the available experimental data.
Nonlinear dynamics of liquid columns: A comparative study
Authors: Schulkes R. M. S. M.
Published: July 2002

One-dimensional models have been used extensively over the past decade to study liquid columns. While the range of validity of these models is well known in the linear limit, this is not the case when nonlinear effects are important. By comparing results of a number of one-dimensional models with results based on a velocity-potential model in which no approximations have been made, the present aim is to establish exactly when the one-dimensional models are applicable. First of all it is shown how the Cosserat equations in the inviscid limit may be obtained formally from the Euler equations. Subsequently, a linearized form of the Cosserat equations is derived and results of this model are compared with results obtained by means of the well-established inviscid-slice model and results obtained by the velocity-potential approach. It is found that the applicability of the inviscid-slice model is limited by short-wavelength effects rather than amplitude effects. The range of validity of the inviscid-slice model can be extended by including radial momentum contributions. However, even with the inclusion of radial momentum effects the one-dimensional models are not well suited to describe the behavior close to the bifurcation point.
The evolution of unstable regions in impulsively started pipe entrance flows
Authors: Moss E. A. , da Silva D. F.
Published: July 2002

A unified stability curve was generated for impulsively started pipe entrance flows, comprising the variation of critical Reynolds number with a novel dimensionless velocity profile shape parameter. Time dependent regions of stability and instability were obtained, explaining qualitatively the measured almost instantaneous upstream propagation of turbulence in a starting pipe flow. In so doing they provide a formal alternative to the widely held view that the observation of turbulence far downstream under steady-state conditions is purely from the evolution and washdown of turbulent structures in the unstable entrance region of the pipe, suggesting the possibility that local downstream instabilities and turbulence from an earlier time, play a role.
Hydrodynamic instability of a fluid layer flowing down a rotating cylinder
Authors: Dávalos-Orozco L. A. , Ruiz-Chavarría G.
Published: July 2002

In this paper the linear stability of a fluid layer flowing down the inside and outside of a rotating vertical cylinder is investigated. To this end, two approximations are made: the small wave number approximation and the small Reynolds number approximation. In the former, only the radial destabilizing effect of surface tension is important and may be counteracted by the centrifugal force at a critical value. In the latter, the analysis integrates the azimuthal modes different from m=0. It is shown that for flow outside the cylinder, the magnitude of centrifugal force and wave number may change the dominant mode of instability. For flow inside the cylinder, only the mode m=0 may be unstable. These results generalize those of Boudourides and Davis [Z. Angew. Math. Phys. 37, 597 (1986)] for swirling viscous flows.
Linear-stability theory of thermocapillary convection in a model of the float-zone crystal-growth process
Authors: Neitzel G. P. , Chang K.-T. , Jankowski D. F. , Mittelmann H. D.
Published: July 2002

Linear-stability theory has been applied to a basic state of thermocapillary convection in a model half-zone to determine values of the Marangoni number above which instability is guaranteed. The basic state must be determined numerically since the half-zone is of finite, O(1) aspect ratio with two-dimensional flow and temperature fields. This, in turn, means that the governing equations for disturbance quantities are nonseparable partial differential equations. The disturbance equations are treated by a staggered-grid discretization scheme. Results are presented for a variety of parameters of interest in the problem, including both terrestrial and microgravity cases; they complement recent calculations of the corresponding energy-stability limits.
Instabilities in two-dimensional spatially periodic flows. Part III: Inviscid triangular lattice
Authors: Thess André
Published: July 2002

The instability of a two-dimensional triangular array of vortices with respect to inviscid perturbations is investigated. A numerical treatment in the framework of Floquet theory provides critical parameters for instability onset and the spatial structure of unstable oscillatory modes which are in agreement with experiments of Sommeria et al. [Mechanics of Fluids and Transport Processes (Kluwer Academic, Dordrecht, The Netherlands, 1989), Vol. 10] in electromagnetically driven flows of a liquid metal layer. A point vortex model allows one to relate the dynamics of infinitesimal displacements of vortices to the concept of waves in a lattice of linearly coupled oscillators.
Observation of a stable high-beta axisymmetric plasma equilibrium
Authors: Kuthi A. , Zwi H. , Schmitz L. , Wong A. Y.
Published: July 2002

Stable, steady-state plasma equilibrium is generated in an axisymmetric configuration. The diamagnetic current is maintained by electromagnetic fields rotating in the electron diamagnetic sense. The stable, free-standing equilibrium exists for all values of beta up to 0.98, limited only by the available rf power. The plasma is centered on the axis well removed from the metal chamber walls, the limiters, and the rf antenna. The equilibrium pressure balance, J×B=grad p, is quantitatively verified. Radial profiles of pressure and magnetic field show that the equilibrium is that of a rigid rotor.
Internal kink modes in the ion-kinetic regime
Authors: Pegoraro F. , Porcelli F. , Schep T. J.
Published: July 2002

The m=1 kink mode is investigated in the high temperature regime where the width of the singular layer is determined by the mean ion gyroradius. This regime is reached in a number of present-day fusion experiments with strong auxiliary heating. A dispersion relation that contains the full kinetic response of the ions is derived and analyzed. The growth rates are larger than the corresponding ones obtained from fluid theory. Diamagnetic stabilization is weaker than in the fluid case. Ion temperature gradients are shown to be stabilizing at low values of the diamagnetic frequency and destabilizing at large values.
Suppression and control of magnetic islands in toroidal plasmas
Authors: Hegna C. C. , Bhattacharjee A. , Nakamura Y. , Wakatani M.
Published: July 2002

Magnetic islands play an important role in determining the stability and confinement properties of toroidal plasmas. The nonlinear growth of magnetic islands can lead to major disruptions in tokamaks. In stellarators, which do not have a continuous symmetry, the formation of magnetic islands can set equilibrium beta limits. In the first part of this paper, a novel method is proposed for reducing drastically the size of m=2, n=1 islands in tokamaks by introducing a beamlet of energetic ions just outside the q=2 surface via parallel neutral-beam injection. A simple physical picture is given of the nonlinear stability of a tearing mode in the Rutherford regime in the presence of energetic ions. This physical picture is supported by a kinetic calculation in the long mean-free-path regime in which the effect of bootstrap currents and resistive interchanges are retained. Estimates show that the energy of the beamlet required for the suppression is a small fraction of that used for Ohmic or beam-heating of the background plasma. In the second part of the paper, an equilibrium beta limit is obtained for stellarators by calculating the island widths induced by finite plasma pressure; the widths are then constrained by the criterion of island overlap. The theory is applied to the Heliotron-E device [Nakamura et al., Phys. Fluids B 2, 2528 (1990)]. It is shown that some aspects of the experimental observations on internal disruptions in Heliotron-E can be interpreted as signatures of the equilibrium beta limit.
High concentration of deuterium in palladium from plasma ion implantation
Authors: Uhm Han S. , Lee W. M.
Published: July 2002

Based on a theoretical calculation, a new scheme to increase deuterium density in palladium over its initial value is presented. This deuterium enrichment scheme makes use of plasma ion implantation. A cylindrical palladium rod (target) preloaded with deuterium atoms, coated with a diffusion-barrier material, is immersed in a deuterium plasma. The palladium rod is connected to a high-power modulator which provides a series of negative-voltage pulses. During these negative pulses, deuterium ions fall into the target, penetrate the diffusion barrier, and are implanted inside the palladium. For reasonable system parameters allowed by present technology, it is found from theoretical calculations that the saturation deuterium density after prolonged ion implantation can be several times the palladium atomic number density. Assuming an initial deuterium density, n0=4×1022 cm−3, it is also found that the deuterium density in palladium can triple its original value within a few days of the ion implantation for a reasonable target size. Because of the small diffusion coefficient in palladium, the incoming ions do not diffuse quickly inward, thereby accumulating near the target surface at the beginning of the implantation.
Strong turbulence equations derived from kinetic theory
Authors: Goodman Simon
Published: July 2002

Two coupled wave equations, very similar to the Zakharov equations, are derived from the Vlasov–Maxwell system. For low-temperature ions they reduce to the Zakharov equations. Corrections include a nonlinear damping term of significance to the turbulent ionospheric plasma.
Scattering of ordinary-mode electromagnetic waves by density fluctuations in tokamaks
Authors: Smith Gary R. , Cook Daniel R. , Kaufman Allan N. , Kritz Arnold H. , McDonald Steven W.
Published: July 2002

Discussion and applications are presented for two approaches for estimating the effects of scattering of electromagnetic waves by turbulent density fluctuations in tokamaks. Ordinary-mode waves propagating nearly perpendicular to the equilibrium magnetic field are considered. The multiple-scattering approach provides analytic results for the angular and spatial spreading of a microwave beam by the turbulence. The single-scattering approach yields numerical results and is derived by a compact technique involving Wigner functions. Both approaches are applied to idealized tokamaks to clarify relationships between the approaches and to test limits of applicability of the multiple-scattering approach.
Ion ring propagation in a magnetized plasma
Authors: Schamiloglu E. , Greenly J. B. , Hammer D. A.
Published: July 2002

The propagation of an ion ring in a 2.5 m long, 0.30 m diam magnetized plasma column was studied using an axial array of magnetic probes and fast proton detectors, a microwave interferometer, and a grating spectrometer. The ring propagated with an initial axial velocity 3×106 m/sec, about four times the Alfvén speed in the plasma, and excited damped magnetosonic waves whose peak amplitude depended on the plasma return current. The plasma electrons were heated by about 1 eV in response to the ring, as measured by the Hγ line-to-continuum intensity ratio. This heating is primarily attributed to classical Coulomb collisions, although about 1%–10% can be attributed to the collective ring–plasma interaction. The collective interaction had no measurable effect on the dynamics of the ion ring, consistent with theoretical models, given the beam, plasma, and magnetic-field parameters in the experiment.
A kinetic model of fast wave propagation in the vicinity of the minority ion cyclotron resonance in a toroidal magnetic field
Authors: Catto Peter J. , Lashmore-Davies C. N. , Martin T. J.
Published: July 2002

Nearly all kinetic treatments of fast wave minority heating of inhomogeneous plasma in the cyclotron range of frequencies assume the magnetic field varies in the direction perpendicular to the magnetic field. However, the toroidal magnetic field of a tokamak varies along a field line due to the rotational transform and causes a small number of trapped particles to turn in the region of cyclotron resonance. In order to include the effects of rotational transform and, hence, trapped particles in the kinetic plasma response, a simplified, concentric circle flux surface model of a tokamak is employed. The most important result of this work is the derivation of response functions for Maxwellian and bi-Maxwellian minority ions which generalize and extend previous replacement Z function forms obtained from a slab approximation of a tokamak (which also retains the variation of the strength of the magnetic field along a field line). The plasma response functions obtained include both passing and trapped ions, off-axis heating, and are valid for arbitrary minority ion concentrations. The response function for a bi-Maxwellian in the case of strong anisotropy substantially modifies the Maxwellian result. Anisotropy and the effects of toroidal geometry are illustrated graphically and tend to enter at higher toroidal mode numbers. For minority concentrations of the order or less than a critical value, the plasma response functions are used to obtain the standard transmission coefficient previously obtained for straight magnetic-field models. The expression for the transmission coefficient is shown to be valid for more general unperturbed distribution functions of pitch angle and speed on each flux surface provided k∥ρ≪1, where k∥ is the parallel wave number and ρ the minority gyroradius.
Plasma transport in mixed magnetic topologies
Authors: Hegna C. C. , Callen J. D.
Published: July 2002

A simple model is introduced to illustrate some features concerning anomalous transport associated with magnetic turbulence. For magnetic topologies that are described as bands of stochasticity separated by regions with good flux surfaces, the transport coefficients deviate significantly from those describing completely stochastic magnetic fields. It is possible to have the electron heat diffusivity exceed a runaway electron diffusion coefficient, despite the existence of widespread magnetic stochasticity. Comparing the ratios of transport coefficients is not a sufficient method to dismiss the possibility that electromagnetic fluctuations play a prominent role in anomalous plasma transport.
Relativistic and ponderomotive self-focusing of a laser beam in a radially inhomogeneous plasma. I. Paraxial approximation
Authors: Brandi H. S. , Manus C. , Mainfray G. , Lehner T. , Bonnaud G.
Published: July 2002

The propagation of a high-irradiance laser beam in a plasma whose optical index depends nonlinearly on the light intensity is investigated through both theoretical and numerical analyses. The nonlinear effects examined herein are the relativistic decrease of the plasma frequency and the ponderomotive expelling of the electrons. This paper is devoted to focusing and defocusing effects of a beam assumed to remain cylindrical and for a plasma supposed homogeneous along the propagation direction but radially inhomogeneous with a parabolic density profile. A two-parameter perturbation expansion is used; these two parameters, assumed small with respect to unity, are the ratio of the laser wavelength to the radial electric-field gradient length and the ratio of the plasma frequency to the laser frequency. The laser field is described in the context of a time envelope and spatial paraxial approximations. An analytical expression is provided for the critical beam power beyond which self-focusing appears; it depends strongly on the plasma inhomogeneity and suggests the plasma density tailoring in order to lower this critical power. The beam energy radius evolution is obtained as a function of the propagation distance by numerically solving the paraxial equation given by the two-parameter expansion. The relativistic mass variation is shown to dominate the ponderomotive effect. For strong laser fields, self-focusing saturates due to corrections of fourth order in the electric field involved by both contributions.
Stimulated Raman up-conversion of electromagnetic waves by a gyrating electron beam
Authors: Sharma O. P. , Patel V. L.
Published: July 2002

A gyrating electron beam supports negative energy modes near the harmonics of electron-cyclotron frequency. An electromagnetic wave passing through such a beam parametrically up-converts into high-frequency electromagnetic modes separated from the pump frequency by the electron-cyclotron harmonics. The growth rate for this process varies directly as the oscillatory velocity of beam electrons caused by the pump and as square root of the beam density. It has a maximum at values of scattering angle close to 180° and is also implicitly dependent on the beam velocity and the cyclotron frequency of electrons. The effect of a cold electron component is to reduce the growth rate.
Motion of a sphere in a rarefied gas. II. Role of temperature variation in the Knudsen layer
Authors: Law W. S. , Loyalka S. K.
Published: July 2002

The motion of a sphere in a rarefied gas is considered with the use of the BGK model and a boundary condition of diffuse reflection. The role of temperature variation in the Knudsen layer is studied; results show that velocity and pressure in the layer and the drag on the sphere are not sensitive to this variation.
Reply to comments of Montgomery and Matthaeus
Authors: Horiuchi Ritoku , Sato Tetsuya
Published: July 2002

The essence of nonlinear driven reconnection, which does not seem to be well understood by the reader as of yet, is described in order to avoid unnecessary misunderstanding of the magnetohydrodynamic self-organization mechanism proposed by the present authors[Phys. Fluids 29, 1161 (1986)].
Long-time simulation of the single-mode bump-on-tail instability
Authors: Simon Albert , Radin Shelden , Short Robert W.
Published: July 2002

A Vlasov code developed by Denavit [Phys. Fluids 28, 2773 (1985)] was modified and used to study long-time behavior of the single-mode bump-on-tail instability. Large oscillations, which interrupted his original runs at ω0 T≊1300 shortly after reaching the O’Neil trapping level (OTL), were identified and controlled by heating the cold background electrons. A run to ω0T =30 000 showed growth well beyond the OTL and eventually saturated at about the level predicted by Simon and Rosenbluth (SR) [Phys. Fluids 19, 1567 (1976)], before oscillations set in. A run with warmer background electrons was again interrupted by oscillations. A weakly unstable case was followed to ω0T =60 000; it also showed growth well beyond the OTL but saturated at an amplitude that was significantly below that predicted by SR. In all cases, the velocity distribution developed strong ripples near v=0. These are shown to be caused by a numerical grid effect, and they may be responsible for the eventual development of the large oscillations and for the low level of saturation in the weakly unstable case.
Direct simulations of the transitional regime of a circular jet
Authors: Verzicco R. , Orlandi P.
Published: July 2002

Accurate numerical simulations of temporal evolving round jets at a low Reynolds number have revealed the same features observed in experiments and vortex filament simulations. The initial layer of azimuthal vorticity, by the Kelvin–Helmholtz instability, produces vortex rings undergoing successive pairings leading to larger rings. Axisymmetric simulations have shown that the initial roll-up is not affected by the Reynolds number, consequently insights of practical importance on the transitional regime, can be obtained from low Reynolds number simulations affordable by numerics. The 3-D simulations displayed the formation of longitudinal structures, and their role in the spreading of the jet is described. Streamwise rib vortices develop in the braid region and these vortices are responsible for the creation of small scales, premonitory of turbulence. In analogy to the plane mixing layer, the pairing reduces the growth of longitudinal and radial vorticity components and triggers the transition to turbulence. Finally comparisons between azimuthal vorticity and passive scalar surfaces have revealed that the latter collects in fat structures while the vorticity is found in thin regions where it is augmented by stretching.
Macroscopic behavior of vibrating beds of smooth inelastic spheres
Authors: Lan Yidan , Rosato Anthony D.
Published: July 2002

Three-dimensional granular dynamics simulations are carried out to investigate macroscopic behavior of granular materials subjected to vibrations. Particles, idealized as smooth inelastic, uniform spheres, are gravitationally loaded into a rectangular periodic cell having an open top and plane floor. Vibrations to the bed are subsequently imposed through the sinusoidally oscillated floor. Significant differences in the character of the bed are found, depending on the strength of the applied floor accelerations Γ=aω2, even if the boundary input energy is fixed. At high acceleration values, a dense upper region is supported on a fluidized low-density region near the floor. The temperature is maximum at the floor and monotonically attenuates upward, while the solids fraction profile peaks at some intermediate depth. When lower accelerations are applied, the granular temperature no longer decreases monotonically from the bottom to the top and the solids fraction depth profile bulges at approximately three diameters from the floor. The surface of the bed appears chaotic and fluidized, where a low solids fraction and high temperature occurs. The bed height, which remains almost constant below 1.2g, undergoes a pronounced expansion when 1.2g≤Γ≤2.0g, and subsequently flattens out at Γ≂2.8g. Computed granular temperature and solids fraction depth profiles are in good agreement with recent kinetic theory predictions when the acceleration is large enough, while bed expansion at lower accelerations is quantitatively consistent with existing experimental data.
Nonlinear interaction of wave trains in a supersonic boundary layer
Authors: Tumin Anatoli
Published: July 2002

Nonlinear interaction of disturbances caused by a harmonic point source in supersonic boundary layer over a flat plate is considered. It is assumed that wave lengths are much less than a characteristic scale of nonlinear interaction and the averaging technique on the intermediate scales may be used. The wave trains are considered as sums of narrow wave packets. The parameters of flow and harmonic point source are chosen in accordance with the experiments carried out by Kosinov et al. [Nonlinear Instability of Nonparallel Flows (Springer, New York, 1994)].
Density variations in a one-dimensional granular system
Authors: Grossman E. L. , Roman B.
Published: July 2002

In this work we examine a system of inelastic particles confined to move on a line between an elastic wall and a heat source. Solving a Boltzmann equation for this system leads to an analytic expression for steady state behavior. Numerical simulations show that the system is in fact capable of simultaneously displaying both the uniform density of the analytic solution, and a state in which the particles are collected into a cluster adjacent to the elastic wall. The boundary conditions for the Boltzmann treatment are then reworked to provide a theoretical description of how smooth particle distributions and clumping phenomena can coexist. From this, we gain a prediction for the time scale of clump formation in this system.
Predictability in two-dimensional decaying turbulence
Authors: Boffetta G. , Celani A. , Crisanti A. , Vulpiani A.
Published: July 2002

Predictability problem for two-dimensional decaying turbulence is addressed by means of numerical simulations. Qualitative and quantitative comparisons with previous results obtained by closure approximations are critically examined. It is found that, as for other features of two-dimensional turbulence, the role of coherent vortices is essential for a correct interpretation of the results. A Lagrangian, vortex-based, definition for the growth of incertitudes leads in general to an enhancement of the predictability time.
Electrocapillary instability in annular geometry
Authors: González H. , Néron de Surgy G. , Chabrerie J.-P.
Published: July 2002

Previous investigations on electrocapillary instability in a liquid metal confined in a circular cylindrical vessel are extended to annular geometry. The number of peaks arising on an initially flat surface when a strong electric field acts on it is determined in terms of the inner and outer ring radii, as well as the critical electric field needed for destabilization. The limiting case of an infinite, straight recipient is independently solved and compared to the annular geometry results for appropriate values of these radii. Experimental observations with mercury are included and confronted to the theory.
Filtered density function for large eddy simulation of turbulent reacting flows
Authors: Colucci P. J. , Jaberi F. A. , Givi P. , Pope S. B.
Published: July 2002

A methodology termed the “filtered density function” (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities. A transport equation is derived for the FDF in which the effect of chemical reactions appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The FDF transport equation is solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of the equivalent stochastic differential equations (SDEs) are obtained. These solutions preserve the Itô-Gikhman nature of the SDEs. The consistency of the FDF approach, the convergence of its Monte Carlo solution and the performance of the closures employed in the FDF transport equation are assessed by comparisons with results obtained by direct numerical simulation (DNS) and by conventional LES procedures in which the first two SGS scalar moments are obtained by a finite difference method (LES-FD). These comparative assessments are conducted by implementations of all three schemes (FDF, DNS and LES-FD) in a temporally developing mixing layer and a spatially developing planar jet under both non-reacting and reacting conditions. In non-reacting flows, the Monte Carlo solution of the FDF yields results similar to those via LES-FD. The advantage of the FDF is demonstrated by its use in reacting flows. In the absence of a closure for the SGS scalar fluctuations, the LES-FD results are significantly different from those based on DNS. The FDF results show a much closer agreement with filtered DNS results.
Second-order conditional moment closure for the autoignition of turbulent flows
Authors: Mastorakos E. , Bilger R. W.
Published: July 2002

The conditional moment closure with second-order approximation for the reaction rate and an equation for the conditional fluctuations of the temperature increments before autoignition of a turbulent nonpremixed flow has been developed for one-step chemistry. The explicit incorporation of conditional variances is necessitated due to the temperature fluctuations induced by heat losses from the reaction zone before ignition, as indicated by recent direct numerical simulations (DNS). Predicted ignition times and reaction zone structure are in very good agreement with DNS data and the differences between the first- and second-order closure are discussed.
Numerical investigation of the entrainment and mixing processes in neutral and stably-stratified mixing layers
Authors: Cortesi A. B. , Smith B. L. , Yadigaroglu G. , Banerjee S.
Published: July 2002

The direct numerical simulation (DNS) of a temporally-growing mixing layer has been carried out, for a variety of initial conditions at various Richardson and Prandtl numbers, by means of a pseudo-spectral technique; the main objective being to elucidate how the entrainment and mixing processes in mixing-layer turbulence are altered under the combined influence of stable stratification and thermal conductivity. Stratification is seen to significantly modify the way by which entrainment and mixing occur by introducing highly-localized, convective instabilities, which in turn cause a substantially different three-dimensionalization of the flow compared to the unstratified situation. Fluid which was able to cross the braid region mainly undisturbed (unmixed) in the unstratified case, pumped by the action of rib pairs and giving rise to well-formed mushroom structures, is not available with stratified flow. This is because of the large number of ribs which efficiently mix the fluid crossing the braid region. More efficient entrainment and mixing has been noticed for high Prandtl number computations, where vorticity is significantly reinforced by the baroclinic torque. In liquid sodium, however, for which the Prandtl number is very low, the generation of vorticity is very effectively suppressed by the large thermal conduction, since only small temperature gradients, and thus negligible baroclinic vorticity reinforcement, are then available to counterbalance the effects of buoyancy. This is then reflected in less efficient entrainment and mixing. The influence of the stratification and the thermal conductivity can also be clearly identified from the calculated entrainment coefficients and turbulent Prandtl numbers, which were seen to accurately match experimental data. The turbulent Prandtl number increases rapidly with increasing stratification in liquid sodium, whereas for air and water the stratification effect is less significant. A general law for the entrainment coefficient as a function of the Richardson and Prandtl numbers is proposed, and critically assessed against experimental data.
Modeling of Richtmyer–Meshkov instability-induced turbulent mixing in shock-tube experiments
Authors: Valerio E. , Jourdan G. , Houas L. , Zeitoun D. , Besnard D. C.
Published: July 2002

A turbulence transport model for the analysis of shock interface interaction-induced turbulent mixing is presented. Results given by the one-dimensional (1-D) version of this model are compared with data obtained in shock-tube experiments. Calibrations are made from an air/He interface destabilized by a 1.3 incident shock wave Mach number, taking into account the successive interactions with the different reshocks on the shock tube end wall. Then, using the same set of model constants, different gas pairs with both various Atwood and incident shock wave Mach numbers are considered, in order to point out the influence of these main parameters on the results. Mixing zone thickness time evolutions and 1-D density profiles are presented and directly compared with experimental results. Profiles of other variables such as the space integral of the turbulent kinetic energy ∫k dx, translation energy ∫ρux2 dx, and the ratio ∫ρk dx/∫ρux2 dx, given by the computations, are also shown. Using two different initializations, in particular, to better describe the first phases of the phenomenon under study (i.e., taking into account the initial membrane in a horizontal shock tube configuration), we have found good agreement between calculations and experiments.
Laboratory evidence of three-dimensional frequency downshift of waves in a long tank
Authors: Trulsen Karsten , Stansberg Carl Trygve , Velarde Manuel G.
Published: July 2002

Experiments show that the evolution of Stokes waves can lead to significant growth of transverse standing wave oscillations across the tank at a large distance from the wave maker. The peak power intensity of narrow-banded transverse standing waves can reach a similar level as that of the collinear waves, and a significant downshift is observed for the transverse waves. Dissipation may be less important for the downshift than previously anticipated.
On a three-dimensional volume tracking model of droplet impact
Authors: Bussmann M. , Mostaghimi J. , Chandra S.
Published: July 2002

A three-dimensional model has been developed of droplet impact onto asymmetric surface geometries. The model is based on RIPPLE, and combines a fixed-grid control volume discretization of the flow equations with a volume tracking algorithm to track the droplet free surface. Surface tension is modeled as a volume force acting on fluid near the free surface. Contact angles are applied as a boundary condition at the contact line. The results of two scenarios are presented, of the oblique impact of a 2 mm water droplet at 1 m/sec onto a 45° incline, and of a similar impact of a droplet onto a sharp edge. Photographs are presented of such impacts, against which the numerical results are compared. The contact angle boundary condition is applied in one of two ways. For the impact onto an incline, the temporal variation of contact angles at the leading and trailing edges of the droplet was measured from photographs. This data is applied as a boundary condition to the simulation, and an interpolation scheme proposed to evaluate contact angles between the leading and trailing edges. A simpler model is then proposed, for contact angle as a function of contact line velocity, and applied to both geometries. The model requires values of only two contact angles, at a rapidly advancing and a rapidly receding contact line. Simulation results compare well with photographic data.