bluuebunny/crossref_metadata_2025 huggingface dataset:
Resolution of simple singularities yielding particle symmetries in a space–time
Authors: Rainer Martin
Published: July 2002

A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The homological intersection graph of these cycles is the Dynkin graph of an ADE Lie group, i.e., a Lie group from the cartan series A, D, or E. The deformation of the simple singularity corresponds to ADE symmetry breaking. A (3+1)-dimensional topological model of observation is constructed, transforming consistently under SL(2,C), as an evolving three-dimensional system of world tubes, which connect ‘‘possible points of observation.’’ The existence of an initial singularity for the four-dimensional space–time is related to its global topological structure. Associating the geometry of ADE singularities to the vertex structure of the topological model puts forward the conjecture on a likewise relation of inner symmetries of elementary particles to local space–time structure.
Wave scattering in a strip
Authors: Tsay W. J.
Published: July 2002

The scattering problem of the discrete random Schrödinger equation in a strip is studied. The wave is considered to be incoming from one side of the disordered section. The main result is that transmission of a wave packet is improbable.
Cocycles for boson and fermion Bogoliubov transformations
Authors: Langmann Edwin
Published: July 2002

Unitarily implementable Bogoliubov transformations for charged, relativistic bosons and fermions are discussed, and explicit formulas for the two-cocycles appearing in the group product of their implementers are derived. In the fermion case this provides a simple field theoretic derivation of the well-known cocycle of the group of unitary operators on a Hilbert space modeled on the Hilbert–Schmidt class and closely related to the loop groups. In the boson case the cocycle is obtained for a similar group of pseudo-unitary (symplectic) operators. Formulas are also given for the phases of one-parameter groups of implementers and, more generally, families of implementers which are unitary propagators with parameter-dependent generators.
On a ferromagnetic spin chain. II. Thermodynamic limit
Authors: Knauf Andreas
Published: July 2002

The existence of the thermodynamic limit of the free energy for the ferromagnetic spin chain connected with the Riemann zeta function is proven.
Continued fraction as a discrete nonlinear transform
Authors: Bender Carl M. , Milton Kimball A.
Published: July 2002

The connection between a Taylor series and a continued fraction involves a nonlinear relation between the Taylor coefficients {an} and the continued fraction coefficients {bn}. In many instances it turns out that this nonlinear relation transforms a complicated sequence {an} into a very simple one {bn}. This simplification is illustrated in the context of graph combinatorics.
Symplectic structure and gauge invariance on the cotangent bundle
Authors: Encinas L. Hernández , Masqué J. Muñoz
Published: July 2002

The cotangent bundle of a manifold M can be identified with the bundle of connections of the trivial bundle M×U(1). Hence, there exists a natural representation of the U(1)-invariant vector fields on M×U(1) extending the gauge representation into the Lie algebra of vector fields on T*(M). It is proved herein that a differential form on T*(M) is invariant under this representation (resp. gauge invariant) if and only if it belongs to the R-algebra [resp. to the Ω ̇ (M)-algebra] generated by the canonical symplectic form of the cotangent bundle.
Modular systems induced by trace functionals on algebras of unbounded operators
Authors: Inoue Atsushi
Published: July 2002

The purpose of this article is to study the unbounded Tomita–Takesaki theory by trace functionals on O*-algebras, and to apply the results to the algebras associated with the canonical commutation relation, pq−qp=−i1 (CCR-algebras).
Comments on the Gribov ambiguity
Authors: Kalogeropoulos Nikolaos
Published: July 2002

The existence of Gribov ambiguities in SU(m)×U(1) gauge theories over the n-spheres is discussed herein. The goal of this article is achieved by showing that there is exactly one conjugacy class of groups of gauge transformations for the theories given above. This implies that these transformation groups are conjugate to the ones of the trivial SU(m)×U(1) fiber bundles over the n-spheres. By using properties of the space of maps Map*(Sn,G) where G is one of U(1), SU(m), we are able to determine the homotopy type of the groups of gauge transformations in terms of the homotopy groups of G. The nontriviality of these homotopy groups gives the desired result.
Properties of q-entropies
Authors: Raggio G. A.
Published: July 2002

Basic properties of the q-entropy Sq[ρ]=(q−1)−1(1−tr(ρq)) (0<q≠1) for states of a quantum system are established: concavity, quasi-convexity, continuity, and failure of ‘‘additivity’’ and ‘‘subadditivity’’ for composite systems.
Statistical mechanics of hard spheres
Authors: Baeyens Bruno , Verschelde Henri
Published: July 2002

A theoretical equation of state for a system of hard spheres is proposed. It is based on the ideas of the scaled-particle theory that has been developed by Reiss et al. [J. Chem. Phys. 31, 369 (1959)]. In this paper, their method is generalized by expanding the function G(y,r) in a set of functions ti(r) so that the low-density behavior is described exactly, not only for asymptotically large values of r, but for the full range of r values. As a consequence the virial coefficients B3 and B4 come out exactly in the approach to the scaled particle theory. For the compressibility factor, a Padé-like expression is obtained that gives exact values for B3 and B4 and reproduces B5, B6, B7, and B8 to within 1.3%, 1.4%, 0.74%, and 5.5%, respectively. Furthermore, the equation of state agrees with the simulation data up to high densities, where the fluid is metastable. An expression for the surface tension is also found.
Massive NGT and spherically symmetric systems
Authors: Clayton M. A.
Published: July 2002

The arguments leading to the introduction of the massive Nonsymmetric Gravitational action are reviewed [J. W. Moffat, J. Math. Phys. 36, 3722 (1995), Phys. Lett. B 355, 447 (1995)], leading to an action that gives asymptotically well-behaved perturbations on General Relativity (GR) backgrounds. Through the analysis of spherically symmetric perturbations about GR (Schwarzschild) and Nonsymmetric Gravitational Theory (NGT) (Wyman-type) static backgrounds, it is shown that spherically symmetric systems are not guaranteed to be static, and hence Birkhoff’s theorem is not valid in NGT. This implies that in general one must consider time dependent exteriors when looking at spherically symmetric systems in NGT. For the surviving monopole mode considered here there is no energy flux as it is short ranged by construction. Further work on the spherically symmetric case will be motivated through a discussion of the possibility that there remain additional modes that do not show up in weak field situations, but nonetheless exist in the full theory and may again result in bad global asymptotics. A presentation of the action and field equations in a general frame is given in the course of the paper, providing an alternative approach to dealing with the algebraic complications inherent in NGT, as well as offering a more general framework for discussing the physics of the antisymmetric sector.
Imaging of velocity singularities with multiscale operators
Authors: Song Shougen , Qu Chaoshun , He Jishan
Published: July 2002

In this paper, by using the multiscale operator and based on the Beylkin’s formula [J. Math. Phys. 26, 99–108 (1985)], the inversion method of velocity singularities is presented, and by applying the multiscale operator to upward scattered data represented by the Kirchhoff approximation, the multiscale imaging formula is shown. For the band-limited inverse problem, based on the multiscale imaging formula in this paper, the behavior of the velocity singularities can be analyzed across the multiscale and the formula to reconstruct the velocity is obtained from the output of the multiscale operator interpreted in the terms of the Kirchhoff-approximate data. Particularly, at wide offset and even postcritical case, for the full-band input data, the same result with Beylkin’s in the above reference about the velocity discontinuities is obtained. Our method in this paper can suppress the effects of the noise in the real world data and analyze the effect produced by band-limited input data.
On some representations of current algebras in two dimensions and their central extensions
Authors: Donkov Sava , Stoytchev Orlin
Published: July 2002

A class of unitary representations of the group of maps from a Riemannian manifold to a compact semisimple Lie group which are a modification of the so-called energy representations is considered. Their irreducibility is proved in any dimension ≥2. This extends the known results of irreducibility for certain cases in dimension 2. Next, the corresponding algebra representations are studied and their irreducibility in dimension 2 is also proved. These are extended in a natural way to representations of certain central extensions of the algebras. Very explicit formulas are given, particularly on the two-dimensional torus, for the algebra extensions and the representations.
The Dirac equation in the Robertson–Walker space–time
Authors: Zecca Antonio
Published: July 2002

The Dirac equation is considered, via the Newman–Penrose formalism, in the context of the Robertson–Walker geometry. The solution of the equation, which contrary to the neutrino case is not directly separable, is reduced to the study of decoupled spatial and temporal equations. The spatial equations are explicitly integrated and show the existence of discrete energy levels in case of closed universe. Besides the neutrino, the time equation is discussed in limiting situations of the standard cosmology.
Geometric phase for isotopic spin coherent states
Authors: Kar T. K. , Ghosh Gautam
Published: July 2002

The concept of geometric phase for a closed circuit in the ray space is applied to the manifold of generalized coherent states defined as the eigenstates of isotopic spin charges. The geometry of the state manifold is elucidated through a calculation of the Gaussian curvature.
Gentle perturbations of the free Bose gas. The critical regime
Authors: Gielerak Roman , Olkiewicz Robert
Published: July 2002

The modular structure of the free Bose gas in the critical regime of couplings is completely described by certain Gaussian Markovian (on a circle) nonergodic thermal process. Gentle perturbations of the arising Gaussian stochastic structure are controlled rigorously and the arising non-quasi-free W* KMS structure is shown to be nonergodic in certain range of couplings. The preserved nonergodicity seems to be connected to the presence of the Bose–Einstein condensate in the constructed models of interacting bosons.
Energy level correlations in disordered metals: Beyond universality
Authors: Andreev A. V. , Simons B. D. , Altshuler B. L.
Published: July 2002

This short review is concerned with energy level statistics in weakly disordered metallic grains. In particular, we concentrate on how these statistics deviate from the universal ones. Using a nonperturbative approach we evaluate the large frequency asymptotics of the two-point correlator of the density of states. This allows us to describe the behavior of the system at arbitrary times.
Ergodic properties of the quantum ideal gas in the Maxwell–Boltzmann statistics
Authors: Lenci Marco
Published: July 2002

It is proved that the q uantization of the Volkovyski–Sinai model of ideal gas (in the Maxwell–Boltzmann statistics) enjoys at the thermodynamical limit the property of quantum mixing in the following sense: lim|t|→∞ limm/L→ρm,L→∞ ωβ ,Lm(eiHmt/ℏ×Ae−iHmt/ mCB)=limm/L→ρm,L→∞ ωβ,Lm( A)⋅limm/L→ρm,L→∞ ωβ,Lm(B ). Here Hm is the Schrödinger operator of m free particles moving on a circle of length L; A and B are the Weyl quantization of two classical observables a and b; ωmβ,L(A) is the corresponding quantum Gibbs state. Moreover, one has limm/L→ρm,L→∞ ωβ,m(A)=Pρ,β (a), where Pρ,β(a) is the classical Gibbs measure. The consequent notion of quantum ergodicity is also independently proven.
Becchi–Rouet–Stora cohomology of zero curvature systems. I. The complete ladder case
Authors: Carvalho M. , Vilar L. C. Q. , Sasaki C. A. G. , Sorella S. P.
Published: July 2002

We present here the zero curvature formulation for a wide class of field theory models. This formalism, which relies on the existence of an operator δ which decomposes the exterior space–time derivative as a BRS commutator, turns out to be particularly useful in order to solve the Wess–Zumino consistency condition. The examples of the topological theories and of the B−C string ghost system are considered in detail.
A null-tetrad approach to Kerr–Schild gravitational fields in matter
Authors: Udeschini Elisa Brinis , Magli Giulio
Published: July 2002

The null tetrad formalism is used to investigate the structure of the Einstein field equations for Kerr–Schild gravitational fields in the presence of an elastic solid source. It is shown that such equations may be reduced to five nonlinear partial differential equations for five variables. It turns out that, when the interior solutions admit the same preferred null congruence of the vacuum ones and some compatibility conditions hold, it is possible to reduce them to a linear system and to develop a method of solution which closely resembles the ‘‘variation of the arbitrary constants’’ for ordinary differential equations. In the present paper, the above technical framework is developed in general and applied to two simple examples, deferring to future work the approach to the Kerr–interior problem.
Ergodic properties of infinite quantum harmonic crystals: An analytic approach
Authors: Graffi Sandro , Martinez André
Published: July 2002

We prove that the quantum dynamics of a class of infinite harmonic crystals becomes ergodic and mixing in the following sense: if Hm is the m-particle Schrödinger operator, ωβ,m(A)=Tr(A exp−βHm)/Tr(exp−βHm) the corresponding quantum Gibbs distribution over the observables A,B,ψm,λ the coherent states in the mth particle Hilbert space, gm,λ=(exp−βHm)ψm,λ then limt→∞ limn→∞ limm→∞(1/T)∫T0〈eiHntAe−iHntψm,λ,ψm,λ〉dt=limm→∞ ωβ,m(A) if the classical infinite dynamics is ergodic, and limt→∞ limn→∞ limm→∞ ωβ,m(e /iiHntAe−iHntB)=limm→∞ ωβ,m(A)limm→∞ωβ,m(B) if it is in addition mixing. The classical ergodicity and mixing properties are recovered as ℏ→0, and limm→∞ ωβ,m(A) turns out to be the average over a classical Gibbs measure of the symbol generating A under Weyl quantization.
Symmetries of preon interactions modeled as a finite group
Authors: Bellinger James N.
Published: July 2002

I model preon interactions as a finite group. Treating the elements of the group as the bases of a vector space, I examine those linear mappings under which the transformed bases may be treated as members of a group isomorphic to the original. In some cases these mappings are continuous Lie groups.
Initial value problem of the linearized Benjamin–Ono equation and its applications
Authors: Matsuno Y. , Kaup D. J.
Published: July 2002

We consider the initial value problem of the Benjamin–Ono (BO) equation linearized about the N-soliton solution. By establishing the completeness relation for the eigenfunctions of the linearized BO equation, we construct the explicit solution to this problem. As an application of the above result, we investigate the linear stability of the N-soliton solution. We show that the wave under consideration is stable against infinitesimal perturbations. Thus we have a direct multisoliton perturbation theory for the BO equation without recourse to the inverse scattering transform. In particular, we can handle the first-order solution beyond the adiabatic approximation. The completeness relation established here enables us to give a general scheme for evaluating the first-order correction to the leading-order N-soliton solution. We also demonstrate that the first-order solution satisfies an infinite set of conservation laws modified by the perturbations. Finally, in the one-soliton case, we perform explicit calculations of the first-order corrections for two different dissipative perturbations that arise in real physical systems and analyze their large time asymptotics.
The perturbed Korteweg–de Vries equation considered anew
Authors: Mann E.
Published: July 2002

The perturbed Korteweg–de Vries equation is studied in a new way by a Green’s function formalism without use of inverse scattering methods. The Green’s function is determined by employing the Bäcklund transformation and Green’s theorem. After a thorough analysis of the exact first-order solution with regard to secular terms, a two-time scale expansion leads to the adiabatic approximation and the first-order correction, in accordance with the results of Karpman and Maslov. Contrary to statements in the literature, the term tanh2 z in the expression for the modified phase of the perturbed soliton arises as a consequence of the systematically conducted first-order perturbation theory.
A length operator for canonical quantum gravity
Authors: Thiemann T.
Published: July 2002

We construct an operator that measures the length of a curve in four-dimensional Lorentzian vacuum quantum gravity. We work in a representation in which an SU(2) connection is diagonal and it is therefore surprising that the operator obtained after regularization is densely defined, does not suffer from factor ordering singularities, and does not require any renormalization. We show that the length operator admits self-adjoint extensions and compute part of its spectrum which, like its companions, the volume and area operators already constructed in the literature, is purely discrete and roughly quantized in units of the Planck length. The length operator contains full and direct information about all the components of the metric tensor which facilitates the construction of so-called weave states which approximate a given classical three-geometry.
Canonical and quasicanonical realizations of the osp(D|d) superalgebra and the Coulomb problem in superspaces
Authors: Daumens Michel , Minnaert Pierre
Published: July 2002

Canonical and quasi-canonical realizations of the osp(D|d) superalgebra are presented. In these realizations there is only one independent Casimir operator: The quadratic one C, the eigenvalues of which allow specification of the involved representations. Pauli’s method for solving the spectrum of the Coulomb problem through quantization of the Runge–Lenz vector is extended to an arbitrary dimension superspace E(D|d) with D bosonic coordinates and d (even) fermionic coordinates. The symmetry algebra of the Hamiltonian is the superalgebra osp(D+1|d). It is shown how the energy spectrum is related to the Casimir operator C′ of osp(D+1|d) in its quasicanonical realization. Then the energy levels are given in terms of the eigenvalues of the operator C′.
On stationary black holes of the Einstein conformally invariant scalar system
Authors: Zannias T.
Published: July 2002

The circularity property of stationary-axisymmetric asymptotically flat solutions of the coupled Einstein conformally invariant scalar field equations is investigated. It is proven that as a result of the coupling of the scalar field to the background scalar curvature, in general such solutions fail to be circular. Consequently, it is argued that the space of stationary, black hole equilibrium states may contain states which are not circular. However, the circular stationary-axisymmetric sector is nonempty and in fact it is proven that: All circular, stationary-axisymmetric asymptotically flat black hole solutions are those and only those black holes states described by the two parameter family of Kerr black holes.
Canonical general relativity: Matter fields in a general linear frame
Authors: Clayton M. A.
Published: July 2002

Building on the results of previous work [M. A. Clayton, “Canonical general relativity: Diffeomorphism constraints and spatial frame transformations,” J. Math. Phys. 39, 3805–3816 (1998)], we demonstrate how matter fields are incorporated into the general linear frame approach to general relativity. When considering the Maxwell one-form field, we find that the system that leads naturally to canonical vierbein general relativity has the extrinsic curvature of the Cauchy surface represented by gravitational as well as nongravitational degrees of freedom. Nevertheless the metric compatibility conditions are undisturbed, and this apparent derivative-coupling is seen to be an effect of working with (possibly orthonormal) linear frames. The formalism is adapted to consider a Dirac Fermion, where we find that a milder form of this apparent derivative-coupling appears.
Second-order second-degree Painlevé equations related with Painlevé I–VI equations and Fuchsian-type transformations
Authors: Muğan U. , Sakka A.
Published: July 2002

One-to-one correspondence between the Painlevé I–VI equations and certain second-order second-degree equations of Painlevé type is investigated. The transformation between the Painlevé equations and second-order second-degree equations is the one involving the Fuchsian-type equation.
Estimates for the spectral shift function of the polyharmonic operator
Authors: Pushnitski Alexander
Published: July 2002

The Lifshits–Krein spectral shift function is considered for the pair of operators H0=(−Δ)l, l>0 and H=H0+V in L2(Rd), d⩾1; here V is a multiplication operator. The estimates for this spectral shift function ξ(λ;H,H0) are obtained in terms of the spectral parameter λ>0 and the integral norms of V. These estimates are in a good agreement with the ones predicted by the classical phase space volume considerations.
On the scaling laws of thermal turbulent convection
Authors: She Zhen-Su
Published: July 2002

A new dimensional analysis for high Rayleigh number thermal convection is proposed to give an alternative interpretation of the scaling laws observed recently by Castaing et al. [J. Fluid Mech. (in press)]. The key assumption in the present approach is that the central fluctuating temperature field actively interacts with the turbulent velocity field, and this interaction leads to a velocity inertial subrange that deviates significantly from Kolmogorov’s freely cascading inertial range.
Numerical calculation of stable three-dimensional tertiary states in grooved-channel flow
Authors: Amon Cristina H. , Patera Anthony T.
Published: July 2002

Numerical simulations of the early transition process in periodic grooved-channel flow are presented. For Reynolds numbers, RRc,2 >Rc,1 the wavy two-dimensional flow is unstable to a classical linear three-dimensional secondary instability; and for some range of Reynolds number above Rc,2 the secondary instability saturates in a steady-periodic, three-dimensional, low-order equilibrium. The three-dimensional equilibria owe their existence and stability to the narrow band nature of grooved-channel-flow secondary instability, which in turn reflects the low-Reynolds-number supercritical form of the grooved-channel-flow primary bifurcation. The contrast between the low-order, weak transition in ‘‘inflectional’’ complex-geometry channels and the abrupt, snap-through transition in (subcritical-primary broadband-secondary) planar channels illustrates the important role of primary criticality in the early transition process.
Propagation of surface waves over an undulating bed
Authors: Kirby James T.
Published: July 2002

Recent results of Davies et al. [Phys. Fluids A 1, 1331 (1989)], which cast the problem of scattering of long surface waves by sinusoidal bed undulations into a Mathieu equation, are extended here to include the case of dispersive, intermediate depth waves. The present formulation is restricted to linear monochromatic wave motions and the bed undulation amplitude is assumed to be small relative to the total water depth.
Mobility functions for two unequal viscous drops in Stokes flow. II. Asymmetric motions
Authors: Fuentes Yuris O. , Kim Sangtae , Jeffrey David J.
Published: July 2002

Analytical results are obtained for mobility functions that describe the hydrodynamic interactions for transverse motions of two unequal viscous drops. In conjunction with the results of an earlier paper on axisymmetric motions, the motion induced by external forces in an arbitrary direction, i.e., the solution of the general mobility problem, is thus obtained. In the problem of interest, the drops are small and the surface tension is sufficiently high so that the drops retain a spherical shape. Exact solutions for the velocity images for Stokeslets and higher-order Stokes singularities near a viscous drop are introduced and then these image solutions are used to generate expressions valid for all two-sphere geometries except those for which the gap is much smaller than the diameter of the smaller drop. For rigid spheres, these results are used to obtain a closed-form expression for the Stokes–Einstein Brownian diffusion coefficient.
Turbulent energy at accelerating and shocked interfaces
Authors: Mikaelian Karnig O.
Published: July 2002

The turbulent energy generated at accelerating or shocked interfaces between two fluids is calculated. Assuming a linear density profile across the mix region it was found that Eturb/Edir=2.3A2% for a constant acceleration and 9.3A2% for a shock, where A is the Atwood number of the two fluids. Somewhat less turbulent energy is generated if density profiles based on self-similar solutions to nonlinear diffusion equations were used. These equations also predict eddy sizes: λ/h=26%–29% and λ/h=16%–18% were found for a constant acceleration and a shock, respectively, where λ is the eddy size controlling the diffusion coefficient and h is the mixing depth into the heavier fluid. The present results were compared with other models and with experiments conducted at AWE.
On falling-film instabilities and wave breaking
Authors: Joo S. W. , Davis S. H. , Bankoff S. G.
Published: July 2002

Long-wave instabilities of thin viscous films flowing down inclined planes are studied. Numerical solutions of the full long-wave evolution equation show that wave profiles grow superexponentially and evolve toward breaking when the surface tension takes on realistically small values. This contrasts with the solutions of the Kuramoto–Sivashinsky equation, which do not tend toward breaking. The use of the full equation thus dispenses with the need to introduce the formally small curvature terms into the Kuramoto–Sivashinsky equation, as suggessted by Rosenau and Oron [Phys. Fluids A 1, 1763 (1989)].
An experimental investigation of the natural transition of an untuned planar jet
Authors: Thomas F. O. , Prakash K. M. K.
Published: July 2002

The result of an experimental investigation into the natural near-field transition of an untuned planar jet at moderate Reynolds number is presented. Here the term ‘‘untuned’’ refers to the case where the ratio of the thin shear layer instability frequency to the jet column frequency is not given by an integer power of 2, so that a sequence of shear layer vortex pairing or amalgamation events is incapable of yielding the jet column frequency near the end of the potential core. This case is of interest because the jet shear layer instability must undergo more dramatic frequency and phase adjustments in order to satisfy the downstream jet column constraint. This provides a unique opportunity to investigate how instabilities that scale with the jet column interact with those that scale with the nascent shear layer instability to configure the initial evolution of the natural planar jet. Auto-bicoherence spectra are used in conjunction with conventional power spectra in order to provide quantitative measurements of the nonlinear phase coupling between wave triads that characterizes the near-field transition of the natural planar jet. These measurements are complemented by two-point correlation, coherence, and phase spectra that document the streamwise evolution and cross-stream symmetry of structural patterns in the flow throughout the initial, interaction, and early self-preserving regions. These measurements indicate that the wave interactions that characterize the planar jet near-field transition are quite different from the sequence of subharmonic instabilities that typically characterize the planar mixing layer. In particular, suppression of the subharmonic instability and the formation of modulating sidebands are observed. The modulation occurs at the jet column frequency and the measurements suggest that this has an origin that is due to a kinematic effect associated with the lateral oscillation of the nascent shear layers near the nozzle lip. The origin of this oscillation appears fully consistent with Biot–Savart induction from the downstream region of the flow associated with the loss of symmetry of the large-scale vorticity field.
Joint probability density function of a scalar and its gradient in isotropic turbulence
Authors: Gao Feng , O’Brien Edward E.
Published: July 2002

The joint probability density function (pdf) of a scalar and its gradient are investigated. Under isotropic conditions, a relation is derived between this pdf and the joint pdf of a scalar and its x derivative. Physical properties of the scalar derivative are analyzed quantitatively to show that its pdf conditional on a given scalar value is close to a Gaussian distribution. The conditional pdf of the scalar derivative is then expanded according to the Gram–Charlier expansion. The coefficients of this expansion are evaluated using direct numerical simulation (DNS) of stationary turbulent scalar fields. Results obtained from a number of simulations support the assumption of a near-Gaussian distribution for the scalar derivative. Finally, the intermittency of the scalar gradient is discussed.
The dynamics and mixing of small spherical particles in a plane, free shear layer
Authors: Gañán-Calvo Alfonso M. , Lasheras Juan C.
Published: July 2002

The equation of motion of small rigid spheres settling under gravity in a two-dimensional inviscid flow given by the Stuart solution of the Euler equations is analyzed as a four-dimensional dynamical system. It is shown that depending on the values of the Stokes, Grashof, and a scaled Reynolds number, particles may either sediment or remain permanently suspended in the flow. When suspension occurs, the particle trajectories are shown to be attracted by a single period, quasiperiodic, or chaotic orbits. A consequence of the existence of a strange attractor (chaotic orbit) is that heavy particles can reach a stage of fluidization by which they remain indefinitely suspended in a layer of finite height located above the center of the Stuart vortices.
Shear flow disturbance due to a hole in the plane
Authors: Davis A. M. J.
Published: July 2002

An exact solution, using pairs of dual integral equations that arise from mixed boundary conditions, is presented for the interaction, due to a circular hole in the bounding wall, of a shear flow with otherwise stationary fluid. Together with a suction-driven flow through the hole, this flow has been used by Yan, Acrivos, and Weinbaum [J. Fluid. Mech. (in press)] to asymptotically model fluid skimming and particle entrainment into a small circular side pore. The Cartesian velocity components and dynamic pressure can be quite simply expressed in terms of toroidal coordinates.
Evidence for solitary wave behavior in Marangoni–Bénard convection
Authors: Weidman P. D. , Linde H. , Velarde M. G.
Published: July 2002

Recent studies have elucidated the possibility of solitary wave behavior in Marangoni–Bénard instability flows. The present paper takes a look at experiments in both heat-transfer- and mass-transfer-driven Marangoni systems to discern nonlinear behavior of the type associated with solitary wave interactions. Direct observation of phase shifts incurred by two Marangoni waves having undergone a head-on collision are reported. Analysis of experiments exhibiting wave reflection at a solid wall and obliquely interacting waves in Marangoni instability flows also show remarkable similarities with nonlinear behavior in Korteweg–de Vries systems.
On the merging of double-diffusive convection cells at a vertical boundary
Authors: Kerr Oliver S.
Published: July 2002

When a body of fluid with a vertical salinity gradient is subjected to an increase in temperature at a vertical wall instabilities may form. These instabilities take the form of almost horizontal convection cells with a height scale of approximately H=‖αΔT‖/(−βS̄z), where ΔT is the instantaneous perturbation wall temperature, S̄z the vertical salinity gradient, and α and β are the coefficient of thermal expansion and the equivalent coefficient for salt. As the wall temperature increases further, these cells merge. At later times, experimental observations show that the average cell height is approximately 2/3H. A simple model of cell merging is presented in which the interfaces between cells remain fixed except when adjacent cells merge to form combined cells of height H, and, as a result, the average cell height is found to be 0.6805H, in reasonable agreement with observations.
A model for pattern selection in wake flows
Authors: Park D. S. , Redekopp L. G.
Published: July 2002

A model for the selection of vortex roll-up patterns in finite-aspect-ratio, two-dimensional wakes at low to moderate Reynolds number is studied. Two primary patterns are found: a chevron pattern encompassing the entire spanwise domain and one with regions adjacent to the side-wall boundaries, which are divorced from the central region by means of dislocation layers. These patterns can be understood in terms of spanwise-propagating phase waves, wave-number shocks, and the criterion for sustained global modes. Selection criteria for the frequency and scale of internal cells in the wake behind tapered cylinders are also discussed.
Buckling of a columnar vortex
Authors: Marshall J. S.
Published: July 2002

The instability of a columnar vortex under axial compression is studied analytically. Prediction of the change with time of an initial perturbation in the form of a small-amplitude helical wave on the vortex core is reduced to solution of a system of two linear, second-order ordinary differential equations. For small rates of compression, a closed-form asymptotic solution of these equations is obtained using a two-variable expansion in time. The results indicate that a vortex under compression may bend (or ‘‘buckle’’) or it may remain columnar with an increase in core radius. The choice of which of these possible outcomes will occur is found to depend on the value of a single dimensionless parameter given by the product of the wave number k of the helical perturbation and the radius σ of the vortex core. When kσ is greater than a critical value, found to be approximately 1.77, the perturbation amplitude will decrease with axial compression and no ‘‘buckling’’ will occur. When kσ is less than this critical value, the perturbation amplitude will increase as the vortex axis is compressed and ‘‘buckling’’ will be observed.
Unsteady force on a spherical bubble at finite Reynolds number with small fluctuations in the free-stream velocity
Authors: Mei Renwei , Klausner James F.
Published: July 2002

Unsteady flow over a stationary spherical bubble with small fluctuations in the free-stream velocity is considered for Reynolds number ranging from 0.1 to 200. Solutions to the Navier–Stokes equations of both steady and unsteady components are obtained using a finite-difference method and a regular perturbation scheme based on the amplitude of the fluctuations being small. The dependence of the unsteady drag on the frequency of the fluctuations is examined at finite Reynolds number. It is shown that the quasisteady drag can be represented by using the steady-state drag coefficient and the instantaneous velocity. Numerical results indicate that the unsteady force at low frequency, ω, increases linearly with ω rather than increasing linearly with ω1/2, which results from the creeping flow solution of the Stokes equation. The added-mass force at finite Reynolds number is found to be the same as in creeping flow and potential flow. The history force at finite Re is identified and carefully evaluated. The imaginary component of the history force increases linearly with ω when ω is small and decays as ω−1/2 as ω becomes large. The implication is that the history force has a much shorter memory in the time domain than predicted by the solution of the unsteady Stokes equation. Numerical results suggest that the history force, which is due to the combination of the viscous diffusion of the vorticity and the acceleration of the flow field, at low frequency is finite even at large Reynolds number.
Numerical simulations of three-dimensional natural transition in the compressible confined shear layer
Authors: Gathmann Ralf Jens , Si-Ameur Mohammed , Mathey Fabrice
Published: July 2002

The spatial supersonic shear layer in a rectangular channel is investigated by numerical simulation with the piecewise parabolic method, a high-order Godunov-type scheme. Both streams are supersonic with Mach number 4.5 and 1.6, respectively. A weak broadbanded noise is introduced at the inflow boundary and the growth of multiple unstable modes is observed. In order to extract detailed information from the computed data, the time-dependent flow field is Fourier transformed in time and in the spanwise direction. For a given frequency and a given spanwise wave number the complex eigenfunction and streamwise wave number can be compared to results from linear stability theory. This work aims at investigating in detail the limit of the linear development of the flow and to describe the transition to turbulence. In particular, this technique enables one to distinguish between oblique subsonic instabilities of the Kelvin–Helmholtz (KH) type and supersonic wall modes. A good agreement with linear stability theory is obtained in two and three dimensions until a characteristic streamwise distance is reached, where the flow becomes nonlinear. It is shown that it is mainly the oblique KH modes which are responsible for an increase in the spreading rate during transition and that the nonlinear regime in three dimensions is therefore essentially different from that in two dimensions. The most unstable mode in our configuration is a wall mode and the frequency spectra are largely dominated by the wall modes. However, it turns out that the transition is not governed by the wall modes, but by the oblique KH modes, which evolve into longitudinal streaks.
Skewed, exponential pressure distributions from Gaussian velocities
Authors: Holzer Mark , Siggia Eric
Published: July 2002

A simple analytical argument is given to show that the distribution function of the pressure and that of its gradient have exponential tails when the velocity is Gaussian. A calculation of moments implies a negative skewness for the pressure. Explicit analytical results are given for the case of the velocity being restricted to a shell in wave number. Numerical pressure distributions are presented for Gaussian velocities with realistic spectra. For real turbulent flows, one expects that the pressure distribution should retain exponential tails while the pressure gradients should develop stretched-exponential distributions. In the context of the theory, available numerical and laboratory data are examined for the pressure, along with data for the wall shear stress in a boundary layer.
A quiver-kinetic formulation of radio-frequency heating and confinement in collisional edge plasmas
Authors: Catto Peter J. , Myra J. R.
Published: July 2002

The near fields in the collisional edge plasma of a radio-frequency-heated tokamak can cause one or more charged species to oscillate in the applied field with a quiver (or jitter) speed comparable to its thermal speed. By assuming the quiver motion dominates over drifts and gyromotion a completely new kinetic description of the flows in an edge plasma is formulated that retains Coulomb collisions and the relevant atomic processes. Moment equations are employed to obtain a description in which only a lowest-order quiver-kinetic equation need be solved to evaluate the slow time particle fluxes and current induced by the applied fields. The electron heating by collisional randomization of their quiver motion (inverse bremsstrahlung) is balanced by impact excitation losses since equilibration with the ions is too weak. A model plasma of electrons, neutrals, and a single cold ion species is considered to illustrate the utility of the quiver-kinetic formulation. The model predicts local electrostatic potential changes and a local E×B convective flux that is of the same magnitude and scaling as would be predicted by Bohm diffusion.
Thermal diffusivity induced by resistive pressure-gradient-driven turbulence
Authors: Carreras B. A. , Diamond P. H.
Published: July 2002

The calculation of the thermal diffusivity induced by resistive pressure-gradient-driven turbulence is revisited. The relevant correlation length for the magnetic fluctuations is shown to be different from estimates made with a mixing-length approach and with dimensional analysis. This leads to different scaling predictions for the electron heat diffusivity. The root of this difference is the fact that the flux and current perturbations are related by two scale lengths, the poloidal wavelength and the mode width.
Resistive instabilities in a flowing plasma. II. Effects of viscosity
Authors: Einaudi Giorgio , Rubini Franco
Published: July 2002

The influence of kinematic viscosity on the properties of resistive instabilities developing in equilibrium configurations in which flows are present is examined. The cross-field viscosity (ν⊥ ) is retained in the linearized resistive magnetohydrodynamic equations, which are solved numerically. The magnetic and velocity equilibrium configurations are the same as those studied in a previous paper [Phys. Fluids 29, 2563 (1986)] neglecting viscosity, so that its effect can be easily studied in the present work. The results show that the inclusion of the viscosity changes the stability properties considerably when τν≤τr, and where τν and τr are the viscous and magnetic time scales, respectively. Depending on the relative importance of the velocity with respect to the Alfvén velocity and of the velocity scale length with respect to the magnetic one, the viscosity can have both a stabilizing and a destabilizing effect.
The coupling of stimulated Raman and Brillouin scattering in a plasma
Authors: Umstadter D. , Mori W. B. , Joshi C.
Published: July 2002

The observation of an anti-Stokes satellite in the spectrum of light backscattered from a CO2 laser plasma is reported. Its origin is found to be Thomson scattering of the incident light from a counterpropagating mode-coupled plasma wave. The parent electron and ion waves in the mode-coupling process were driven by stimulated Raman and Brillouin backscattering. The parent and daughter plasma waves were detected by ruby laser Thomson scattering. A computer simulation modeling the experiment shows further cascading of the Stokes backscattered light to lower frequencies, apparently a result of its rescattering from another, higher phase velocity, counterpropagating coupled mode. Comparisons with theoretical predictions are presented.
Effect of plasma noise spectrum on stimulated scattering in inhomogeneous plasma
Authors: Berger R. L. , Williams E. A. , Simon A.
Published: July 2002

The flux of radiation emitted from an inhomogeneous plasma by stimulated Raman and Brillouin scattering is calculated with a source that includes both bremsstrahlung and longitudinal plasma wave noise sources. Significant enhancement of the flux above that found for a bremsstrahlung source alone are found for stimulated Brillouin scattering and for nonthermal but stable velocity distributions.
Expanding plasma structure and its evolution toward long wavelengths
Authors: Sgro A. G. , Peter Gary S. , Lemons Don S.
Published: July 2002

The expansion of a plasma slab across an initially uniform magnetic field is simulated by the use of a two-dimensional electromagnetic hybrid (particle ions, fluid electrons of nonzero mass) computer code. The expanding plasma develops magnetic-field-aligned structure on time scales faster than an ion gyroperiod. Through the full duration of the mi/me =100 simulation, the structure wavelength is well predicted by the wavelength at maximum growth rate from the linear Vlasov theory of the lower hybrid drift instability modified by deceleration. At mi/me =400, the late time structure wavelength is about 1.5 times the early time value. At mi/me =1836, the structure wavelength at early times is close to that corresponding to the maximum growth rate of linear theory, while at later times the structure wavelength becomes about twice as long as its early time value. These three results suggest that the ratio of the late time wavelength to the early time value gradually increases with mi/me. Extrapolation of this scaling to larger mi/me values is consistent with structure wavelengths observed in an expanding aluminum plasma experiment [J. Appl. Phys. J. 20, 157 (1981)], as well as the observed wavelength in the expanding barium plasma of the AMPTE magnetotail experiment [J. Geophys. Res. 92, 5777 (1987)].
Experimental simulation of a gaseous plasma collector
Authors: Fiksel G. , Kishinevsky M. , Hershkowitz N.
Published: July 2002

Hydrogen plasma with a density of 3×1014 cm−3 and electron temperature of 20 eV is injected parallel to a 0.1 T B field, into hydrogen (and helium) neutral gas at 0.1–2 Torr. This plasma is opaque to molecular hydrogen but transparent to Franck–Condon neutrals. The axial density and temperature scale length increased with decreasing gas pressure but were insensitive to plasma density and axial magnetic field strength. The plasma decay is explained by radial ion diffusion resulting from collisions with fast neutrals while the fast neutral density is determined by the radial pressure balance between fast neutrals and the cold background gas.
Advances in the analytical theory of plasma turbulence and transport: Realizable Markovian statistical closures
Authors: Ottaviani M. , Bowman J. C. , Krommes J. A.
Published: July 2002

Explaining anomalous plasma transport in magnetic confinement devices requires a deeper understanding of the underlying turbulent processes than presently exists. In this work, Markovian closures are built by imposing the constraints of realizability, conservation of quadratic invariants, and covariance to arbitrary linear transformations. One such closure is solved numerically. The results compare favorably to the data available from numerical simulations.
The resistive tearing instability for generalized resistivity models: Applications
Authors: Birk G. T. , Otto A.
Published: July 2002

The dispersion relation for the resistive tearing mode is investigated with a general form of the resistivity that allows for evaluating the dependence of the mode on the anomalous dissipation caused by the lower-hybrid-drift turbulence and the ion-acoustic turbulence. The coupling of the plasma dynamic and radiative processes due to a temperature-dependent Spitzer resistivity are also discussed. The dispersion relation is solved numerically for two-dimensional equilibrium configurations with applications to the Earth’s magnetosphere and the solar corona. In the case of the parameter regimes of the magnetopause and the solar corona, growth rates that result in realistic time scales for the respective dynamic processes as flux transfer events and solar flares were found. Moreover, the influence of a nonvanishing component of the magnetic field normal to the current sheet on the dispersion relation is examined. The normal field component leads to overstable modes and the growth rate of the pure tearing mode is not altered, whereas the radiative tearing mode is damped effectively.