bluuebunny/crossref_metadata_2025 huggingface dataset:
An equilibrium supercooled liquid’s entropy and enthalpy in the Kauzmann and the third law extrapolations, and a proposed experimental resolution
Authors: Johari G. P.
Published: July 2002

In our current discussion of the thermodynamics and molecular kinetics of glass-forming liquids, the entropy is extrapolated below a liquid’s vitrification temperature Tg along a curve of progressively increasing slope until a temperature Tk is reached. Here the entropy and heat capacity, Cp, of the equilibrium liquid become equal to those of its crystal. Several observations have indicated fundamental difficulties with this extrapolation, thus suggesting the need for an alternative. We propose one alternative, in which Cp of an equilibrium liquid decreases along a sigmoid-shape path stretched over a broad temperature range from above Tg to 0 K. Its entropy and Cp become equal to those of its crystal at 0 K, as required by the third law of thermodynamics, and the enthalpy and volume remain higher. To elaborate, the available Cp data of 12 supercooled liquids have been interpolated between T>Tg and 0 K, and the enthalpy of their equilibrium state at 0 K, as well as the Gibbs free energy and enthalpy at T<Tg, determined. The enthalpy of the equilibrium liquid state at 0 K is 17%–37% of the enthalpy of melting, and for eight out of 12 liquids the Kauzmann extrapolation and our interpolation yield values within 5% of the average. Relative merits of the two resolutions of the entropy situation may be tested by the heat of solution, enthalpy loss and vapor pressure measurements of aged nonionic glasses and emf measurement of ionic glasses forming a half-cell of an electrochemical equilibrium. The anticipated enthalpy, Gibbs energy and vapor pressure change for the Kauzmann extrapolation of Cp and our interpolation are given at T<Tg for triphenylethene. As the equipment time needed for such measurements is only a few hours, such experiments may allow a study of the time-dependent thermodynamics of a glass more conveniently than other experiments.
Spectroscopic and ab initio investigation of the νOH overtone excitation in trans-formic acid
Authors: Hurtmans D. , Herregodts F. , Herman M. , Liévin J. , Campargue A. , Garnache A. , Kachanov A. A.
Published: July 2002

Fourier transform spectroscopy and intracavity laser absorption spectroscopy are used to record the absorption spectrum of formic acid at high spectral resolution, in the ranges of the 2νOH (6968.258 cm−1) and 4νOH (13 284.075 cm−1) vibrational bands of the trans-rotamer, respectively. Numerous perturbations combined with a large line density limit the extent to which the vibration–rotation analysis is performed. Some 689 lines are assigned in the first overtone band and related vibration–rotation constants are determined. Only the band origin and upper state principal A-rotational constant are determined for the n=4 overtone band, because of much higher spectral density. Interpolation, helped by literature data, provides all missing principal rotational constants in the nOH series, for n=1 to 4. All major vibration–rotation parameters appear to evolve very smoothly along the series. This trend is fully supported by ab initio calculations performed at the MP2/cc-pVTZ level of theory and based on an effective one-dimensional model describing the OH local mode stretching vibration. Results of these calculations are detailed in terms of the mean nuclear structure in the excitation series, up to n=4. The related calculated dipole moment surface allows the experimental a:b subband intensity ratio in the series to be interpreted in terms of a decrease in the HOC angle, from Θ≈90° (n=1) to 44°(n=4). The potential occurrence of a proton exchange mechanism between the two oxygen nuclei, close to a tautomerism mechanism, is discussed.
Si–H bending modes as a probe of local chemical structure: Thermal and chemical routes to decomposition of H2O on Si(100)-(2×1)
Authors: Weldon M. K. , Queeney K. T. , Gurevich A. B. , Stefanov B. B. , Chabal Y. J. , Raghavachari Krishnan
Published: July 2002

Surface infrared spectroscopy and density functional cluster calculations are used to study the thermal and atomic hydrogen-induced decomposition of water molecules on the clean Si(100)-(2×1) surface. We report the first observation of the Si–H bending modes associated with the initial insertion of oxygen into the dimer and backbonds of a silicon dimer. We find that, while one and two oxygen-containing dimers are formed almost simultaneously during the thermal decomposition of water on this surface, atomic H can be used to drive the preferential formation of the singly oxidized dimer. This work highlights the sensitivity of Si–H bending modes to the details of local chemical structure in an inhomogeneous system, suggesting that the combined experimental and theoretical approach demonstrated herein may be extremely useful in studying even more complex systems such as the hydrogenation of defects in SiO2 films.
Bi-Hamiltonian formulation of the Kadomtsev–Petviashvili and Benjamin–Ono equations
Authors: Fokas A. S. , Santini P. M.
Published: July 2002

It was shown recently that the Kadomtsev–Petviashvili (KP) equation (an integrable equation in 2+1, i.e., in two-spatial and one-temporal dimensions) admits a bi-Hamiltonian formulation. This was achieved by considering KP as a reduction of a (3+1)-dimensional system (in the variables x,y1, y2,t). It is shown here, using the KP as a concrete example, that equations in 2+1 possess two bi-Hamiltonian formulations and two recursion operators. Both Hamiltonian operators associated with the x direction are local; in contrast only one of the Hamiltonian operators associated with the y direction is local. Furthermore, using the Benjamin–Ono equation as a concrete example, it is shown that intergrodifferential equations in 1+1 admit an algebraic formulation analogous to that of equations in 2+1.
The geometry of the space of null geodesics
Authors: Low R. J.
Published: July 2002

The topology and geometry of the space of null geodesics N of a space-time M are used to study the causal structure of the space-time itself. In particular, the question of whether the topology of N is Hausdorff or admits a compatible manifold structure carries information on the global structure of M, and the transversality properties of the intersections of skies of points tell whether the points are conjugate points on a null geodesic.
Local differential geometry of null curves in conformally flat space-time
Authors: Urbantke H.
Published: July 2002

The conformally invariant differential geometry of null curves in conformally flat space-times is given, using the six-vector formalism, which has generalizations to higher dimensions. This is then paralleled by a twistor description, with a twofold merit: first, sometimes the description is easier in twistor terms and sometimes in six-vector terms, which leads to a mutual enlightenment of both; and, second, the case of null curves in timelike pseudospheres or 2+1 Minkowski space could only be treated twistorially, making use of an invariant differential found by Fubini and Čech [Geometria Proiettiva Differenziale (Zanichelli, Bologna, 1926), Vol. 1; Introduction à la Géométrie Projective Differentielle des Surfaces (Gauthier–Villars, Paris, 1931)]. The result is the expected one: apart from the stated exceptional cases there is a conformally invariant parameter and two conformally invariant curvatures that, when specified in terms of this parameter, serve to characterize the curve up to conformal transformations.
Chern–Simons forms on principal superfiber bundles
Authors: Bartocci Claudio , Bruzzo Ugo , Landi Giovanni
Published: July 2002

A graded Weil homomorphism is defined for principal superfiber bundles and the related transgression (or Chern–Simons) forms are introduced. As an example of the application of these concepts, a ‘‘superextension’’ of the Dirac monopole is discussed.
Cosmic censorship and pseudoconvexity
Authors: Beem John K. , Krolak Andrzej
Published: July 2002

It is shown that conditions of causal simplicity and pseudoconvexity are closely related. It is proved that under certain reasonable conditions space-time is maximally null pseudoconvex. It is indicated that pseudoconvexity may play the role of global hyperbolicity even though it is a weaker condition. Consequently, obtained results provide some tentative evidence for the validity of the cosmic censorship hypothesis.
The unified approach to integrable relativistic equations: Soliton solutions over nonvanishing backgrounds. II
Authors: Barashenkov I. V. , Getmanov B. S.
Published: July 2002

In Part I of this work the N-soliton solution has been constructed for the generic system associated with the sl(2,C) case of the scheme for the unified description of integrable relativistic massive fields. Here, solutions are isolated for reductions of this system, including the (conventional) complex sine-Gordon equation, the massive Thirring model and another complexification of the sine-Gordon equation defined by the Lagrangian L= ‖∂μφ‖2/1−‖φ‖2 +‖φ‖2−J 2μ/2‖φ‖2(1−‖φ‖2) , Jμ=i(φ*∂μφ−φ∂μφ*). The latter model is shown to exhibit decays and fusion of (subluminal) solitons. The reduction to the conventional complex sine-Gordon appears to be even more interesting as it cannot be defined by simply restricting the linear problem to some real form of sl(2,C) algebra, and the relevant involution turns out to be quite nontrivial. When the background is flat, this involution degenerates and so the N-kink solution for the reduction cannot be extracted from the generic N-kink solution directly. This difficulty is bypassed by seeing the flat background case as a limit of an exponential one.
On exact solutions of the regularized long-wave equation: A direct approach to partially integrable equations. I. Solitary wave and solitons
Authors: Parker A.
Published: July 2002

Hitherto, the bilinear transformation method has been used to obtain analytic solutions of completely integrable (or nonlinear evolution) equations. In this first of two studies (designated I and II), it is shown that the method may apply equally well to those nonlinear wave equations dubbed partially integrable. Here the regularized long-wave (RLW) and RLW Boussinesq (RLWB) equations are considered as examples. In each case, the bilinear form is found to have an ‘‘extra’’ equation which would appear to signal their nonintegrability. Their solitary-wave solutions are reconstructed and the nonexistence of multisoliton solutions is demonstrated. The present work provides the basis for the construction of periodic solutions in II.
Helicity conservation via the Noether theorem
Authors: Yahalom Asher
Published: July 2002

The conservation of helicity in ideal barotropic fluids is discussed from a group theoretical point of view. A new symmetry group is introduced, i.e., the alpha group of translations. It is proven via the Noether theorem that this group generates helicity conservation.
Asymptotic algebra for charged particles and radiation
Authors: Herdegen Andrzej
Published: July 2002

A C*-algebra of asymptotic fields which properly describes the infrared structure in quantum electrodynamics is proposed. The algebra is generated by the null asymptotic of electromagnetic field and the time asymptotic of charged matter fields which incorporate the corresponding Coulomb fields. As a consequence Gauss’ law is satisfied in the algebraic setting. Within this algebra the observables can be identified by the principle of gauge invariance. A class of representations of the asymptotic algebra is constructed which resembles the Kulish–Faddeev treatment of electrically charged asymptotic fields.
Exact interaction of solitary waves for certain nonintegrable equations
Authors: Liu Q. M. , Fokas A. S.
Published: July 2002

Physically interesting exact solutions are constructed for a large class of nonlinear nonintegrable evolution equations. These solutions describe the interaction of traveling waves. They exhibit rich phenomenology including breaking of solitary waves. Generalized conditional symmetries and bilinearity are used to derive these exact results.
Groupoid approach to noncommutative quantization of gravity
Authors: Heller Michael , Sasin Wiesław , Lambert Dominique
Published: July 2002

We propose a new scheme for quantizing gravity based on a noncommutative geometry. Our geometry corresponds to a noncommutative algebra A=Gc∞(G,C) of smooth compactly supported complex functions (with convolution as multiplication) on the groupoid G=E◃Γ being the semidirect product of a structured space E of constant dimension (or a smooth manifold) and a group Γ. In the classical case E is the total space of the frame bundle and Γ is the Lorentz group. The differential geometry is developed in terms of a Z(A)-submodule V of derivations of A and a noncommutative counterpart of Einstein’s equation is defined. A pair (A,Ṽ), where Ṽ is a subset of derivations of A satisfying the noncommutative Einstein’s equation, is called an Einstein pair. We introduce the representation of A in a suitable Hilbert space, by completing A with respect to the corresponding norm change it into a C*-algebra, and perform quantization with the help of the standard C*-algebraic method. Hermitian elements of this algebra are interpreted as quantum gravity observables. We introduce dynamical equation of quantum gravity which, together with the noncommutative counterpart of Einstein’s equation, forms a noncommutative dynamical system. For a weak gravitational field this dynamical system splits into ordinary Einstein’s equation of general relativity and Schrödinger’s equation (in Heisenberg’s picture) of quantum mechanics. Some interpretative questions are considered.
Coexistent observables and effects in a convexity approach
Authors: Lahti Pekka , Pulmannova Sylvia , Ylinen Kari
Published: July 2002

We characterize functionally coexistent observables in terms of biobservables and joint observables. Coexistent sets of effects are characterized in terms of projective systems of simple observables.
Product integral formalism and non-Abelian Stokes theorem
Authors: Karp Robert L. , Mansouri Freydoon , Rno Jung S.
Published: July 2002

We make use of the properties of product integrals to obtain a surface product integral representation for the Wilson loop operator. The result can be interpreted as the non-Abelian version of Stokes’ theorem.
Noncommutative geometry and fundamental physical interactions: The Lagrangian level—Historical sketch and description of the present situation
Authors: Kastler Daniel
Published: July 2002

These notes comprise (i) a descriptive account of the history of the subject showing how physics and mathematics interwove to develop a mathematical concept of quantum manifold relevant to elementary particle theory; (ii) a detailed technical description, from scratch, of the spectral action formalism and computation.
Reference Data for the Thermal Conductivity of Saturated Liquid Toluene Over a Wide Range of Temperatures
Authors: Ramires Maria L. V. , Nieto de Castro Carlos A. , Perkins Richard A. , Nagasaka Yuchi , Nagashima Akira , Assael Marc J. , Wakeham William A.
Published: July 2002

Efficient design of industrial processes and equipment requires accurate thermal conductivity data for a variety of fluids, such as alternative refrigerants, fuels, petrochemicals, aqueous systems, molten salts, and molten metals. The accuracy of experimental thermal conductivity data is a function of the operating conditions of the instrument. Reference data are required over a wide range of conditions to verify the claimed uncertainties of absolute instruments and to calibrate relative instruments, since either type may be used to measure the thermal conductivity of fluids. Recently, accurate experimental data for the thermal conductivity of liquid toluene near the saturation line have been obtained, which allow the upper temperature limit of the previous reference-data correlation to be extended from 360 to 553 K. The thermal conductivity was measured using two transient hot-wire instruments from 300 to 550 K, the first with a bare 12.7 μm platinum wire and the second using an anodized 25 μm tantalum wire. Uncertainties due to the contribution of thermal radiation and the purity of the samples are discussed. The proposed value of the thermal conductivity of liquid toluene at 298.15 K and 0.1 MPa is 0.13 088±0.000 85. The quality of the data is such that new improved recommendations and recommended values can be proposed with uncertainties at 95% confidence of 1% for 189 <T< 440 K, 1.5% for 440 <T< 480 K, and 2% for 480 <T< 553 K, near the saturation line.
Diffusion of hydrogen in rare gas solids: neutral H atoms and H+ protons
Authors: Beyer M. , Savchenko E. V. , Niedner-Schatteburg G. , Bondybey V. E.
Published: July 2002

In this letter we review and compare the available information about the stability and spectroscopy of the hydrogen atoms and protons in rare-gas solids. Mechanism of the H+ diffusion involving protonated rare-gas dimer Rg2H+ formation in the lattice is discussed. We suggest that the puzzling differences in their behavior and the stability are due to the fact that diffusion of hydrogen atoms is thermally activated, while that of the protons is activated by vibrational excitation of the Rg2H+ under ambient temperature blackbody radiation.
Effect of superconducting transition on the low-temperature jumplike deformation of metals and alloys (Review)
Authors: Pustovalov V. V.
Published: July 2002

The available experimental data on the effect of the superconducting transition on the low-temperature jumplike deformation of metals and alloys are examined. Different hypotheses as to the mechanism for this effect are stated and compared with experiment. The experimental and theoretical papers on the low-temperature jumplike deformation are discussed, and conjectures as to the mechanism for the effect are set forth.
Oscillatory flow in a curved annular pipe
Authors: Karahalios George T. , Panagopoulos Alkis
Published: July 2002

A theoretical study of oscillatory flow in a curved annular pipe is presented. The equations of motion are expanded in powers of a nondimensional radius ratio ε and the linearized equations are solved for the cases of small and large frequency parameter α. It is shown that the presence of the axial core affects essentially the flow and the wall shear stress. In addition, and only when α is large, the secondary flow exhibits a large number of vortices, depending on the phase and on the size of the annular gap.
On the interaction of vortex rings and pairs with a free surface for varying amounts of surface active agent
Authors: Bernal L. P. , Hirsa A. , Kwon J. T. , Willmarth W. W.
Published: July 2002

Observations are reported of the interaction with a free surface of vortex rings and vortex pairs moving normal to the surface when different amounts of surface active agents are present on the surface. At a vortex ring Reynolds number Γ/ν≈3800, the interaction with a contaminated free surface results in the generation of secondary and tertiary vortex rings that limited the outward motion of the vortex ring core. When the experiment was repeated with a cleaner surface the formation of the secondary vortex ring was delayed so that the outward motion and stretching of the vortex ring core was much more than for the contaminated surface. At a Reynolds number Γ/ν≈18 000, the vortex pair was observed to rebound from the free surface contrary to what one would expect for an inviscid flat boundary. When the surface was cleaned by draining away a portion of the contaminated surface water the amount of rebound was reduced. These changes in interaction are believed to be caused by the reduction in concentration of the surface active agent which, in turn, results in a reduced generation of secondary vorticity ahead of the vortex ring or pair before and during the interaction with the surface.
An experimental study of the effect of suspension concentration on the stability and efficiency of inclined settlers
Authors: Borhan A.
Published: July 2002

Observations of the instability wave growth in a series of continuously operated low and high aspect-ratio inclined settling experiments are reported. The effect of wave rollover and breakup on the efficiency of operation of such devices is also examined through measurements of the contamination of the clarified overflow product. The general trends of the stability and efficiency in low aspect-ratio settlers are found to be consistent with those set forth by the linear stability analysis of Borhan and Acrivos [Phys. Fluids 31, 3488 (1988)]. In particular, settler stability and efficiency are enhanced with increasing suspension concentration and fluid viscosity. It is also shown that high aspect-ratio inclined settlers not only provide the largest enhancement in the settling rate but are also more stable and efficient than their low aspect-ratio counterparts.
The tuning of a splash
Authors: Shin Jordan , McMahon Thomas A.
Published: July 2002

A water drop falling into a shallow pool of water can give rise to a splash that ejects droplet fragments high into the air. The height reached by the highest-flying ejected droplet is greatest when the depth of the target liquid is equal to the radius of the hemispherical crater formed by the impact of the incident drop. This phenomenon, referred to here as the tuning of a splash, is still observed when liquids of very different viscosity and surface tension are substituted for water, but a thin sponge layer cemented over the floor of the pan all but destroys the tuning behavior. Cine images reveal a possible explanation for the tuning phenomenon based on a delay of the upward retraction of the collapsing crater.
Core instability of the spanwise vortices in a plane mixing layer
Authors: Nygaard Kris J. , Glezer Ari
Published: July 2002

A spanwise core instability of the primary vortices in a plane mixing layer has been identified as a viable mechanism for the generation of streamwise vortical structures far downstream of the flow partition. The core instability is excited by a time-harmonic wave train with spanwise phase variation, synthesized by a mosaic of individually controlled surface heaters flush mounted on the flow partition. The flow is visualized in planes of constant cross-stream elevation by means of a schlieren system. As a result of the forcing, the primary vortices undergo spanwise deformations that induce secondary vortical structures, the shape and strength of which depends on the magnitude of the prescribed spanwise phase variation. The appearance of small-scale structures within the large coherent vortices suggests that core instability is an important contributor to mixing.
Lagrangian and Eulerian statistics obtained from direct numerical simulations of homogeneous turbulence
Authors: Squires Kyle D. , Eaton John K.
Published: July 2002

Lagrangian statistics have been obtained from direct numerical simulations of isotropic turbulence and homogeneous shear flow. Quantities presented include properties of the dispersion tensor 〈Xi(t)Xj(t)〉, isoprobability contours of particle displacement, Lagrangian and Eulerian velocity autocorrelations and time scale ratios, and the eddy diffusivity tensor. The dispersion measurements from the simulations of isotropic turbulence are in good agreement with those of Warhaft [J. Fluid Mech. 144, 363 (1984)] and Stapountzis et al. [J. Fluid Mech. 165, 401 (1986)]. ‘‘Integral’’ time scales were defined as the time required for the temporal correlations to decrease to 1/e of their initial value. The ratio of TeL/TeE from the simulations of isotropic turbulence was approximately 0.8, in good agreement with the data of Sato and Yamamoto [J. Fluid Mech. 175, 183 (1987)]. The principal angle of 〈Xi(t)Xj(t)〉 from the shear flow simulations shows reasonable agreement with a similar study done by Riley (Ph.D. dissertation, The Johns Hopkins University, Baltimore, 1971). The Lagrangian time microscale was found to be consistently larger than the Eulerian microscale, presumably due to the advection of the small scales by the large scales in the Eulerian reference frame. A comparison made between the measured diffusivity tensor and measurements of Tavoularis and Corrsin [Int. J. Heat Mass Transfer 28, 265 (1985)] show reasonable agreement.
Nonparallel instability of supersonic and hypersonic boundary layers
Authors: El-Hady Nabil M.
Published: July 2002

Multiple scaling technique is used to examine the nonparallel instability of supersonic and hypersonic boundary-layer flows to three-dimensional (first mode) and two-dimensional (second mode) disturbances. The method is applied to the flat plate boundary layer for a range of Mach numbers from 0 to 10. Growth rates of disturbances are calculated based on three different criteria: following the maximum of the mass-flow disturbance, using an integral of the disturbance kinetic energy, and using an integral of the square of the mass-flow amplitude. By following the maximum of the mass-flow disturbance, the calculated nonparallel growth rates are in good quantitative agreement with the experimental results of Kendall at Mach number 4.5.
Development of singular solutions to the axisymmetric Euler equations
Authors: Pumir Alain , Siggia Eric D.
Published: July 2002

A variety of initially smooth axisymmetric flows with swirl are simulated with a variable mesh, finite-difference code with particular attention paid to the production of large (divergent) vorticity. Away from the symmetry axis, the evolution is entirely consistent with expectations based on the isomorphism with two-dimensional convection. Vortex sheets form on the leading face of ‘‘plumes’’ and their trailing edges roll up. When a ‘‘plume’’ begins to fission, a cusp develops at the cleavage point via a Rayleigh–Taylor-like instability and the maximum (three-dimensional) vorticity diverges, approximately, as inverse time squared. For technical reasons, the Boussinesq approximation was employed for this part of the simulation which observed, overall, a 106 increase in vorticity. The diverging strain was generated progressively more locally, justifying the approximation. Analytic estimates are provided which significantly constrain the singular solutions.
Measurement of the diffusion coefficient in a heated plane airstream
Authors: Pemha E. , Gay B. , Tailland A.
Published: July 2002

In order to measure the diffusion coefficient of a heated plane airstream, a single laser beam is passed through the jet, perpendicularly to the flow direction. The thermic turbulence in the airstream causes random fluctuations of the refractive index. Consequently, the beam direction undergoes, in the flow, random perturbations. After having traversed the jet, the beam produces a luminous trace on a photoelectric cell placed outside the jet. An experimental setup for measuring the probabilities of the beam impact positions on the cell is described. From the Markovian process model, applied along the whole random path of the beam, it has been possible to compute these probabilities by solving the Einstein–Fokker–Kolmogorov equation. The diffusion coefficient can be determined by adjusting the numerical solution to agree with the experimental results. In addition, the calculation procedure gives the order of magnitude of an integral scale, characterizing the dimension of the turbulent structures in which the propagation of light can be considered rectilinear. A good agreement between the results and the published data obtained by means of the cold-wire anemometer technique proves the validity of the method.
An experimental investigation of vortex motions near surfaces
Authors: Chu Chin-Chou , Wang Chi-Tzung , Hsieh Chang-Shyue
Published: July 2002

Laminar vortex rings approaching a solid planar surface and a free surface have been investigated experimentally over the range of Reynolds numbers based on the circulation, ReΓ, from 900 to 2350. The emphasis is on the process of vortex stretching, induction of boundary layer on the surface, formation of secondary vortices, and rebounding of the primary vortex ring. Detailed measurements were made using laser-induced photochemical anemometry (LIPA), a nonintrusive visualization technique which enables multipoint simultaneous measurement of the unsteady velocity field. Results show that enstrophy, rather than circulation, clearly signifies three stages of the behavior of the primary vortex ring—free-traveling stage, vortex stretching stage, and vortex rebounding stage. Although the flow phenomena are very similar when a vortex ring approaches a solid surface or a slightly contaminated free surface, the difference between the induced boundary layers under two surface conditions is obvious in terms of the circulation and the enstrophy. In addition, the surface deformation and subsequent surface waves resulting from the impacting vortex ring on the contaminated free surface are also discussed. The present study provides a basis for validation and comparison with numerical simulations.
Reynolds stress description of opposed and impinging turbulent jets. Part I: Closely spaced opposed jets
Authors: Champion Michel , Libby Paul A.
Published: July 2002

The flow arising from two, closely spaced turbulent jets flowing counter to one another is analyzed for both two-dimensional and axisymmetric configurations. By closely spaced it is indicated that the diameter of the jets is large compared to their separation distance. Two parameters, one a measure of the integral scale of the turbulence compared with half the separation distance of the jets, and a second, a measure of the intensity of the turbulence issuing from the jets, are assumed small and form the basis of an asymptotic analysis. As a consequence, the mean velocity components are given by the mean Euler equations, except in a thin layer that is centered about the plane containing either the stagnation line or point and within which discontinuities in the flow from each jet are adjusted. Thus, outside of this layer, the turbulence characteristics in a known mean velocity field are determined, in the present study, in terms of a Reynolds stress description. The rate of strain field associated with the stagnating flow results in anisotropy of the turbulence as the plane containing the stagnation line or point is approached. Differences in the mean velocities in two-dimensional and axisymmetric configurations result in significant differences in the evolution of the gradient of the Reynolds shear stress from the exit planes of the jets and thus in the thin layer at the stagnation plane. For two-dimensional flows, the velocity characteristics in the thin layer satisfy to lowest order in an expansion parameter the requisite symmetry conditions, whereas this is not the case for axisymmetric flows. The temperature in the two streams is assumed to be slightly different but uniform so that there is also a thermal layer at the stagnation plane. Comparison is made with the applicable experimental data for the mean velocity and the turbulence intensities with good and reasonable agreement, respectively.
The pressure moments for two rigid spheres in low-Reynolds-number flow
Authors: Jeffrey D. J. , Morris J. F. , Brady J. F.
Published: July 2002

The pressure moment of a rigid particle is defined to be the trace of the first moment of the surface stress acting on the particle. A Faxén law for the pressure moment of one spherical particle in a general low-Reynolds-number flow is found in terms of the ambient pressure, and the pressure moments of two rigid spheres immersed in a linear ambient flow are calculated using multipole expansions and lubrication theory. The results are expressed in terms of resistance functions, following the practice established in other interaction studies. The osmotic pressure in a dilute colloidal suspension at small Péclet number is then calculated, to second order in particle volume fraction, using these resistance functions. In a second application of the pressure moment, the suspension or particle-phase pressure, used in two-phase flow modeling, is calculated using Stokesian dynamics and results for the suspension pressure for a sheared cubic lattice are reported.
Probability distribution functions in turbulent flows and shell models
Authors: Biferale Luca
Published: July 2002

In the multifractal framework some recent results [Phys. Rev. Lett. 67, 2295 (1991)] on the probability distribution functions (pdf) in fully developed turbulence are reviewed, for the increments of the velocity field in the inertial range and for transversal gradients. New comparisons are also produced, in the same scenario, with clusters of isogradients and with pdf evaluated from a numerical simulation of a shell model. The Reynolds dependence of the flatness in the multifractal model is discussed.
The optical analogy for vector fields
Authors: Parker E. N.
Published: July 2002

This paper develops the optical analogy for a general vector field F(r), noting that the projection Fs of F onto any surface locus S of ∇×F can be expressed as the gradient of a scalar, Fs=−∇φ. It follows that the field lines of Fs pass across S as if refracted by an index of refraction ‖Fs‖. A sufficiently localized maximum in ‖Fs‖ refracts the field so as to produce a gap in the field pattern in S, with the field bifurcating and passing around the sides, rather than across, the maximum. Such a disruption of the field pattern produces a discontinuity in F. The optical analogy allows the examination of certain aspects of a vector field that are not otherwise readily accessible. In particular, in the cases of a stationary Eulerian flow v of an ideal fluid and a magnetostatic field B, the vectors v and B have surface loci in common with their curls. The intrinsic discontinuities around local maxima in ‖v‖ and ‖B‖ take the form of vortex sheets and current sheets, respectively, the former playing a fundamental role in the development of hydrodynamic turbulence and the latter playing a major role in heating the x-ray coronas of stars and galaxies.
Stability theorem for off-axis states of a non-neutral plasma column
Authors: O’Neil Thomas M. , Smith Ralph A.
Published: July 2002

A sufficient condition is given for the stability of a long non-neutral plasma column that obeys two-dimensional E×B dynamics. The column is confined by a uniform magnetic field and bounded by a conducting cylinder aligned with the field. The variational approach used here generalizes the well-known stability of a centered, axisymmetric column, whose density is a monotonically decreasing function of radius. Displacement of such a column away from the axis by excitation of an l=1 diocotron mode yields a dynamical equilibrium stationary in a frame rotating with the mode. This new equilibrium is shown to be stable if the column is not too large. The analysis may explain, in part, the remarkable longevity observed for l=1 diocotron modes in experiments.
Experiments on impulsive spin-down to rest
Authors: Mathis D. M. , Neitzel G. P.
Published: July 2002

Experiments were performed to determine the stability characteristics of impulsive spin-down to rest in a circular cylinder of moderate aspect ratio. The characteristics measured include the onset time, onset wavelength, and time history of the wavelength for the Taylor–Görtler instability, as well as the global stability limit of the apparatus. Results compare favorably with earlier theoretical, numerical, and experimental investigations.
Channel cooling by turbulent convective mixing
Authors: Greig J. R. , Pechacek R. E. , Raleigh M.
Published: July 2002

Results from a series of experiments are described which show that hot, reduced-density channels in the atmosphere usually cool by a process of turbulent convective mixing. Five different types of channels were created: (a) by the interaction of a pulsed CO2 laser with aerosols in the atmosphere, (b) by electric discharges in the atmosphere, (c) by laser-guided electric discharges in the atmosphere, and (d) and (e) by the absorption of CO2 laser radiation in nitrogen doped with sulfur hexafluoride. For channels in which the energy deposition was almost cylindrically symmetric and axially uniform, (e), the rate of cooling, after reaching pressure equilibrium, was within an order of magnitude of thermal conduction. But for channels in which the energy deposition was asymmetric and/or axially nonuniform, the rate of cooling was typically one thousand times faster than thermal conduction (for channels whose radius at pressure equilibrium was ∼1 cm). These channels were seen to be turbulent and to cool by mixing cold surrounding air into the hot channel. Such turbulence has been explained by Picone and Boris [Phys. Fluids 26, 365 (1983)] in terms of a residual vorticity that is caused by the noncylindrical energy deposition. A simple empirical formula is deduced relating the rate of cooling (growth of channel envelope) to the radius of the channel at pressure equilibrium and to the ambient sound speed, which indicates that the effect of vorticity/turbulence saturates for variations in the energy deposition of greater than about 2 to 1.
Resonance absorption in a microwave plasma interaction
Authors: Lee Ann Y. , Nishida Y. , Luhmann N. C. , Randall C. , Rhodes M. , Obenschain S. P.
Published: July 2002

A detailed study of resonance absorption and the resultant plasma wave electric field evolution is reported. At sufficiently low input power levels, convective saturation of the localized electric field is observed. At higher input power levels, wave-breaking saturation begins, resulting in hot electron production. The transition from the convective to the wave breaking regime occurred at much lower powers than expected. The temporal and spatial evolution of the harmonic fields of the excited plasma wave as well as the quasisteady magnetic field were also investigated and compared with existing theories.
Trajectories of charged particles traversing a plasma sheath in an oblique magnetic field
Authors: DeWald A. B. , Bailey A. W. , Brooks J. N.
Published: July 2002

A particle-in-cell technique is used to model a plasma sheath in which the magnetic field intersects the surface at an oblique angle. The angle of impact of deuterium and impurity ions striking the surface is examined and found to depend on the relative sizes of the ion gyroradii and the Debye length.
Turbulent magnetic diffusion and magnetic field reversal
Authors: Hameiri Eliezer , Bhattacharjee A.
Published: July 2002

The behavior of compressible plasmas caused by small fluctuations superimposed on slowly varying profiles is investigated self-consistently within the framework of resistive magnetohydrodynamics. The effect of the fluctuations is shown to be the generation of an additional ‘‘eddy’’ resistivity, and not of a dynamo. This effect, nevertheless, suffices to explain magnetic field reversal in pinches. The functional form of the turbulent resistivity is derived from the dynamics of the fluctuations, taken as a bath of local and global modes that are believed to be responsible for field reversal. It is shown that the fluctuations tend to flatten the pressure and parallel current profiles and thus produce plasmas near a ‘‘Taylor state.’’
A criterion for vortex breakdown
Authors: Spall R. E. , Gatski T. B. , Grosch C. E.
Published: July 2002

A criterion for the onset of vortex breakdown over a wide range of the Reynolds number is proposed. Based upon previous experimental, theoretical, and numerical studies, as well as a new numerical study, an appropriately defined local Rossby number is used to delineate the region where breakdown occurs. Comparisons are made with previously suggested criticality parameters and the unique features of the proposed Rossby number parameter are shown. A number of previous theoretical studies concentrating on inviscid standing-wave analyses for trailing wing-tip vortices are reviewed and reinterpreted, along with the previous numerical and experimental studies, in terms of the Rossby number parameter. For the case of trailing wing-tip-type vortices, it is shown that previous numerical studies were performed at lower Reynolds numbers than the corresponding laboratory experiments. Utilizing a consistently defined Reynolds number, Rossby number–Reynolds number plots of these previous vortex breakdown studies, for both trailing wing-tip and leading-edge vortices, are obtained. A criticality condition is identified for both types of vortices.
Experimental observations of the tearing of an electron current sheet
Authors: Gekelman W. , Pfister H.
Published: July 2002

A neutral magnetic sheet, in which the current is carried mainly by the electrons, is set up in a laboratory plasma. By forcing the current through a thin slot, the ratio of the length to height t of the sheet may be varied; the current is observed to tear when t≳30. The structure of the magnetic islands and their associated currents is fully three dimensional, although a linear two-dimensional theory gives a very good estimate of the tearing mode growth time. Tearing is accompanied by the generation of significant Hall currents, and magnetic disturbances are observed to propagate at the whistler wave speed.
The effects of optical smoothing techniques on filamentation in laser plasmas
Authors: Schmitt Andrew J.
Published: July 2002

The effect of the induced spatial incoherence (ISI) and the random phase screen (RPS) optical smoothing techniques on the filamentation instability in laser plasmas has been investigated numerically and analytically. A two-dimensional time-dependent laser–plasma propagation code, including both ponderomotive and thermal-conduction dominated filamentation, is used to simulate the laser–plasma interaction. The results of these simulations are compared to the predictions of a simple theory that describes the filamentation of both coherent light and spatially and temporally incoherent light. It is shown that filaments driven by the thermal mechanism tend to cluster together and produce greater large scale nonuniformities in the laser illumination than the ponderomotively driven filaments. The RPS optical smoothing technique is found to reduce filamentation only if fast focusing optics (f/♯≲5) are used. The ISI smoothing method suppresses filamentation for fast or slow focusing optics, and requires only moderate laser bandwidth (Δω/ω≂0.1%). In general, the ISI smoothing method provides the best suppression of filamentation. Under common laboratory conditions, filamentation is pronounced at longer laser wavelengths (1.06 μm–0.53 μm), suggesting that current experiments may be dominated by filamentation effects. Optical smoothing methods can suppress, but not eradicate, filamentation effects at these wavelengths. The optical smoothing methods are most effective in short-wavelength (0.25 μm) laser-driven plasmas. At 0.25 μm laser wavelength, ISI is found to completely eliminate filamentation effects in both time-averaged and instantaneous intensity distributions.
Rayleigh–Taylor and shear driven mixing with an unstable thermal stratification
Authors: Snider Dale M. , Andrews Malcolm J.
Published: July 2002

A new water channel experiment has been used to study turbulent mixing driven by buoyancy, and by combined buoyancy and shear. Density differences were produced by thermal stratification. The experiment was statistically steady, and a space–time transformation in the streamwise direction permitted a continuous study of the mixing evolution. Dye and digitized photographs were used to study the mixing process. An ensemble average of images gave the average mixing layer growth rate and the distribution of light and heavy fluid in the mixing layer. The structure of the early growth of buoyancy dominated mixing and of combined shear and buoyancy mixing is presented. The mixing transition from combined shear and buoyancy mixing to buoyancy dominated mixing occurred at Richardson numbers from −5 to −11. It was found that buoyancy dominated a self-similar mixing stage for the range of flows (ΔU=0 to 2 cm/s) and density differences (Δρ=0.38 to 2.4 kg/m3). Transition to self-similar mixing occurred at a Reynolds number from 670 to 1200. The self-similar mixing width for all tests had a quadratic growth rate with an average acceleration constant of 0.070 and a standard deviation of 0.011.
Interaction between short-scale Marangoni convection and long-scale deformational instability
Authors: Golovin A. A. , Nepomnyashchy A. A. , Pismen L. M.
Published: July 2002

Nonlinear evolution of two interacting modes of the Marangoni convection, a long-scale deformational mode and a short-scale stationary convective pattern, is considered. It is shown that the interaction between modes stabilizes surface deformation and leads to formation of various convective structures: stationary long-scale modulated roll patterns, traveling and standing long waves, and can also cause chaotic convection (interfacial turbulence).
Proper orthogonal decomposition applied to turbulent flow in a square duct
Authors: Reichert R. S. , Hatay F. F. , Biringen S. , Huser A.
Published: July 2002

The proper orthogonal decomposition method is used to extract empirical eigenfunctions from an incompressible turbulent flow in a square duct. The two-dimensional eigenfunctions, corresponding to the two inhomogeneous duct directions, are optimal in the energy sense. The database used to form the two-point correlation tensor is obtained from a low Reynolds number direct numerical simulation of the flow field. The symmetries inherent in the square cross section allow the formulation of the integral eigenvalue problem over one octant, producing an eigensystem of manageable size without losing any spatial scales. The extraction process reveals a gradual decrease of modal energies rather than a single dominant eigenfunction. Reconstructions of instantaneous velocity fields and Reynolds stresses indicate the efficiency, as it pertains to identifying structures and storing data, of the proper orthogonal decomposition method for this problem.
Subgrid-scale energy transfer in the near-wall region of turbulent flows
Authors: Härtel Carlos , Kleiser Leonhard , Unger Friedemann , Friedrich Rainer
Published: July 2002

Direct numerical simulation databases of turbulent channel and pipe flow have been used in order to assess the energy transfer between resolved and unresolved motions in large-eddy simulations. To this end, the velocity fields are split into three parts: a statistically stationary mean flow, the resolved, and the unresolved turbulent fluctuations. The distinction between the resolved and unresolved motions is based on the application of a cutoff filter in spectral space. Within the buffer layer a backward transfer of averaged kinetic energy from subgrid to grid-scale turbulent motions has been found to exist, which is primarily caused by subgrid-scale stresses aligned with the mean rates of strain. Such reverse transfer generally cannot be described by the simple eddy-viscosity-type subgrid models usually applied in large-eddy simulations. The use of a conditional averaging technique revealed that the reverse transfer of energy within the near-wall flow is strongly enhanced by coherent motions, such as the well-known bursting events.
Weightless bubble lattices: A case of froth wicking
Authors: Noever David A. , Cronise Raymond J.
Published: July 2002

In the absence of gravity drainage, froth wicking draws excess fluid onto a bubble lattice. Capillary forces only cause fluid transport; a moving front moves stably and without fluid fingering along a constant velocity bubble–fluid contact line. This percolation of fluid crawling up the lattice shows (1) fluid coverage on lattice borders varies linearly with available surface area (proportional to lattice perimeter); (2) fluid accelerates through regions or nests of high bubble density (number of bubbles cm−2). The development of nearly two-dimensional bubble lattices in variable gravity (step function between 0.01 and 1.8 times earthly gravity) are examined experimentally and a zeroth-order model for froth wetting is presented, which captures many of the principal observations. Possible applications for bubble lattices include adhesion casting of metals and separation of biological cells, bacteria, and particles.