bluuebunny/crossref_metadata_2025 huggingface dataset:
Anchoring transitions in the nematic-substrate system: Study of the Landau–de Gennes model
Authors: Poniewierski A. , Samborski A.
Published: July 2002

We study the phenomenon of anchoring and anchoring transitions in the nematic-substrate system using the Landau–de Gennes formalism. The free-energy functional is expanded around the bulk tensor nematic order parameter up to the second-order terms. This quadratic approximation is used to find an explicit condition for the anchoring direction in a semi-infinite system, and then the phase boundaries between the homeotropic, planar, and conical anchorings are determined. In the cases that we have studied the quadratic approximation predicts a first order homeotropic–conical transition and a first order or continuous planar–conical transition. It also predicts a simple asymptotic expression for the free energy of a finite system, when the sample thickness is large and the deviation of the director from the anchoring direction is small. This asymptotic formula leads in a natural way to the definition of the geometrical measure of the anchoring strength b̄. However, the quadratic approximation is insufficient to predict the correct behavior of b̄ close to a continuous anchoring transition, although it can serve as a rough estimate of b̄ far from the transition.
The excitation energy dependence of the Raman–Stokes shift: The resonance Raman spectra of phenol blue in methanol
Authors: Yamaguchi T. , Kimura Y. , Hirota N.
Published: July 2002

We found that the Raman–Stokes shift of the C=N stretching mode of Phenol Blue changes with excitation energy; the frequency of this Raman band increased with an increase of the excitation energy, whereas the bandwidth was almost the same. The origin of the excitation energy dependence is discussed in connection with the correlation of the effect of the solvent fluctuation on the electronic transition energy and the vibrational frequency.
Proton rotating frame spin-lattice relaxation study of slow motion of pore water
Authors: Holly R. , Peemoeller H. , Choi C. , Pintar M. M.
Published: July 2002

Proton rotating frame spin-lattice relaxation times of water in hydrated porous silica glass, with pore diameters of 7.4, 23.7, 49.1, and 54.8 nm, are reported. Experiments were limited to hydrations corresponding to more than one-third hydrated pore volumes. The frequency dependence of the relaxation rates reveals a slow motion of pore water with a characteristic correlation time of ∼10−5 s. Within the limits given above, this correlation time depends on pore dimension and hydration only slightly. This indicates that the surface water molecules, which reorient with a characteristic time of ∼10−8 s, are changing their orientational axis with the slower correlation time ∼10−5 s. This process, which disrupts the nearby water molecules, depends primarily on the environment in the vicinity of the molecule’s original binding site. The analysis, based on the two-site fast exchange model, indicates that in small pores all the water may be affected by these slow jumps.
Realistic master equation modeling of relaxation on complete potential energy surfaces: Partition function models and equilibrium results
Authors: Ball Keith D. , Berry R. Stephen
Published: July 2002

To elucidate the role that potential surface topography plays in shaping the evolution of a cluster toward equilibrium, entire sets of kinetically accessible bound-state configurations and transition states on the model potential energy surfaces of (KCl)5 and Ar9 are mapped and compared. To describe the stochastic dynamics on these surfaces in terms of transition-state theory, we require adequate approximations of the partition functions of the minima and transition states. In this paper we introduce several partition function models derived from harmonic and anharmonic approximations and compare their predicted equilibrium population distributions with those determined from canonical-ensemble molecular dynamics. We perform this comparison for both (KCl)5 and Ar9 in order to evaluate the relative performance of the models for two different types of potential surfaces. For each system, particular models are found to give results that agree better with simulation than do the results using the simple harmonic approximation. However, no one unparameterized model gives acceptable results for all minima, and the best parameter-free strategies differ for (KCl)5 and Ar9. Nevertheless, a one-parameter version of one of the models is shown to give the best agreement with simulation for both systems. In an accompanying paper, the best partition function models are used to construct a stochastic master equation which makes predictions of relaxation behavior. These predictions are compared with results from molecular dynamics.
Rotationally resolved Ã 2Πg←X̃ 2Πu electronic spectrum of triacetylene cation by frequency modulation absorption spectroscopy
Authors: Sinclair Wayne E. , Pfluger David , Linnartz Harold , Maier John P.
Published: July 2002

The spectrum of the Ã 2Πg←X̃ 2Πu 000 band system of the triacetylene cation and isotopic derivatives DC6H+ and C6D2+ have been studied at Doppler-limited resolution using frequency modulation absorption spectroscopy. The ions were generated in a liquid-nitrogen-cooled hollow cathode discharge incorporated in a White cell. A discharge modulation in combination with the frequency modulation technique was used to enhance the detection sensitivity. Analyses of the rotational structure yield accurate rotational and spin-orbit interaction constants of triacetylene cation in the two electronic states and information on its geometry.
Ion conductance in electrolyte solutions
Authors: Chandra Amalendu , Bagchi Biman
Published: July 2002

We develop a new theoretical formulation to study ion conductance in electrolyte solutions, based on a mode coupling theory treatment of the electrolyte friction. The new theory provides expressions for both the ion atmosphere relaxation and electrophoretic contributions to the total electrolyte friction that acts on a moving ion. While the ion atmosphere relaxation term arises from the time-dependent microscopic interaction of the moving ion with the surrounding ions in the solution, the electrophoretic term originates from the coupling of the ion’s velocity to the collective current mode of the ion atmosphere. Mode coupling theory, combined with time-dependent density functional theory of ion atmosphere fluctuations, leads to self-consistent expressions for these two terms which also include the effects of self-motion of the ion under consideration. These expressions have been solved for the concentration dependence of electrolyte friction and ion conductance. It is shown that in the limit of very low ion concentration, the present theory correctly reduces to the well-known Debye–Huckel–Onsager limiting law which predicts a linear dependence of conductance on the square root of ion concentration (c). At moderate and high concentrations, the present theory predicts a significant nonlinear and weaker dependence on c which is in very good agreement with experimental results. The present theory is self-contained and does not involve any adjustable parameter.
Hydride nucleation and formation of hydride growth centers on oxidized metallic surfaces—kinetic theory
Authors: Ben-Eliyahu Y. , Brill M. , Mintz M. H.
Published: July 2002

The initial stage of hydrogen–metal reactions leading to the formation of metallic hydrides, frequently proceeds (on massive metallic samples) by the appearance of hydride “spots” (or “patches”) on the surface of the metal. These spots (henceforth denoted as growth centers, GC’s) grow at a certain velocity, overlap, and finally cover the whole surface by a hydride layer (which continues to thicken into the bulk of the metal). In certain systems it has experimentally been verified that the total available number of such GC’s is limited to a certain fixed number (typical to the given metallic surface and the reaction conditions). The kinetics of formation of these GC’s is characterized by a rate function which depends on the reaction conditions, i.e., temperature and pressure, and on the metal surface characteristics. Qualitatively, these rate functions initially accelerate, reach a maximum rate, and finally decay to zero. In the present article, a kinetic theory, which accounts for that behavior, is proposed. The model assumes that the initiation of the growth process can take place only at certain sites, with a limited number of such sites available on the surface. Also, the probability for the start-up of the growth process increases with increasing supersaturation of the hydrogen concentration at these sites. The interplay between these two factors (i.e., available GC’s sites and local hydrogen concentrations) reproduces the observed kinetics of formation of the GC’s. Analytical expressions for these rate functions are derived and compared with the experimental kinetic data reported for some metal–hydrogen systems. Universal forms of the rate function and its parameters provide a simple procedure for the evaluation of specific kinetic parameters from experimentally available data.
Response to “Comment on ‘Remarks on the information entropy maximization method and extended thermodynamics’ ” [J. Chem. Phys. 111, 6144 (1999)]
Authors: Eu Byung Chan
Published: July 2002

In this reply to B. Robertson’s comment on the paper published in J. Chem. Phys. [108, 5834 (1998)], the author points out that Robertson’s assertion made in his comment is not based on rigorous mathematical proofs on the entropy production and associated quantities that characterize the energy dissipation in nonequilibrium systems. His claimed proofs, in fact, are no proofs at all. Therefore he has not shown that the Robertson projection method gives rise to a theory of irreversible processes consistent with the thermodynamic laws. An error, which is irrelevant to the basic conclusions in the aforementioned paper by the present author, is also acknowledged.
Two-field-NOESY for precise determination of proton–proton distances and correlation times
Authors: Mao Xi-An , Zhang Tao , Baur Matthias , Kessler Horst
Published: July 2002

A nuclear magnetic resonance (NMR) method for the precise determination of internuclear distances is proposed. This method, called two-field-NOESY or simply 2F-NOESY, is based on the fact that cross-relaxation rates between spins, which can be measured by nuclear Overhauser enhancement spectroscopy (NOESY), are intrinsically frequency dependent. The method has the advantage that the reorientational correlation times for individual dipole–dipole vectors can be simultaneously determined along with the internuclear distances.
Thermodynamic study of a phase transition between the ordered and disordered phases and orientational disorder in crystalline p-chloronitrobenzene
Authors: Tozuka Yoshitaka , Yamamura Yasuhisa , Saito Kazuya , Sorai Michio
Published: July 2002

Heat capacities of the disordered and ordered crystalline phases of p-chloronitorobenzene were measured by adiabatic calorimetry between 6 and 303 K. The disordered phase stable at room temperature shows a glass transition around 245 K, which arises from the freezing of molecular reorientation as evidenced from the magnitude of the residual entropy. The ordered phase that is stable below 279 K was obtained through annealing the disordered phase around 260 K for a long time. The thermodynamic quantities concerning the first-order phase transition between the ordered and disordered phases were determined as Ttrs=279.0 K, ΔtrsH=(4468±5) J mol−1 and ΔtrsS=(16.01±0.05) J K−1 mol−1. Standard thermodynamic functions are tabulated.
Critical cluster size and droplet nucleation rate from growth and decay simulations of Lennard-Jones clusters
Authors: Vehkamäki Hanna , Ford Ian J.
Published: July 2002

We study a single cluster of Lennard-Jones atoms using a novel and physically transparent Monte Carlo simulation technique. We compute the canonical ensemble averages of the grand canonical growth and decay probabilities of the cluster, and identify the critical cluster, the size for which the growth and decay probabilities are equal. The size and internal energy of the critical cluster, for different values of the temperature and chemical potential, are used together with the nucleation theorems to predict the behavior of the nucleation rate as a function of these parameters. Our results agree with those found in the literature, and roughly correspond to the predictions of classical theory. In contrast to most other simulation studies, we are able to concentrate on the properties of the clusters which are most important to the process of nucleation, namely those around the critical size. This makes our simulations computationally more efficient.
Rotationally resolved A 2Π←X 2Π electronic absorption spectrum of cyanotriacetylene cation in the gas phase
Authors: Sinclair Wayne E. , Pfluger David , Verdes Dorinel , Maier John P.
Published: July 2002

The origin band of the A 2Π←X 2Π electronic transition of cyanotriacetylene cation has been detected in the gas phase. The ions were generated in a liquid-nitrogen cooled hollow cathode discharge incorporated in a multiple reflection cell. The technique of frequency modulation absorption spectroscopy is used to observe the band at Doppler-limited resolution. Analysis of the rotational structure yields accurate values of the rotational constants in the two electronic states, confirming a linear geometry. Comparison with astronomical measurements of diffuse interstellar bands is made.
Explicit calculation of a model for diffusion in nonconstant temperature
Authors: van Kampen N. G.
Published: July 2002

As a model for diffusion in a nonhomogeneous medium, Landauer [Phys. Lett. A 68, 15 (1978)] proposed a pipe filled with a Knudsen gas. The wall temperature varies along the pipe, and the gas molecules, on colliding with the wall, assume its temperature. Here, by explicit calculation, in the limit of small diameter, an equation is derived for the flow of the gas through the pipe. The derivation is possible because the transverse motion of the gas particles rapidly establishes thermal equilibrium. It can therefore be eliminated using the method of eliminating fast variables. The surviving equation for the slow longitudinal flow has the form of a diffusion equation with nonconstant coefficients.
Canonical quantization of supersymmetric second-order systems
Authors: de Azeredo Campos R.
Published: July 2002

The canonical quantization of systems described by Lagrangians containing second-order time derivatives of both even and odd variables is developed. It is shown that a correct application of Dirac’s method eliminates the ambiguity of different quantized versions associated with the same superclassical dynamics.
Modes in n-dimensional first-order systems
Authors: Kauderer Mark
Published: July 2002

Properties of the extended Hermite polynomials are studied. It is proved, apparently for the first time, that these functions (times Gaussian functions) are the modes of an n-dimensional first-order system, thus generalizing an earlier result due to Hardy, Sheng, and Siegman for one dimension. Misalignment, nonlosslessness, and the exact normalization constant are explicitedly included in the treatment. Phase conjugators are also analyzed.
Space–times admitting a three-parameter similarity group
Authors: Carot J. , Mas L. , Sintes A. M.
Published: July 2002

Space–times admitting a similarity group are considered. Among them, special attention is given to the three-parameter ones. A classification of such space–times is given based on the Bianchi type of the similarity group H3, and the general form of the metric is provided in each case assuming the orbits are non-null.
Solution of Nester’s gauge conditions
Authors: Bruzzo Ugo , Venzano Francesca
Published: July 2002

We give a rigorous proof of the existence of solutions to the nonlinear gauge conditions on orthonormal frames introduced by Nester to prove the positive energy theorem in general relativity. The proof holds in all dimensions n≥2. If the second de Rham cohomology group vanishes one also proves uniqueness.
Quasitriangularity and enveloping algebras for inhomogeneous quantum groups
Authors: Podleś P.
Published: July 2002

Coquasitriangular universal ℛ matrices on quantum Lorentz and quantum Poincaré groups are classified. The results are extended (under certain assumptions) to inhomogeneous quantum groups. Enveloping algebras on those objects are described.
Integration on quantum Euclidean space and sphere
Authors: Steinacker Harold
Published: July 2002

Invariant integrals of functions and forms over q-deformed Euclidean space and spheres in N dimensions are defined and shown to be positive definite, compatible with the star structure and to satisfy a cyclic property involving the D matrix of SOq(N). The definition is based on spherical and radial integration. Stokes theorem is proved with and without spherical boundary terms, as well as on the sphere.
Extremal eigenvalue gaps for the Schrödinger operator with Dirichlet boundary conditions
Authors: Karaa Samir
Published: July 2002

We consider the problems of minimizing and maximizing the gap between the two lowest Dirichlet eigenvalues of the Schrödinger operator −Δ+V(x) on a bounded domain in Rn, when the potential V is subjected to a p-norm constraint. We give characterization theorems for extremizing potentials. We prove in particular that a second eigenvalue corresponding to a minimizing potential is always single.
Acoustic magnetic resonance in absorption and dispersion of surface elastic waves in multilayers
Authors: Okulov V. I. , Ustinov V. V. , Pamyatnykh E. A. , Slovikovskaya V. V.
Published: July 2002

It is shown that magnetic resonances related to excitation of oscillations of the layer magnetization can appear in the spectrum and absorption of the Love acoustic surface waves propagating in a multilayered film with a Fe/Cr type magnetic ordering on a massive substrate. The magnetoelastic resonant contribution to the elastic shear modulus of the film is calculated and the relation between the resonant frequencies and the frequencies of electromagnetically excited uniform ferromagnetic resonance is established.
Inverse energy cascade in a time-dependent flow
Authors: Hefer David , Yakhot Victor
Published: July 2002

It is shown that the finite lifetime of anisotropic flow structures inhibit the inverse energy cascade discussed by Yakhot and Sivashinsky [Phys. Rev. A 35, 815 (1987)] and Bayly and Yakhot [Phys. Rev. A 34, 381 (1986)]. The possibility of the inverse energy cascade by strongly anisotropic velocity fluctuations in turbulent flows is discussed.
Acceleration of a slab driven by a constant pressure piston
Authors: Diez J. A. , Thomas L. P.
Published: July 2002

The sequence of shock and rarefaction waves, which occur in a plane layer of ideal gas initially at rest when it is driven toward the vacuum by a very high constant pressure piston, is studied. In the rarefaction flow that relaxes the layer compressed by the first strong shock, a second shock is generated. The time and position of its formation are obtained by an exact analytical expression. The subsequent motion and intensity of the shock wave are approximated by the Chester–Chisnell–Whitham (CCW) method. Then, the Lagrangian distribution of entropy in the layer is analytically derived.
Transition to Soret-driven convection in a system with nearly impermeable boundaries
Authors: Hadji Layachi , Schell Mark
Published: July 2002

The transition to Soret-driven convection in a binary fluid located in a system with nearly impermeable boundaries is analyzed. An expansion is carried out around the critical conduction state in terms of the Biot number, the ratio of the solute diffusivity in the material composing the boundaries to the solute diffusivity in the binary fluid. At a large enough separation ratio three spatial convective structures, rolls, squares, and hexagons, can arise through a supercritical bifurcation and each of these structures is stable with respect to disturbances that possess wave vectors coincident to those of the steady solutions. However, it is shown that only squares are stable with respect to disturbances with wave vectors pointed in an arbitrary direction. The convective contributions to the heat flux and a concentration flux are calculated for each of the three spatial structures and they are found to be largest for squares. This result is in agreement with a stated relative stability criterion.
On the neutral stability of cross-waves
Authors: Kit E. , Shemer L.
Published: July 2002

The neutral stability of parametrically excited cross-waves in a rectangular tank is studied. Model equations considered include complex coefficients describing dissipation of the side walls of the tank and at the wavemaker. The results of this study are compared with the available experimental data. It is shown that for certain experimental conditions, the dissipation at the wavemaker becomes important and sometimes dominant. Analysis of the experimentally obtained neutral stability curves and their comparison with the present theory provide an opportunity to estimate the complex dissipation coefficients.
New instability modes for bounded, free shear flows
Authors: Macaraeg Michéle G. , Streett Craig L.
Published: July 2002

A class of highly amplified supersonic disturbances are found for high-speed, bounded mixing layers at high values of streamwise wavenumber. Their amplification is an order of magnitude greater than the most amplified modes, which occur at 60°–65° at low streamwise wavenumber. These disturbances are stabilized by increasing Mach number, viscosity, and sweep; however, the effect of sweep on the most amplified mode is not significant until the wave propagation angle reaches 30°. The maximum growth rate of the unstable disturbances decreases as the temperature of the higher Mach number stream is increased. The structure of these disturbances is such that the phase speed with respect to the mean flow is subsonic in a small region in the center of the shear layer, and supersonic on either side of this region.
Compressible rotational flows generated by the substitution principle. II.
Authors: Rodriguez Azara J. L. , Emanuel George
Published: July 2002

The substitution principle is a transformation of the dependent variables that leaves invariant the steady Euler equations. In Part I [J. L. Rodriguez Azara and G. Emanuel, Phys. Fluids 31, 1058 (1988)] the principle is applied to several well-known compressible flows. In this communication, the most general forms of the transformation are derived, including a generalization of the vorticity transformation. From a thermodynamic analysis and the energy shock wave jump condition, we conclude that a thermally perfect gas is usually the only assumption compatible with the principle. The nonlinear equations for rotational flow of a perfect gas are derived in the hodograph plane. By means of the substitution principle, the solutions of the linear, irrotational hodograph equations can be transformed into solutions of the new rotational equations. As a result of the invariance of the physical coordinates under the substitution principle, the transformation does not alter the form of the solutions. A cylindrical source flow is used to illustrate the hodograph theory.
The crisis of transport measures in chaotic flow past a cylinder
Authors: Karniadakis George Em , Triantafyllou George S.
Published: July 2002

The dynamics of the flow past a cylinder is drastically affected when external periodic disturbances are present in the flow. For a certain range of amplitude and frequency of disturbances the flow bifurcates to a chaotic state, even at low Reynolds numbers. In this Letter, the effect of these chaotic responses on transport measures (e.g., the heat transfer coefficient) by direct numerical simulations using spectral element methods is investigated. It is found that transport quantities oscillate aperiodically in time; their time-averaged value increases slightly from the undisturbed state. However, their amplitude increases dramatically from that of the undisturbed flow or any other excited, resonant, or quasiperiodic neighboring state.
Shock-cell and instability-wave eigenmodes for supersonic round jets with finite momentum thickness
Authors: Koshigoe Shozo , Tubis Arnold
Published: July 2002

The study of large-scale structures in the presence of shock cells is important for understanding the mechanism of noise generation in, and means for control of, supersonic mixing layers. As a preliminary to the investigation of the dynamical interactive effects of shock cells on large-scale structures, linear instability theory is used to calculate both shock-cell and spatial instability modes for supersonic round jets with finite momentum thickness. The shock-cell eigenmodes are determined from the zero-frequency limit of the usual instability equations. The dependence of the results on Mach number is also investigated. The main effects of increasing momentum thickness are to saturate the spatial growth rates at lower frequencies and to reduce the shock-cell spacing: The latter effect is most prominent at low Mach number. The spatial growth rates of modes that track from the zero-frequency shock-cell modes are, at very low frequencies, negligible compared to those of the regular instability mode (whose associated wavenumber vanishes at zero frequency). However, at sufficiently high Mach number, the most unstable modes in certain frequency regions are actually the ones that track from shock cells. These regions occur at lower and lower frequencies as the momentum thickness and Mach number increase.
An advanced model of dissipation cascade in locally isotropic turbulence
Authors: Hosokawa Iwao
Published: July 2002

Based on the recognition that the spatial probability density of velocity gradients and vorticity in a fully developed turbulence is nearly exponential, the scale-similar dissipation cascade in a locally isotropic turbulence is reconsidered. With this, a new model of dissipation cascade that has a quality different from the other models known at present is constructed. Various aspects of the model are outlined and compared with the existing models and further experiments.
Measurement of the hydrodynamic surface roughness of noncolloidal spheres
Authors: Smart Jeffery R. , Leighton David T.
Published: July 2002

A new technique for measuring the surface roughness of noncolloidal spheres is presented. The time for a sphere initially in contact with a smooth surface to fall away under the influence of gravity through a viscous fluid is shown to be related to the largest scale of surface roughness of sufficient surface coverage to support the particle. The ratio of the time taken for a sphere to fall one particle diameter from a smooth mica plane to that for the sphere to fall between one radius and one diameter from the plane thus provides a means of measuring the effective hydrodynamic surface roughness of spheres. This technique was employed to measure the roughness of eight types of particles ranging from 43–6350 μm in diameter. The roughnesses were found to be on the order of 10−2 to 10−3 particle radii, and were in agreement with independent observations using a scanning electron microscope and an optical profilometer.
Linear stability of a rotating film flow attached inside a circular cylinder
Authors: Fujimura Kaoru
Published: July 2002

Stability of a rotating film flow attached inside a circular cylinder was analyzed on a linear basis, where the cylinder is at rest and the basic flow is assumed to be kept rotating under the imposition of an artificial body force acting in the azimuthal direction. A traveling-wave mode that is intrinsic for a film flow on a vertical or an inclined flat plate and a centrifugal instability mode are obtained as unstable modes. The effect of a superimposed shear flow in the axial direction was also examined and it was shown that the shear flow exerts a stabilizing effect on the centrifugal instability mode.
The dynamics and geometry of a two-dimensional turbulent front
Authors: Tseng Ruo-Shan , Maxworthy Tony
Published: July 2002

The formation and evolution of a front between turbulent and nonturbulent fluid in a two-dimensional flow are studied using a combined experimental-numerical technique. Turbulence was created by towing a grid of vertical bars partway through a tank that was filled with a two-layer stratified fluid. The velocity field at several times during the evolution of the turbulence was obtained by photographing neutrally buoyant particles suspended in the sharp density interface. Each realization was used to compute the advance of lines of particles released in the flow near the initial location of the grid. The computed location and shape of the turbulent/nonturbulent front, representing the distribution of a passive scalar in the flow, correlate well with the ‘‘zero contour’’ of the absolute-vorticity field. It is shown that the turbulent/nonturbulent front, in the most distorted cases, may be described by a fractal dimension over a restricted range of length scales. Certain geometric characteristics of the frontal region, in particular the probability distribution of a passive scalar, the frontal width, and length are also examined; the latter appears to grow with a power of time related to the fractal dimension of the interface.
On the forces of droplets in Poiseuille flow
Authors: Puri Ishwar K. , Libby Paul A.
Published: July 2002

The forces on droplets in Poiseuille flow in the Reynolds number range from 0.7 to 27 are determined experimentally. It is found that droplets migrate toward the centerline and experience drag considerably in excess of that prevailing in uniform flow. Rough correlations for the drag and lift coefficients as functions of the Reynolds number and a parameter characterizing the flow nonuniformity are developed.
Stabilization of a molten-metal/coolant-gas interface by electromagnetic fields
Authors: Hull John R. , Rote Donald M.
Published: July 2002

Experiments were conducted in which nitrogen gas flowed at a uniform velocity in a rectangular channel over the surface of a shallow horizontal dish containing liquid tin in the presence of a 10 kHz magnetic field above the tin surface. The threshold gas velocity for wave formation was determined with the magnetic field oriented parallel or perpendicular to the gas flow. In both orientations, the threshold velocity increased as magnetic-field strength increased at a rate much larger than predicted by linear stability theories, and the enhanced wave suppression was attributed to the influence of electromagnetic stirring.
Spatial effects of removal and creation processes on the dynamics of gases
Authors: Zanette Damián H.
Published: July 2002

Exact similarity solutions are presented for the spatial-dependent McKean–Boltzmann equation, when creation and removal processes are allowed. The effects of such processes on the spatial dynamics of the gas are analyzed through these solutions.
The added mass, Basset, and viscous drag coefficients in nondilute bubbly liquids undergoing small-amplitude oscillatory motion
Authors: Sangani A. S. , Zhang D. Z. , Prosperetti A.
Published: July 2002

The motion of bubbles dispersed in a liquid when a small-amplitude oscillatory motion is imposed on the mixture is examined in the limit of small frequency and viscosity. Under these conditions, for bubbles with a stress-free surface, the motion can be described in terms of added mass and viscous force coefficients. For bubbles contaminated with surface-active impurities, the introduction of a further coefficient to parametrize the Basset force is necessary. These coefficients are calculated numerically for random configurations of bubbles by solving the appropriate multibubble interaction problem exactly using a method of multipole expansion. Results obtained by averaging over several configurations are presented. Comparison of the results with those for periodic arrays of bubbles shows that these coefficients are, in general, relatively insensitive to the detailed spatial arrangement of the bubbles. On the basis of this observation, it is possible to estimate them via simple formulas derived analytically for dilute periodic arrays. The effect of surface tension and density of bubbles (or rigid particles in the case where the no-slip boundary condition is applicable) is also examined and found to be rather small.
Nonlinear free-surface flows past a submerged inclined flat plate
Authors: Vanden-Broeck J.-M. , Dias Frédéric
Published: July 2002

Steady two-dimensional free-surface flows past an inclined flat plate submerged in a channel of finite depth are calculated numerically. The flow is assumed to be supercritical. The numerical scheme is based on finite differences. It is shown that there are families of solutions for which there is no force exerted on the plate. In addition, solutions for a horizontal semi-infinite plate are calculated by series truncation.
Comparison of velocity distribution functions in an argon shock wave between experiments and Monte Carlo calculations for Lennard-Jones potential
Authors: Matsumoto Hiroaki , Koura Katsuhisa
Published: July 2002

The velocity distribution functions (VDF’s) in an argon normal shock wave at an upstream high Mach number 7.183 and low temperature 16 K are calculated using the null-collision direct-simulation Monte Carlo method for the Lennard-Jones (LJ) potential to compare with the experimental results of Holtz and Muntz [Phys. Fluids 26, 2425 (1983)]. The convolved VDF’s for the LJ potential are in reasonable agreement with the measured data in early and late regions of the shock wave but significantly different in the middle region. This discrepancy cannot be explained by a possible uncertainty in the potential well depth. Moreover, the difference in the convolved VDF’s between the LJ potential and the softest and hardest unrealistic molecular models with no attractive force, i.e., the Maxwell molecule and hard sphere, is much smaller than the discrepancy between the experiments and Monte Carlo calculations.
Self-dilating viscous fingers in wedge-shaped Hele–Shaw cells
Authors: Ben Amar Martine , Hakim Vincent , Mashaal Maurice , Couder Yves
Published: July 2002

Viscous fingering in a wedge-shaped Hele–Shaw cell is analyzed. The shape of a self-dilating viscous finger is shown to obey a time-independent nonliner integrodifferential equation that is solved numerically. The results show that there is a continuum of zero-surface-tension solutions for any wedge angle between 0 and π/2. When surface tension is taken into account only a discrete set of solutions exist. In contrast to the classical case, different branches merge for finite values of the surface tension parameter.
Axial forcing of an inviscid finite length fluid cylinder
Authors: Lyell M. J.
Published: July 2002

Current interest in microgravity materials processing has focused attention upon the finite fluid column. This configuration is used in the modeling of float zones. In this Brief Communication, the incompressible inviscid finite length fluid column is subjected to an axial, time-dependent disturbance. The response of the fluid system and the resulting interface location are determined via Laplace transform methods.
The lubrication analysis for two spheres in a two-dimensional pure-straining motion
Authors: Jeffrey D. J.
Published: July 2002

The stresslets of two spheres in a low Reynolds number flow are calculated asymptotically for the case in which the imposed flow field tends, far from the spheres, to a two-dimensional pure-straining motion perpendicular to the line of centers. The spheres are assumed to be nearly touching. The analysis is based on a complementary problem in which lubrication theory is used to calculate the flow between two deforming spheres. As well as providing asymptotic estimates of the singular nature of the stresslets, the solution shows an unexpected feature for a lubrication flow, this being the fact that, for one special case, the pressure in the flow field is zero.
Laboratory experiments on turbulent mixing across sheared density interfaces
Authors: Stephenson Philip , Fernando Harindra J. S.
Published: July 2002

An experimental study was carried out to investigate turbulent mixing and entrainment across a density interface subjected to velocity shear. The flow configuration consisted of a salinity (stably) stratified two-fluid system with a driven upper turbulent layer and a quiescent lower layer. The experiments were performed in an Odell–Kovasznay tank and the mean flow in the upper layer was generated by using a conventional disk pump. The velocity and salinity measurements were made using a laser-Doppler anemometer and conductivity probes, respectively, and (quantitative) flow visualization was performed using the laser-induced fluorescence LIF technique. The refractive indices of upper and lower layers were matched, using salt and alcohol, to facilitate the use of laser-based flow diagnostic techniques. The measurements show that the rms velocity fluctuation u in bulk of the mixed layer scales well with the mean velocity jump Δu across the interface. The Thorpe, buoyancy, overturning, and integral length scales, as well as the maximum Thorpe displacement in the mixed layer, were also found to be proportional to the depth h of the upper mixed layer.

The structure of the entrainment interface was found to depend strongly on the bulk Richardson number Ri (=Δb h/u2), where Δb is the buoyancy jump across the interfacial layer. At lower Ri, the entrainment occurred rapidly, as in a nonstratified fluid, but as Ri increases, the entrainment rate becomes a strong function of Ri: under the latter conditions, the interfacial wave breaking and Kelvin–Helmholtz instabilities were common features. At still higher Ri, the entrainment rate becomes vanishingly small and the interfacial mixing events were found to be controlled by the molecular diffusive effects. The measurement of the interfacial-layer thickness using LIF shows that it is much thinner than that measured using less-accurate techniques such as traversing probes. The nondimensional rms amplitude of the interfacial distortions at moderate and high Ri was found to be a strong function of Ri. The interfacial instabilities cause the formation of isolated mixing patches within the interface, which, when collapsed, form horizontal intrusions. The experimental measurements were in agreement with theoretical formulations based on scaling arguments.
The structure and dynamics of patterns of Bénard convection cells
Authors: Rivier N.
Published: July 2002

Bénard convection, in containers with large aspect ratio, exhibits space-filling cellular patterns, with the degree of disorder varying with the temperature difference driving the convective instability. I shall show that the structure of cellular networks can be explained by elementary topological transformations (which act like collisions in statistical mechanics to keep the network in statistical equilibrium, but also govern the motion of topological dislocations in the network). I shall also discuss the dynamics of cells in the network, in terms of a (molecular dynamics) modelization by Telley, and show why such a simple model can also be realistic. This work relates to the subject ‘‘geometry and topology of stirred fluid regions’’ mentioned in the announcements for the Symposium. [Work at Argonne supported by U.S. Department of Energy Contract No. W-31-109-ENG-38.]
Stability and chaotic advection in the eccentric Taylor problem
Authors: King G. P. , Banas K. , MacKay R. S. , Shaw C. T.
Published: July 2002

Theoretically, Lagrangian chaos or chaotic advection can occur by forcing a steady, two-dimensional velocity field with a time-periodic perturbation. This idea has recently been confirmed experimentally by Chaiken et al.1 and Chien et al.2 In principle, chaotic advection should also occur in a three-dimensional steady flow. To investigate this problem we constructed an eccentric Taylor–Couette apparatus with a rotating inner cylinder and a stationary outer cylinder. We obtain a 3-D steady flow in the following way. We first create a 2-D velocity field at small rotation rates of the inner cylinder by imposing a sufficiently large ecccentricity to obtain separated flow. (That is, an eddy in the region of largest gap is created by the separation of the fluid from the outer boundary and its reattachment downstream.) The inner cylinder rotation rate is then increased until Taylor vortices appear. The Taylor vortices modify the separated flow but do not destroy it. It is in this mixed Taylor vortex-separated flow regime that we carry out our studies of chaotic advection. On account of mathematical difficulties there exist few theoretical or experimental studies of stability of the flows in the eccentric geometry. We have therefore conducted numerical and laboratory experiments to identify the regions of parameter space where 3-D steady flow exists and where a transition of time dependence (i.e., 4-D flows) occurs. In our numerical work we used a commercial computational fluid dynamics program and we will report on our assessment of its accuracy in predicting the three-dimensional flow features observed in the experiments and its potential for investigating chaotic advection. In particular, we use it to find the ‘‘skeleton’’ of the flow and the fluxes between the associated regions of different flow type that it defines, and compare these with experimental observations.
Strong flows of dilute suspensions of microstructure
Authors: Szeri Andrew J. , Wiggins Stephen , Leal L. Gary
Published: July 2002

We consider dilute suspensions that have a microstructure that may be characterized by an axial state vector. Examples include axisymmetric particles, line elements of the fluid itself, or, as an approximation, droplets of fluid or polymer molecules. Past studies, in which sufficient conditions for stretch or coherent orientation of the microstructure are obtained for steady flows with homogeneous velocity gradient tensors are shown not to apply to the general situation. Instead, a careful analysis of the microdynamical equations reveals that stretching and orientation of the microstructure by the flow must be analyzed over a time interval. Using techniques from the theory of dynamical systems, a quantitative measure is developed to determine orientations and/or stretched lengths of the microstructure, that are robust and attractive to nearby states. This leads to a strong flow criterion for unsteady flows with inhomogeneous velocity gradient tensors in which the effects of history dependence are apparent.

A particular model system is treated in the case of general two-dimensional flow. The sensitivity of the results to changes in the modeling assumptions is investigated.
The evolution of diffusive thermohaline staircases
Authors: Stegen G. R. , Muench R. D. , Fernando H. J. S. , Ching C. Y.
Published: July 2002

Diffusive thermohaline staircases have been observed over wide regions of the Northwestern Weddell Sea in the March 1986 AMERIEZ experiments.1 The spatial distribution and temporal evolution of these staircases suggests that these layers may migrate upwards and also may bifurcate into multiple layers. These observations provided the motivation for a laboratory study of the evolution of thermohaline staircases. In the present study, a thermohaline staircase was generated by heating a stable salinity gradient from below. The thicknesses of the convecting layers, heat and salt transports across the interfaces, and migration of the interfaces due to interfacial turbulent mixing were measured. During the experiments, the interfaces and convecting layers evolve with time, ultimately assuming steady positions and thicknesses h.

The experimental measurements of h, away from the bottom boundary, were found to be in good agreement with a theoretical prediction based on the assumption that a balance between the kinetic and potential energies of the turbulent eddies within the convecting layers sets the thicknesses of the convecting layers. Further, the laboratory data showed an excellent agreement with the oceanic data gathered by the previous investigators. Because of buoyancy transport across the interfaces, the stratification in the system weakens and the buoyancy jump Δb across the interfaces reduces. When the interfacial Richardson number Ri=Δbδ/w*2, where δ is the thickness of the interface and w* is the convection velocity in the layers, drops below a critical value Ric, which is about 1.5, the interfaces showed rapid migration to new quasiequilibrium levels, at which they remain stationary until Ri drops below Ric again. Flow visualization studies show that these rapid migrations are caused by engulfment of the interfacial layer fluid by the eddies of the lower, strongly convecting, layers. The experiments also show that, under certain conditions involving low heat fluxes and high density stratifications, heating of a stable salinity gradient does not lead to the formation of a thermohaline staircase structure; a criterion is developed to predict the conditions favorable for their formation. In addition, when the stratification is small and heat flux is high, the convectively mixed layer propagates upward as in a nonstratified fluid and the stratification tends to be destroyed without forming layers. The laboratory results successfully explain some of the field observations, while providing insight into the physics of thermohaline convection.