Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

Scaling in large Prandtl number turbulent thermal convection

We study the scaling properties of heat transfer Nu in turbulent thermal convection at large Prandtl number Pr using a quasi-linear theory. We show that two regimes arise, depending on the Reynolds number Re. At low Reynolds number, NuPr ^-1/2 and Re are a function of RaPr ^-3/2. At large Reynolds number NuPr ^1/3 and RePr are function only of RaPr ^2/3 (within logarithmic corrections). In practice, since Nu is always close to Ra ^1/3, this corresponds to a much weaker dependence of the heat transfer in the Prandtl number at low Reynolds number than at large Reynolds number. This difference may solve an existing controversy between measurements in SF₆ (large Re) and in alcohol/water (lower Re). We link these regimes with a possible global bifurcation in the turbulent mean flow. We further show how a scaling theory could be used to describe these two regimes through a single universal function. This function presents a bimodal character for intermediate range of Reynolds number. We explain this bimodality in term of two dissipation regimes, one in which fluctuation dominate, and one in which mean flow dominates. Altogether, our results provide a six parameters fit of the curve Nu(Ra, Pr) which may be used to describe all measurements at Pr≥0.7. Received 27 February 2002 / Received in final form 29 May 2002 Published online 31 July 2002     

Order-parameter fluctuations (OPF) in spin glasses: Monte Carlo simulations and exact results for small sizes

The use of parameters measuring order-parameter fluctuations (OPF) has been encouraged by the recent results reported in referenece [2,3] which show that two of these parameters, G and G _c, take universal values in the . In this paper we present a detailed study of parameters measuring OPF for two mean-field models with and without time-reversal symmetry which exhibit different patterns of replica symmetry breaking below the transition: the Sherrington-Kirkpatrick model with and without a field and the Ising p-spin glass (p = 3). We give numerical results and analyze the consequences which replica equivalence imposes on these models in the infinite volume limit. We give evidence for the transition in each system and discuss the character of finite-size effects. Furthermore, a comparative study between this new family of parameters and the usual Binder cumulant analysis shows what kind of new information can be extracted from the finite T behavior of these quantities. The two main outcomes of this work are: 1) Parameters measuring OPF give better estimates than the Binder cumulant for T _c and even for very small systems they give evidence for the transition. 2) For systems with no time-reversal symmetry, parameters defined in terms of connected quantities are the proper ones to look at. Received 20 September 2000 and Received in final form 10 January 2001     

Effect of tangential interface motion on the viscous instability in fluid flow past flexible surfaces

The stability of linear shear flow of a Newtonian fluid past a flexible membrane is analysed in the limit of low Reynolds number as well as in the intermediate Reynolds number regime for two different membrane models. The objective of this paper is to demonstrate the importance of tangential motion in the membrane on the stability characteristics of the shear flow. The first model assumes the wall to be a “spring-backed” plate membrane, and the displacement of the wall is phenomenologically related in a linear manner to the change in the fluid stresses at the wall. In the second model, the membrane is assumed to be a two-dimensional compressible viscoelastic sheet of infinitesimal thickness, in which the constitutive relation for the shear stress contains an elastic part that depends on the local displacement field and a viscous component that depends on the local velocity in the membrane. The stability characteristics of the laminar flow in the limit of low are crucially dependent on the tangential motion in the membrane wall. In both cases, the flow is stable in the low Reynolds number limit in the absence of tangential motion in the membrane. However, the presence of tangential motion in the membrane destabilises the shear flow even in the absence of fluid inertia. In this case, the non-dimensional velocity (Λ_t) required for unstable fluctuations is proportional to the wavenumber k ( Λ _t∼k) in the plate membrane type of wall while it scales as k² in the viscoelastic membrane type of wall ( Λ _t∼k ²) in the limit k→ 0. The results of the low Reynolds number analysis are extended numerically to the intermediate Reynolds number regime for the case of a viscoelastic membrane. The numerical results show that for a given set of wall parameters, the flow is unstable only in a finite range of Reynolds number, and it is stable in the limit of large Reynolds number. Received 8 November 2000 and Received in final form 20 March 2001     

Spatial variations of the mean and statistical quantities in the thermal boundary layers of turbulent convection

We have studied the dynamics of the contact line of a viscous liquid on a solid substrate with macroscopic random defects. We have first characterized the friction force f₀ at microscopic scale for a substrate without defects; f₀ is found to be a strongly nonlinear function of the velocity U of the contact line. In presence of macroscopic defects, we find that the applied force F(U) is simply shifted with respect to f₀(U) by a constant: we do not observe any critical behavior at the depinning transition. The only observable effect of the substrate disorder is to increase the hysteresis. We have also performed realistic numerical simulation of the motion of the contact line. Using the same values of the parameters as in the experiment, we find that the experimental data is qualitatively well reproduced. In light of experimental and numerical results, we discuss the possibility of measuring a true critical behavior.Received: 6 October 2003, Published online: 19 February 2004PACS: 46.65. + g Random phenomena and media - 64.60.Ht Dynamic critical phenomena - 68.08.Bc Wetting     

Renormalization group treatment of the scaling properties of finite systems with subleading long-range interaction

The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a field-theoretic ɛ-expansion scheme under periodic boundary conditions. We suppose a van der Waals type long-range interaction falling apart with the distance r as r ^{- (d + σ)}, where 2 < σ < 4, which does not change the short-range critical exponents of the system. Despite that the system belongs to the short-range universality class it is shown that above the bulk critical temperature T _c the finite-size corrections decay in a power-in-L, and not in an exponential-in-L law, which is normally believed to be a characteristic feature for such systems. Received 8 August 2001     

Two-particle dispersion in model two-dimensional velocity fields

We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v ²(r) ∝r ^α and the corresponding correlation time scales as τ(r) ∝r ^β, and fix α = 2/3, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For α/2 + β < 1 the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, α/2 + β > 1, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation. In this case, depending on the particular parameters of the flow, the dispersion behavior can be rather diffusive or rather ballistic. Received 13 March 2001     

Gamow-Teller transitions from 58Ni to discrete states of 58Cu

Under the assumption that isospin is a good quantum number, symmetry is expected for the transitions from the ground states of T = 1, T _z = ±1 nuclei to the common excited states of the T _z = 0 nucleus situated between the two nuclei. The symmetry can be studied by comparing the strengths of Gamow-Teller (GT) transitions obtained from a (p, n)-type charge-exchange reaction on a target nucleus with T _z = 1 with those from the β-decay of the T _z = - 1 nucleus. The A = 58 system is the heaviest for which such a comparison is possible. As a part of the symmetry study, we measured the GT transitions from ⁵⁸Ni (T _z = 1) to ⁵⁸Cu (T _z = 0) by using the zero-degree (³ He, t) reaction at 150 MeV/nucleon. With the achieved resolution of 50 keV, many hitherto unresolved GT states have been identified. The GT transition strengths were obtained for states up to 8 MeV excitation, i.e., near to the Q window limitation ( Q _EC = 9.37 MeV) of the β-decay from ⁵⁸Zn (T _z = - 1) to ⁵⁸Cu. The strength distribution is compared with that from shell-model calculations. Received: 24 November 2001 / Accepted: 30 January 2002     

Low-energy Compton scattering and the polarizabilities of the proton

Differential cross-sections for Compton scattering from the proton have been measured at the MAMI tagged photon facility using the TAPS setup. The data cover an angular range of θ^lab _γ = 59^°-155^° and photon energies ranging from 55 MeV to 165 MeV. Our results are in good agreement with those from previous experiments, but yield higher precision. Using dispersion relations the proton polarizabilities have been determined to be = [11.9±0.5_stat.±1.3_syst.±0.3_mod.] ^. 10^-4 fm ³ and = [1.2±0.7_stat.±0.3_syst.±0.4_mod.)] ^. 10^-4 fm ³. These results confirm the Baldin sum rule which was re-evaluated to be + = [13.8±0.4] ^. 10^-4 fm ³. We can also conclude that there is no significant additional asymptotic contribution to the backward spin polarizability γ_π beyond the t-channel π⁰-exchange. Received: 9 January 2001 / Accepted: 13 February 2001     

New evidence for supernarrow dibaryons production in pd interactions

The analysis of new experimental data, obtained at the Proton Linear Accelerator of INR, with the aim to search for supernarrow dibaryons in the pd↦ppX ₁ and pd↦pdX ₂ reactions is presented. Narrow peaks with an experimental width of 5 MeV at masses of 1904±2, 1926±2, and 1942±2 MeV have been observed in missing mass M _pX1 spectra. In the missing mass M _X1 spectra, the peaks at M _X1 = 966±2, 986±2, and 1003±2 MeV have been found. The analysis of the data obtained leads to the conclusion that the observed peaks in M _pX1 spectra are most likely supernarrow dibaryons, the decay of which into two nucleons is forbidden by the Pauli exclusion principle. An alternative interpretation of the spectra by assuming a decay of the supernarrow dibaryons in “exotic baryon states” with masses M _X1 is discussed. Received: 22 October 2001 / Accepted: 15 November 2001     

On the theory of light scattering in molecular liquids

The theory of light scattering for a system of linear molecules with anisotropic polarizabilities is considered. As a starting point for our theory, we express the result of a scattering experiment in VV and VH symmetry as dynamic correlation functions of tensorial densities ρ _lm(q) with l = 0 and l = 2. l, m denote indices of spherical harmonics. To account for all observed hydrodynamic singularities, a generalization of the theory of Schilling and Scheidsteger [1] for these correlation functions is presented, which is capable to describe the light scattering experiments from the liquid regime to the glassy state. As a microscopic theory it fulfills all sum rules contrary to previous phenomenological theories. We emphasize the importance of the helicity index m for the microscopic theory by showing, that only the existence of m = 1 components lead to the well known Rytov dip in liquids and to the appearance of transversal sound waves in VH symmetry in the deeply supercooled liquid and the glass. Exact expressions for the phenomenological frequency dependent rotation translation coupling coefficients of previous theories are derived. Received 3 July 2000 and Received in final form 7 November 2000     

Solvation and chemical reaction of sodium in water clusters

Na_m(H₂O)_n Clusters ( n = 1...200, m = 1...50) are formed in a recently build pick-up arrangement. Preformed water clusters traverse a sodium oven, where sodium atoms are picked up. At low sodium vapour pressure ( < 1×10^-4 mbar) pure Na(H₂O)_n clusters are observed in the mass spectra. At high sodium vapour pressure ( > 1×10^-3 mbar) the water cluster pick up more than 50 Na atoms and reaction products Na(NaOH)_n ( n = 2, 4...50) dominate the mass spectra. The even number of NaOH units in the products indicate that also in a finite cluster the reaction occurs in pairs as in the macroscopic reaction. Received 4 December 2000     

Optical functions of InGaP/GaAs epitaxial layers from 0.01 to 5.5 eV

In_0.49Ga_0.51P films, both undoped and doped n- and p-type (up to 10¹⁸ cm^-3), were grown lattice matched on GaAs substrates, with different miscut angles, by Metal-Organic Vapour Phase Epitaxy (MOVPE) at different temperatures. The shift of the fundamental gap E₀, caused by “ordering effect” was measured as a function of temperature by photoluminescence. The complex refractive index = n + ik and the dielectric function = ɛ ₁ + iɛ ₂ at room temperature were determined from 0.01 to 5.5 eV by using complementary data from fast-Fourier-transform far-infrared (FFT-FIR), dispersive, and ellipsometric spectroscopies. The effect of the native oxide was accounted for and the self-consistency of the optical functions was checked in the framework of the Kramers-Kronig causality relations. In the restrahlen region the dielectric function was well fitted by classical Lorentz oscillators; in the transparent region below E₀, the refractive index was modelled by a Sellmeier dispersion relation; in the interband region the dielectric function was well reproduced by analytical lineshapes associated to seven critical points. Thus parametrized analytical expressions were obtained for the optical functions all over the spectral range, without discontinuities, to be used in the modelling and characterization of multi-layer structures, also on opaque substrates. Received 13 December 2001 Published online 25 June 2002     

Harmonically trapped ideal quantum gases

We solve the problem of a Bose or Fermi gas in d-dimensions trapped by δ ⩽ d mutually perpendicular harmonic oscillator potentials. From the grand potential we derive their thermodynamic functions (internal energy, specific heat, etc.) as well as a generalized density of states. The Bose gas exhibits Bose-Einstein condensation at a nonzero critical temperature T _c if and only if d + δ > 2, along with a jump in the specific heat at T _c if and only if d + δ > 4. Specific heats for both gas types precisely coincide as functions of temperature when d + δ = 2. The trapped system behaves like an ideal free quantum gas in d + δ dimensions. For δ = 0 we recover all known thermodynamic properties of ideal quantum gases in d dimensions, while in 3D for δ = 1, 2 and 3 one simulates behavior reminiscent of quantum wells, wires anddots, respectively. Good agreement is found between experimental critical temperatures for the trapped boson gases ₃₇ ⁸⁷Rb, ₃ ⁷Li, ₃₇ ⁸⁵Rb, ₂ ⁴He, ₁₉ ⁴¹K and the known theoretical expression which is a special case for d = δ = 3, but only moderate agreement for ₁₁ ²⁷Na and ₁ ¹H. Received 17 July 2002 / Received in final form 14 October 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: mdgg@hp.fciencias.unam.mx     

A shell-model approach to fractal-induced turbulence

We present a shell-model of fractal induced turbulence which predicts that structure function scaling exponents decrease in absolute value as the fractal dimension of the turbulence-inducing fractal object increases. This qualitative prediction is in agreement with laboratory measurements. Finer details of the fractal induced turbulence statistics and dynamics depend on the fractal force's phases, i.e. on the detailed construction of the fractal stirrer. In a case of deterministic forcing phases, a critical fractal dimension exists below which the average rate of inter-scale energy transfer <T _n> is a decreasing function of the wavenumber k_n and the structure function scaling exponents take close to Kolmogorov values. Above this critical fractal dimension, <T _n> is an increasing function of k_n and the structure function scaling exponents deviate significantly from Kolmogorov values. Received 25 June 2001 / Received in final form 5 April 2002 Published online 19 July 2002     

Magnetic properties of the cyclic spincluster Fe6:bicine

The magnetic properties of the cyclic compound [Fe₆(bicine)₆] LiClO₄ ^. 2MeOH are reported. The cluster Fe₆(bicine)₆ forms an antiferromagnetically coupled ring structure of Fe ^III ions. The magnetic susceptibility is measured between 2 and 300 K and yields the exchange coupling of J/k _B = - 27.5±0.5 K. The field dependence of the magnetic moment is studied at 3 and 6 K in magnetic fields up to 5 T. The zero-field splitting of the first excited spin states with S = 2 and 3 are determined by ESR at 94 GHz. The intra-molecular interactions of the Fe ^III ions are analyzed and the on-site anisotropy of the Fe ^III due to the ligand-configuration is determined to d /k _B = - 0.633±0.008K. Received 28 October 2002 / Received in final form 22 February 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: bernd@piobelix.physik.uni-karlsruhe.de     

Surface and flexoelectric polarization in a nematic liquid crystal 5CB

The temperature dependence of the surface polarization has been measured for both the planar and homeotropic orientation of a nematic liquid crystal at a solid substrate. A conventional liquid crystal 5CB, pure and doped with an azo-dye, was used in cells with controlled asymmetry for light absorption. The measurements have been made by a pyroelectric technique using short pulses of a YAG laser to create a temperature increment. The latter, in turn, was measured independently by a novel time-resolved “optical thermometer” technique monitoring temperature-dependent birefringence by a He- Ne laser beam. In accordance with the symmetry of the order parameter, the surface polarization has different sign for the two orientations, its magnitude ranges from -4 to +2pC/m. The same technique has been used for the measurement of the flexoelectric polarization in hybrid cells. The sum of the flexoelectric coefficients is e ₁ + e ₃ = - 13pC/m at 25°C. Received 28 February 2000 and Received in final form 5 September 2000