Magnetic field generation by convective flows in a plane layer

Hydrodynamic and magnetohydrodynamic convective attractors in a plane horizontal layer 0≤z≤1 are investigated numerically. We consider Rayleigh-Bénard convection in Boussinesq approximation assuming stress-free boundary conditions on horizontal boundaries and periodicity with the same period L in the x and y directions. Computations have been performed for the Prandtl number P=1 for and Rayleigh numbers 0<R≤4000, and for L=4, 0<R≤2000. Fifteen different types of hydrodynamic attractors are found, including two types of steady states distinct from rolls, travelling waves, periodic and quasiperiodic flows, and chaotic attractors of heteroclinic nature. Kinematic dynamo problem has been solved for the computed convective attractors. Out of the 15 types of the observed attractors only 6 can act as kinematic dynamos. Nonlinear magnetohydrodynamic regimes have been explored assuming as initial conditions convective attractors capable of magnetic field generation, and a small seed magnetic field. After initial exponential growth, in the saturated regime magnetic energy remains much smaller than the flow kinetic energy. The final magnetohydrodynamic attractors are either quasiperiodic or chaotic.     

Chaotic travelling rolls in Rayleigh-Bénard convection

In this paper we investigate two-dimensional (2D) Rayleigh-Bénard convection using direct numerical simulation in Boussinesq fluids with Prandtl number P = 6.8 confined between thermally conducting plates. We show through the simulation that in a small range of reduced Rayleigh number r (770 < r < 890) the 2D rolls move chaotically in a direction normal to the roll axis. The lateral shift of the rolls may lead to a global flow reversal of the convective motion. The chaotic travelling rolls are observed in simulations with free-slip as well as no-slip boundary conditions on the velocity field. We show that the travelling rolls and the flow reversal are due to an interplay between the real and imaginary parts of the critical modes.     

Unsteady conjugate thermogravitational convection in a cylindrical region with local energy source

The mathematical modelling of unsteady regimes of natural convection in a closed cylindrical region with a heat-conducting shell of finite thickness was carried out in the presence of a local heat source under the conditions of convective heat exchange with the ambient medium. The mathematical model was constructed in dimensionless variables “stream function — vorticity vector — temperature” in the cylindrical coordinate system. The influence of the Rayleigh number, 10⁴ ≤ Ra ≤ 10⁶, of the unsteadiness factor 0 < τ < 300, of the thermal conductivity ratio λ _2,1 = 5.7·10⁻⁴, 4.3·10⁻², and the energy source sizes on both local characteristics (streamlines and temperature fields) and on the integral complex (the mean Nusselt number on typical boundaries) was analysed in detail. Thermohydrodynamic peculiarities due to the geometry of the object of research were established.     

Application of the multi distribution function lattice Boltzmann approach to thermal flows

Numerical methods able to model high Rayleigh (Ra) and high Prandtl (Pr) number thermal convection are important to study large-scale geophysical phenomena occuring in very viscous fluids such as magma chamber dynamics (10⁴ < Pr < 10⁷ and 10⁷ < Ra < 10¹¹). The important variable to quantify the thermal state of a convective fluid is a generalized dimensionless heat transfer coefficient (the Nusselt number) whose measure indicates the relative efficiency of the thermal convection. In this paper we test the ability of Multi-distribution Function approach (MDF) Thermal Lattice Boltzmann method to study the well-established scaling result for the Nusselt number (Nu ∝ Ra ^1/3) in Rayleigh Bénard convection for 10⁴ ≤ Ra ≤ 10⁹ and 10¹ ≤ Pr ≤ 10⁴. We explore its main drawbacks in the range of Pr and Ra number under investigation: (1) high computational time N _c required for the algorithm to converge and (2) high spatial accuracy needed to resolve the thickness of thermal plumes and both thermal and velocity boundary layer. We try to decrease the computational demands of the method using a multiscale approach based on the implicit dependence of the Pr number on the relaxation time, the spatial and temporal resolution characteristic of the MDF thermal model.     

Logarithmic corrections to scaling in turbulent thermal convection

We use a simplified model of turbulent convection to compute analytically heat transport in a horizontal layer heated from below, as a function of the Rayleigh and the Prandtl number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we recover power classical scaling regimes of the Nusselt versus Rayleigh number, with exponent 1/3 or 1/4. At larger Reynolds number, velocity and temperature fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the Nusselt versus Rayleigh or Prandtl. Instead, we obtain logarithmic corrections to the classical soft (exponent 1/3) or ultra-hard (exponent 1/2) regimes, in a way consistent with the most accurate experimental measurements available nowadays. This sets a need for the search of new measurable quantities that are less prone to dimensional theories.     

Mode-to-mode energy transfers in convective patterns

We investigate the energy transfer between various Fourier modes in a low-dimensional model for thermal convection. We have used the formalism of mode-to-mode energy transfer rate in our calculation. The evolution equations derived using this scheme is the same as those derived using the hydrodynamical equations for thermal convection in Boussinesq fluids. Numerical and analytical studies of this model show that convective rolls appear as the Rayleigh number R is raised above its critical value R _c. Further increase of Rayleigh number generates rolls in the perpendicular directions as well, and we obtain a dynamic asymmetric square pattern. This pattern is due to Hopf bifurcation. There are two sets of limit cycles corresponding to the two competing asymmetric square patterns. When the Rayleigh number is increased further, the limit cycles become unstable simultaneously, and chaotic motion sets in. The onset of chaos is via intermittent route. The trajectories wander for quite a long time almost periodically before jumping irregularly to one of the two ghost limit cycles.     

Observation of the muon inner bremsstrahlung at?LEP1

Muon bremsstrahlung photons converted in front of the DELPHI main tracker (TPC) in dimuon events at LEP1 were studied in two photon kinematic ranges: 0.2<E _γ ≤1 GeV and transverse momentum with respect to the parent muon p _T <40 MeV/c, and 1<E _γ ≤10 GeV and p _T <80 MeV/c. A good agreement of the observed photon rate with predictions from QED for the muon inner bremsstrahlung was found, contrary to the anomalous soft photon excess that has been observed recently in hadronic Z ⁰ decays. The obtained ratios of the observed signal to the predicted level of the muon bremsstrahlung are 1.06±0.12±0.07 in the photon energy range 0.2<E _γ ≤1 GeV and 1.04±0.09±0.12 in the photon energy range 1<E _γ ≤10 GeV. The bremsstrahlung dead cone is observed for the first time in the direct photon production at LEP. Deceased.     

The high-pressure-induced spin-reorientation transition in a ferromagnetic semiconductor Cd<Subscript>0.7</Subscript>Mn<Subscript>0.3</Subscript>GeAs<Subscript>2</Subscript>

The dependences of the longitudinal magnetoresistance (Δρ _zz /ρ₀)(P), transverse magnetoresistance (Δρ _xx /ρ₀)(P), and magnetic susceptibility (χ/χ₀(P)) on hydrostatic pressure P ≤ 7 GPa in the ferromagnetic semiconductor Cd_0.7Mn_0.3GeAs₂ at room temperature were investigated.     

Scattering of Rayleigh waves by a statistical inhomogeneity of the mass density

The problem of the scattering of a Rayleigh wave by a surface inhomogeneity of the mass density of an isotropic solid is solved in the Born approximation of perturbation theory. The inhomogeneity is statistical with a Gaussian correlation function in the plane parallel to the surface and is deterministic with an exponentially decaying dependence on the coordinate perpendicular to the surface. Expressions are derived for the displacement fields in the scattered longitudinal (P), transverse (SV and SH), and Rayleigh (R) waves at large distances from the inhomogeneity. The Rayleigh wave energy scattering coefficients are calculated as functions of the wavelength λ, the correlation length a of the inhomogeneity, the depth d of the defective layer, and the Poisson ratio of the medium, σ. The angular distribution of the scattered Rayleigh wave energy is determined. Asymptotic expressions are obtained for the scattering coefficient in various limiting cases with respect to the parameters a/λ and λ/d. The relation between the energies in the scattered P, SV, SH, and R waves is established. The resulting equations are used to calculate the scattering coefficients numerically over a wide range of variation of the parameters a/λ, λ/d, and σ; the results are presented in the form of graphs and a table. A physical pattern of the scattering process is constructed and used as a basis for interpreting the results of the study. Fiz. Tverd. Tela (St. Petersburg) 39, 267–274 (February 1997)     

EPR Studies of Tl0.5Pb0.5Sr1.6Ba0.4CaCu2?xRuxO7?δ Superconductor

Bulk superconducting samples of type Tl_0.5Pb_0.5Sr_1.6Ba_0.4CaCu_2−x Ru _x O_7−δ, (Tl, Pb)/Sr-1212, with 0.0 ≤ x ≤ 0.525 were prepared by the conventional one-step solid-state reaction technique. The prepared samples were investigated using X-ray powder diffraction, electrical resistivity and electron paramagnetic resonance (EPR) measurements. Enhancement of the phase formation, superconducting transition temperature T _c and hole carriers concentration P was observed up to x = 0.075. For x > 0.075, a reverse trend was observed. EPR spectra were measured at different temperatures (120–290 K) for all prepared samples. The number of spins N participating in the resonance and the paramagnetic susceptibility χ were calculated as a function of both Ru-content and temperature. N and χ increased as the Ru-content increased. A linear relationship between logN and 1/T was established, from which the activation energy E _a was calculated as a function of the Ru-content. The temperature dependence of χ was fitted according to Curie–Weiss type of magnetic behavior. Curie constant C, Curie temperature θ, the effective magnetic moment μ and the electronic specific heat γ were estimated as a function of the Ru-content.     

Spin-Flip and Elastic Processes in Slow Collisions of Mesic Atoms

The reduced adiabatic hyperspherical (RAHS) basis suggested previously is used for the calculation of elastic and spin-flip cross sections in the processes (aμ) _F + a → (aμ) _F′ + a, a = (p, d, t), for collision energies 10⁻³ ≤ ε ≤ 10² eV. The rapid convergence of the method is demonstrated. A comparison of the obtained results with previous ones is presented. This revised version was published online in August 2006 with corrections to the Cover Date.     

A study on electrodeposited Ni x Fe1−x alloy films

Ni _x Fe_1−x (0.22 ≤x ≤ 0.62) alloy films were grown by electrodeposition technique. A shift in diffraction peaks of NiFe and Ni₃Fe was detected with increasing Ni content. The highest positive magnetoresistance ratio was detected as 5% in Ni0.₅₁Fe0.₄₉. Positive and negative anisotropic magnetoresistance were observed in longitudinal and transverse geometries respectively. The highest anisotropic magnetoresistance ratio of 9.8% was also detected in Ni0.₅₁Fe0.₄₉. The angular variation of magnetoresistance was studied. Magnetisation loop curves show that NiFe alloy films have a linear decreasing anisotropy constant with increasing Ni deposit content and show a decreasing behavior of coercivity which indicates soft magnetic property with increasing Ni deposit content     

Infinite Prandtl Number Convection

We prove an inequality of the type NCR ^1/3(1+log₊ R)^2/3 for the Nusselt number N in terms of the Rayleigh number R for the equations describing three-dimensional Rayleigh–Bénard convection in the limit of infinite Prandtl number.     

Bounds on charged lepton mixing with exotic charged leptons

We examine the effects of mixing induced light heavy charged lepton neutral currents on the partial wave amplitude for the process l⁺l⁻ →ZZ (withl = e,μ or τ). By imposing the constraints that the amplitude should not exceed the perturbative unitarity limit at high energy (√s = Λ), we obtain bounds on light heavy charged lepton mixing parameter sin²(2θ _L ^a ) where θ _L ^a is the mixing angle of the ordinary charged lepton with its exotic partner. For Λ = 1 TeV, no bound is obtained on sin² (2θ _L ^a ) form _E < 0.69 TeV. However, sin² (2θ _L ^a ) ≤ 1.52×10⁻⁵ form _E = 5 TeV, sin² (2θ _L ^a ) ≤ 2.41 ×10⁻⁷ form _E = 10 TeV. Similarity for Λ = ∞ no bound is obtained on sin² (2θ _L ^a ) for m_E < 1.97 TeV and sin² (2θ _L ^a ) ≤ 0.15 form _E = 5 TeV and sin² (2θ _L ^a ) ≤ 3.88×10^-2 form _E = 10 TeV.     

A multi agent model for the limit order book dynamics

By means of the Howard-Busse method of the optimum theory of turbulence we investigate numerically the effect of strong rotation on the upper bound on the convective heat transport in a horizontal fluid layer of infinite Prandtl number Pr. We discuss the case of fields with one wave number for regions of Rayleigh and Taylor numbers R and Ta where no analytical asymptotic bounds on the Nusselt number Nu can be derived by the Howard-Busse method. Nevertheless we observe that when R > 10⁸ and Ta is large enough the wave number of the optimum fields comes close to the analytical asymptotic result α₁ = (R/5)^1/4. We detect formation of a nonlinear structure similar to the nonlinear vortex discussed by Bassom and Chang [Geophys. Astrophys. Fluid Dyn. 76, 223 (1994)]. In addition we obtain evidence for a reshaping of the horizontal structure of the optimum fields for large values of Rayleigh and Taylor numbers.     

The attenuation of rayleigh surface waves by surface roughness

This paper presents a calculation of the attenuation length of Rayleigh surface waves in the presence of surface roughness. We consider Rayleigh waves on the surface of a semi-infinite isotropic elastic continuum, and the method we use produces the contribution to the attenuation rate proportional to the square of the rms amplitude of the roughness. We obtain explicit expressions for the contribution to the attenuation rate from roughness-induced scattering into bulk transverse and longitudinal acoustic waves, and into Rayleigh waves. Our derivation makes use of a Green's function method. When the wavelength λ of the Rayleigh wave is long compared to the transverse correlation length a that characterizes the surface roughness, all contributions to the attenuation rate are proportional to the fifth power of the frequency. When λ is comparable to or smaller than a, the attenuation constant varies more slowly with frequency. For a model of the surface roughness, we present numerical calculations of the relative magnitude and frequency dependence of the various contributions to the attenuation rate. The Green's functions used here may be applied to a number of calculations. A derivation of their form is provided in an Appendix.     

Control of material removal of fused silica with single pulses of few optical cycles to sub-picosecond duration

Surface ablation of a dielectric material (fused silica) by single femtosecond pulses is studied as a function of pulse duration (7–450 fs) and applied fluence (F _th<F<10F _th). We show that varying the pulse duration gives access to high selectivity (with resolution ∼10 nm) for axial removal of matter but does not influence the transverse ablation selectivity, which only depends on the normalized applied fluence F/F _th. The ablation efficiency is shown to be inversely dependent on the pulse duration and saturates with respect to the applied fluence earlier at ultra-short pulse durations (≤30 fs). The deduced optimal fluence F _opt corresponding to the highest ablation efficiency for each pulse width defines two regimes of laser application. Below F _opt, the removed material depth can be accurately adjusted in a large range (∼40–200 nm) as a function of the applied fluence and the morphology of the ablated pattern almost reproduces the Gaussian beam distribution. Above F _opt, the material removal depth tends to saturate and the morphology of the ablated pattern evolves to a top-hat distribution. The coupled evolution of depth and morphology is related to the dynamics of formation of dense plasma at the surface of the material, acting as an ultra-fast optical shutter.     

Use of the wake of a small cylinder to Control unsteady loads on a circular cylinder

Simultaneous measurements of lift and drag forces have been performed in order to study passive control of unsteady loads induced on a circular cylinder. For this purpose, an aerodynamic balance has been developed. The balance, developed for a cylinder of 25.4 mm in diameter, was designed to operate in the subcritical regime (Re=32000). This instrument is characterized by its sensitive element that forms a small central part of the cylinder. The static and dynamic calibrations of the balance show the appropriateness of the present design. Moreover, qualification experiments carried out with a single cylinder gave results (mean and rms values of the lift and drag coefficients) that are in good agreement with those found in the literature. The purpose of this paper is to present a passive control experiment performed by means of the wake of a smaller cylinder interacting with a larger one. Firstly, a parametric study was performed by varying the following: i) the diameterdS of the small cylinder for one large cylinder diameterd (7 values in the range 0.047≤d _S /d≤0.125); ii) the center-to-center spacingS/d (11 values in the range 1.375≤S/d≤2.5); and iii) the stagger anglea(0≤a≤90 with a fine angular stepDa fora≤15). A maximum mean drag reduction of about 48% is achieved. Ata=4 to 8, one can observe a peak of mean lift coefficient. Then unsteady fluid forces, vortex shedding frequency and flow pattern were systematically investigated for the small cylinder having a diameterdS=2.4 mm (0.094d). Reductions of 78% and 56% of the rms lift and drag fluctuations respectively were obtained with the small cylinder placed at a slight stagger angle in the range 6<a<9. This leads to an instantaneous force vector that exhibits more steadiness both in angle and amplitude. Moreover, at these stagger angles, the energy of the lift fluctuations at the shedding frequency is significantly reduced compared to the single cylinder case.     

Differing Averaged and Quenched Large Deviations for Random Walks in Random Environments in Dimensions Two and Three

We consider the quenched and the averaged (or annealed) large deviation rate functions I _q and I _a for space-time and (the usual) space-only RWRE on \mathbbZ^d{\mathbb{Z}^d} . By Jensen’s inequality, I _a  ≤ I _q . In the space-time case, when d ≥ 3 + 1, I _q and I _a are known to be equal on an open set containing the typical velocity ξ _o . When d = 1 + 1, we prove that I _q and I _a are equal only at ξ _o . Similarly, when d = 2 + 1, we show that I _a  < I _q on a punctured neighborhood of ξ _o . In the space-only case, we provide a class of non-nestling walks on \mathbbZ^d{\mathbb{Z}^d} with d = 2 or 3, and prove that I _q and I _a are not identically equal on any open set containing ξ _o whenever the walk is in that class. This is very different from the known results for non-nestling walks on \mathbbZ^d{\mathbb{Z}^d} with d ≥ 4.     

μ + SR studies of antiferromagnetic chromiumSR studies of antiferromagnetic chromium

μ ⁺ SR measurements have been performed on Cr single crystals at temperatures 60 mK≤T≤295 K in applied magnetic fields 0≤B _appl≤1.5 T. The temperature dependence of the observed precession frequencies and transverse relaxation rates can be explained by the assumption that theμ ⁺ are hopping between adjacent tetrahedral interstices. At temperaturesT≤11 K evidence for an interaction between theμ ⁺ and the spin-density waves in Cr has been found. The directions and magnitudes of the lattice magnetic moments are unaffected by the applied magnetic fields.