Effect of the induced magnetic field on peristaltic flow of a couple stress fluid

We have analyzed the MHD flow of a conducting couple stress fluid in a slit channel with rhythmically contracting walls. In this analysis we are taking into account the induced magnetic field. Analytical expressions for the stream function, the magnetic force function, the axial pressure gradient, the axial induced magnetic field and the distribution of the current density across the channel are obtained using long wavelength approximation. The results for the pressure rise, the frictional force per wave length, the axial induced magnetic field and distribution of the current density across the channel have been computed numerically and the results were studied for various values of the physical parameters of interest, such as the couple stress parameter γ, the Hartmann number M, the magnetic Reynolds number Rm and the time averaged mean flow rate θ. Contour plots for the stream and magnetic force functions are obtained and the trapping phenomena for the flow field is discussed.     

A buoyant flow structure in a magnetic field: Quasi-steady states and linear-nonlinear transitions

The confined evolution of a buoyant blob of fluid subject to a vertical magnetic field is investigated in the limit of low magnetic Reynolds number. When the applied magnetic field is strong, the rise velocity of the blob is small. As the vorticity diffuses along the magnetic field lines, a quasi-steady state characterised by a balance between the work done by buoyancy and Ohmic dissipation is eventually reached at time tqs∼(L²/δ²)τ, where L is the axial dimension of the fluid domain, δ is the radius of the buoyant blob and τ is the magnetic damping time. However, when the applied magnetic field is weak or the axial length is sufficiently large compared to the blob size, the growth of axial velocity eventually makes the advection of vorticity significant. The typical time for the attainment of this nonlinear phase is , where N₀ is the magnetic interaction parameter at time t=τ. The order-of-magnitude estimates for the timescales tqs and tnl are verified by computational experiments that capture both the linear and nonlinear phases.     

Three-dimensional simulations of instabilities in a Marangoni-driven, low Prandtl number liquid bridge with magnetic stabilization to verify linear stability theory

The Full-Zone model of a liquid bridge encountered in crystal growth is analyzed via linear stability analysis and three-dimensional spectral element simulations, neglecting gravitational forces, for Prandtl number 0.02. The base state is axisymmetric and steady state. Linear stability predicts the character of flow transitions and the value of Re _FZ , the thermocapillary Reynolds number, at which instabilities occur. Previous linear stability findings show that application of a steady, axial magnetic field stabilizes the base state. Previous three-dimensional simulations with no magnetic field predict a first transition that agrees well with linear stability theory. However, these simulations also demonstrated that continued time integration at just slightly higher Re _FZ leads to what appears to be periodic flow. Closer inspection and comparison with linear stability theory revealed that this apparent periodicity was actually competition between two steady modes with different axial symmetries. Here an axial magnetic field is applied in three-dimensional simulations and it is verified that the magnetic field does have the intended effect of stabilizing the flow and removing modal competition. The azimuthal flow shows excellent agreement with eigenvectors predicted by linear stability theory.     

Nonlinear magnetic induction by helical motion in a liquid sodium turbulent flow

We report an experimental study of the magnetic field B--> induced by a turbulent swirling flow of liquid sodium submitted to a transverse magnetic field B-->(0). We show that the induced field can behave nonlinearly as a function of the magnetic Reynolds number, R(m). At low R(m), the induced mean field along the axis of the flow, , and the one parallel to B-->(0), , first behave like R(2)(m), whereas the third component, , is linear in R(m). The sign of is determined by the flow helicity. At higher R(m), B--> strongly depends on the local geometry of the mean flow: decreases to zero in the core of the swirling flow but remains finite outside. We compare the experimental results with the computed magnetic induction due to the mean flow alone.     

Diffusion Effects on the Breakdown of a Linear Amplifier Model Driven by the Square of a Gaussian Field

We investigate solutions to the equation ? _t ?? $\mathcal{D}$ Δ?=λS ²?, where S(x, t) is a Gaussian stochastic field with covariance C(x?x′, t, t′), and x∈ $\mathbb{R}$ ^d . It is shown that the coupling λ _cN (t) at which the N-th moment <? ^N (x, t)> diverges at time t, is always less or equal for $\mathcal{D}$ >0 than for $\mathcal{D}$ =0. Equality holds under some reasonable assumptions on C and, in this case, λ _cN (t)=Nλ _c (t) where λ _c (t) is the value of λ at which <exp[λ ∫ ^t ₀ S ²(0, s) ds]> diverges. The $\mathcal{D}$ =0 case is solved for a class of S. The dependence of λ _cN (t) on d is analyzed. Similar behavior is conjectured when diffusion is replaced by diffraction, $\mathcal{D}$ →i $\mathcal{D}$ , the case of interest for backscattering instabilities in laser-plasma interaction.     

On the basic states of one-dimensional disordered structures

The purpose of this paper is to study a limit probability distribution of the set of the first κ eigenvalues λ₁(?)<λ₂(?)<...<λ_κ(?) (with a fixed κ and ?→∞) of the boundary problem on the interval [0, ?] wherea(t, ω),q(t, ω) are the random stationary processes. Particularly the question of the repulsion between the first eigenvalues (small energetic levels) is studied. It has been proved that in the “divergent” case (q(t, ω)=0,a(t, ω)≠0) levels repulsion exists. As for the “potential” case (a(t, ω)≡1,q(t, ω)≠0) there is not any repulsion at all. This is one of the main differences between these two cases.     

Electronic transport through a Majorana bound state coupled to a T-shaped quantum-dot system with Coulomb interaction

Using the Green’s function technique, we respectively investigate the electron transport properties of two spin components through the system of a T-shaped double quantum dot structure coupled to a Majorana bound state, in which only one quantum dot is connected with two metallic leads. We explore the interplay between the Fano effect and the MBSs for different dot-MBS coupling strength λ, dot-dot coupling strength t, and MBS-MBS coupling strength ε_M in the noninteracting case. Then the Coulomb interaction and magnetic field effect on the conductance spectra are investigated. Our results indicate that G_↓(ω) is not affected by the Majorana bound states, but a “0.5” conductance signature occurs in the vicinities of Fermi level of G_↑(ω). This robust property persists for a wide range of dot-dot coupling strength and dot-MBS coupling strength, but it can be destroyed by Coulomb interaction in quantum dots. By adjusting the size and direction of magnetic field around the quantum dots, the “0.5” conductance signature damaged by U can be restored. At last, the spin magnetic moments of two dots by applying external magnetic field are also predicted.     

The correlation function for a quantum oscillator in a low-temperature heat bath

The momentum autocorrelation function c(t) for a quantum oscillator coupled with harmonic forces to a heat bath of oscillators is calculated at low temperatures. It is found that c(t) contains two distinct terms: one, the zero-point contribution c₀(t), is temperature independent, and the other, c₁(t), does depend on temperature. We concentrate our attention on the low-temperature case. An expression for c₁(t) is obtained, which is valid for arbitrary strenghts of the coupling and for arbitrary times. It is shown that c₁(t) is governed by the low-frequency behaviour of F(λ) = A²(λ)ϱ(λ), where ϱ(λ) is the density of normal modes and A(λ) is the central-oscillator component of the λth normal mode; other details of the problem are irrelevant. It is found that c₁(t) decays in time as an inverse-power law, with a relaxation time t_q ≈ ħ/kT.     

Flow field and acoustic properties of a Mach number 0·9 jet at a low Reynolds number

An experimental study of the flow field and acoustic properties of a low Reynolds number (Re ? 3600), M = 0·9 jet has been performed in our low pressure anechoic test chamber. The mean flow field was surveyed with a conventional Pitot pressure probe and flow fluctuations were detected with a normal hot wire probe. Also, condenser microphone measurements were made in the acoustic field. The major goal of the study was to develop a better understanding of the noise generation mechanisms of subsonic jets. The flow fluctuations within the jet were found to be dominated initially by a relatively discrete, large-scale, wave-like instability centered around a Strouhal number of 0·44. The axial wavelength of this instability was determined to be 1·45 jet diameters and its azimuthal character includes the n = 0 and n = ± 1 modes. The growth of this instability coupled with its non-linear breakdown are major contributors to the termination of the potential core region of the jet. The acoustic field of the jet, in contrast to the flow field, has a broad frequency spectrum with a peak amplitude near a Strouhal number of St = 0·2. The results indicate that a non-linear mechanism involving the large scale flow instability is responsible for a dominant portion of the noise generated from this jet.     

Temperature measurements in small holes drilled in superconducting bulk during pulsed field magnetization

The time dependence of the temperatures T(z, t) has been measured along the thickness direction z in several drilled holes in a superconducting bulk during pulsed field magnetization (PFM) and the heat generation and heat transfer in the bulk have been discussed. In the previous paper [H. Fujishiro, S. Kawaguchi, K. Kakehata, A. Fujiwara, T. Tateiwa, T. Oka, Supercond. Sci. Technol. 19 (2006) S540], we calculated the T(z, t) profiles in the bulk by solving a three-dimensional heat-diffusion equation to reproduce the measured T(t) on the bulk surface; the heat generation took place adiabatically and the calculated T(z, t) was isothermal along the z direction. In this study, the measured T(z, t) at the top surface was higher than that at the bottom surface just after the pulse field application at t < 0.5 s, and then became isothermal with increasing time. These results suggest that the magnetic flux intrudes inhomogeneously into the bulk from the edge of the top surface and the periphery at the early stage. The inhomogeneous magnetic flux intrusion and the flux trap during PFM change depending on the strength of the pulsed field and the pulse number in the successive pulse field application.     

Hall effect on Hartmann flow and heat transfer of a Burgers' fluid

The effect of Hall current on the steady magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible Burgers' fluid between two parallel electrically insulating infinite planes is studied. The MHD flow is generated by applying constant pressure gradient. An external uniform magnetic field normal to the disks is applied. The disks are kept at two different constant temperatures. Exact solutions are obtained for the governing momentum and energy equations. The effects of Hartmann number M, Reynolds number Re, Prandtl number Pr, Eckert number Ec, pressure gradient dp/dx and Hall parameter η are examined.     

Time evolution of a fractal distribution: Particle concentrations in free-surface turbulence

Steady-state turbulence is generated in a tank of water and the trajectories of particles forming a compressible system on the surface are tracked in time. The initial uniformly distributed floating particles coagulate and form a fractal structure, a rare manifestation of a strange attractor observable in real space. The surface pattern reaches a steady state in approximately 1 s. Measurements are made of the fractal dimensions D_q(t) (q=1 to 6) of the floating particles starting with the uniform distribution D_q(0)=2 for Taylor Microscale Reynolds number Re_λ?160. Focus is on the time evolution of the correlation dimension D₂(t) as the steady state is approached. This steady state is reached in several large eddy turnover times and does so at an exponential rate.     

Effect of magnetic field on the IR optical properties of dielectrics

Magnetic-field induced changes revealed in reflectance spectra R(λ) of nonmagnetic dielectrics Al₂O₃, LiF, and MgO in the IR range (λ = 2.5–25 μm) are reported. The reflectance spectra are shown to have specific features in the vicinity of the wavelengths corresponding to optical phonon mode excitation in these crystals, with the magnetic field giving rise to a noticeable change of reflectance ΔR/R(λ) at these wavelengths. The value of ΔR/R(λ) for p-(s-) polarized IR radiation in a magnetic field of ～13 kOe is ～0.6% (～0.4%) for Al₂O₃ at λ ≈ 9.6 μm, ～1.63% (～1.15) for LiF at λ ≈ 11.1 μm, and ～ 0.07 (～0.2%) for MgO at λ ≈ 11.7 μm, respectively. These changes can be increased substantially by irradiating the dielectric crystals by x-ray radiation. It is shown that the optical and magnetooptical properties of the above dielectrics in the IR spectral region can be described in terms of the polaron excitation theory.     

Eigenvalue comparisons for quantum systems in a box

Comparison theorems are obtained for the first even and odd solutions of Schrödinger's equation −v″ + Q(t)v = λv, −l ≤ t ≤ l with boundary conditions v(−l) = v(l) = 0. The comparison functions Q_i(t), i = 1, 2, may intersect at a finite number of points within [−l,l]. Immediate extensions are possible for a more general class of Sturm-Liouville problems, and for problems in unbounded regions.     

Co-Si-B and Fe-Co-B amorphous alloys: Induced anisotropy and various magnetic properties

The dependence on the metalloid content of some magnetic properties of Co_100−x(Si_0.6B_0.4)_x (22.5 ⩽ x ⩽ 30) and Co₇₅Si_25−xB_x (10 ⩽ x ⩽ 25) amorphous alloys has been studied.Ribbons were subjected to different kinds of heating treatments: field annealing, stress annealing and stress-field annealing (tensile stress and longitudinal magnetic field applied simultaneously). While the anisotropies induced by simple field annealings are of the order of magnitude of 0.1 kJm^-3, the anisotropy induced by stress-field annealing can reach values up to 0.5 kJm^-3. The preferred axis is longitudinal for most of the annealing conditions. The temperature and composition dependence of the magnetostriction have been studied too.Stress, field and stress-field induced anisotropies have also been measured in Co₆₆Fe₉B₂₅ samples (λ_s > 0). In this case the preferred axis is transverse to the ribbon axis.     

Solution to the paradox of the linear stability of the Hagen-Poiseuille flow and the viscous dissipative mechanism of the emergence of turbulence in a boundary layer

It has been shown that the conclusion of the linear instability of the Hagen-Poiseuille flow at finite Reynolds numbers requires the refusal of the use of the traditional “normal” form of the representation of disturbances, which implies the possibility of separation of variables describing disturbances as functions of the radial and longitudinal (along the axis of a tube) coordinates. In the absence of such separation of variables in the developed linear theory, it has been proposed to use a modification of the Bubnov-Galerkin theory that makes it possible to take into account the difference between the periods of the longitudinal variability for different radial modes preliminarily determined by the standard application of the Galerkin-Kantorovich method to the evolution equation of extremely small axisymmetric disturbances of the tangential component of the velocity field. It has been shown that the consideration of even two linearly interacting radial modes for the Hagen-Poiseuille flow can provide linear instability only in the presence of the mentioned conditionally periodic longitudinal variability of disturbances along the axis of the tube, when the threshold Reynolds number Re_th(p) is very sensitive to the ratio p of two longitudinal periods each describing longitudinal variability for its radial disturbance mode. In this case, the threshold Reynolds number can tend to infinity, Re_th(p) → ∞, only at p = p _k = k, p = p _1/k = 1/k, and \(p = p_{\sqrt k } = [k + 1 \pm \sqrt {(k + 1)^2 - 4} ]/2\) , where k = 1, 2, 3, …. The minimum Reynolds number Re_th(p) ≈ 448 (at which p ≈ 1.527) for the linear instability of the Hagen-Poiseuille flow quantitatively corresponds to the condition of the excitation of Tollmien-Schlichting waves in the boundary layer, where Re_th = 420. Similarity of the mechanisms of linear viscous dissipative instability for the Hagen-Poiseuille flow and Tollmien-Schlichting waves has been discussed. Good quantitative agreement has been obtained between the phase velocities of the vortex disturbances and the experimental data on the velocities of the leading and trailing edges of turbulent “puffs” propagating along the axis of the tube.     

The self-similarity of wall-bounded temporally accelerating turbulent flows

From the study of viscous flow it is known that certain time-dependent laminar problems, such as the impulsively started flat plate and the diffusion of a vortex sheet, possess self-similar solutions. Previous studies of turbulent channel and pipe flows accelerating between two steady states have shown that the flow field evolves in three distinct stages. Furthermore, recent direct numerical simulations have shown that the perturbation velocity, i.e. the surplus velocity from the initial value, in an impulsively accelerating turbulent channel and pipe flow also possesses a self-similar distribution during the initial stage. In here, these results are developed analytically and it is shown that accelerating flows in which the centreline velocity develops as U^∧_c(t) = U₀(t/t₀)^m will possess a self-similar velocity distribution during the initial stage. The displacement thickness of the perturbation velocity is shown to be dependent only on the type of acceleration, and not on the initial Reynolds number, the acceleration rate or the change in Reynolds number. The derived formulas are verified with good agreement against measurements performed in a linearly accelerating turbulent pipe flow and with data from channel flow simulations.     

Dynamic and spatial behavior of a corrugated interface in the driven lattice gas model

The spatiotemporal behavior of an initially corrugated interface in the two-dimensional driven lattice gas (DLG) model with attractive nearest-neighbors interactions is investigated via Monte Carlo simulations. By setting the system in the ordered phase, with periodic boundary conditions along the external field axis. i.e. horizontal, and open along the vertical directions respectively, an initial interface was imposed, that consists in a series of sinusoidal profiles with amplitude A₀ and wavelength λ set parallel to the applied driving field axis. We studied the dynamic behavior of its statistical width or roughness W(t), defined as the root mean square of the interface position. We found that W(t) decays exponentially for all λ and lattice longitudinal sizes L_x, i.e., the lattice side that runs along the axis of the external field. We determined its relaxation time τ, and found that depends on λ as a power law τ∝λ^p, where p depends on the temperature and L_x. At low T’s (T?T_c(E)) and large L_x, p approaches to p=3/2. At intermediate T’s (T<T_c(E)), p decreases up to p≈1, and is free of finite effects. This indicates that the interface stabilizes faster than in the equilibrium model, i. e. the Ising lattice gas (E=0) where p=3. At higher T’s p increases for T?T_c(E), and the finite size dependence is recovered. Also, if T is fixed, p increases with L_x until it saturates at large values of it, while this regime is vanishing at T?T_c(E). In this way, the dynamic relaxation process of a sinusoidal interface is improved by the external driving field with respect to its equilibrium counterpart, if the system is set in an intermediate temperature stage far from T_c(E) and in a lattice with a sufficiently large longitudinal side. The behavior of τ was also investigated as a function of E and in the intermediate stage T<T_c(E). It was found that τ decreases exponentially with E in the interval 0<E?1, while for higher fields it remains constant. The exponential decay depends on the wavelength of the initial profile.In order to study the spatial evolution of the profiles, we evaluated the structure factor of the interface, and the Fourier coefficients corresponding to the same wave vector of the initial profile. The obtained results allowed us to conclude that the spatial evolution of the profile maintains its initial wavelength, does not travel along the external field axis, and its shape is preserved over all the relaxation process.     

Investigation of the optical constants of arsenic chalcogenide films in the wavelength range 0.5–2.5 μm

Thin films of chalcogenide glasses deposited on quartz glass substrates by thermal evaporation in vacuum have been investigated. The dependences n(λ) and k(λ) for films of different composition have been determined from the transmission spectra. Expressions of the n = A + BL + CL ² + Dλ ² + Eλ ⁴ type (L = (λ ² ? 0.028)^?1 and A, B, C, D, and E are constants) for calculating the refractive indices of As₂Se₃, AsSe₄, AsS₄, and AsS_16.2Se_16.2 films in the wavelength range from 0.5 to 2.5 μm are reported.     

Study of the K − → μ − νπ 0 decay

The decay K ^? → μ ^? νπ ⁰ has been studied using in-flight decays detected with the ISTRA+ setup operating in the 25-GeV negative secondary beam of the U-70 PS. About 112K events were used for the analysis. The λ ₊ and λ ₀ slope parameters of the decay form factors f ₊(t) and f ₀(t) have been measured: λ ₊=0.0321±0.004(stat.)±0.002(syst.), λ ₀=0.0209±0.004(stat.)±0.002(syst.); the correlation dλ ₀/dλ ₊=?0.46. The limits on the possible tensor and scalar couplings have been derived: f _T/f ₊(0)=?0.021±0.028(stat.)±0.014(theor.), f _S/f ₊(0)=0.004±0.005(stat.)±0.005(theor.).