Magnetohydrodynamic stratified flow past a sphere

This paper considers the uniform, steady, horizontal flow of a vertically stratified, electrically conducting, non-diffusive fluid over a non-conducting sphere in the presence of a uniform magnetic field. The force exerted on the sphere is investigated on the basis of the method of matched asymptotic expansions, for small values of a stratification parameter α, $\text{R}{}_{\mathrm{e}}\text{? ¦α¦}{}^{\mathrm{<mtext>1</mtext><mtext>3</mtext>}}$, $\text{F}{}_{\mathrm{r}}{}^2\text{? ¦α¦}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>3</mtext>}}$ and for $\text{M}{}^2\text{= 0(α}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$. Up to the first order of calculations the drag is computed for a few typical values of magnetic interaction parameter when, (a) The applied magnetic field lies in the vertical plane and inclined with the ambient flow direction. (b) The applied magnetic field lies in the horizontal plane and perpendicular to the flow direction. Further it is shown that the sphere has no tendency to rotate nor it experiences a lift force upto the order of calculations which we have made. The drag experienced by the sphere is found to be increased due to the combined effects of stratification and magnetic field.     

Studies in convergence of stochastic models in rough-surface hydrodynamic lubrication theory

The stochastic Reynolds equation for hydrodynamic lubrication with random homogeneous roughness of the lubricated surface is studied using series expansions. In the case in which the roughness function $\text{δ ? C}{}^0\text{(}\text{}\text{?}\text{gW)}$, we show convergence of the series for pressure and its expectation in the Sobolev space $\text{H}{}^1\text{(Ω)}$, whereas in the case in which $\text{δ ? C}{}^1\text{(}\text{}\text{?}\text{gW)}$, the series converge in $\text{C}{}^2\text{(Ω)}$ provided ▽δ is uniformly bounded.     

The elastic field around an elliptical crack in an anisotropic medium under an applied stress of polynomial forms

A general form is presented for the stress disturbance caused by an elliptical crack in an anisotropic medium under an arbitrary stress field in the form of polynomials. Somigliana's dislocation method is employed for analysis as Willis [4] did, but a different integral process is taken. The results are expressed in the integral forms defined on the subspace of the surface of a unit sphere. The following theorem is proved: If the displacement discontinuity of the elliptical Somigliana's dislocation has the form where is a homogeneous polynomial of degree $\text{N}$ in the coordinates $\text{x′}{}_1$ and $\text{x′}{}_2$ and $\text{a}{}_1$ and $\text{a}{}_2$ are the semi-axes of the elliptical Somigliana's dislocation, the stresses on the plane of the Somigliana's dislocation are inhomogeneous polynomials in the coordinates, whose terms are of degree $\text{N, (N ? 2}$), $\text{(N ? 4),4.}$     

Pressure drop in selected porous materials used for thermal regenerators

The isothermal pressure drop of porous iron whisker matrices, bronze wire mesh screens and small stainless steel spheres has been measured in the region of very small Reynolds-numbers $\text{Re}\text{? 10}{}^{\mathrm{?2}}$. The results are discussed applying physical models for laminar flow producing small wakes downstream and the influence of the filling factor k of the different samples is considered. Using the porous material as a low temperature thermal regenerator, the pressure drop is shown to reduce the thermal efficiency of the regenerative cooling process.     

Observation of magnetic flux frozen in high conductivity metal during flux jumping in a type II superconductor

In the concentric arrangement of a superconducting tube and a high-conductivity aluminium cylinder, the magnetic flux variation arising from flux jumps occurred only within the superconducting tube itself, whereas the magnetic flux in the normal metal was almost completely frozen during the flux jumps. Provided that the magnetic flux was completely frozen in the normal metal, the energy released by a flux jump was calculated to be equal to a quarter that released by a complete flux jump. It was found that the magnetic diffusion time-constant was much larger than that given by $\text{L}{}^2\text{π}{}^2\text{D}{}_{\mathrm{m}}$.     

On the thermal and mechanical properties of slender-fibre reinforced materials at non-dilute concentration

The slender-body theory as applied to a dilute suspension of nearly-rigid and nearly-perfect conducting fibres in an elastic matrix predicts an increase in the composite Young modulus and thermal conductivity along the direction of the applied field of the order $\text{l}{}^2\text{/R}{}_0{}^2$, where 2$\text{l}$ is the length of the fibre and $\text{R}{}_0$ is its representative radius. As a consequence of the diluteness assumption, the fibre-contributed stress or heat flux is never more than a perturbation of the stress or the heat flux due to the ma rix. At non-dilute concentration range, where the average distance between neighbouring fibres is very much less than $\text{l}$ but yet much greater than $\text{R}{}_0$, Batchelor's ideas can be applied to show that the dilute formulae continue to give accurate predictions, and that an order of magnitude increase in Young modulus or thermal conductivity is possible at this level of concentration.     

Electronic and spin configurations of Co3+ and Ni3+ ions in oxides of K2NiF4 structure: A magnetic susceptibility study

In La₄LiCoO₈, Li⁺ and Co³⁺ ions are ordered in two dimensions and Co³⁺ ions undergo transitions from the low-spin to the intermediate as well as the high-spin states. Both Sr₄TaCoO₈ and Sr₄NbCoO₈ exhibit low to intermediate-spin state transitions of Co³⁺ ions. In the system LaSr_1?xBa_xNiO₄, the e_g electrons are essentially in extended states forming a band. With increase in x, the band width decreases accompanying an increase in unit cell volume; high-spin Ni³⁺ ions are formed to a small extent with increasing x, but there is no spin-state transition. In LaSrAl_1?xNi_xO₄, at small x, there is a small proportion of high-spin Ni³⁺; when x ≈ 0.6, there is an abrupt decrease in the $\text{c}$/$\text{a}$ ratio, signalling the formation of the band. In LnSrNiO₄, the $\text{c}$/$\text{a}$ ratio decreases sharply between Ln = La and Nd; this is likely to be accompanied by a broadening of the band.     

Drag force acting on a neuromast in the fish lateral line trunk canal. II. Analytical modelling of parameter dependencies

In Part I of this two-part study, the coupled flows external and internal to the fish lateral line trunk canal were consecutively calculated by solving the Navier–Stokes (N–S) equations numerically in each domain. With the external flow known, the solution for the internal flow was obtained using a parallelepiped to simulate the neuromast cupula present between a pair of consecutive pores, allowing the calculation of the drag force acting on the neuromast cupula. While physically rigorous and accurate, the numerical approach is tedious and inefficient since it does not readily reveal the parameter dependencies of the drag force. In Part II of this work we present an analytically based physical–mathematical model for rapidly calculating the drag force acting on a neuromast cupula. The cupula is well approximated as an immobile sphere located inside a tube-shaped canal segment of circular cross section containing a constant property fluid in a steady-periodic oscillating state of motion. The analytical expression derived for the dimensionless drag force is of the form |FN|/(|PL−PR|π(D/2)2)=f(d/D,Lt/D,ωD*), where |F_N| is the amplitude of the drag force; |P_L−P_R| is the amplitude of the pressure difference driving the flow in the interpore tube segment; d/D is the ratio of sphere diameter to tube diameter; L_t/D is the ratio of interpore tube segment length to tube diameter; and ωD*=ω(D/2)2/ν is the oscillating flow kinetic Reynolds number (a dimensionless frequency). Present results show that the dimensionless drag force amplitude increases with decreasing L_t/D and maximizes in the range 0.65≤d/D≤0.85, depending on the values of L_t/D and ωD*. It is also found that in the biologically relevant range of dimensionless frequencies 1≤ωD*≤20 and segment lengths 4≤L_t/D≤16, the sphere tube (neuromast–canal) system acts as a low-pass filter for values d/D≤0.75, approximately. For larger values of d/D the system is equally sensitive to all frequencies, but the drag force is significantly decreased. Comparisons with N–S calculations of the drag force show good agreement with the analytical model results. By revealing the parameter dependencies of the drag force, the model serves to guide biological understanding and the optimized design of corresponding bioinspired artificial sensors.     

Vaporization reactions of manganese gallium sulfide

The vaporization of manganese gallium sulfide was investigated in the temperature range 500–975°. Manganese gallium sulfide was found to vaporize incongruently by the reaction:

$\text{3}\text{MnGa}{}^2\text{S}{}^4\text{(s) =}\text{Mn}{}^3\text{Ga}{}^2\text{S}{}^6\text{(s) + 2}\text{Ga}{}^2\text{S}\text{(g) + 2}\text{S}{}^2\text{(g)}$

and

$\text{Mn}{}^3\text{Ga}{}^2\text{S}{}^6\text{(s) = 3}\text{MnS(s)}\text{+}\text{Ga}{}^2\text{S}\text{(g) +}\text{S}{}^2\text{(g)}$

Approximate vapor pressures were measured by the Knudsen effusion technique. Lattice parameters, density, and chemical analysis of the new ternary compound Mn₃Ga₂S₆ are reported.     

Recrystallization of InSb thin films obtained by cathode sputtering

Thin polycrystalline n-type InSb films were prepared by cathode sputtering. The Hall mobility of the films was about $\text{300 cm}{}^2\text{V}\text{s}$. When the films were recrystallized by melting in an argon atmosphere at normal pressure, an influence of the sputtering conditions on the properties of the recrystallized films was found. Room temperature mobilities of $\text{4000 cm}{}^2\text{V}\text{s}$ were achieved after recrystallization.     

Carburization and decarburization kinetics of iron in CH4 — H2 mixtures between 1000 – 1100 °C

In this study the rate constants of the methane decomposition reaction on iron surfaces were determined in the 1000–1100°C temperature range, by grav? metric methods. Earlier works showed that the reaction velocity was given by The results indicate that the constant values vary from 2.72 × 10^?6 to $\text{16.74 × 10}{}^{\mathrm{?6}}\text{mol C/cm}{}^2\text{/sec/atm}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ for k and 2.61 × 10^?8 to $\text{8.62 × 10}{}^{\mathrm{?8}}\text{mol C/cm}{}^2\text{/sec/atm}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}$ for k′ between 1000 and 1100°C.     

Stress in the vicinity of a griffith crack at the interface of a layer bonded to a half plane—an approximate method

Approximations to the stress field in the vicinity of a Griffith crack located at the interface of a layer bonded to a dissimilar half plane are determined. A systematic use of Fourier transforms reduces the problem to that of solving a set of simultaneous dual integral equations with trigonometric kernels and weighting functions. This latter problem is reduced to the solution of an uncoupled pair of singular integral equations. An approximate technique using Legendre polynomial expansions is discussed. The analysis shows that when a constant pressure is applied to the faces of the crack, the stress components have the distinctive oscillatory singularities at the crack tip. Expressions up to the order of $\text{h}{}^{\mathrm{?4}}$, where $\text{h}$ is the thickness of the layer and is much greater than 1, are derived for the stress components.     

Nouveaux conducteurs ioniques caracterises par une structure a tunnels entrecroises

The ionic conductivity of pyrochlores A_1+α(Ta_1+αW_1?α)O₆ was investigated for A = Na and T1. The thallium compounds are rather good conductors (0.34 ≤ ΔE ≤ 0.40 eV and $\text{5 10}{}^{\mathrm{?8}}\text{(Θ}\text{cm}\text{)}{}^{\mathrm{?1}}\text{≤}{}^{\mathrm{\sigma }}\text{25°}\text{C}\text{≤ 5.5 10}{}^{\mathrm{?5}}\text{(Θ}\text{cm}\text{)}{}^{\mathrm{?1}}$); the sodium oxides are poor conductors (0.76 eV ≤ ΔE ≤ 1.48 eV and $\text{10}{}^{\mathrm{?7}}\text{(Θ}\text{cm}\text{)}{}^{\mathrm{?1}}\text{≤}{}^{\mathrm{\sigma }}\text{500}\text{K}\text{≤ 10}{}^{\mathrm{?5}}\text{(Θ}\text{cm}\text{)}{}^{\mathrm{?1}}$). The differences between these two classes of pyrochlores are explained in terms of structure. New non-stoechiometric oxides T1_12+x(M_30+xW_3?x)O₉₀, with M = Ta, Nb, and 0 ≤ x ≤ 3, were isolated. They are, like pyrochlores, characterized by an intersecting tunnel structure, which is an intergrowth of pyrochlore and A₂M₇O₁₈ structures. These oxides show ionic conduction properties which are very close to those of pyrochlores: the tantalum oxides are better conductors (0.30 eV ≤ ΔE ≤ 0.37 eV ; $\text{3.6 10}{}^{\mathrm{?7}}\text{(Θ}\text{cm}\text{)}{}^{\mathrm{?1}}\text{≤}{}^{\mathrm{\sigma }}\text{25°}\text{C}\text{≤ 1.4 10}{}^{\mathrm{?6}}\text{(Θ}\text{cm}\text{)}{}^{\mathrm{?1}}$) than the niobium oxides (0.36 eV ≤ ΔE ≤ 0.42 eV ; $\text{10}{}^{\mathrm{?7}}\text{(Θ}\text{cm}\text{)}{}^{\mathrm{?1}}\text{≤}{}^{\mathrm{\sigma }}\text{25°}\text{C}\text{≤ 3.8 10}{}^{\mathrm{?7}}\text{(Θ}\text{cm}\text{)}{}^{\mathrm{?1}}$). The evolution ofionic conduction properties of all these compounds is discussed.     

Copper doped zinc oxide Y2BaZnO5: ERS and optical investigation

In copper doped Y₂BaZnO₅ oxides, copper exhibits a distorted square pyramidal coordination which is consistant with the values of g and A tensors obtained from O band ERS spectrum for a sample containing about 1 % Cu. Three values for g and A are observed, g₁ = 2.049₅, g₂ = 2.051₅, g₃ = 2.275, $\text{¦}\text{A}{}_1\text{¦ = 13 10}{}^{\mathrm{?4}}\text{cm}{}^{\mathrm{?1}}$, $\text{¦}\text{A}{}_2\text{¦ = 10 10}{}^{\mathrm{?4}}\text{cm}{}^{\mathrm{?1}}$ and $\text{¦}\text{A}{}_3\text{¦ = 147.5 10}{}^{\mathrm{?4}}\text{cm}{}^{\mathrm{?1}}$. Since $\text{g}{}_1\text{?}\text{g}{}_2$ an approximate C_4v point symmetry can be assumed for copper. The electronic spectrum shows three bands at 11700, 14500 and 20500 cm^?1 which can be assigned to the transitions A₁ → B₁, B₂ → B₁ and E → B₁ respectively. The orbital reduction parameters are calculated and the bonding covalency is discussed.     

Thermal expansion of corundum structure Rh2O3

The directional thermal expansion coefficients of the corundum structure form of Rh₂O₃ were determined from room temperature to 850°C by x-ray diffraction methods. Rh₂O₃ has a lower thermal expansion and is less anisotropic in thermal expansion than alumina. The directional thermal expansion coefficients of Rh₂O₃ expressed in second degree polynominal form are: $\text{“α}{}_{\mathrm{<mtext>a</mtext>}}\text{” = 5.350 ×10}{}^{\mathrm{?6}}\text{+ 1.281 ×10}{}^{\mathrm{?9}}\text{T}\text{? 1.133 ×10}{}^{\mathrm{?14}}\text{T}{}^2\text{/°}\text{C}$ and $\text{“α}{}_{\mathrm{<mtext>c</mtext>}}\text{” = 5.246 ×10}{}^{\mathrm{?6}}\text{+ 6.369 ×10}{}^{\mathrm{?9}}\text{T}\text{? 7.480 ×10}{}^{\mathrm{?14}}\text{T}{}^2\text{/°}\text{C}$.     

Formation and properties of metallic organotin films

Semiconductive and conductive films of metallic appearance are formed by glow discharge of appropriate organometallic compounds. Tetramethyltin is used as a starting compound for the film-forming experiments. The resulting films contain carbon, tin and hydrogen with a carbon-to-tin atomic ratio of 2.5 or less. These films are semiconductors with conductivities between 2 × 10^-1 and $\text{1 × 10}{}^{-2}\text{Ω}{}^{-1}\text{cm}{}^{-1}$. Transmission electron microscopy shows the films to be amorphous. Films of a certain composition are transformed to β-Sn on exposure to an electron beam. Thermal treatment increases the conductivity gradually to values of about $\text{1 × 10}{}^2\text{Ω}{}^{-1}\text{cm}{}^{-1}$.     

A cooled photoresistor based on n-type germanium alloyed with copper

A photoresistor cooled with liquid nitrogen is described based on n-type Ge alloyed with Cu with a detection sensitivity of $\text{10}{}^{14}\text{cmHz}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{W}{}^{\mathrm{?1}}$ in the spectral range from 0.8 to 1.7 μm.     

Effect of mechanical properties of material on rate of fatigue crack propagation

Many experimental and analytical equations on a rate of a fatigue crack propagation have been proposed. However, it seems that they can not fully express its complex behavior. There are still many problems remaining to be solved in order to clarify its mechanism. One of them is to clarify the relation between the rate of the crack propagation and the mechanical properties of material. In this paper, the rate of the crack propagation is analysed to clarify this problem. This analysis is based on the observation results of the fatigue crack propagation behavior previously by the authors. The analytical result is compared with the experimental one to make sure that they agree with each other. The conclusion obtained is; the rate of fatigue crack propagation is expressed by using the stress intensity factors as

$\text{dl}\text{dN}\text{= {}\text{c}\text{[Y}{}^2\text{F}{}^{\mathrm{a}}\text{E}{}^{\mathrm{a(1?n)}}\text{]}\text{} (K}{}_{\max }\text{)}{}^2\text{(K}{}_{\mathrm{a}}\text{)}{}^{\mathrm{a(2?n)}}$

. where C is a constant; E, Young's modulus; F, plastic coefficient; Y, yield stress; K_max and K_a, maximum and amplitude of the stress intensity factor, and α and n, exponents of the Manson-Coffin's law and work-hardening.     

A model for fatigue crack growth in a threshold region

The prediction of fatigue crack growth at very low ΔK values, and in particular for the threshold region, is important in design and in many engineering applications. A simple model for cyclic crack propagation in ductile materials is discussed and the expression

$\text{da}\text{dN}\text{=}\text{2}{}^{\mathrm{1+n}}\text{(1?2v)(ΔK}{}^2{}_{\mathrm{eff}}\text{?ΔK}{}^2{}_{\mathrm{c,eff}}\text{)}\text{4(1+n)π σ}{}^{\mathrm{1?n}}{}_{\mathrm{yc}}\text{E}{}^{\mathrm{1+n}}\text{?}{}^{\mathrm{1+n}}{}_{\mathrm{f}}$

developed. Here, n is the cyclic strain hardening exponent, σ_yc is cyclic yield, and ε_f is the true fracture strain. The model is successfully used in the analysis of fatigue data BS 4360-50D steel.     

Theorems of zaremba type for thermoelastic solid

It was shown in [2] that any solution of the equation of coupled dynamic thermoelasticity (a) $\text{[(?}{}^2\text{??}{}_{\mathrm{t}}{}^2\text{)(?}{}^2\text{??}{}_{\mathrm{t}}\text{)?∈?}{}_{\mathrm{t}}\text{?}{}^2\text{]phi = 0, (?}{}_{\mathrm{t}}\text{= ?/?t)}$, subject to homogeneous initial conditions admits the representation $\text{phi = phi}{}_1\text{+ phi}{}_2$, where (b) $\text{(?}{}^2\text{??}{}_{\mathrm{t}}{}^2\text{?∈?}{}_{\mathrm{t}}\text{?∈?∈K 1)phi}{}_1\text{= 0}$, and (c) $\text{?}{}^2\text{??}{}_{\mathrm{t}}\text{+∈+teK (s)phi}{}_2\text{= 0}$. Here $\text{K = K(t, epsi)}$ is a given function and ¹ denotes the operation of convolution with respect to time $\text{t}$. In the present paper three uniqueness theorems associated with (a), (b) and (c) are given, and a domain of influence theorem for (b) is established. Next, these theorems are used to show that there exist such couplings between the external mechanical and thermal fields applied to the boundary of a thermoelastic solid that inside the body the temperature is either of a wave type or of a diffusive type, but not of both types.