On a simple wave approximation of a set of linear dispersive wave equations

Summary The validity of an approximation ₀ of one of the solutions of a set of two linear coupled dispersive wave equations has been discussed. ₀ is the solution of a linear Korteweg-de Vries equation and satisfies the same initial condition as . It is shown that for square integrable solutions having a spectral range not exceeding [–, ] the approximation is useful if ^{5 2}t«1 in the sense that –₀(t)« (t)(L ₂ -norm). is a measure for the dispersion. The approximation fails in that sense ast . Some remarks to a similar nonlinear problem are made.     

Singularities of Ionization-Field Instability and Structurization of Plasma of High-Pressure Non-Self-Maintained Free-Localized Discharge in the Field of a Quasi-Monochromatic Microwave

A self-consistent set of the equations for the electromagnetic field and balance of plasma concentration in view of ambipolar diffusion and the equation for the fast oscillating component of electron motion in a variable field are used to investigate the linear stage of ionization-field instability of the plasma of high-pressure non-self-maintained discharge in the approximation of unbounded plasma in a plane quasi-monochromatic microwave packet. Greens function is constructed. In the simplest one-dimensional formulation of the problem, assuming that all parameters of the plasma and field vary only in the direction of propagation of the wave packet, the saddle point approximation is used to derive the dominant terms of asymptotic expansion of Greens function in two limiting cases; namely, for t , |z– z ₀| 0, and for t 0, |z– z ₀| . It is demonstrated that, contrary to the existing notion of insignificant importance of ionization-field instability in a high-pressure plasma, this instability may produce a high rate of development of perturbations in such a plasma and have a decisive effect on the structure of plasma inhomogeneity being formed. A method is suggested of stabilizing ionization-field instability of a microwave plasma by selecting a proper shape of the wave packet, including an increase in the effective width of the frequency band emitted by the source.     

Investigation of the gapless state induced by pressure in Hg1−x Cd x Te alloys

We report the results of an experimental study of the gapless state (GS) induced inp-type semimetallic alloys Hg _1–x Cd _x Te (0<x<0.15) by pressure. Galvanomagnetic effects in weak magnetic fields (2T<300 K) and the Shubnikov-de Haas effect have been investigated in the pressure interval 1p<15 kbar. Direct evidence for the existence inp-type semimetallic alloys of an impurity hole band overlapping with the conduction band by 3–4 me V is obtained. At liquid helium temperatures the Fermi level is located in the impurity band, so that two groups of carriers take part in transport effects: light electrons in the conduction band and heavy holes in the impurity band. The electron Fermi energyE _F is proved to be essentially constant during the transition to the GS. A linear dependence of the electron effective mass at the band edgem* (0) upon the gapE _g is obtained. A significant role of scattering of electrons into the impurity band at liquid helium temperatures is revealed.     

Relationship between superconductivity and band structures of electrons and phonons

The relationship between superconductivity and band structures of electrons and phonons is established on the basis of a generalized Bardeen-Cooper-Schrieffer model in which the interaction strengths (V ₁₁,V ₁₂,V ₁₂) among and between electron (1) and hole (2) Cooper pairs are differentiated. Elemental superconductors must have local hyperboloidal Fermi surfaces called necks or inverted double caps.     

Investigation of the excitonic insulator phase in bismuth-antimony alloys

Pressure-induced metal-semiconductor transitions in bismuth-antimony alloys in a strong magnetic field (up to 70 kOe) at helium temperatures have been investigated. It is found that for values of the overlap-gap |G|1 meV the alloy forms an excitonic insulator (EI) in magnetic fields above a certain threshold (30–40 kOe). It is inferred that the EI energy gap increases with the magnetic field. The maximum gap observed in fields of 70 kOe turns out to be ₀₀7.5 K. An analysis of the results shows that transitions to the EI phase are observed from both the semimetal and the semiconducting states. The critical transition temperatureT _c is related to the EI gap by the expressionT _c0.7. Arguments are advanced in support of the fact that the formation of the EI phase involves the pairing of electrons at theL point with holes at theT point.     

Kondo Impurity in a Mesoscopic Ring: Charge Persistent Current

We study the influence of a magnetic impurity or ultrasmallquantum dot on the charge persistent current of a mesoscopicring. The system consists of electrons in a one-dimensionalring threaded by spin-dependent Aharonov–Bohm/Casher fluxes,coupled via an antiferromagnetic exchange interaction to alocalized electron. By passing to a basis of electron stateswith definite parities, the problem is mapped onto a Kondomodel for the even-parity channel plus free electrons in theodd-parity channel. The twisted boundary conditionsrepresenting the fluxes couple states of opposite parityunless the twist angles satisfy =f,where f are integers, with spin index=, . For these special values of, the model is solved exactly by a Bethe ansatz.Special cases are investigated in detail. In particular weshow that the charge stiffness in the case= is insensitive to the presenceof the magnetic impurity/quantum dot.     

Thermodynamic investigations of liquid Bi-Na and Sn-Na alloys by coulometric titration using β″-alumina

The following double galvanic cell was assembled and the thermodynamic properties of liquid Bi-Na and Sn-Na alloys, and the ion selectivity of -alumina during coulometric titration, were investigated. Mo, Na(I)¦-alumina¦M-Na(I), Mo [I] M-Na(I)¦-alumina¦Au + Au₂Na, Mo [II] (M = Bi or Sn) where M-Na(1) and Au + Au₂Na were used as the common electrode and reference electrode, respectively. Sodium was coulometrically titrated through the -alumina electrolyte of cell I both ways, and the EMFs were measured. It was found that no ion-exchange reaction occurs between the liquid alloys and the -alumina, and only Na was transferred in the -alumina during coulometric titrations. The thermodynamic properties of liquid Sn-Na and Bi-Na alloys were found to be in agreement with the literature.     

Proximity-effect-induced superconductivity at millikelvin temperatures

A systematic study is reported of the proximity effect in superconductivity of thick Cu layers (4d _n105 µm) in contact with Nb or Nb-Ti (46D _s1041 µm) from measurements of the ac susceptibility and of the thermal conductivity. The induced superconducting properties of Cu are studied as a function of temperature (7 mKT1 K), field (0.4 mGH 10 G), and electronic mean free path (0.2l14 µm). The Meissner screening length in Cu increases faster than the coherence length with decreasing temperature and eventually saturates, making the Cu fully superconducting. In this case, superconductivity can be destroyed sharply at a breakdown fieldH _b; the transition atH _b is hysteretic. The data are in agreement with numerical solutions of the de Gennes/Ginzburg-Landau theory, as demonstrated by the dependence of the Meissner screening length and of the breakdown field on temperature, field, and electronic mean free path. The data indicate that observation of a reduction in thermal conductivity requires a substantially larger induced pair potential than is necessary even for total field shielding. The concentration of Cooper pairs in Cu in contact to Nb is larger than in Cu in contact to Nb-Ti, even for Nb-Ti/Cu samples with a larger electron mean free path in the Cu part. No measurable superconducting field screening could be induced in the investigated temperature range in Pd (26d _n72 µm) in contact to Nb/Cu or to Nb (D _s5d _n). This is explained by the fact that the coherence length is at least an order of magnitude smaller in Pd than in Cu. Evaporating a layer of Fe on Cu in the Nb/Cu samples results in a strong depression of the proximity effect.     

On the dispersion of gases under the action of the medium

Some general regularities of dispersion of a gas emerging from a nozzle submerged in a liquid are considered. A condition for establishment of the so-called maximum dispersion state is formulated.Notation ₀ coefficient of surface tension at the liquidgas boundary - contact angle of wetting of the nozzle material surface by the liquid - p_at atmospheric pressure - p air pressure - density of the liquid - g gravitational acceleration - h height of the liquid column - ₁, and _g dynamic viscosity coefficients of the liquid and gas, respectively - R and r radii of the bubble and nozzle, respectively - Q and F dimensionless criteria - , , , , and undetermined coefficients - ratio of the circumference of a circle to its diameter     

Similarity solutions in axisymmetric mixed-convection boundary-layer flow

The similarity equations for mixed-convection axisymmetric boundary-layer flow are considered. The equations involve a buoyancy parameter and a curvature parameter . The equations are solved numerically and it is found that for large , and of O(1), an asymptotic solution is approached, the nature of which is discussed. When is also large, of O(^1/4), the problem, at leading order, becomes independent of the mainstream and the free-convection limit is obtained. This problem is also discussed, including the behaviour for large values of ₀, the free-convection curvature parameter. For < 0 we find that the solution can be continued past the point where the wall heat transfer becomes zero (where previous mixed-convection similarity solutions in plane geometry were terminated) with the solution ending as 0^–. The nature of this limit is also discussed. For < 0 it is also found that there are solutions only in _b = < 0 with two branches of solution bifurcating out of = _b , and values of _b are computed for a range of . The behaviour of the solution for large values of the curvature parameter , and of O(1), is discussed where it is shown that the solution proceeds in inverse powers of log .     

The variation of the index of refraction in a vortex tube

Three models of a vortex tube (isentropic, isothermal, and isochoric) are considered as optical inhomogeneities. Expressions relating the index of refraction to the coordinate are obtained. The possibility of obtaining Schlieren pictures of such flows is discussed.Notation a speed of sound - n index of refraction - p pressure - r radius - T absolute temperature - v linear velocity - angular deflection of the beam - x adiabatic exponent - density - angular velocity - ¯v, ¯p etc. dimensionless parameters - v₀, ₀ values at the core bounboundary - p, etc. stagnation values - n_c index of refraction at center of vortex     

Fatigue microcrack growth in a nickel-base superalloy

The growth of very small fatigue microcracks was studied in a powder metallurgy nickel-base superalloy. A novel specimen containing a small crack was used, with crack growth rates being measured optically at high magnification. Interaction between the crack and the material microstructure was observed in a cyclic loading stage within a scanning electron microscope.It was found that microcracks grew initially at rates more rapid than those corresponding to conventional fracture mechanics (large crack) specimens. The rate undergoes a transient decrease with increasing crack length, dropping below the corresponding plot for large cracks, before beginning to increase in accordance with large crack results, ultimately merging with the latter. These results are discussed in terms of microstructure and crack growth mode, and the findings considered in light of the few studies of cyclic microcrack growth which have previously been correlated with fracture mechanics.     

Dislocations in extruded Co-49.3at% Al

Polycrystalline Co-49.3at% Al which had been extruded at 1505 K was examined using transmission electron microscopy. Diffraction contrast analysis showed that b = 100 as well as b = 111 dislocations contribute to elevated temperature deformation in CoAl. Therefore, it was concluded that sufficient slip systems exist in CoAl to allow for general plasticity in the absence of diffusional mechanisms. Since no examples of b = 110 dislocations were found, the importance of 110{1¯10} slip in CoAl at 1505 K is unclear. Dislocations of the type b = 001 were observed on both {110} and {100} planes while b = 111 dislocations were observed on {1¯10} planes.     

Synthesis, crystal structure and X-ray powder diffraction data of the phosphor matrix 4SrO·7Al2O3

The white phosphor matrix 4SrO·7Al₂O₃ has been synthesized by firing the appropriate mixture of SrCO₃, Al(OH)₃ and H₃BO₃ in the molar ratios 1:3.5:0.135 at 1300°C for 4–7 h. The crystal structure of 4SrO·7Al₂O₃ has been determined as a orthorhombic Pmma space group with a=24.7451(2)Å, b=8.4735(6)Å, c=4.8808(1)Å, V=1023.41(3)ų, Z=2, and D=3.66 g cm^–3 by the Rietveld analysis. The refinement figures of merit are R_p=8.26, R_wp=11.60, R_bragg=4.44 and s=2.61 for 844 reflections with 2<119.94°. And the corresponding X-ray powder diffraction data are presented for search/match analysis.     

Stress-induced phase transformations in a hot-deformed two-phase (α2+γ) TiAl alloy

Stress-induced 2, 2 and 9R phase transformations in a hot-deformed Ti–45 at% Al–10 at% Nb alloy have been investigated using high-resolution transmission electron microscopy. The 2 phase transformation is an interface-related process. The interfacial superdislocations emitted from the misoriented semicoherent 2– interface react with each other or with the moving dislocations in the phase, resulting in the formation of the 2 phase. The nucleation of the 2 phase transformation takes place either at the 2– interfaces or at the stacking faults on the basal plane of 2 phase, and the growth of plate is accomplished by the moving of a/61 0 1 0 Shockley partials on alternate basal plane (0 0 0 1)2. The 9R structure was usually found to form at incoherent twin or pseudotwin boundaries. During deformation the interfacial Shockley partial dislocations of these incoherent twin and pseudotwin boundaries may glide on (1 1 1) planes into the matrix, resulting in the formation of 9R structure. The interfaces (including 2– and – interfaces) as well as the crystallographic orientation relationship between the as-received or stress-induced 2, and 9R phase have been analysed. The mechanisms for the stress-induced 2, 2 and 9R phase transformations were also discussed. © 1998 Chapman & Hall     

The effect of quenching on the martensitic transformation in ß1 phase of Au-Cd alloys

The effect of quenching on the martensitic transformation mechanism in ₁ Au-Cd alloys has been investigated by measurements of the electrical resistivity and X-ray diffraction. In the case of the Au-47.5 at%Cd alloy, the ₂-martensite is the characteristic product under quenching conditions, but it always exists with the equilibrium ₂-martensite phase. Consequently, the _{1 2} and ₂transformations occur simultaneously during the heating and cooling cycles. The corresponding resistivity behaviour is very complicated and extremely sensitive to thermal treatments such as quenching temperature and thermal cycling. On the other hand, in the case of the Au-49.0 at%Cd alloy, only the _{1 2} transformation occurs even when quenched, and the transformation is unaffected structurally by quenching. A distinct resistivity anomaly, which is considered to be due to the disappearance of quenched-in vacancies, is observed in quenched alloys. Some important characteristics of this anomaly are determined. In particular, the quenching effect disappears when the specimen is heated above the temperature at which the resisitivity anomaly begins. This result suggests that the quenched-in vacancies play an essential role in the martensitic transformation process under quenching conditions.     

Interfacial and mechanical properties of environment-friendly “green” composites made from pineapple fibers and poly(hydroxybutyrate-co-valerate) resin

Physical and tensile properties of pineapple fibers were characterized. Tensile properties of pineapple fibers, like most natural fibers, showed a large variation. The average interfacial shear strength between the pineapple fiber and poly(hydroxybutyrate-co-valerate) (PHBV) was 8.23 MPa as measured by the microbond technique. Scanning electron microscopy (SEM) photomicrographs of the microbond specimens revealed an adhesive failure of the interface. Fully degradable and environment-friendly green composites were prepared by combining pineapple fibers and PHBV with 20 and 30% weight content of fibers placed in a 0°/90°/0° fiber arrangement. Tensile and flexural properties of these green composites were compared with different types of wood specimens. Even though tensile and flexural strength and moduli of these green composites were lower than those of some wood specimens tested in grain direction, they were significantly higher than those of wood specimens tested in perpendicular to grain direction. Compared to PHBV virgin resin, both tensile and flexural strength and moduli of these green composites were significantly higher. SEM photomicrographs of the fracture surface of the green composites, in tensile mode, showed partial fiber pull-out indicating weak bonding between the fiber and the matrix.     

Formation of Friction Layers and Wear Resistance of Steels under Conditions of Boundary Friction

We studied the influence of the lubricant compositions Grafitol with 10% graphite (1), Aerol containing 17% MoS₂ (2), Limol containing 60% MoS₂ (3), Limol + 10% chlorine-paraffin (4), and Limol + 10% copper powder (5) on the wear rate and formation of the fine structure of surface friction layers of structural steels. We established a correlation between the tribological characteristics of steels and lubricants. The abrasive wear of 40KhFA steel was minimum if it was lubricated with Limol + 10% copper powder. In this case, its wear was smaller by a factor of 10, 2, 1.25, and 7.25 as compared with lubricant compositions 1–4, respectively. In the course of minimum wear of 40KhFA steel, in the surface friction layers, we observed the minimum values of second-kind distortions (a/a) and of the true size of domains of X-ray coherent scattering (D) as well as the minimum difference between the crystal lattice constants (a) of steel before and after friction.     

Structural and magnetic characterization of nanocrystalline Ni-20%Fe permalloy films

Samples of nanocrystalline Ni-20%Fe permalloy, obtained by electrodeposition, were studied using an X-ray diffraction technique and magnetic force microscopy. After deposition, the alloy exhibited strong fiber texture with the major component being 1 0 0 and a lesser contribution from 1 1 1. An increase in deposition current density led to a reduction in the strength of the 1 0 0 texture. Despite the small magnitude of the magnetic interaction, images of magnetic domains were obtained using magnetic force microscopy. The images were, however, unstable and changed significantly with the scanning time. Annealing of the permalloy above 573 K caused rapid grain growth and a transformation of the 1 0 0 fiber to 1 1 1 fiber. Numerical analysis of the texture data was conducted to assess the atomic structure of grain boundaries in the as-deposited and annealed states.     

Phase equilibria and thermodynamic properties in the system Ni-Mo-O

Coexisting phases in the Ni-Mo-O ternary system at 1373 K have been identified by X-ray diffraction, optical microscopy and scanning electron microscopy. The samples were equilibrated in evacuated quartz capsules. Only one ternary phase, NiMoO₄, was found to exist in the system. The reversible e.m.f. values of the following solid-state galvanic cells were measured in the temperature range 900 to 1500 K: (I) Pt, Ni + NiO/(CaO) ZrO₂/NiO + MoO₂ + NiMoO₄, Pt; (II) Pt, Mo + MoO₂/(CaO) ZrO₂/O₂, Pt; and (III) Pt, Mo + MoO₂/(CaO) ZrO₂/Ni-Mo + MoO₂, Pt. The Gibbs energies of formation of NiMoO₄ and MoO₂ and activities in Ni-Mo alloys were derived from the e.m.f. data. For the reaction NiO + MoO₂ + 2(02) NiMoO₄ we obtain G _r ⁰ = -201 195 + 69.70T (±400) J mol^–1; for Mo + (02) MoO₂ we obtain G _f ⁰ = –578880 + 168.5T (+500) J mol^–1. Based on the information from phase identification studies and thermodynamic stabilities, the isothermal section and oxygen potential diagram for the Ni-Mo-O system at 1373 K have been developed.