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.     

The crystal growth and thermoelectric properties of chromium disilicide

Single crystals of chromium disilicide about 8 mm in diameter and 35 mm long were grown using the floating zone technique. Measurements of electrical resistivity , Hall coefficient R and thermoelectric power were carried out in the temperature range from 85 to 1100 K. The values of and showed the anisotropy over the temperature range studied. The ratios parallel and perpendicular to the c-axis were / =1.9 and /=1.7 respectively, at room temperature. It was found to be a degenerate semiconductor having the hole concentration of 6.3×10²⁰ cm^–3 below 600 K. The effective masses of holes parallel and perpendicular to the c-axis determined from the thermoelectric power and the hole concentration near room temperature were estimated to be five and three times as large as a free electron mass, respectively. The calculation on the values of and was made using those effective masses. These values showed good agreement with the observed values in the temperature range from 150 to 1100 K.     

A nonlinear composite shell element with continuous interlaminar shear stresses

A numerical model for layered composite structures based on a geometrical nonlinear shell theory is presented. The kinematic is based on a multi-director theory, thus the in-plane displacements of each layer are described by independent director vectors. Using the isoparametric apporach a finite element formulation for quadrilaterals is developed. Continuity of the interlaminar shear stresses is obtained within the nonlinear solution process. Several examples are presented to illustrate the performance of the developed numerical model.List of symbols reference surface - convected coordinates of the shell middle surface - ⁱ coordinate in thickness direction - ⁱ h thickness of layer i - X_o position vector of the reference surface - ⁱX_o position vector of midsurface of layer i - t _k orthonormal basis system in the reference configuration - ⁱ a _k orthonormal basis system of layer i - ⁱW axial vector - R_o orthonormal tensor in the reference configuration - ⁱ R orthonormal tensor of layer i - ⁱ Cauchy stress tensor - ⁱ P First Piola-Kirchhoff stress tensor - ⁱ q vector of interlaminar stresses - ⁱ n, ⁱ m vector of stress resultants and stress couple resultants - v _x components of the normal vector of boundary - ⁱ N, ⁱ Q, ⁱ M stress resultants and stress couple resultants of First Piola-Kirchhoff tensor - stress resultants and stress couple resultants of Second Piola-Kirchhoff tensor - ⁱ , ⁱ , ⁱ strains of layer i - _K transformation matrix - u_o displacement vector of layer 1 - ⁱ local rotational degrees of freedom of layer i     

Tilted and Crossing Vortex Chains in Layered Superconductors

No Heading In presence of the Josephson vortex lattice in layered superconductors, small c-axis magnetic field penetrates in the form of vortex chains. In general, structure of a single chain is determined by the ratio of the London [] and Josephson [_J] lengths, = /_J. The chain is composed of tilted vortices at large s (tilted chain) and at small s it consists of crossing array of Josephson vortices and pancake-vortex stacks (crossing chain). We study chain structures at the intermediate s and found two types of phase transitions. For 0.6 the ground state is given by the crossing chain in a wide range of pancake separations a [2–3]_J. However, due to attractive coupling between deformed pancake stacks, the equilibrium separation can not exceed some maximum value depending on the in-plane field and . The first phase transition takes place with decreasing pancake-stack separation a at a = [1 – 2]_J, and rather wide range of the ratio , 0.4 0.65. With decreasing a, the crossing chain goes through intermediate strongly-deformed configurations and smoothly transforms into the tilted chain via the second-order phase transition. Another phase transition occurs at very small densities of pancake vortices, a [20 – 30]_J, and only when exceeds a certain critical value 0.5. In this case small c-axis field penetrates in the form of kinks. However, at very small concentration of kinks, the kinked chains are replaced with strongly deformed crossing chains via the first-order phase transition. This transition is accompanied by a very large jump in the pancake density.PACS numbers: 74.25.Qt, 74.25.Op, 74.20.De     

The optical properties and a.c. conductivity of magnesium phosphate glasses

Magnesium phosphate [X MgO-(100–X) P₂O₅] glasses in the composition range [X=20, 25, 30, 40, 45, 50 mol %] have been made. The optical properties and a.c. conductivities were measured and their amorphous nature confirmed by X-ray diffraction technique. The variation of relative density with x was anomalous. In the ultraviolet/visible regions it was found that the fundamental absorption edge is a function of glass compositions and lower absorption coefficients, () follow the so-called Urbach edge. At lower absorption levels (1<<10⁴cm^–1), the width of the tail of localized states in the band gap, E _g, did not vary significantly with glass composition and lay in the range (0.26–0.343) eV. In the high absorption region (()>10⁴ cm^–1), the behaviour of () suggests that there are two different transition energies for electrons in k-space, namely direct allowed transitions and non-direct transitions. In the infrared region at wavelengths =2.5–30 m, the transmission spectrum has four absorption bands. Using the Kramers-Kronig theory, the optical constants (refractive index n and extinction coefficient k) have been determined from the transmission spectrum. The a.c. conductivity, (), real and imaginary dielectric constants, ₁, ₂, and loss factor, tan , have been determined at room temperature in the frequency region, = 2×10⁴–10⁶ Hz. It has previously been established theoretically that () ^s and s was found to be in the range 0.64–0.73, depending on glass composition.     

A Method for Calculating Thermal Radiation Properties of Multilayer Films from Optical Constants

A calculation method for the incident angle dependence of the solar absorptance _S and the temperature dependence of the total hemispherical emittance _H of multilayer films is proposed. The method is based on calculation of _S and _H from optical constants in the wavelength region from 0.25 to 100 m for thin polymer films and deposited metal. In this paper we provide values of _S in the incident angle region from 0 to 90° and _H in the temperature range from 173.15 to 373.15 K for two-layer samples of aluminum-deposited polyimide film. The results obtained for _S and _H by the present method are compared with experimental results measured by both spectroscopic and calorimetric methods. The calculated results of _S and _H agree well with the experimental results.     

Correlation between magnetic hysteresis and magnetic relaxation in YBaCuO single crystals

The dependence of the magnetic momentm obtained from the hysteresis loops on the speed of the magnetic field sweep =dH _ext/dt is explained on the basis of Anderson's interpretation of the magnetic flux creep. In addition, a phenomenological model is suggested which predicts a linear dependence ofm on ln with the slope m/ ln , numerically equal to the relaxation rate m/ ln(t) from the usual magnetic relaxation. Such linear relations betweenm and ln were observed experimentally in single crystals of YBaCuO. Preliminary experiments on the complementary time dependent relaxation ofm after a simulated step change ofH _ext gave mostly relaxation rates close to the predicted values. The model here presented also enables one to compare the critical state in the superconductor at a field sweep rate with the critical state at some timet _eff after a step change ofH _ext. The values of analyzed in our experiments actually correspond to the critical state at timest _eff between0.04 and4 sec after an imaginary large step change ofH _ext.     

Standard free energies of formation of rare earth sesquisulphides

An e.m.f. technique is used for the measurement of the Gibbs' energy changes involved in the conversion of the rare earth oxysulphides to the corresponding sesquisulphides in the temperature range 870 to 1120 K. The cell arrangement is Au, Ag + Ag₂SR₂O₂S + R₂S₃ (Y₂O₃)ThO₂ Fe + Fe_0.95O, Au where R = La, Pr, Nd, Sm, Eu and Gd. Yttria-doped thoria is used as the solid electrolyte because it has predominant ionic conduction at the low oxygen potentials developed at the R₂O₂S + R₂S₃ electrode, especially for systems containing heavier rare earth elements. The sulphur potential at the left-hand electrode is established by the dissociation of Ag₂S to silver in a closed system. The changes in the standard free energy, enthalpy and entropy associated with the conversion of the rare earth oxysulphide to the sesquisulphide all show a smooth variation with rare earth atomic number. Based on these empirical trends, the corresponding thermodynamic functions for terbium, dysprosium and holmium systems are estimated. The measured free energy values are combined with recent data on the standard free energies of formation of the rare earth oxysulphides to obtain the Gibbs' energies of formation of the corresponding sesquisulphides.     

Investigations of the copper isotope effect in oxygen-deficient YBa2Cu3O7−δ

We present data on the copper isotope effect (⁶³Cu-⁶⁵Cu), C_u =-nT_c/nm_Cu, for two isotopic pairs of oxygen-deficient YBa₂Cu₃O_7–, where varies between 0.06 and 0.52. _Cu is below 0.01 at =0.06 (fully oxygenated), it takes values between –0.14 and –0.34 in the 60 K plateau. Larger negative values of _Cu are observed away from the plateau. The dependence of _Cu is similar to that of the pressure effect dnT_c/dP.     

Preparation of micaceous iron oxide by the oxidation of iron with pressurized oxygen in concentrated sodium hydroxide solution at elevated temperatures

Iron powders were oxidized in NaOH solutions of 5–25 mol kg^–1 at 403–563 K and 5 MPa of oxygen partial pressure. Various types and morphologies of iron compounds such as fine particles of Fe₃O₄, micaceous -Fe₂O₃, and coagulated particles of -NaFeO₂ were formed depending on the experimental conditions. The observed critical concentrations of NaOH above which -NaFeO₂ was formed was in good agreement with those thermodynamically calculated for the hydrolysis equilibrium of -NaFeO₂.     

Kinetic interpretation ofα- andβ-Si3N4 formation from oxide-free high-purity silicon powder

A kinetic analysis of the isothermal nitridation of high-purity oxide-free silicon powder is described. The kinetic analysis suggests that the and polymorphs of Si₃N₄ are formed by separate and parallel reaction paths. This analysis provides for the decoupling and quantitative kinetic interpretation of- and-Si₃N₄ formation reactions. Consistent with existing microstructural and thermodynamic evidence, the-forming reaction is shown to obey a first-order rate law, whereas a phase-boundary controlled rate law describes the-forming reaction. A kinetic model employing these rate laws is developed and is used to predict the/ phase ratio as a function of isothermal reaction temperature and extent of reaction. The/ phase ratios so obtained are shown to be in good agreement with experimental observations made under a variety of reaction conditions.     

Phase diagram and some properties of Cu2−xSe(2.01≥2−x≥1.75)

The temperatures of phase transformation from low-temperature -phase to high-temperature -phase were measured for copper selenide Cu_2–x Se in the composition range 2.012–x1.75. The -phase was found to be unstable in air, and further experiments should be performed in a good vacuum. The phase diagram of Cu_2–x Se was redetermined by the X-ray parametric method and the possible reasons why the phase diagrams reported by several authors do not coincide with each other are discussed.     

Optical and photoelectric properties of Cd<Subscript>1 - <Emphasis Type="Italic">x</Emphasis></Subscript>Zn<Subscript>x</Subscript>As<Subscript>2</Subscript> single crystals

The optical absorption, photoconductivity, and short-circuit photocurrent spectra of structurally perfect Cd_{1 - x} Zn_xAs₂ (x = 0.03, 0.05, 0.06) single crystals are studied for the first time near the intrinsic edge in the range 80–300 K. The results demonstrate that the intrinsic edge in the solid solutions is due to indirect transitions involving the formation of excitons for both the E c and E c polarizations. The indirect gaps _g ⁱ of the solid solutions are determined. In the range 80–300 K, the data for x = 0–0.06 and both polarizations are well fitted by _g ⁱ (x) = _g ⁱ (0) + 0.0866x + 2.35x ². The introduction of 6 mol % ZnAs₂ into CdAs₂ increases its _g ⁱ by 14 meV.Translated from Neorganicheskie Materialy, Vol. 41, No. 3, 2005, pp. 268–272.Original Russian Text Copyright © 2005 by Morozova, Marenkin, Mikhailov, Koshelev.This revised version was published online in April 2005 with a corrected cover date.This revised version was published online in April 2005 with a corrected cover date.     

Relative diffusion resistance in drying wheat

An apparatus is described for examining various methods of convective drying.Notation tan=N_I drying rate in the first period - tan =(dW^c/d)_II drying rate in the second period - drying time - W _e ^c equilibrium water content - W^c water content of grain on dry mass - N^*=(1/N_I)(dW^c/d) dimensionless drying rate - T_sur surface temperature - T_a ambient temperature - T_w wet-bulb temperature - A,, experimental coefficients Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 31, No. 5, pp. 839–843, November, 1976.     

A new approach to detect and size closed cracks by ultrasonics

The effect of a crack on time-of-flight of shear waves (4.5 MHz) polarized in perpendicular (t ) and parallel (t ) directions to the crack surface, propagating parallel to the direction of crack growth is investigated. The first and second back-wall echoes are used instead of the weak crack-tip echo for the measurement of time-of-flight. The measurement is made for fatigue cracks grown by different loading histories in ferritic steel (pressure vessel steel A533B-1) under the condition of no loading. The normalized time-of-flight (t –t )/t at the crack position is found to change proportionally as the ratio of crack depth to specimen width increases. The change is mainly due to the effect of plastic deformation occurring around the crack ont . It is shown that the depth of tightly closed fatigue crack in austenitic stainless steel (AISI 304) also can be evaluated under the condition of no loading by using this relationship.     

Study on the α2/γ interfacial structures in a two-phase (α2?+?γ) alloy deformed at elevated temperature

The details of structure modification on ₂/ interface induced by deformation in a hot-deformed Ti-45Al-10Nb alloy were investigated by conventional and high-resolution transmission electron microscopy. A new type of dislocation ledge containing 1/3[111] partials was identified. The Burgers vectors of these dislocation ledges were determined to be 1/2[110] or 1/2101]. The formation mechanism of this new type of dislocation ledge is discussed. Also, two types of hot deformation induced ₂/ interfaces, coherent interfaces with high density of ledges and misoriented semi-coherent ₂/ interfacial boundaries were observed. For the misoriented semi-coherent ₂ interfaces, the density of dislocation ledges in these interfaces increases with the misoriented angle between the (111) and (0001) planes, and 1/3[111] partial dislocations were involved in all the dislocation ledges. The formation mechanism of these deformation-induced ₂/ interfaces were discussed related to the role of ₂/ interfaces adjusting the deformation as a dislocation sink absorbing the slipping dislocations in the phase. Moreover, misoriented semi-coherent ₂ interface related deformation twinning and structure transformation induced by deformation were analyzed and discussed related to the role of ₂/ interfaces as a dislocation source during deformation.     

Analysis of the effect of the decomposition of char-forming heat-insulating materials on the free discharge of a gas mixture

The article presents results of a numerical solution of a nonsteady problem on the free discharge of a mixture of gases from a hemispherical volume with allowance for thermal decomposition of heat-insulating materials.Notation V volume - S area - t - P p - T - u v - Q q, dimensional and dimensionless time, pressure, temperature, TIM decomposition rate, and heat flux - adiabatic exponent - R gas constant - density - H specific enthalpy - c specific heat - thermal conductivity - , , _s dimensionless complexes - coefficient expressing the radiative properties of the gas medium and the heat-transfer surface - Stefan-Boltzmann constant Indices 0 initial state and scale factors - s surface - coke - M TIM material - P pyrolysis front - A ablation front - v volatile degradation products - adiabatic conditions - c completion of discharge Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 54, No. 5, pp. 787–793, May, 1988.     

Isochoric specific heat of sulfur hexafluoride at the critical point: Laboratory results and outline of a spacelab experiment for the d1-mission in 1985

The specific heat at constant volume c_v shows a weak singularity at the critical point. Renormalization group techniques have been applied, predicting a universal critical behavior which has to be experimentally confirmed for different systems. In this paper an experiment is presented to measure the specific heat of SF₆ along the critical isochore (_c=0.737 g·cm^–3), applying a continuous heating method. The results cover a temperature span of –1.5×10^–2< <1.70×10^–2 [=(T–T _c)/T _c] and were strongly affected by gravity effects that emerge in the sample of 1-mm hydrostatic height near the critical point. Using regression analysis, data were fitted with functions of the form c _v/R=A × ¦¦^– + B for the one-phase state and c _v/R=A × ¦¦^– + B for the twophase state. Within their error bounds the critical values (==0.098, A/A=1.83) represent the measurements for the temperature span 3.5×10^{–5< ¦¦<2.0×10 –3}, in good agreement with theoretical predictions. In order to exclude density profiles in the specimen, which are unavoidable in terrestrial experiments due to the high compressibility of fluids at the critical point and the gravity force, a space-qualified scanning ratio calorimeter has been constructed, which will permit long-term c_v measurements under microgravity (-g) conditions. The experiment will be part of the German Spacelab mission in October 1985. The significant features of the apparatus are briefly sketched.Paper presented at the Ninth Symposium on Thermophysical Properties, June 24–27, 1985, Boulder, Colorado, U.S.A.     

Bone formation induced by calcium phosphate ceramics in soft tissue of dogs: a comparative study between porous α-TCP and β-TCP

Two kinds of tri-calcium phosphate ceramics (Ca/P = 1.50), -TCP and -TCP, which has the same macrostructure and microstructure, but different phase composition, were implanted in dorsal muscles of dogs. The samples were retrieved at 30, 45 and 150 days, respectively, after implantation, and were analyzed histologically. There were critically different tissue responses between -TCP ceramic and -TCP ceramic. Higher cell populations were observed inside the pores of -TCP than those of -TCP, bone tissue was found in -TCP at 45 and 150 days, but no bone formation could be detected in any -TCP implants in this study. On the other hand, the bone tissue in -TCP seemed to degenerate at 150 days. The results indicate that porous -TCP can induce bone formation in soft tissues of dogs; while the rapid dissolution of the ceramic and the higher local Ca²⁺, PO ₄ ^3- concentration due to the rapid dissolution of -TCP may resist bone formation in -TCP and the less rapid dissolution of -TCP may be detrimental to already formed bone in -TCP.     

Microstructure and mechanical properties of metastable lath martensite wires in the Fe-Ni-Cr-Al-C system produced by melt spinning in rotating water

Metastable lath martensite ( _L ) phase wires with high strengths have been produced in the Fe-Ni-Cr-Al-C alloy system by melt spinning in rotating water. These wires have a circular cross section and a white lustre and the wire diameter is in the range of 100 to 140m. The width and length of each lath in the _L phase are as small as about 0.3 and 2m, respectively. The _y, _f and _p are about 900 and 1650 MPa and 2.0% for the _L wires. The subsequent annealing causes an increase in _p as well as _y and _f and the attained values are about 1000 and 1700 MPa and 3.0% for Fe-10Ni-10Cr-6.5 Al-1.0C wire annealed at 773 K for 1 h owing to the precipitation strengthening of a very fine unidentified carbide and to a high density of dislocations and lath boundaries in the _L phase. Further annealing causes a significant decrease in _p through decomposition of _L to+M₇C₃+M₂₃C₆. Therefore, the high strength combined with relatively good ductility for the _L wires is interpreted as due to the suppression of the phase transformation of _L to a mixed structure of+M₇C₃+M₂₃C₆ by melt quenching.