Chebyshev approximation for the roots of the equation BiWГ(μ)=μVГ(μ)

A minimax approximation, uniform for Bi [0, ), is developed for the roots of the equation BiW()=V(), by means of Chebyshev polynomials.Translated from Inzhenero-Fizicheskii Zhurnal, Vol. 28, No. 4, pp. 710–715, April, 1975.     

Initial permeability studies on A13+ and Cr3+ substituted Ni–Zn ferrites

The chemical formula of the samples investigated is Ni0.7Zn0.3Alx/CrxFe2-xO4, where x=0.00, 0.05, 0.10, 0.15, 0.20 and 0.25. The samples were obtained by the usual ceramic technology from high-purity oxides. The initial permeability was calculated from the inductance measurements with a torroidal core of 100 turns, using the formula L=0.0046 iN2h log d2/d1. The initial permeability i decreases in Ni0.7Zn0.3Alx/CrxFe2-xO4 with increase in Al3+/Cr3+. The decrease in i is attributed to a decrease of grain size D from 4.9 m to 4.4 m with Al3+ and to 1.9 m with Cr3+ and to variations in the anisotropy constant K1. The main contribution to the variation of permeability with content of Al3+/Cr3+ in the system is the effect each of them has on domain wall motion. The trivalent substituents (Al3+/Cr3+) cause impedance to the domain wall motion, which increases as the content of these ions increases. Al3+ has a stronger effect than Cr3+. The initial permeability components and do not exhibit much variation with temperature, except near Tc, where they fall sharply. The maximum of near Tc has been attributed to a damping effect of domain wall motion. © 1998 Chapman & Hall     

Fabrication of a new class of porous media models for visualization studies of multiphase flow processes

The conventional wet-chemistry techniques used for the fabrication of porous media models exhibit some shortcomings with regard to the control of the structural parameters of pores etched either on glass or on plastic plates. A new method of fabrication of pore network micro-models, using an excimer laser LIGA technique, is presented. First, the microstructure is etched on a thin PMMA layer by using as input data the pore depth distribution (10–25 m) and the pore width-to-depth aspect ratio distribution (1–4). Then, the void space is filled with a layer of nickel (total thickness300 m) which, in turn, is covered by a thick layer of copper (1700 m) by using micro-electroforming. Finally, and after a series of mechanical treatments, a metal insert, which is a negative replica of the target microstructure, is produced and used for the printing of a large number of identical structures on PMMA plates with hot embossing. Each plastic model is glued with a thin PMMA cover foil by using a spin coating technique. In this manner, pore network models of well-controlled pore dimensions are produced. It is found that the depth of pores is well-controlled, whereas the depth of each intersection region (node) is almost equal to the sum of the depths of the two intersected capillaries (bonds). The aforementioned features in combination with the broad pore depth and width range (10–100 m) make the new micro-models representative of real porous media such as natural formations (e.g. sedimentary rocks, soils). Preliminary experiments of two-phase immiscible displacement performed on the new models confirm their applicability to visualization studies of multiphase transport processes in porous media.     

Eutectic solidification characteristics of Bridgman grown AI-3Fe-0.1V alloy

Eutectic solidification characteristics of Al-2.85 wt%Fe-0.12 wt% Valloy have been investigated by steady-state growth over the range of solidification front velocity from 51 to 1030m/s and temperature gradient 8 to 15 K/mm. Increasing growth velocity displaced the Al-Al3Fe eutectic by Al-AlxFe eutectic rather than by the Al-Al6Fe eutectic obtained for the binary Al-3 wt%Fe alloy. A fully Al-AlxFe eutectic structure has been obtained for the first time in the vanadium-containing alloy over the growth velocity range from 71 to1030m/s except at 100 and 510m/s where some Al dendrites were present in the eutectic matrix. TheAl-AlxFe eutectic was observed to undergo a morphological transition from lamellar to rod-like with increasing growth velocity concurrently with formation of a cellular eutectic structure. It was found that the relationship = Av–1/2, between eutectic spacing and growth velocity v, was applicable with A = 22.4 ± 1.8 and 13.8 ± 2.1 m3/2s–1/2 for lamellar and rod-like Al-AlxFe eutectics, respectively.     

Electron-phonon coupling as a mechanism for high-temperature superconductivity

We have solved the Eliashberg gap equations which are valid for arbitrary phonon frequency, (_ph), electron-phonon coupling constant, (), and screened Coulomb interaction, ( ^*). We have used values of (_ph),, and ( ^*) appropriate to the cuprate superconductors, and calculated the density of states, the pair potential., and the value of the gap at T=0 K. Using the linearized Eliashberg equations in the matrix representation, we have calculatedT _c and 2/k T _c . We have found that we can account for the highT _c 's in the cuprates with reasonable values for, ^*, and _ph.     

Dielectric and pyroelectric properties of KNO3 thin-layers

A series of thin monocrystalline KNO₃ layers has been grown from the melt by a special technique. The changes of the dielectric constant, d.c. resistivity, activation energy and pyro-electric current behaviour with the layer thickness and temperature have been investigated. Also, the effect of the a.c. frequency on the dielectric constant is checked in the frequency range 1 to 10 kHz. A sharp drop in dielectric constant could be recorded up to 6 kHz. The layers exhibit essentially the same dielectric and pyroelectric properties as bulk KNO₃ single crystals. The various measured parameters of these layers were found to be thickness-dependent. TheI-V characteristics of the layers (5m thickness) reveal the presence of breakdown voltage at 10.95V. Maximum pyrocurrent was obtained at positive d.c. biasing voltage. Also, the layers show a high pyroelectric coefficient, e.g. for layer thickness 8.9m, = 60C cm^–2 K^–1 at 180° C. The study proved that thin layers of potassium nitrate have good pyroelectric properties and should be useful as pyroelectric thermal detector material.     

Microdeformation of a polydomain, smectic liquid crystalline thermoset

The microdeformation and fracture mechanisms of a densely crosslinked, polydomain, smectic liquid crystalline thermoset (LCT) were investigated in order to gain some insight into its interesting mechanical properties (e.g. improved fracture toughness). A difunctional LC epoxy monomer, diglycidyl ether of 4,4-dihydroxy--methylstilbene (DGDHMS), was crosslinked with the tetrafunctional, aromatic crosslinker, 4,4-methylene dianiline (MDA) to produce the LCT. Thermoset films (30 m in thickness) were bonded to copper grids, strained in tension, and observed under the polarizing optical microscope. A new type of microdeformation and fracture mechanism was observed for the smectic LCT. At small strains, numerous microcracks formed which were oriented at various angles to the straining direction. Many smaller isolated and interconnected defects (of the order of a single LC domain, 1 m in size) surrounded and emanated from the crack tips. At larger strains, the microcracks propagated slowly and stably until reaching a critical size of 250 m, at which time they began to widen and change direction, indicative of plastic deformation which extended over many LC domains. Film failure occurred through microcrack interconnection. A fracture mechanism for the LCT is proposed based on microscopic voiding near the crack tip through the failure of individual LC domains.     

In situ X-ray Diffraction Studies of a Multilayered Membrane Fluid under Confinement and Shear

The structure of a fluid membrane system composed of surfactant-co-surfactant-oil-water mixtures has been investigated under confinement and shear conditions. Small angle x-ray scattering (SAXS) was employed with a second generation x-ray surface forces apparatus (XSFA-II) to study the time evolution of the orientational structure of the lamellar fluid under oscillatory shear. In a regime of relatively big confinement gap (800 m) and small shear amplitude (40 m), direct evidence of an orientational phase separation behavior, where a surface boundary layer adopts different orientation and separates from the bulk region, was observed for the first time. Under continuous shearing, the surface boundary layer grows in thickness and aligns towards a shear-favored (low friction) state while the bulk orientation remains unchanged. To further investigate the effects of surface confinement, we spatially mapped, in 1 m sections, the orientation structure of the lamellar fluid sample confined between two glass surfaces using a micro-focused x-ray beam produced by a linear Bragg–Fresnel lens at the Advanced Photon Source. The data confirmed the expected trend that the smectic domains align progressively better with respect to the surface as they approach the surface.     

A note on the similarity solutions for free convection on a vertical plate

Summary The similarity solutions for free convection on a vertical plate when the (non-dimensional) plate temperature is x and when the (non-dimensional) surface heat flux is –x are considered. Solutions valid for 1 and 1 are obtained. Further, for the first problem it is shown that there is a value ₀, dependent on the Prandtl number, such that solutions of the similarity equations are possible only for >₀, and for the second problem that solutions are possible only for >–1 (for all Prandtl numbers). In both cases the solutions becomes singular as ₀ and as –1, and the natures of these singularities are discussed.     

Change of mechanical properties of rigid poly(vinylchloride) during photochemical ageing

Thermally stabilised, unpigmented, rigid PVC samples, were exposed to accelerated photoageing at 40°C, 55°C and 70°C. The concentration profiles of photoproducts were determined on microtome slices ( 20 m) parallel to the irradiated surface using IR (carbonyls) and UV (polyenic double bonds) spectrophotometry and by steric exclusion chromatography (Mn and Mw). They indicate that carbonyls and chain scissions predominate only in a thin superficial layer whereas polyconjugated double bonds and crosslinks predominate in a subcutaneous layer (300–400 m). Tensile measurements show that the ultimate elongation decreases after an induction period whose duration is a decreasing function of temperature. The change of mechanical behaviour can be described in terms of a ductile-brittle transition shift mechanism in which crosslinking plays an important role. A tentative explanation of a such crosslinking induced transition is proposed in the discussion.     

Experimental hydration of two synthetic glassy blast furnace slags in water and alkaline solutions (NaOH and KOH 0.1 N) at 40° C: structure,composition and origin of the hydrated layer

The hydration of blast furnace slags has been modelled using two synthetic (CaO, SiO₂, Al₂O₃, MgO) glasses with different Al₂O₃/MgO values. Experiments (duration: 16 h to 150 d) were performed at 40° C in deionized water (pH 6.5) and in NaOH and KOH (0.1 N) solutions (pH=12.9). The hydrated layer was characterized from a combination of several techniques at different scales: surface analysis by XPS and SEM; TEM of ultrathin diamond-cut sections including electron microdiffraction and EDS analysis; X-ray diffraction of scratched powders. In water, the hydrated zone is only about 0.5m thick after 150 d with a leached layer covered by a thin siliceous film on which are scattered rare amorphous lamellae. In alkali media, the hydrated zone is composed of three parts: an inner layer made of modified residual glass, calcium-depleted and richer in magnesium and aluminium than the initial glass; an intermediate lamellar of constant thickness (O.3m) after 15 d with magnesium and aluminium as major components (hydrotalcite type composition) and labelling the initial solid-solution interface, an outer layer with initially abundant C-S-H more or less carbonated after reaction with atmospheric CO₂. The hydrotalcite-type layer separates the inner domain dominated by the formation and evolution of a leached glass layer from an outer one, where the precipitation of C-S-H and other amorphous or crystalline compounds, followed by carbonation, are the major processes.     

Mössbauer studies of α″-Fe16N2 and α′-Fe8N films

Conversion-electron Mössbauer spectra of epitaxial -Fe₁₆N₂ and -Fe₈N films have been studied and their differences are discussed in detail. The Mössbauer spectrum of -Fe₁₆N₂ can be decomposed into three subspectra, which correspond to the 4d, 8h and 4c sites. The Mössbauer spectrum of -Fe₈N can be fitted using four spectra based on a nitrogen-atom-random-distribution model. The average hyperfine field is larger (3%) for -Fe₁₆N₂ than for -Fe₈N, which is approximately consistent with a 4.1% enhancement of the magnetic moments for -Fe₁₆N₂. The iron moments tend to locate in the film plane for -Fe₁₆N₂ and to arrange perpendicularly to the film plane for -Fe₈N.     

Field and excitation dependent ultrasonic attenuation in3He-B

Sound absorption of³He-B at 0 bar was studied at a frequency of 10 MHz. We performed pulsed experiments with different pulse lengths (4 to 15 s) and pulse powers (0.1 to 160 W) in the temperature range 0.2 < T/T_C < 2. For pulse power less than pth 50 W, and in the temperature range 0.4 to 0.8 T_c and zero field, the attenuation coefficient a decreases monotonically at about 0.2 cm^–1 per decade of power. Above pth. increases up to values of 3.5 cm^–1 and 1.9 cm^–1 at highest power for temperatures of 0.8 T_c and 0.4 T_c, respectively. At pulse power around 100 W and at the lowest temperatures, the attenuation changes within the first 200 s after the application of the pulse; also increases with increasing field. In the normal fluid decreases with increasing power. All of our observations are lacking a rigorous theoretical understanding.     

Measurement of the Thermal Diffusivity of Metallic Foils and Films by the Photoacoustic Method1

The thermal diffusivities of four kinds of metallic foils from 20 to 200m in thickness were measured by a photoacoustic method on the basis of the Rosencwaig and Gersho theory. The measured data for continuous foils of uniform microscopic structure almost agreed with the literature values. Measurements were also carried out on two kinds of metallic thin films with of 10m thickness produced by sputtering. The difference in thermal diffusivity between the foils and the sputtered films depended on the uniformity of the microscopic structure.     

Application of coherent-optical methods in physical studies of evaporation

The application of the methods of laser and holographic interferometry to the problems of measuring evaporation rates is examined. Mass transfer accompanying evaporation in the region of extradiffusion monitoring is studied.Notation j_v specific mass flux of the vapor, kg/(m²·sec) - _c coefficient of condensation - _v coefficient of evaporation - D coefficient of diffusion - m²/sec, wetting angle - R radius of the vessel, m - time, sec - h height of the segment, m - wavelength of the laser radiation, m - N order of the interference fringe or the number of fringes passing through a given point - density of the matter, kg/m³ - length of the cell with the liquid of interest, m - T temperature, K - n refractive index of the medium - m mass - kg, V volume of the spheroidal segment, m³ - _liq and _g molar mass, kg/mole - C₀ and C_p concentration of vapor in the gas, kg/m³ - a and b semiaxes of the spheroid, m - _e ellipsoidal coordinate of a point on the surface, m² - c/n derivative along the normal - r coordinate of a point on the surface of evaporation, m - n change in the refractive index of the medium Indices st standard liquid - liq liquid - g gas - 0 starting state - p equilibrium pressure Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 55, No. 4, pp. 605–611, October, 1988.     

The Interplay of Electronic and Nuclear Magnetism in PtFe x at Milli-, Micro-, and Nanokelvin Temperatures

We have measured ac susceptibility, nuclear magnetic resonance, and nuclear heat capacity of two PtFe _x samples with concentrations of magnetic impurities x = 11 ppm and 41 ppm at magnetic fields (0 ± 0.05) mTB248 mT. The susceptibility data have been measured at temperatures of 0.3 KT100 mK, no hint for nuclear magnetic ordering could be detected to a temperature of 0.3 K. The nuclear heat capacity data taken at 1.4 KT10 mK show enhanced values which scale with x at low polarization. This effect is described by a model assuming an internal magnetic field caused by the impurities. No indication for nuclear magnetic ordering could be detected to 1.4 K. The nuclear magnetic resonance experiments have been performed on these samples at 0.8 KT0.5 mK and 2.5 mTB22.8 mT as well as on three other samples with x = 5, 10, 31 ppm in a different setup at 40 KT0.5 mK and at 5.4 mTB200 mT. Spin-lattice and effective spin-spin relaxation times ₁and ₂ ^* of ¹⁹⁵ Pt strongly depend on x and on the external magnetic field. No temperature dependence of ₁and ₂ ^* could be detected and the NMR data, too, give no hint for nuclear magnetic ordering to 0.8 K.     

Numerical Calculation of the Flow Regimes of a Fluid Partially Filling a Horizontal Rotating Heat‐Exchange Cylinder

Consideration is given to a numerical determination of a twodimensional unsteady viscous flow with the free surface in a stationarily rotating horizontal cylinder in which heatexchange processes are carried out. The markerandcell method in a polar coordinate system is used. The features of modeling of the walllayer regime and the circulating flow regime that occur in rapid and slow rotation of the cylinder, respectively, are discussed. Based on the given results of numerical calculations, the influence of the Reynolds number on the character of flow is analyzed.     

A note on the μ-zeros of combinations of cross-product bessel functions

Summary In the problem of diffraction of elastic waves in annular circular, or cylindrical (doubly connected) domains, the zeros of complicated combinations of cross-products of cylinder functions as analytic functions of the index =n+i (in general complex) are required. In this note, the imaginary -zeros of two such combinations of cross-products of two identical doubly connected domains, however with two different boundary conditions on one boundary, are asymptotically computed and graphically displayed. It is shown that even for such a comparison of different boundary conditions, one can obtain with a minimum effort in mathematics asymptotic distributions and the relative dispositions of the respective -zeros. It is then rather simple to determine with a computer the exact positions of the -zeros.

---

Zusammenfassung Bei der Behandlung des Beugungsproblems elastischer Wellen in kreisringförmigen oder zylindrischen (zweifach zusammenhängenden) Bereichen werden die Nullstellen komplizierter Produktkombinationen von Zylinderfunktionen benötigt, und zwar als analytische Funktionen ihrer im allgemeinen komplexen Ordnung =n+i . In dieser Arbeit werden die imaginären -Nullstellen zweier solcher Produktkombinationen in zwei identischen, zweifach zusammenhängenden Bereichen, jedoch mit an einem Rand verschiedenen Randbedingungen, asymptotisch berechnet und graphisch dargestellt. Es wird gezeigt, daß man selbst bei einem solchen Vergleich verschiedener Randbedingungen mit einem Minimum an mathematischem Aufwand asymptotische Verteilungen und die relativen Lagen der entsprechenden -Nullstellen erhalten kann. Es ist dann ziemlich einfach, mit Hilfe eines Rechners die exakten Lagen der -Nullstellen zu bestimmen.

---

---

With 1 Figure     

Coaxial variable-length resonator for determining the electromagnetic parameters of materials at normal and higher temperatures

Conclusions It is possible by means of the above resonator, according to our analysis and in the absence of air gaps between the sample and the line, to evaluate the real components and of permeability and permittivity respectively in the range of 2 to 100 with an error between ±3% and ±10% in the temperature range from room temperature to +400°C, and the imaginary components and (for tan and tan in the range of 0.001 to 2) with an error of 7 to 20% over the same temperature range.     

Single-Mode As–S Glass Fibers

Single-mode As–S glass fibers with a core diameter from 3 to 20 m and a clad diameter of 125 m are prepared by the double-crucible method. The cutoff wavelength of the fibers is 0.9–6 m. The lowest transmission losses in the fibers at 2.2–2.3 m are 100 dB/km, and their mean bending strength is 800–1000 MPa.