On the flow of a stratified fluid over a barrier

Summary The flow of a stratified fluid over a barrier is considered. The initial-value problem is solved, and it is shown that there is no disturbance far upstream of the barrier whent . The stationary solution which is obtained by lettingt, is given in a simple closed form for a barrier of an arbitrary shape.     

Amplifier based on a field-effect triode with negative current feedback

Conclusions A field-effect triode amplifier with series negative current feedback allows a voltage gain of the order of 200–300 to be obtained for a load resistance R_s1 M. The coefficient K_u begins to decrease noticeably only for a feedback resistance above 500 .The current gain reaches (8–10)·10³. Increasing the resistances R_s and R_L to hundreds of ohms has practically no effect on K_i. For a further increase of R_s and R_L the coefficient K_i decreases.The power gain reaches its maximum value (of the order of 10⁴ or more) for R_s100 and R_L=10–100 k. An increase in R_s leads to a reduction of K_pmax and to a shift of the extremum of the function K_p=f(R_L) into the range of higher values of R_L.A large input resistance of the amplifier (tens of megohms and higher) is obtained when R_s increases to 10–100 M. The maximum input resistance is obtained for R_L and R_s and may exceed values of from hundreds of megohms to several gigaohms. The minimum input resistance is hundreds of kilohms for R_L and R_s0.The minimum input resistance (5–10 k or less) is ensured for R_g and R_L0. An increase of the output resistance to hundreds of megohms or higher occurs for R_g and R_s.Translated from Izmeritel'naya Tekhnika, No. 9, pp. 67–70, September, 1971.     

On extraneous solutions with uniformly bounded difference quotients for a discrete analogy of a nonlinear ordinary boundary-value problem

Summary For a discrete analogy with n – 1 N grid points of a nonlinear ordinary boundary-value problem with an implicit differential equation of the second order, the existence of 2 ^n–1–2 extraneus solutions is shown, whose sequences of difference quotients of the first and the second order are uniformly bounded as n . For selected explicitly represented sequences of extraneous solutions, the limiting function as n is explicitly given. These functions either do not solve the differential equatin or only in a non-classical sense.This paper is dedicated to Professor Dr. J. Weissinger on the occasion of his 70th birthday.     

Reinvestigation of Elastic-Plastic Growth of Mode III Cracks in Power Law Hardening Materials

This work deals with asymptotic analysis of near tip fields for mode III cracks growing quasi-statically in steady in power law hardening materials. In the analysis the stress expansion originally suggested by Gao and Hwang was modified. Attention was focused on the behavior of the asymptotic solutions as hardening exponent n. Analytical expressions of the dominant terms of deformation velocity and flow factor in the centered fan sector have been obtained by expanding them in series of the small parameter s=2/(n-1). Results showed that the asymptotic solution of near tip fields for power hardening materials goes, as , to its corresponding solution for elastic-perfectly plastic materials.     

Half-solitons in superfluid3He-A: Novel π/2-quanta of phase slippage

Core structures of nontopological solitons between inequivalent vacua in superfluid³He-A are considered. We analyze the symmetries of these A-A interfaces, and compute their hard-core structures in the Ginzburg-Landau regime. We discuss both domain walls where the orbital anisotropy l-vector is flipped (l–l), and those with the same l(x=–) and l(x=+) asymptotics. In particular, we find new classes of A-A boundaries: these novel /2-solitons, which can occur in the absence of a change in the asymptotic l-vector field, constitute the elementary quanta of phase slippage in superfluid³He-A. We ascribe these half-solitons to a new topological scenario for the flaring-out of vorticity in the extended (k, r)-space. Edges of such walls serve to provide vortices with 1/4 quantum of circulation in³He-A. In analogy with the B-B domain walls in superfluid³He-B, solitons of pure phase slippage by —with a normal core—prove unstable in³He-A; they either fission into a pair of ordinary l-solitons—domain walls with superfluid cores both flipping the orbital anisotropy axis (i.e., l–ll), or form a bound pair of walls, each of which constitutes an l-soliton with a phase shift of /2. Our investigation of the superfluid A-A vacuum interfaces may prove useful in a broader context since the A-A boundaries exemplify the possible domain walls relevant for the Higgs-field solitons (cosmic domain walls) within the Weinberg-Salam model.     

Suppression of Anomalous Allotropic Transformations at High Pressures

Anomalous allotropic transformations accompanied by a reduction in the density of the substance can be suppressed by applying a high pressure equal to the ratio of the heat of transition to the difference in the volumes of the phases involved. The estimated pressures necessary to suppress the (ZrO₂), (Fe), and (Sn) phase transitions are 4.34, 3.00, and 0.495 GPa, respectively.     

Transport in the low-temperature limit of a Landau Fermi liquid

The Boltzmann equation for Landau quasiparticles is solved for T 0 by a specialization of a method discussed by Sykes and Brooker. The quasiparticle distribution function is expanded in Legendre polynomials, assuming a boundary condition which imposes axial symmetry, and even-order terms are assumed to relax together with relaxation time _e , odd-order terms with relaxation time _o . By letting wavelength , with finite, one obtains a first-sound solution, and by lettingT 0, and then , one obtains a zero-sound solution. When these solutions are used to calculate the pressure, it is found that the first-sound solution is consistent with hydrodynamics, exhibiting viscosity = _s , while the zero-sound velocityc ₁=[^–1(B₁+4/3_s)]^1/2, so that phenomenologically zero-sound propagates like a longitudinal elastic wave in a glass. A higher zero-sound mode is also predicted, but is heavily damped. The heat flux is calculated and found to obey Vernotte's equation, which contains an intertial term, added to Fourier's law, that becomes significant asT 0.     

Ohm resistivity of electroless copper layers as a function of their thicknesses

The electric Ohm resistivity of electroless Cu depositions on dielectric substrates as a function of their thicknesses is studied. Substantial deviations (up to 10–20 times) from the standard resistivity ( = 1.7 cm^–1) below 0.5 (m thicknesses are observed. The experimental data show for the entire region of thicknesses (d 0.07–5 m) a power function between the relative resistivity changes (/) and the inverse thickness of depositions (d )–(/ (1/d )^0.8. This empirical relation is discussed as an effect of the porous structure of the metallic layers deposited on the substrate. A scanning electron micrography was applied in order to visualize the morphology of the depositions. The micrographs clearly show the evolution of the deposition profile: starting from separate islands at the very beginning of the process, and gradually covering the entire area with continuous but porous metal layers.     

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.     

Axisymmetric stagnation-point flow impinging on a transversely oscillating plate with suction

The viscous fluid motion generated by axisymmetric stagnation-point flow of strain rate a impinging on a flat plate oscillating in its own plane with velocity amplitude U0 and frequency , including uniform suction of strength W0 is considered. A coordinate decomposition transforms the full Navier-Stokes equations into a primary equation describing the steady flow and a secondary equation describing the unsteady motion coupled to the primary solution. The solution to the boundary-value problem is governed by two dimensionless groups: the suction parameter S = W0 a and the frequency parameter = /a, where is the kinematic viscosity. Numerical integrations performed with a Runge-Kutta routine provide an exact solution to the Navier-Stokes equations. Values of the steady shear stress are found to agree with asymptotic results for large values of |S|, with S>0 representing suction and S<0 representing blowing. The magnitude and phase of the unsteady shear stress are given over a range of frequencies sufficient to recover analytical asymptotic results at large values of . The unsteady shear stress lags the wall motion by radians for 0 and by 5/4 radians when . Velocity profiles at selected parameter values during a period of plate oscillation are presented and discussed.     

Theory of the hall effect in strongly correlated Fermi systems

The anomalous properties of the Hall constant in the normal state of high-T_c superconductors are investigated within the Hubbard model. In Mori theory, the frequency dependent Hall constant is given as the sum of its infinite frequency limit and a memory function contribution. The first term (R _H ) was already considered by Shastry et al.¹ In perturbation theory and in the limit of infinite spatial dimensions, the memory function contribution causes the Hall constant to change sign as a function of doping () and to decrease as a function of temperature, if we allow U to be 2W (U: Coulomb repulsion; W: bandwidth). In the limit U , the memory function is calculated via its moments. For frequencies W U, this leads to a decrease of R _H by a factor of (1 + )/2.     

Temperature dependence of the experimental penetration depth of superconducting thin films

Experimental magnetic field penetration depths (t, d, H) of the stable and superheated Meissner state were calculated as a function of temperature for various applied magnetic fields and various film thicknesses for two cases: (1) (t)/d and (2) 2(t)/d ( is the Ginzburg-Landau penetration depth,d is the film thickness, is the GL parameter). The results of the first case should be a useful tool for obtaining (0) of amorphous superconducting thin films.¹ This work was supported in part by NSF Grant No. INT 8006927.     

Quantum Transition to Supersolid Phase

We study a possible coexistence of superconducting state and charge density waves which, in a broad sense, might be called a supersolid phase. We investigate the infinite dimensional (d=) attractive Hubbard model by applying a sublattice dependent Gutzwiller wave function |BCS as a variational wave function describing the ground state. One may naively expect that the BCS superconducting state evolves continuously to the Bose–Einstein condensed state of bipolarons as the attractive interaction increases, as far as the system is dilute. However, we show that our variational wave function has lower energy than the simple BCS wave function for all electron densities and the interaction strengths. Our variational parameters increase (g _A,B) as we increase the interaction strength (U). The energy gap turns out to be a mixture of s and extended-s waves. In the vicinity of half-filling, we find a quantum transition from a simple superconducting phase to a supersolid phase with increase of the electron density and/or the interaction strength.     

Complex Model of the Efficiency of Rectification Plates. 8. Comparison with Other Models with Respect to Experimental Data

A complex model is compared with the Murphree and Hausen models for the cases of concurrent and cross motion of vapor and liquid phases. Use is made of results of experimental studies involving separation of an acetic acidwater mixture and industrial data on rectification of furfurol and ethanol. It is proved that the efficiencies in the complex and Murphree models coincide as the coefficient of phase equilibrium m approaches unity but when this coefficient increases, the first model and the Hausen model coincide. The possibility of using the Murphree model at m 1 and the Hausen model at m is shown.     

A proof for the quasisteady method of solving the Stefan problem

The location limit for the interphase boundary is found in the region exterior to a sphere with a finite radius. It is shown that the solution to the Stefan problem for this region by the method of quasisteady states approaches the same limit as t .Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 24, No. 1, pp. 135–137, January, 1973.     

On irreducible polynomials of small height over finite fields

It is shown that, for an arbitrary function(x) , for almost all prime numbersp of any interval of the form [N–,N] there exists an irreducible modulop polynomial with coefficients of orderO((p)).     

The preparation of alumina fibre by sol-gel processing

Attempts have been made to prepare alumina fibre from the colloidal sol and polymerized alkoxides. The aluminium chloride or aluminium nitrate systems were found to be potential methods for producing continuous alumina fibre: the aluminium nitrate system had a better sintering behaviour than the aluminium chloride system. The aluminium isopropoxide system, however, was unsuitable for preparing alumina fibre but was suitable for the preparation of monoliths, membranes, powders, and multicomponent ceramics. The thermal changes of these precursors were studied by transmission electron microscopy, Fourier-transform infrared spectroscopy and X-ray diffraction. The results demonstrated the different routes of phase transformation as the temperature increases. The aluminium chloride system exhibits two routes for phase transformation: (a) boehmite -Al₂O₃, and (b) gibbsite -Al₂O₃.     

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.     

Mixed state odd Hall effect in YBa2Cu3O7−δ with unidirectional twins

We have studied the mixed state Hall effect in YBa₂Cu₃O_7– single crystals with unidirectional twins: _xy=f(H). An analysis of the Hall conductivity _xy in free flux flow regime reveals that _xy can be successfully described by two terms which are related to the quasiparticle excitations and the motion of free vortices respectively. We have discovered the strong twin dependence of the Hall conductivity _xy in the pinning (TAFF) regime and detected the sign reverse of the Hall conductivity _xy at changing angle (+45 °–45 °) between current and twin plane that indicated the presence of backflow of vortices. We have observed that _xy tends to - while approaching the melting line. These results provide the evidence of strong planar pinning influence on the Hall conductivity.     

Magnetic order in thet-J andt-t′-J models

The magnetic structure of thet-J andt-t-J models are investigated. Assuming that the ground state has magnetic long-range order, we calculated the energy of some magnetically ordered states using a simple transformation of the models and theS approximation. The result shows that the Néel state is destroyed by doped holes unless the next-nearest neighbor hoppingt is finite, and that the ferromagnetic phase appears at moderate doping. Mean field analysis shows that the intermediate phase between the Néel and ferromagnetic phase has spiral spin order, although the spiral phase is shown to be unstable against density fluctuations.On leave from the Department of Materials Science, Faculty of Science, Hiroshima University, Higashi-Hiroshima 724, Japan.