Artificially layered Bi2Sr2Ca n−1Cu n O2n+4 (n≥3) films by sequential sputter deposition

Uniformly layered mixture of the succeeding members in the structure series was found in artificially layered Bi₂Sr₂Ca _n?1Cu _n O_2n+4 films synthesized by a three-target sequential sputter deposition technique. The intergrowth structure was quantitatively evaluated by X-ray analysis technique. An averagedc-axis (half) unit length and a plane spacing d₀～-0.31 nm $\left( { \simeq d_{CaCuO_2 } } \right)$ in the intergrowth structure are considered as a modulation wavelength and an average lattice of superlattice in the analysis. It is shown that the X-ray diffraction patterns observed in our films are in good agreement with that predicted by the superlattice model.     

A note on the turbulent energy as a parameter of turbulent flow

The art of modeling turbulence is a needed tool in the construction of computer codes for turbulent flows. The state to which this art has been developed is inadequate, and quotations from authoritative sources support this point of view. The energy contained in the turbulent fluctuations, i.e., the turbulent energy, is often used as a parameter in the modeling process. The present article attempts to examine this quantity as it is being created, transported, and dissipated. For this purpose experimental evidence from the author's own experiments (free jets), as well as theoretical conclusions from the elementary deductions of the basic equations, the concept of turbulent potential flow, and a general solution to the Navier-Stokes-Reynolds equations, is drawn to attention. Recirculating flow is given special attention. The paper concludes with recommendations for principles that must be satisfied if improved modeling is to be achieved. These principles are necessary; whether they are also sufficient is open to question.Nomenclature A ₀ Constant - b _1/2 Jet's half-width - b ₁ ^2/(0) Jet's half-width at z=z(in0) - E _z Kinetic energy contained in the jet's axial velocity at a given profile - E _r Kinetic energy contained in the jet's radial velocity at a given profile - f() Dimensionless velocity profile [f(0)=1] - F(), H() Defined functions - L _char Jet's characteristic length - m, n Exponents - p Pressure - q Kinetic energy in the turbulent fluctuations - Heat flux - q ² - r, , z Cylindrical coordinates - t Time - û Internal energy - u, v, w Velocity components - Mean velocity components - Mean velocity components - U ₀ Constant - U _plate Plate's velocity - Uskc/(0) Centerline velocity at z=z₀ - X, Y, Z Components of body force - W Total work done by surface stresses - W ₁ Recoverable work done by surface stresses - W ₂ Dissipated work - z ₀ Downstream distance from the nozzle beyond which self-similar velocity profiles occur - Fluid's kinematic viscosity - Fluid's density - Normal stresses - Shear stresses - Normal stresses with the pressure removed - Dimensionless Crossflow coordinate - ₀ Constant - Stress functions - Stress potential Paper dedicated to Professor Joseph Kestin.Definitions of symbols are given under Nomenclature.     

Computer-aided design of small patch antenna using (Al, Mg)TaO2 ceramics

The microwave dielectric properties of (AMT) ceramics and the design of small coplanar waveguide fed antenna (CPWFA) have been investigated. ( and ( have orthorhombic and tetragonal structure, respectively. As ( concentration increased, AMT ceramics transformed into the tetragonal structure. Specimens having tetragonal single phase could be obtained above x=0.6. As ( concentration increased, the grain size, dielectric constant and quality factor (Q) significantly increased and the temperature coefficient of resonant frequency changed from negative to positive. The of was realized at x=0.65 and the Q · f _O value and for this composition were 112 470 GHz and 26.1, respectively. Newly developed dielectric materials were used for 1.5 GHz band CPWFA design and fabrication. The size of the CPWFA can be reduced by using high dielectric constant AMT ceramics, insetting slits into the patch, and fabricating CPW feed line in the ground plane. The slits play a role in not only lowering a center frequency but also fine tuning for the proposed antenna together with the open stub of CPW feed line. The CPWFA with slits has a lower center frequency than the conventional CPWFA, which suggests that the antenna size can be reduced by as much as 16.3%. The structure simulations of the CPWFAs have been performed to obtain impedance matching and to investigate the effects of slits. Experimental results of the fabricated device were in good agreement with the simulation.     

Stresses in a cylindrical shell supported by a core of a different material

Summary The stress problem of a thin cylindrical shell supported by an elastic core of a different material and subjected to arbitrary loading on its curved surface is considered. The problem is solved by applying the three-dimensional theory of elasticity to the core and using membrane or bending solutions for the shell. Equilibrium and compatibility equations are satisfied at the junction of the shell and the core. It is pointed out that the procedure can easily be extended to the case of a hollow core with or without another shell of another material in it. Numerical results are presented to illustrate the effectiveness of even a weak core in reducing the shell stresses.

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Zusammenfassung Gegenstand der Untersuchung ist eine dünne Kreiszylinderschale, die durch einen elastischen Kern aus einem anderen Werkstoff gestützt ist und eine beliebige Belastung trägt. Die Lösung verbindet die strenge, dreidimensionale Theorie des zylindrischen Kerns mit der Membran- oder Biegetheorie der Schale. An der Grenze zwischen beiden Teilen müssen die Verschiebungen und gewisse Spannungskomponenten stetig übergehen. Es wird darauf hingewiesen, daß die Lösung leicht auf den Fall ausgedehnt werden kann, daß der Kern ein Hohlzylinder ist, der möglicherweise auf der Innenseite mit einer zweiten Zylinderschale verbunden ist. Zahlenergebnisse zeigen, daß selbst ein verhältnismäsig nachgiebiger Kern einen großen (und günstigen) Einfluß auf die Spannungen in der Schale ausübt.

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Principal Symbols a Radius of the middle surface of the shell - t Thickness of the shell - =1–t/2a - u _c,v _c,w _c Displacements respectively in the axial, circumferential and radial directions of a point in the core - X(x), (), (r/a) 3×3 square matrices - ,m Parameters - l Length of the cylinder - c A vector containing constantsc ₁,c ₂ andc ₃ - =r/a - =m+4(1–v _e) - E _c,v _e Elastic constants for the core material - Stresses at a point in the core - D _c - A vector containing _rx , _r and _r - (r/a) A 3×3 matrix - Displacements at the surfacer=a of the core - A vector containing - Amplitudes of displacements - A vector containing - =(x, ,a) - _ij Constants - A A square matrix containing constants _ij - Stress resultants in the shell as defined in reference [3] - p _x,p ,P _r Components of applied loading per unit area of shell's middle surface - () - ()· - u, v, w Displacements of a point on the middle surface of the shell - E _s,v _s Elastic constants for the shell material - D _s - K - k - p _xmn,p _mn,p _rmn Amplitudes of loadsp _x,p , p_r - u _mn, v_mn,w _mn Amplitudes of displacementsu, v, With 1 Figure     

Structural features of Σ = 19, [110] GaAs tilt grain boundaries

= 19, [110] tilt grain boundaries have been observed to facet parallel to particular planes; the facets lie along _A/ _B, ( )_A/ )_B and ( )_A/( )_B. The structural unit of the = 19 ( )_A/( )_B [110] boundaries consists of 5- and 7-member rings, which are similar to the core structure of a/2[110] edge dislocations. The polarities in each grain on either side of the boundaries has been confirmed by CBED methods; a lower number of anti-site type cross-boundary bonds occur along the boundaries compared to when the polarity of one grain is reversed. The presence of 7-member rings and anti-site cross-boundary bonds results in a more open atomic structure at the boundary, shortening the distance between the first and the second {331} atomic planes from the boundary plane by 40%.     

On strong Dickson pseudoprimes

It is known that the Lucas sequenceV _n(,c)=aⁿ + bⁿ,a, b being the roots ofx ² – x + c=0 equals the Dickson polynomial .^n–2i Lidl, Müller and Oswald recently defined a number b to be a strong Dickson pseudoprime to the parameterc (shortlysDpp(c)) if [itg_n(b, c)b modn for all b. These numbers seem to be very appropriate for a fast probabilistic prime number test. In generalizing results of the above mentioned authors a criterion is derived for an odd composite number to be ansDpp(c) for fixedc. Furthermore the optimal parameterc for the prime number test is determined.     

Fabrication and electrical properties of lead zirconate titanate thick films using a new sol-gel processing technique

Lead zirconate titanate (Pb ( , PZT) ferroelectric films 2–60 m in thickness have been successfully fabricated on Pt-coated oxidized Si substrates by a new sol-gel-based process. The films are a 0-3 ceramic–ceramic composite formed by dispersing ceramic powders in a sol-gel solution. The precursor solution for spin coating was prepared from lead acetate, tetrabutyl titanate, and zirconium nitrate. The microstructure and morphology of the prepared PZT thick films were investigated via X-ray diffractometry (XRD) and scanning electron microscopy techniques. XRD analysis shows that the thick films possess single-phase perovskite-type structure, no pyrochlore phase exists in thick films, and SEM micrographs suggest that the PZT thick films were uniform, dense, and crack free. A dielectric constant of 860, loss tangent of 0.03, remanent polarization of , and a coercive field of were measured on 50 m thick films.     

On primitive and free roots in a finite field

In this paper them-dimensional extension of the finite field of orderq is investigated from an algebraic point of view. Looking upon the additive group as a cyclic module over the principal ideal domain , we introduce a new family of polynomials over which are the additive analogues of the cyclotomic polynomials. Two methods to calculate these polynomials are proposed. In combination with algorithms to compute cyclotomic polynomials, we obtain, at least theoretically, a method to determine all elements in of a given additive and multiplicative order; especially the generators of both cyclic structures, namely the generators of primitive normal bases in over , are characterized as the set of roots of a certain polynomial over .     

μ+SR Study on Bi2Sr2Ca1−x Y x (Cu1−y Zn y )2O8+δ around the Hole Concentration of \frac{1} {8} per Cu

In order to study the effect in different high-T _c oxides from the La-system, muon spin relaxation measurements were applied to the Zn-substituted Bi-2212 system, Bi ₂ Sr ₂ Ca _1–x Y _x (Cu _1–y Zn _y ) ₂ O ₈₊ , around the hole concentration p= per Cu. It has been revealed that the magnetic correlation between Cu spins is anomalously enhanced in the Zn-substituted samples at per Cu, proving the existence of the effect" in the Bi-2212 system as well.