Path-independent integrals around two circular holes in an infinite plate under biaxial loading conditions

An analytic solution is presented for stresses induced in an infinite plate with two unequal circular holes by remote uniform loadings and arbitrary internal pressures in the holes. The solution is obtained by using the general expression for a biharmonic function in bipolar coordinates. The Airy stress function is decomposed in the sum of a fundamental stress function for an infinite plate remotely loaded, which gives non vanishing tractions on the circular boundaries, and an auxiliary stress function required to satisfy the boundary conditions on the pressures at the edges of the holes, which produces vanishing stresses at infinity. Correspondingly, the variations of the stress concentration factor are determined in terms of the holes geometry and loading conditions. The path independent J_k- (k = 1, 2), M- and L-integrals are analytically calculated on a closed contour encircling the two holes, under remote loading, in order to evaluate the energy release rates accompanying unit translation, self similar expansion and rotation of the holes, respectively. Results are then presented for varying loading orientation angle, biaxial loading ratio and holes geometry.     

Notes on multiple periodic solutions for second-order discrete Hamiltonian system

By a new orthogonal direct sum decomposition E_M = Y⊕Z, where Z is related to Δu_i(i = 1, 2, 3, …, M), and a new functional I(u), the method by Guo and Yu is improved to obtain new multiple periodic solutions with a negativity hypothesis on F for a second-order discrete Hamiltonian system. Moreover, we exhibit an instructive example to make our result more clear, which has not been solved by known results.     

Integral formulation for elastodynamic T-stresses

In this paper, a path independent integral formulation is presented for the computation of dynamic T-stresses in a two-dimensional body with a stationary crack. The mutual M-integral expressed through dynamic Ĵ-integrals provides sufficient information for determining T-stresses on the basis of the relationship found between the M-integral and T-stresses. The elastodynamic fields required for the evaluation of the Ĵ-and M-integrals are obtained by the boundary element method. The time-domain approach is used for the solution of the boundary value crack problem and numerical results for two crack problems are presented. In the first a rectangular plate with a central crack is considered and in the second two cracks at a hole in an infinite sheet. A comparison is made with the results obtained by the boundary layer and displacement field methods based on the asymptotic expansions of stresses and displacements at a crack tip vicinity. This revised version was published online in August 2006 with corrections to the Cover Date.     

Some properties of topological pressure of a semigroup of continuous maps

Based on the work of Ma and Wu,[9 Ma D, Wu M. Topological pressure and topological entropy of a semigroup of maps. Discrete Contin Dyn Syst. 2011;31:545–557.[Crossref], [Web of Science ®] , [Google Scholar]] some equivalent definitions of topological pressure of a semigroup of continuous maps are given and several of their basic properties are provided by using separated sets and spanning sets. We also answer an open problem of Bi? and Urbański.[19 Bi? A, Urbański M. Some remarks on topological entropy of a semigroup of continuous maps. Cubo. 2006;8:63–71. [Google Scholar]] That is, letting f_i, i = 2, … , k, be homeomorphisms acting on a compact metric space, G₁ = {id_X, f₂, … , f_k}, G^{? 1}₁ = {id_X, f^{? 1}₂, …, f_k^{? 1}} and letting G and G^?1 denote the semigroups generated by G₁ and G^{? 1}₁, respectively, we give an example showing that the topological entropy of G does not equal the topological entropy of G^?1.     

Structure and cation distribution in perovskites with small cations at the A site: the case of ScCoO3

Abstract

We synthesize ScCoO₃ perovskite and its solid solutions, ScCo_1?xFe_xO₃ and ScCo_1?xCr_xO₃, under high pressure (6 GPa) and high temperature (1570 K) conditions. We find noticeable shifts from the stoichiometric compositions, expressed as (Sc_1?xM_x)MO₃ with x = 0.05–0.11 and M = Co, (Co, Fe) and (Co, Cr). The crystal structure of (Sc_0.95Co_0.05)CoO₃ is refined using synchrotron x-ray powder diffraction data: space group Pnma (No. 62), Z = 4 and lattice parameters a = 5.26766(1) Å, b = 7.14027(2) Å and c = 4.92231(1) Å. (Sc_0.95Co_0.05)CoO₃ crystallizes in the GdFeO₃-type structure similar to other members of the perovskite cobaltite family, ACoO₃ (A³⁺ = Y and Pr-Lu). There is evidence that (Sc_0.95Co_0.05)CoO₃ has non-magnetic low-spin Co³⁺ ions at the B site and paramagnetic high-spin Co³⁺ ions at the A site. In the iron-doped samples (Sc_1?xM_x)MO₃ with M = (Co, Fe), Fe³⁺ ions have a strong preference to occupy the A site of such perovskites at small doping levels.     

Laserstrukturierte nitridische und oxinitridische Beschichtungen abgeschieden mittels Mittelfrequenz‐Magnetron‐Sputtering

The presented work adresses the investigation of the influence of the variation of laser parameters such as pulse energy and the number of pulses on uncoated and coated surfaces with nitride and oxynitride coatings. Three different oxygen gas flows j(O₂) = 10 sccm, j(O₂) = 15 sccm and j(O₂) = 20 sccm in the coating process and correspondingly three different resulting coating compositions with x_{j(O2) = 10 sccm} = (39.8±4.2) atomic‐%, x_{j(O2) = 15 sccm} = (31.6±1.4) atomic‐% and x_{j(O2) = 20 sccm} = (58.4±6.0) atomic‐% were investigated. The analysis of the structure depth using confocal laser scanning microscopy showed that the structure depth is increased with increasing pulse energy and number of pulses. The line‐like interference structures with constant periodicity were detected by scanning electron microscopy. In addition, laser‐induced periodic surface structures with higher spatial frequency and smaller periodicity can be observed more clearly on all coated surfaces in the vertical direction. For coating with x_{j(O2) = 20 sccm} = (58.4±6.0) atomic‐% a formation of microcracks on the flanks of the interference structure is observed after laser structuring.     

A Lanczos-based method for structural dynamic reanalysis problems

In this paper, a new solution method for the modified eigenvalue problem with specific application to structural dynamic reanalysis is presented. The method, which is based on the block Lanczos algorithm, is developed for multiple low rank modifications to a system and calculates a few selected eigenpairs. Given the solution to the original system Ax = λx, procedures are developed for the modified standard eigenvalue Problem (A + ΔA)x? = λ x?, where

• 1 ΔA = Σ_jBS_jB^T, where S_j = S ∈ ?^{p × p}, p ? n and B ∈ ?^{n × p} is constant for all the perturbations S_j.
• 2 ΔA = Σ_iΣ_j B_iS_jB_i^T, where B_i ∈ ?^{n × p} may vary with the pertubations S_j.

The procedures are then extended for the reciprocal and generalized eigenvalue problems so that they are directly applicable to the structural dynamic reanalysis problem. Numerical examples are given to demonstrate the applications of the method.     

Concentration and mobility of charge carriers in thin polycrystalline films of bismuth

We studied bismuth polycrystalline films evaporated onto substrates of Corning 7059 glass to thicknesses d of 200–3000 Å. The resistivity ?, Hall coefficient R_H, magnetoresistance Δ?/? and thermoelectric power α for the temperature range 80–293 K were measured. From the data obtained, the concentrations of electrons (n) and of holes (p) as well as their mobilities μ_n and μ_p were determined without assuming that n = p. The dependences n = ?(d) and ? = ?(d) at a temperature of 90 K confirm the pertinence of the film model according to which the wavefunction of the electrons satisfies a boundary condition in the form ?Ψ = 0 on the film surface.     

The general solutions of an infinite plate with doubly periodic cracks under bending and twisting

The objective of the present paper is to use the basic theorem of Jacobi elliptic functions and residues to find the general solutions of the stress intensity factor of a plate with doubly periodic cracks subjected to a pair of concentrated couples $\text{M}{}_{\mathrm{b}}$ and $\text{M}{}_{\mathrm{t}}$ on the faces of each crack. In this paper the general solutions are expressed in simply closed forms, and they can also be applied to solve practical problems of bending and torsion of a rectangular sheet containing a central crack. The general solutions may be used as a fundamental Green's function for finding other solutions of a plate with doubly periodic cracks under arbitrary bending and twisting moments. It is easily proved that all problems of bending and torsion of an infinite plate with a central crack or singly periodic cracks, are the special cases of the general solutions in this paper.     

Mechanical micro-drilling of nimonic 80A superalloy using uncoated and TiAlN-coated micro-drills

Micro-drilling is a complex mechanical machining process. Micro-drilling experiences an early tool damage which is a major drawback for nickel-based superalloy. This paper examines the wear condition on the micro-tool cutting edge, surface roughness of machined holes, and hole diameter analysis in micro-drilling of Nimonic 80A, using two types of micro-drills (uncoated and TiAlN coated) with 0.79?mm diameter. Micro-drilling tests, using cutting speed (V_c), feed rate (f_z), and the micro-drill diameter as experimental parameters were carried out to bring out the best optimized machining conditions in micro-drilling of Nimonic 80A. Wear on the tool cutting edge and burr height occurring at the entrance of drilled holes were measured at constant period to give the lastingness of micro-drill. Quality of holes were analyzed in terms of surface roughness inside the hole and the hole diameter after every five drilled holes. The result obtained from the above analysis showed that TiAlN-coated micro-drill performs way better than the uncoated micro-drill in terms of wear, surface roughness, hole quality, and burr. Thus, the above performed study gives the knowledge to select micro-tool for machining of Nimonic 80A which could be useful in the aerospace industry.     

Film cooling over a concave surface through two Staggered rows of compound angle holes

Abstract

Experimental results of film cooling effectiveness over a concave surface with two staggered rows are presented by employing transient liquid crystal thermography. Four different discrete hole configurations are used for the injection of jet flow, including a straight circular hole configuration with a spanwise injection angle (β) of 0° and three forward‐expanded hole configurations with β = 0°, 45° and 90° respectively. In all test models there are two staggered rows of discrete holes with streamwise injection angle (γ ) of 35°. Blowing ratios (M) are 0.5, 1.0, and 2.0. The effects of blowing ratio, hole expanded angle, and injection angle orientation on film cooling performance are investigated. The jet flow with M = 0.5 is fairly uniform along the wall surface. The lift‐off phenomenon can be found in the jet flow with β = 0° for both cases of simple and compound angles at M = 1.0 and also exists among all test cases at M = 2.0 except for β = 90°. The lift‐off effect results in a decrease in both η and h /h0. At β = 0°, the jet flow with a forward‐expanded hole gives higher η and lower h /h0 than a simple angle hole. At a fixed blowing ratio, the jet flow with compound angle holes has lower q /q0 and thus provides better wall protection than that with simple angle holes. In the present study, the compound angle with β = 0° at M = 2.0 provides the best film‐cooling protection over the concave surface among all the test configurations.     

Maximum Likelihood Estimation of the Parameters of the Beta Distribution from Smallest Order Statistics

Numerical methods, useful with high-speed computers, are described for obtaining the maximum likelihood estimat.es of the two (shape) parameters of a beta distribution using the smallest M order statistics, 0 < u ₁ ≤ … ≤ ≤ … ≤ u _M , in a random sample of size K(≥M). The maximum likelihood estimates are functions only of the ratio, n = M/K, the Mth ordered observation, u _M , and the two statistics, G ₁ = [II ^M _i=1 u _i ]^1/M , and G ₁ = [II ^M _i=1 (1 – u _i )]^1/M . For the case of the complete sample (i.e., R = 1), however, the estimates are functions only of G ₁ and G ₂, and hence, for this case, explicit tables of the estimates are provided. When R < 1, the methods described depend crucially for their usefulness on the availability of a high-speed computer. Some esamples are given of the use of the procedures described for fitting beta distributions to sets of data. In one example, the fit is studied by using beta probability plots.     

The Distribution of a Variate Based on Independent Ranges from a Uniform Population

The statistic of interest in this article is W = R ₁/min_{1 ≤ j ≤ k} R _j where R _i , i = 1, …, k, denote k independent sample ranges from a standard uniform distribution each based on a common sample size n. Expressions are derived for the distribution function and moments of W, and a table of percentage points is included for selected valrles of k and n. The role of the statistic W in the construction of a subset selection procedure is indicated and operating characteristics of the proceduce are derived under a slippage configuration. A numerical example is provided.     

Analysis and optimal control of discrete time‐varying systems Via Hahn polynomials

Abstract

Recently, the problem of analysis and optimal control of discrete time‐invariant systems has been extensively studied using finite series expansion of discrete orthogonal polynomials. This paper is to extend the applicable scope of discrete orthogonal polynomials to discrete time‐varying systems. The finite set of Hahn polynomials {q_ik)], i=0, 1, …, N} is chosen as the finite series expansion basis due to its general form and useful properties. First, for treating the product of two discrete‐time functions by Hahn series expansion, a new algorithm is derived to compute the Hahn series expansion coefficients of products qi(k)q_j (k), i, j=0, 1, …, N. These Hahn coefficients are then used to establish a product operational matrix for relating the Hahn coefficient vector of a product function to those of its component functions. This product operational matrix, along with the relations for connecting the Hahn coefficient vectors of a discrete function x(k) and its time‐shifted x(k+1), is finally applied to derive computational algorithms for solving the problems of analysis and optimal control of discrete time‐varying systems via finite Hahn series. Computed results are provided to illustrate the applicability of the proposed algorithms.     

Standard entropies of compounds: Theoretical aspects of Latimer's rule

Latimer (1921) and others have suggested empirical formulas for the standard entropyS ⁰=S(298 K) of solid compounds. Without any rigorous theoretical analysis, they assume that the explicit dependence on the constituent atomic massesM _i (1 ≤i ≤j) is given byc ₁lnM ₁+ ... +c _j lnM _j , wherec _i , is the concentration of the atom of kindi (0 < c_i < 1). It is shown, from lattice dynamical theory, that this is the correct mass dependence for the high temperature limit of the vibrational entropy. Thus, it is correct in an estimate ofS ⁰ provided that the massesM _j are not too small and the interatomic forces not too strong.     

Analytic Study of the E ⊗ e Jahn–Teller Polaron

A review is given of recent work on the E ? e Jahn–Teller (JT) polaron, i.e., a mobile e_g electron linearly coupled to the local e_g normal vibrations of a periodic array of octahedral complexes. The main ingredient of our theory is a mapping of the Hamiltonian onto a new Hilbert space, belonging to a fixed angular momentum eigenvalue j > 0. In this representation, the Hamiltonian depends explicitly on j and decomposes into a Holstein term and a residual JT interaction. The ground state of the JT polaron belongs to the sector j = 1/2, whereas the Holstein polaron is obtained for the “unphysical” value j = 0. The new Hamiltonian is then subjected to a variational treatment, yielding the dispersion relations, effective masses and band widths for both kinds of polarons. The calculated polaron masses are in remarkably good agreement with recent quantum Monte Carlo data.     

Analytic Study of the E ? e Jahn–Teller Polaron

A review is given of recent work on the E e Jahn–Teller (JT) polaron, i.e., a mobile e_g electron linearly coupled to the local e_g normal vibrations of a periodic array of octahedral complexes. The main ingredient of our theory is a mapping of the Hamiltonian onto a new Hilbert space, belonging to a fixed angular momentum eigenvalue j > 0. In this representation, the Hamiltonian depends explicitly on j and decomposes into a Holstein term and a residual JT interaction. The ground state of the JT polaron belongs to the sector j = 1/2, whereas the Holstein polaron is obtained for the unphysical value j = 0. The new Hamiltonian is then subjected to a variational treatment, yielding the dispersion relations, effective masses and band widths for both kinds of polarons. The calculated polaron masses are in remarkably good agreement with recent quantum Monte Carlo data.     

Four-mode coherent entangled state as an entanglement of two bipartite coherent entangled states

By introducing a four-mode unitary operator U = exp[?iλ(X ₁ P ₂ + X ₂ P ₃ + X ₃ P ₄ + X ₄ P ₁)], we show how a four-mode coherent entangled state can be generated by entangling a two bipartite coherent entangled state. The corresponding squeezed vacuum state U|0000? in four-mode Fock space is derived by virtue of the technique of integration within ordered production of operators, which exhibits the standard squeezing for the four-mode quadratures. A new ideal quantum mechanical representation |α, β, γ? is constructed from U|0000? in the limit of infinite squeezing, which possesses the properties of both coherent and entangled states. The entanglement involved in |α, β, γ? is explained. A scheme for generating |α, β, γ? is presented.     

Diffeomorphisms with the s-limit shadowing property

Let Diff(M) be the space of diffeomorphisms of a closed C ^∞ manifold M endowed with the C ¹-topology, and denote by ?(f) the chain recurrent set of f?∈?Diff(M). In this article, we show that C ¹-generically f _|?(f) has the s-limit shadowing property if and only if f satisfies both Axiom A and no-cycle condition.