Influence of stress ratio on the threshold level for fatigue crack propagation in high strength steels

Centrally cracked specimens of JIS SM58Q and HT80 steels were fatigued. The fatigue crack growth rates, da/dn, and the stress intensity threshold levels, ΔK_th were measured over the range of stress ratio, R, from ?1 to 0.8 by the use of an automatic method of continuously decreasing stress intensity factor with crack extension. The measured ΔK_th was well represented as |ΔK_th/2|_R=(1?R)γ|ΔK_th/2|_R=0; and the propagation rate, as da/dn = A(1?R)^γm[(ΔK/2)^m ? {(1 ? R)^γ|ΔK_th/2|R=0}^m] for ?1≦R≦0.33 or da/dn = A(1 ? 0.33)^?γm [(ΔK/2)^m {(1 ? R)^γ |ΔK_th/2|R=0}^m] for 0.33 < ≦ 0.8.     

Dynamics near the tricritical point of a3He-4He mixture

By means of mode-mode coupling we compute damping constants near the tricritical point of a ³ He- ⁴ He mixture. Both on the coexistence curve and in the tricritical region we find : mass diffusion constant≈|?T _t | ^+1/2 , thermal diffusion constantDK _T ～|T?T _t | ^?1/2 , and third viscosity～|T?T _t | ^?3/2 , whereT is the temperature andT _t is the tricritical temperature. These results imply that damping constant of second sound～|T?T _t |S| ^?1/2 in the ordered phase.     

Experimental proof of the existence of a surface electromagnetic wave

Results of experiments for the observation of surface electromagnetic waves (SEWs) in the decameter range (10 and 15 MHz) excited by a vertical dipole and propagating above the ice-coated surface of a salt lake over a distance of up to 1.2 km are considered. It is shown that the SEW decays much more weakly than the “ground” ray. An analysis of the field of radiation from the vertical dipole reveals the presence of a wave with an amplitude decaying with the distance R approximately as 1/R ^1/2, which corresponds to the SEW divergence. The absolute values of the radiation attenuation function |W| are significantly greater than unity and reach |W| ≈ 2, which also corresponds to the SEW. Experimental data on the SEW damping agree with the results of numerical calculations of the electromagnetic field in the system under consideration.     

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.     

An algorithm for spectral factorization using random search techniques

An approximation method for the energy spectrum of a stationary stochastic dynamical system is presented, which allows approximate functional rational factorization.This paper is in three parts. The first deals with a theoretical problem of approximation in Hardy Spaces, whose main result is the following:Let S⁽ⁱⁿ⁾, S be positive functions belonging to L¹(R_gw), such that log S⁽ⁿ⁾ and log S belong to L¹(R_ω, dω/1 + ω²).Let h⁽ⁿ⁾, h be the outer functions of the Hardy Space H²(Π₊) such that S^(g) = |h⁽ⁿ⁾|² and S = |h|² on iR.If S⁽ⁿ⁾ n^→∝ S in L¹(R_ω), and log S⁽ⁿ⁾ n^→∝ log S in L¹(R_ω, dω/1 + ω²), then: h⁽ⁿ⁾ n^→∝ h in H²(Π₊).The second part describes an effective algorithm, using random search methods, and gives an almost sure convergence result for it.The third part treats numerically two examples, permitting comparison of this algorithm with others (whenever there are…): the first example is a problem of approximation for a nonrational process (turbulence) that was considered in Ref. 22: the second example is a problem of model reduction (automatic) considered in Ref. 4.     

Matrix-Product Codes over ? q

Codes C ₁ ,…,C _M of length n over ? _q and an M × N matrix A over ? _q define a matrix-product code C = [C ₁ …C _M ] ·A consisting of all matrix products [c ₁ … c _M ] ·A. This generalizes the (u|u+v)-, (u+v+w|2u+v|u)-, (a+x|b+x|a+b+x)-, (u+v|u-v)- etc. constructions. We study matrix-product codes using Linear Algebra. This provides a basis for a unified analysis of |C|, d(C), the minimum Hamming distance of C, and C ^⊥. It also reveals an interesting connection with MDS codes. We determine |C| when A is non-singular. To underbound d(C), we need A to be `non-singular by columns (NSC)'. We investigate NSC matrices. We show that Generalized Reed-Muller codes are iterative NSC matrix-product codes, generalizing the construction of Reed-Muller codes, as are the ternary `Main Sequence codes'. We obtain a simpler proof of the minimum Hamming distance of such families of codes. If A is square and NSC, C ^⊥ can be described using C ₁ ^⊥, …,C _M ^⊥ and a transformation of A. This yields d(C ^⊥). Finally we show that an NSC matrix-product code is a generalized concatenated code. Received: July 20, 1999; revised version: August 27, 2001     

Improved upper complexity bounds for the discrete fourier transform

The linear complexityL ₂ (G) of a finite groupG is the minimal number of additions, subtractions and multiplications by complex constants of absolute value 2 sufficient to evaluate a suitable Fourier transform of G. Combining and modifying several classical FFT-algorithms, we show thatL ₂(G)8|G|log₂|G| for any finite metabelian groupG.     

Approximate scheme by the coupled-wave theory to efficiently analyze the influences of moiré phenomena in liquid-crystal devices

This work studies an approximate scheme by coupled-wave theory to analyze quickly the large-scale moiré phenomena as seen in common liquid-crystal devices. The moiré phenomena are considered to be caused by two periodic structures (with lattice vectors γ?₁ and γ?₂) and show an interference pattern spanning over a length γ_m=|γ?₁|·|γ?₂|/|γ?₁-γ?₂| (with γ?₁?γ?₂). With the coupled-wave theory, the complete analysis of the moiré optics includes at least 2γ_m/λ (λ: wavelength in vacuum) Fourier components and presents an ineffective computation. This work applies a cos^τ type approximation for the openings of unpatterned liquid-crystal pixels, and considers the first-order coupling between the Fourier components of pixels and other (periodic) optical structures. We hence arrive at an effective evaluation, including 4τ|γ?₁|/λ (or 4τ|γ?₂|/λ) Fourier components, and are able to go back to a complete analysis when considering higher-order couplings at an appropriate τ integer value.     

Quantum Nonlinear Sigma Model with a Damping Term; Finite Temperature Renormalization Group Analysis

We study the behavior of the finite temperature quantum nonlinear sigma model in two dimensions in the presence of the damping of the form f (|w_n|) = g|w_n|^af (|\omega_n|) = \gamma |\omega_n|^\alpha, where α satisfies a 3 1\alpha \ge 1. The analytical calculations will be performed using a = 2\alpha = 2 and the results will be compared with the standard results obtained for the standard quantum nonlinear sigma model. The behavior of such a system is connected with the pseudogap which appears in the normal state of the cuprate superconductors.     

On the location of roots of non-reciprocal integer polynomials

Let P be a polynomial of degree d with integer coefficients such that P(0) ≠ 0. Assuming that P has no reciprocal factors we obtain a lower bound on the modulus of the smallest root of P in terms of its degree d, its Mahler measure M(P) and the number of roots of P lying outside the unit circle, say, k. We derive from this that all d roots of P must lie in the annulus R ₀ < |z| < R ₁, where R ₀ = R ₀(d, k, M(P)) and R ₁ = R ₁(d, k, M(P)) are given explicitly. As an application, for non-reciprocal conjugate algebraic numbers α, α′ of degree d ≥ 2 and of Mahler’s measure M(α), we prove the inequality ${|\alpha\alpha'-1|\,{ > }\,(12M(\alpha)^2 \log M(\alpha))^{-d}}${|\alpha\alpha'-1|\,{ > }\,(12M(\alpha)^2 \log M(\alpha))^{-d}}. Some lower bounds on the moduli of the conjugates of a Pisot number are also given. In particular, it is shown that if α is a cubic Pisot number, then the disc |z| ≤ α ⁻¹ + 0.1999α ⁻² contains no conjugates of α. Here the constant 0.1999 cannot be replaced by the constant 0.2. We also show that if α is a Pisot number of degree at least 4 and α′ is its conjugate, then |α α′ − 1| > (19α ²)⁻¹.     

On the simulation of stochastic processes by spectral representation

In this paper, a modification in the simulation formula for generating stationary stochastic processes, using the spectral representation method developed by Shinozuka, is presented. It is shown that with this modification, the ensemble and temporal autocorrelation function of the simulated stochastic process for fixed values of time lag τ converge to their target autocorrelation function much more quickly. If the sample function is synthesized with N frequencies, then the rate of the convergence is of the order 1/N⁴ instead of 1/N for the original simulation formula. However, for the whole simulation time T₀, the convergences of the autocorrelation functions are not uniform for the time lag τ throughout the range from 0 to T₀/2. It turns out that the proposed modified simulation formula is preferable for the time lag |τ| T₀/2π and the original simulation formula is preferable for the time lag T₀/2π < |τ| T₀/2.     

Dependence of Seebeck coefficient on a load resistance and energy conversion efficiency in a thermoelectric composite

The thermo-emf ΔV and current ΔI generated by imposing the alternating temperature gradients (ATG) at a period of T and the steady temperature gradient (STG) on a thermoelectric (TE) composite were measured as a function of t, where t is the lapsed time and T was varied from 60 to or ∞ s. The STG and ATG were produced by imposing steadily and alternatively a source voltage V in the range from 1.0 to 4.0 V on two Peltier modules sandwiching a composite. ΔT, ΔV, ΔI and V_P oscillate at a period T and their waveforms vary significantly with a change of T, where ΔV and V_P are the voltage drops in a load resistance R_L and in resistance R_P of two modules. The resultant Seebeck coefficient |α| = |ΔV|/ΔT of a composite under the STG was found to be expressed as |α| = |α₀|(1 − R_comp/R_T), where R_T is the total resistance of a circuit for measuring the output signals and R_comp is the resistance of a composite. The effective generating power ΔW_eff has a local maximum at T = 960 s for the p-type composite and at T = 480 s for the n-type one. The maximum energy conversion efficiency η of the p- and n-type composites under the ATG produced by imposing a voltage of 4.0 V at an optimum period were 0.22 and 0.23% at ΔT_eff = 50 K, respectively, which are 42 and 43% higher than those at ΔT = 42 K under the STG. These maximum η for a TE composite sandwiched between two Peltier modules, were found to be expressed theoretically in terms of R_P, R_T, R_L, α_P and α, where α_P and α are the resultant Seebeck coefficients of Peltier modules and a TE composite.     

Heat transfer through subcooled He I layer from distributed heat source in a pressurized He II channel

The subcooled He I layer, in contact with a large heated surface in a channel filled with the pressurized superfluid He II (He II_p), expands the non-boiling region above the Kapitza region up to q_n, above which nucleate boiling sets in. As the bath temperature decreases, q_n is increased more rapidly than q_λ at which the superfluidity is broken at the centre of the heated surface. The value of q_n is increased as the channel gap increases, and is independent of the channel orientation as well as q_λ. Metastabilization of superconducting coils may be enhanced by taking the non-boiling limit q_n into account.     

Reanalysis of Microgravity Heat Capacity Measurements Near the SF<Subscript>6</Subscript> Liquid–Gas Critical Point

The earlier microgravity heat capacity measurements in SF₆ by Haupt and Straub have been reanalyzed in this study. A simple power law as well as the minimal-subtraction renormalization (MSR) scheme were used to fit the measurements. In this paper the unexpected result that the SF₆ heat capacity measurements appear to be within the asymptotic critical region all the way out to a reduced temperature |t| 10^–2 is presented. This conclusion is in contradiction with the smaller asymptotic region |t| < 1.6× 10^–4 found in the original investigation. These heat capacity measurements were found to be inconsistent with renormalization group predictions using SF₆ compressibility measurements.     

Theory of Plane Copper and Oxygen Nuclear Spin–Lattice Relaxation Rates in Lightly Doped La2− x Sr x CuO4

Using a Mori-Zwanzig projection operator procedure the relaxation function theory of doped two-dimensional Heisenberg antiferromagnetic (AF) system in the paramagnetic state is presented taking into account the hole subsystem as well as both the electron and AF correlations. At low temperatures the main contribution to the nuclear spin–lattice relaxation rate, ⁶³(1/T ₁), of plane ⁶³Cu, arises from the AF fluctuations, and ¹⁷(1/T ₁), of plane ¹⁷O, has the contributions from the wave vectors in the vicinity of (π,π) and small q ∼ 0. The effects of thermal spin-wave damping Γ _q on ¹⁷(1/T ₁) in lightly doped regime are investigated, suggesting either a polynomial of up to third order (not simply (T/J)³) or exponential temperature dependence of Γ _q at low temperatures. It is shown that the theory is able to explain the main features of experimental data on temperature and doping dependence of ^17,63(1/T ₁) in the paramagnetic state of La_{2− x} Sr _x CuO₄ compounds.     

The structure of the unidirectionally solidified Al-Al2Au eutectic

The structure of a number of unidirectionally solidified Al-Al₂Au alloys of eutectic and off-eutectic compositions has been investigated over a wide range of growth rates (1.6×10^–4 to 1.66×10^–2cm sec^–1) using a thermal gradient of approximately 80 to 100 lamellar interface || (001)_{Al 2 Au} || (01 1) _Al [ 1 1 0 ]_{Al 2 Au} || [ 1 0 0 ] _Al growth direction of lamellae and rods || [ 1 1 0 ]_{Al2 Au} || [ 1 0 0 ]_Al \begin{gathered} lamellar interface \left\| {(001)_{Al_{ 2} Au} } \right.\left\| {(01 1)} \right._{Al} \hfill \\ \left[ {1 1 0} \right]_{Al_{ 2} Au} \left\| {\left[ {1 0 0} \right]} \right._{Al} \hfill \\ growth direction of \hfill \\ lamellae and rods \left\| {\left[ {1 1 0} \right]_{Al_2 Au} \left\| {\left[ {1 0 0} \right]_{Al} } \right.} \right. \hfill \\ \end{gathered}     

Engineering Co2MnAlxSi1−x Heusler Compounds as a Model System to Correlate Spin Polarization,Intrinsic Gilbert Damping,and Ultrafast Demagnetization

Engineering of magnetic materials for developing better spintronic applications relies on the control of two key parameters: the spin polarization and the Gilbert damping, responsible for the spin angular momentum dissipation. Both of them are expected to affect the ultrafast magnetization dynamics occurring on the femtosecond timescale. Here, engineered Co₂MnAl_xSi_1-x Heusler compounds are used to adjust the degree of spin polarization at the Fermi energy, P, from 60% to 100% and to investigate how they correlate with the damping. It is experimentally demonstrated that the damping decreases when increasing the spin polarization from 1.1 × 10⁻³ for Co₂MnAl with 63% spin polarization to an ultralow value of 4.6 × 10⁻⁴ for the half-metallic ferromagnet Co₂MnSi. This allows the investigation of the relation between these two parameters and the ultrafast demagnetization time characterizing the loss of magnetization occurring after femtosecond laser pulse excitation. The demagnetization time is observed to be inversely proportional to 1 – P and, as a consequence, to the magnetic damping, which can be attributed to the similarity of the spin angular momentum dissipation processes responsible for these two effects. Altogether, the high-quality Heusler compounds allow control over the band structure and therefore the channel for spin angular momentum dissipation.     

Similarity solutions for unsteady shear-stress-driven flow of Newtonian and power-law fluids: slender rivulets and dry patches

Unsteady flow of a thin film of a Newtonian fluid or a non-Newtonian power-law fluid with power-law index N driven by a constant shear stress applied at the free surface, on a plane inclined at an angle α to the horizontal, is considered. Unsteady similarity solutions representing flow of slender rivulets and flow around slender dry patches are obtained. Specifically, solutions are obtained for converging sessile rivulets (0 < α < π/2) and converging dry patches in a pendent film (π/2 < α < π), as well as for diverging pendent rivulets and diverging dry patches in a sessile film. These solutions predict that at any time t, the rivulet and dry patch widen or narrow according to |x|^3/2{|x|^{3/2}} , and the film thickens or thins according to |x|{|x|} , where x denotes distance down the plane, and that at any station x, the rivulet and dry patch widen or narrow like |t|^-1{|t|^{-1}} , and the film thickens or thins like |t|^-1{|t|^{-1}} , independent of N.     

Geometric isomerism of layered complexes of uranyl selenates: Synthesis and structure of (H3O)[C5H14N]2[(UO2)3(SeO4)4(HSeO4)(H2O)] and (H3O)[C5H14N]2[(UO2)3(SeO4)4(HSeO4)(H2O)](H2O)

New uranyl selenates with organic cations (H₃O)[C₅H₁₄N]₂[(UO₂)₃(SeO₄)₄(HSeO₄)(H₂O)] (I) and (H₃O)[C₅H₁₄N]₂[(UO₂)₃(SeO₄)₄(HSeO₄)(H₂O)](H₂O) (II) were synthesized by evaporation of aqueous solutions and studied. Compound I has monoclinic symmetry, space group C2/c, a = 16.7572(13), b = 11.7239(12), c = 19.0490(13) Å, β = 98.875(6)°, V = 3697.6(5) ų, Z = 4. The crystal structure was solved by the direct method and refined to R ₁ = 0.085 for 2868 reflections with |F _hkl | ≥ 4σ|F _hkl |. Compound II has monoclinic symmetry, space group P2₁/n, a = 10.8252(10), b = 19.0007(10), c = 18.6463(15) Å, β = 100.324(7)°, V = 3773.2(5) ų, Z = 4. The crystal structure was solved by the direct method and refined to R ₁ = 0.084 for 5721 reflections with |F _hkl | ≥ 4σ|F _khl |. The structures of I and II are based on layered complexes [(UO₂)₃(SeO₄)₄(HSeO₄)(H₂O)]^3? formed by combination of uranyl pentagonal bipyramids and selenate tetrahedra. H₃O⁺ cations, water molecules, and protonated methylbutylamine cations are located in the interlayer space. Geometric isomerism of two-dimensional complexes [(UO₂)₃(SeO₄)₅(H₂O)] in the structures of uranyl selenates was found and described.     

Unconventional Coherently Precessing Spin States of Superfluid Phases of Liquid 3He and Antiferromagnetic U2D2 Solid 3He

New coherently precessing spin states in superfluid A and B phases of liquid ³ He and antiferromagnetic U2D2 solid ³ He are described. These unconventional dynamical modes are stabilized in the states with nonequilibrium value of the magnitude of the nuclear magnetization. Especially interesting regimes are developed at one half of the equilibrium magnetization (M = M₀/2, M₀ = H₀). One of such exotic dynamical modes has been recently observed in ³ He-B.