A continuous review inventory model with a time discount

This paper presents a continuous review inventory model with a lost sales assumption. The model is unique due to the inclusion of a time discount. Whenever the supplier faces the likelihood of being out of stock, he may issue a discount to motivate customers to accept delayed deliveries and thus avoid the occurrence of lost sales. We propose a control policy with four parameters R₁, Q, R₂ and T where R₁ and Q are the normal reorder point and quantity, respectively and R₂ and T are the triggers for this time discount. During each replenishment cycle, if the on-hand inventory drops to R2 at or before T after the reorder time epoch, the time discount will be granted. A derivation as well as a solution approach for the total cost function are provided. Based on computational results, such a system with a time discount is superior to that without a time discount in terms of minimizing the total system cost. Finally, we compare the performance of the time discount and the emergency ordering approaches.     

Internal friction and elastic modulus of bulk metallic glasses

The mechanical relaxation in binary, ternary, quaternary, and quitary bulk metallic glasses with widely different glass-forming ability, or the critical cooling rate, has been studied. A single-roller melt-spinning apparatus was used for preparing thin specimens. The internal friction Q⁻¹ and the oscillation frequency f of the specimens were measured using an inverted torsion pendulum with the free decay method. The measurements were performed from room temperature, through the glass transition temperature T_g, up to the crystallization temperature T_x. As the temperature is increased, the background Q⁻¹ increases, and peaks can usually be seen near T_g and T_x. The shear modulus, which is proportional to f², is changed near the Q⁻¹ peak. The experimental data are presented and overall features of the results are discussed.     

First principles calculations of thermal equations of state and thermodynamical properties of MgH2 at finite temperatures

We present the first principles calculations of the thermodynamical properties of magnesium hydride (MgH₂) over a temperature range of 0–1000 K. The phonon dispersions are determined within the density functional framework and are used to calculate the free energy of MgH₂ within the quasiharmonic approximation (QHA) at each cell volume and temperature T. Using the free energies the thermal equation of state (EOS) is derived at several temperatures. From the thermal EOS structural parameters such as the equilibrium cell volume (V₀) and elastic properties, namely, bulk modulus (K₀) and its pressure derivative are computed. The free energies are also used to calculate various thermodynamical properties within QHA. These include internal energy E, entropy S, specific heat capacity at constant pressure C_P, thermal pressure P_thermal(V, T) and volume thermal expansion ΔV/V (%). The good agreement of calculated values of S and C_P with experimental data exhibits that QHA can be used as a tool for calculating the thermodynamical properties of MgH₂ over a wide temperature range. P_thermal(V,T) increases strongly with T at all the volumes but it is a slowly varying function of volume for T = 298–500 K. According to Karki [B.B. Karki, Am. Miner. 85 (2000) 1447] such volume based variations can be neglected and so it is possible to estimate the thermal EOS only with the knowledge of the measured P_thermal(V, T) versus temperature at ambient pressure and isothermal compression data at ambient temperature. Temperature dependence of ΔV/V(%) shows that V₀ increased with increase in temperature. However, the percentage decrease in K₀ superseded this percentage increase in V₀ even at temperatures moderately higher than 298 K. Therefore, we suggest application of temperature (T > 298 K) as an approach to enhance the hydrogen storage capacity of MgH₂ because of its better compressibility at these temperatures.     

Moving singularity creep crack growth analysis with the (ΔT)c and C integrals

The physical meaning of (ΔT)_c and its applicability to creep crack growth are reviewed. Numerical evaluation of(ΔT)_c and C^* is discussed with results being given for compact specimen and strip geometries. A moving crack-tip singularity, creep crack growth simulation procedure is described and demonstrated. The results of several crack growth simulation analyses indicate that creep crack growth in 304 stainless steel occurs under essentially steady-state conditions. Based on this result, a simple methodology for predicting creep crack growth behavior is summarized.     

Characterization and modeling of transition edge sensors for high resolution X-ray calorimeter arrays

Characterizing and understanding, in detail, the behavior of a Transition Edge Sensor (TES) is required for achieving an energy resolution of 2 eV at 6 keV desired for future X-ray observatory missions. This paper will report on a suite of measurements (e.g. impedance and I–V among others) and simulations that were developed to extract a comprehensive set of TES parameters such as heat capacity, thermal conductivity, and R(T,I), (T,I), and β_i(T,I) surfaces. These parameters allow for the study of the TES calorimeter behavior at and beyond the small signal regime.     

Icosahedra from liquid droplets?

Quenching of a liquid Pb droplet containing 8217 atoms to T 0.65 T_m is studied on the nanosecond time scale using molecular dynamics and a “glue” force model. Crystallization takes place, and analysis of the final structure reveals an icosahedral-like shape, even if cuboctahedral single crystal structures are energetically favoured by our potential for all sizes. This result appears to be a consequence of the rapid formation of {111} crystallization fronts at the liquid surface and moving inward, and provides an explanation for the rapid structural fluctuations observed in electron microscopy experiments.     

Representation of the displacement rate between the loading points in terms of applied stress and temperature and its relation to creep crack growth rate, C, P and Q parameters

The displacement rate between the loading points in SUS 304 stainless steel has been experimentally obtained under several applied gross stress and high temperatures, and the equation for has been obtained experimentally as a function of applied gross stress σ_g and absolute temperature T. Then, the relation of δ to creep crack growth rate da/dt was clearly shown in terms of equation. Furthermore, the relation has been clarified between the energy rate line integral C^* as affected by , and P parameter. In this way, it is clearly shown why log (da/dt) data plotted against log C^* deviates in some systematic trend with the increase of temperature and gross stress, respectively, whereas log da/dt vs the P parameter becomes exactly the same and one straight line independent of temperature and gross stress. The discussion is made on that the similar relation will hold between the evaluation by C^* and that by _gQ or by Q^*.     

Low-frequency modes in two-dimensional Debye-Yukawa plasma crystals

In a Debye-Yukawa system, charged micro-particles interact with each other through a screened Coulomb potential φ=(Q/r)exp{−r/λ_D} where Q is the charge and λ_D is the screening length. In a strongly coupled Debye-Yukawa system (where Q is much larger than the magnitude of an electron charge), a plasma crystal may be formed. One important feature of such a strongly coupled system is the existence of transverse waves (or shear waves) in low frequency modes. In this paper we present an analytic treatment of longitudinal (or compressional) and transverse low frequency modes in two-dimensional plasma crystals. Dispersion relations of the modes are obtained for two-dimensional triangular lattices. It is also found that the modes (the compressional and the transverse) are strongly damped near the ‘negative dispersion’ regime. Theoretical predictions agree quantitatively with recent experiments, and the effects of neutral gas damping are also discussed.     

Heat pump cycles based on the AF–F transition in Fe–Rh alloys induced by tensile stress

The heat-pumping scheme based on the 1st order antiferromagnetism–ferromagnetism transition induced in FeRh alloy by one-dimensional tensile stress is proposed. Using the model S–T diagram for this alloy, the heat-pump cycles are drawn up based both on the transition latent heat absorption and emission when the transition is induced isothermally and on the change in alloy's temperature when the transition is induced adiabatically by applying tensile stress. The calculated values of heat coefficient φ for the cycles are 30 at ΔT=5 К and 20 at ΔT=10 К, where ΔT is the difference between the temperature surrounding and that of the heat receiver. These values are achieved using the tensile stress of 1·10⁹ Pa. The high values of φ make it possible to consider Fe–Rh alloys near the equiatomic composition as an effective refrigerant for elastocaloric heat-pumping near the room temperature.     

Orientation-dependent mobilities from analyses of two-dimensional TiN(111) island decay kinetics

We present a method for the determination of orientation-dependent mobilities Γ_eff(φ) based upon analyses of the detachment-limited coarsening/decay kinetics of equilibrium-shaped two-dimensional islands. An exact analytical expression relating the orientation-dependence of Γ_eff(φ) to that of the anisotropic step energies β(φ) is derived. This provides relative values of Γ_eff(φ) to within an orientation-independent scale factor that is proportional to the decay rate of the island area. Using in situ high temperature (T = 1550–1700 K) low-energy electron microscopy measurements of two-dimensional TiN island coarsening/decay kinetics on TiN(111) terraces for which β(φ) values are known [Phys. Rev. B 67 (2003) 35409], we demonstrate the applicability of our analytic formulation for the determination of absolute Γ_eff(φ) values.     

An equivalent domain integral method for computing crack-tip integral parameters in non-elastic, thermo-mechanical fracture

The crack-tip parameters, such asJ; T^*, ΔT^* etc, which quantify the severity of the stress/strain fields near the crack-tip in elastic-plastic materials subject to thermo-mechanical loading, are often expressed as integrals over a path that is infinitesimally close to the crack-tip (front). The integrand in such integrals involves the stress-working density, stress, strain and displacement fields arbitrarily close to the crack-tip. In a numerical analysis, such data near the crack-tip are not expected to be very accurate. This paper describes simple approaches and attendant computational algorithms, wherein, the “crack-tip integral” parameters may be evaluated through “equivalent domain integrals” (EDI) alone. It is also seen that the present (EDI) approaches form the generic basis for the popular “virtual crack extension” (VCE) methods. Several examples of thermo-mechanical fracture, including: (i) thermal loading of an elastic material, (ii) arbitrary loading/unloading/reloading of an elastic-plastic material, containing a single dominant crack, are presented to illustrate the present approach and its accuracy.     

Calculation of the ferrite volume in some dual phase steels

The relation between the γ/γ + boundary temperature, T, and the equivalent values of [Cr] and [Ni], as well as the variation of the ferrite volume, V_f, with the temperature in + γ dual-phase steels have been studied. With the aid of a computer, the regressive expressions derived from the experimental results are: T (°C) = T₃ + 21.2 [Cr] − 15.8 [Ni] + 223; V_f (%) = 0.715 exp [0.015(T − T_δ)] − exp[0.015(T_c − T_δ)] + 1.85 exp [0.0083(T − T_c]).     

具有热阻、热漏和内不可逆性的联合卡诺热机生态学优化

用有限时间热力学的方法分析具有热阻、热漏、内不可逆性的定常流联合卡诺型热机循环．导出了在傅立叶导热定律下联合循环功率、效率和生态学指标的性能，并进行优化；得到功率、效率和生态学指标之间的优化关系，并由数值计算分析了功率、效率和循环熵产率之间的关系．所得的结果表明，最大生态学指标下的效率十分接近于联合循环可以达到的最大效率；相应的熵产率也要低于以输出功率为优化目标时的熵产率．     

A dynamic measure of order in structural glasses

Although some patterns of physical behavior are common in the glass transition and in the properties of supercooled liquids and glasses (characteristic viscoelasticity, temperature dependence of viscosity and relaxation times, property evolution through “physical aging”, difficulties in performing equilibrium measurements or simulations, etc.), it is difficult to arrive at a definition of the glass transition which distinguishes it from other phenomena exhibiting similar features. The present paper addresses this problem by defining a dynamical measure of order involving the average “shape” of particle trajectories in supercooled liquids. This dynamic order parameter should provide a measure of “closeness” to the glass transition and some indirect insights into the physical nature of supercooled liquids and glasses. Arguments are given that the proposed dynamic measure of order [“generalized capacity”, C(T)] is related to the temperature-dependent “effective hydrodynamic radius” R_H(T) measured in supercooled liquids and model numerical calculations are given to support this view. Some consequences of the intermittent particle motion at low temperatures for stress relaxation are also discussed.     

Epitaxial growth of AB type compounds under quasi-equilibrium conditions

Single-crystal films of CdS, CdSe and CdTe have been grown in vacuum on mica (fluophlogopite and muscovite) under isothermal conditions, i.e. with T_ev ≈ T_ep ≈ T_gr where T_ev and T_ep are the evaporation and epitaxial temperatures respectively and T_gr is the growth temperature. The synthesis was carried out in the temperature range 430°–800°C in the case of CdS, 300°–650°C for CdSe and 270°–550°C for CdTe. It is shown that the growth rate of single crystal layers (V_gr) depends exponentially on the growth temperature: V_gr (Å/sec) = D exp (−E/RT_gr) Perfect epitaxial CdS, CdSe and CdTe films have a wide range of electrophysical properties. Co-evaporation of CdS and sulphur and of CdSe and selenium allowed high-resistance films of cadmium sulphide and cadmium selenide of both n- and p-types to be obtained.     

Reaction between the tetragonal tungsten bronze niobate K2Sr4Nb10O30 and the perovskite Pb(Mg1/3Nb2/3)O3

The search for dielectric materials with a high dielectric constant and ′_r = ƒ(T) curves with a flat profile fitting the X7R specification is still ongoing. Promising results were obtained by mixing compounds with closely related structures, such as the tetragonal tungsten bronze (TTB) niobate K₂Sr₄Nb₁₀O₃₀ and the perovskite Pb(Mg_1/3Nb_2/3)O₃ (PMN). The present study, based on three methods of synthesis, explores the origin of the spreading out of the dielectric curves ′_r = ƒ(T). For the composition 10x K_0.2Sr_0.4NbO₃ (KSN) + (1 − x)Pb(Mg_1/3Nb_2/3)O₃ (PMN) with x = 0.3–0.6, the three synthesis methods provided similar characteristics and for the highest perovskite ratio (x = 0.3), the ′_r = ƒ(T) curve exhibits a flat profile. When lithium is used as a sintering agent, ′_r = ƒ(T) curves present a linear dependency with the temperature. These materials are also characterized by a structural and a microstructural inhomogeneity. Two phases TTB and perovskite type, different from KSN and PMN, are present after calcination and sintering, but not evenly distributed. The PbO loss during sintering also contributes to the evolution of the properties of the material.     

A modified effective crack-length formulation in elastic-plastic fracture mechanics

In examining the performance of standard effective crack-length formulations, the authors noted quantitative accuracy up to “high” fractions of limit load under loading conditions for which the elastic T-stress was non-negative, while a pronounced deviation from the corresponding continuum elastic-plastic plane-strain finite-element solutions was seen in shallow-cracked geometries having negative T-stress. This trend can be rationalized by noting that, under modified boundary layer (K_I and T) loading, the maximum plastic zone radius strongly increases as the T-stress decreases from zero (J.R. Rice (1974), J. Mech. Phys. Solids 22, 17–26; S.G. Larsson and A.J. Carlsson (1973), J. Mech. Phys. Solids 21, 263–277; N.P. O'Dowd and C.F. Shih (1991), J. Mech. Phys. Solids 39(8), 989–1015.) Accordingly, we formulate a modified effective crack length to account for the effects of the elastic T-stress.

The new formulation consistently extends the load range for which accurate predictions of compliance, J-integral, and crack-tip constraint are obtained in several plane strain specimen geometries. The magnitude of influence of the T-stress varies with specimen type and relative crack depth. The greatest “improvement” to standard effective crack length approximations occurs in specimens of “moderately” negative T-stress.     

Homogenization kinetics of a cast Ti48A12W0.5Si alloy

The homogenization kinetics of a cast Ti48A12W0.5Si alloy with a duplex microstructure was studied in terms of γ-phase dissolution and -grain growth. It was found that the measured volume fraction of remnant γ grains can be well simulated by a model of interface-controlled dissolution in a dislocation mechanism, instead of a diffusion-controlled one. The activation energy for the /γ interface reaction was found to be Q_int = 476 kJ mol⁻¹, which is much higher than the interdiffusion activation energy in TiAl alloy. The grain growth of phase during homogenization can be categorized into three stages. During the first stage, where the volume fraction of remnant γ grains is higher than about 10%, the growth of grains follows the parabolic law D = k₁t^0.2, and the activation energy for grain growth was calculated to be Q₁ = 442 kJ mol⁻¹, very close to the Q_int for /γ interface reaction. In the second stage, where few fine γ grains (1–10 vol.%) remained, a dramatic grain growth occurs. During the final stage, as the single phase is obtained, the coarsening of grains again satisfies the grain growth law D = k₃t^0.4, with the grain growth activation energy Q₃ of 147 kJ mol⁻¹, lower than the reported interdiffusion energy of γ phase.     

Effect of Ca2PbO4 on the formation of the (2223) phase in the Bi---Pb---Sr---Ca---Cu---O system

The effect of excess Ca₂PbO₄ on the superconducting properties of Bi_1.7Pb_0.3Sr₂Ca₂Cu₃O_yB_x (B ≡ Ca₂PbO₄) is investigated through X-ray diffraction, resistivity and a.c. magnetic susceptibility measurements. The Xpray diffraction results show that the volume friction of the low T_c (221s) phase decreases and that of (2223) phase increases with the addition of Ca₂PbO₄. For x = 0.6 and 1.5, only the (2223) phase exists. At higher Ca₂PbO₄ concentrations, i.e. for x = 3.0, the low T_c phase again appears along with the high T_c phase. Diffraction peaks appear at d = 2.02, 2.814 and 2.85, which are characteristic peaks of Ca₂PbO₄, and their intensities increase with increasing x, indicating that Ca₂PbO₄ exists in the lattice in the same form. However, the T_c(0) values decreased gradually from 107 to 98 K with increasing Ca₂PbO₄ concentration. Compared with the undoped sample, the width of the transition δT_c is broad for impurity-added samples and reaches a maximum value for x = 3.0. Pure and Ca₂PbO₄-doped samples showed two peaks in ξ″ vs. T curves and two steps in ξ′ vs. T curves. The first peak is close to the transition temperature and corresponds to the midpoint of the first step in the ξ′ curve. The second peak appears below 98 K and this peak maximum corresponds to the midpoint of the second step. The position of both sets of peaks remained almost the same up to x = 1.5 and shifted towards lower temperatures thereafter. The role of Ca₂PbO₄ in the growth of the (2223) phase and the mechanism of energy loss are discussed.