Statistical Entropy of a Lattice-Gas Model: Multiparticle Correlation Expansion

A formula expressing the statistical entropy of a lattice-gas model as a multiparticle correlation expansion is derived in the grand-canonical and in the canonical ensembles. The differences from the analogous expansion in the continuum case are elucidated. The Ising model in one dimension is discussed as a case study.     

A new analytical model for thermal stresses in multi-phase materials and lifetime prediction methods

Based on the fundamental equations of the mechanics of solid continuum, the paper employs an analytical model for determination of elastic thermal stresses in isotropic continuum represented by periodically distributed spherical particles with different distributions in an infinite matrix, imaginarily divided into identical cells with dimensions equal to inter-particle distances, containing a central spherical particle with or without a spherical envelope on the particle surface. Consequently, the multi-particle-（envelope）- matrix system, as a model system regarding the analytical modelling, is applicable to four types of multi-phase materials. As functions of the particle volume fraction v, the inter-particle distances dl, d2, d3 along three mutually per- pendicular axes, and the particle and envelope radii, R1 and R2, respectively, the thermal stresses within the cell, are originated during a cooling process as a consequence of the difference in thermal expansion coefficients of phases rep- resented by the matrix, envelope and particle. Analytical-（experimental）-computational lifetime prediction methods for multi-phase materials are proposed, which can be used in engineering with appropriate values of parameters of real multi-phase materials.     

关于一类复合幂级数展开式的收敛性定理

本文研究了一类复合型幂级数展开式,证明了一个收敛性定理并举例说明其应用.在注记中指出了可进一步研究的问题.     

高层数印制板对位精度控制

文章讨论了温度、湿度对底片胀缩的影响，并结合底片胀缩、单片胀缩的情况探讨了高层数印制板生产对位精度的控制方法。     

Effect of lateral dimensional scaling on the thermal stability of poly-CoSi2 reacted on Si (001)

The effect of lateral dimensional scaling on the thermal stability of polycrystalline cobalt disilicide wires reacted on Si (001) has been studied down to 0.6 μm linewidth. An unpatterned silicide has been used as a reference sample. The annealing processes were performed in N₂ environment, between 900 and 1050°C, on both blanket and patterned silicide. Transmission electron microscopy analyses in plan-view and cross-section allowed us to study the morphology of lines before and after high-temperature processes. Resistance measurements showed a better thermal stability in blanket silicide layer compared to narrow lines. The electrical behaviour of the lines has been explained in terms of both lateral roughness and hole formation in the silicide layer.     

On the Ising Model with Strongly Anisotropic External Field

In this paper we analyze the equilibrium phase diagram of the two-dimensional ferromagnetic n.n. Ising model when the external field takes alternating signs on different rows. We show that some of the zero-temperature coexistence lines disappear at every positive sufficiently small temperature, whereas one (and only one) of them persists for sufficiently low temperature.     

Dendriform equations

We investigate solutions for a particular class of linear equations in dendriform algebras. Motivations as well as several applications are provided. The latter follow naturally from the intimate link between dendriform algebras and Rota–Baxter operators, e.g. the Riemann integral map or Jackson's q-integral.     

Matrix and vector models in the strong coupling limit

We consider matrix and vector models in the large-N limit: we study N × N matrices and vectors with N² components. In the case of a zero-dimensional model (D = 0), we prove that in the strong coupling limit (g → ∞), the partition functions of the two models coincide up to a coefficient. This also holds for D = 1. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 236–243, May, 2008.     

Kinetics and thermodynamics of thermal decomposition of synthetic AlPO<Subscript>4</Subscript>·2H<Subscript>2</Subscript>O

Cumene hydroperoxide (CHP) and its derivatives have caused many serious explosions and fires in Taiwan as a consequence of thermal instability, chemical contamination, and even mechanical shock. It has been employed in polymerization for producing phenol and dicumyl peroxide (DCPO). Differential scanning calorimetry (DSC) was used to analyze the thermal hazard of CHP in the presence of sodium hydroxide (NaOH), sulfuric acid (H₂SO₄), and sodium bisulfite (Na₂SO₃). Thermokinetic parameters for decomposition, such as exothermic onset temperature (T ₀ ), maximum temperature (T _max ), and enthalpy (ΔH), were obtained from the thermal curves. Isothermal microcalorimetry (thermal activity monitor, TAM) was employed to investigate the thermal hazards during CHP storage and CHP mixed with NaOH, H₂SO₄, and Na₂SO₃ under isothermal conditions in a reactor or container. Tests by TAM indicated that from 70 to 90 °C an autocatalytic reaction was apparent in the thermal curves. According to the results from the TAM test, high performance liquid chromatography (HPLC) was, in turn, adopted to analyze the result of concentration versus time. By the Arrhenius equation, the activation energy (E _a ) and rate constant (k) were calculated. Depending on the process conditions, NaOH was one of the incompatible chemicals or catalysts for CHP. When CHP is mixed with NaOH, the T ₀ is induced earlier and the reactions become more complex than for pure CHP, and the E _a is lower than for pure CHP.