Scaling of Nucleation Rates

The homogeneous nucleation rate, J, for T ≪ Tc can be cast into a corresponding states form by exploiting scaled expressions for the vapor pressure and for the surface tension, σ. In the vapor-to-liquid case with σ = σ0[Tc-T], the classical cluster energy of formation /kT = [16π/3]·Ω3[Tc/T-1]3/(ln S)2 ≡ [x0/x]2, where Ω ≡ σ0[k ñ2/3] and ñ is liquid number density. The Ω ≈ 2 for normal liquids. (A similar approach can be applied to homogeneous liquid to solid nucleation and to heterogeneous nucleation formalisms using appropriate modifications of σ and Ω.) The above [x0/x]2 is sufficiently tenable that in some cases, one can use it to extract approximate critical temperatures from experimental data. In this work, we point out that expansion cloud chamber data (for nonane, toluene, and water) are in excellent agreement with ln J ≈ const. - [x0/x]2 [centimeter-gram-second (cgs) units], and that the constant term is well approximated by ln (Γc), where Γc is the inverse thermal wavelength cubed per second at T = Tc. The ln (Γc) is ≈ 60 in cgs units (74 in SI units) for most materials. A physical basis for the latter form, which includes the behavior at small n, the discrete integer behavior of n, and a configurational entropy term, τ ln (n), is presented

An inventory model for deteriorating items with stock-dependent demand under the conditions of inflation and time-value of money

[[abstract]]In this paper, we incorporate the effects of inflation and time-value of money in inventory decision making when demand, at each time moment rather than being constant, is considered to be dependent upon current stock level. In addition, the shortages are neither completely backlogged nor completely lost assuming the backlogging rate to be linearly dependent on the amount of demand backlogged. We shall be concerned with finding the optimal number of replenishments and service rate to minimize the total relevant costs over a finite planning horizon. Numerical examples are presented to illustrate the proposed models.[[notice]]補正完畢[[incitationindex]]E