The exponential power law: partial wetting kinetics and dynamic contact angles

An equation for the kinetics of partial drop spreading is proposed. This equation was empirically derived from experimental data for the spreading kinetics of partially wetting liquids in terms of the wet area versus time. The equation has the form of an exponential power law (EPL), and transforms into the well-known power law for complete wetting, when the equilibrium contact angle approaches zero. The EPL fits very well available experimental data. To lend additional support to the validity of this generalized equation, it will be demonstrated that when it is transformed to present the dynamic contact angle (DCA), it fits very well DCA experimental data for other wetting processes, such as capillary flow and tape coating.     

ISLAND, revisited

This paper is in answer to the comment on the GRG paper: Lockerbie N.A. Gen. Rel. Grav. 36, 593 (2004), made by A.V. Sanders, G.T. Gillies (ibid.). N. A. Lockerbie is a member of the STEP (Satellite Test of the Equivalence Principle) Science Study Team, and an Associate of the Institute for Gravitational Research at the University of Glasgow, Scotland, UK.     

Evaluation of the drag force by integrating the energy dissipation rate in stokes flow for 2D domains using the FEM

The total drag force on the surface of a body, which is the sum of the form drag and the skin friction drag in a 2D domain, is numerically evaluated by integrating the energy dissipation rate in the whole domain for an incompressible Stokes fluid. The finite element method is used to calculate both the energy dissipation rate in the whole domain as well as the drag on the boundary of the body. The evaluation of the drag and the energy dissipation rate are post-processing operations which are carried out after the velocity field and the pressure field for the flow over a particular profile have been obtained. The results obtained for the flow over three different but constant area profiles—a circle, an ellipse and a cross-section of a prolate spheroid—with uniform inlet velocity are presented and it is shown that the total drag force times the velocity is equal to the total energy dissipation rate in the entire finite flow domain. Hence, by calculating the energy dissipation rate in the domain with unit velocity specified at the far-field boundary enclosing the domain, the drag force on the boundary of the body can be obtained.     

Space–time integrated least squares: a time‐marching approach

A time‐marching formulation is derived from the space–time integrated least squares (STILS) method for solving a pure hyperbolic convection equation and is numerically compared to various known methods. Copyright © 2004 John Wiley & Sons, Ltd.     

Analytical formulas for the velocity field induced by an infinitely thin vortex ring

Three different analytical solutions are presented for a potential vortex ring using three different streamfunctions. Verification studies confirm that all three approaches are valid. It is found that the solution obtained using the Biot–Savart law is the most efficient method due to its simplicity. It is shown that all analytical results are accurate to within machine accuracy and sample calculations are included. Copyright © 2004 John Wiley & Sons, Ltd.     

The Kissinger law and isokinetic effect: Part II. Experimental analysis

On the basis of copper sulphate pentahydrate thermal dissociation, for analyzed reactions I to IV, 6 thermokinetic equations was discussed. Arrhenius law parameters were determined and the isokinetic effect (IE) and Kissinger law appearing was analyzed. It was found that only dependence resulting from isokinetic effect, in the form k _m=q/T _m, relates to the suitable thermokinetic Eq. (2) and Kissinger law in modified form (14). The confirmation was made that the possibility of determining the averaged activation energy from thermokinetic equations using suitable correction coefficients exists.This revised version was published online in November 2005 with corrections to the Cover Date.     

Low detection limit spectrophotometry

An efficient, more sensitive and accurate spectrophotometric process is possible and can be used to obtain qualitative or quantitative results for analytes at limiting concentrations lower than usual. Transmission measurements (incident light power, P₀, or transmitted, P) are performed with a fluorescence spectrometer. One cell only is used to measure standards or unknown solutions, placed between the standard holder cuvette and the emission monochromator of the instrument. The source of the radiant power (P₀) is not the xenon lamp but the fluorescence or scattered radiation from the holder cuvette filled with an appropriate solution. The analyte concentration is found from a calibration graph, based upon Beer’s law or the approximate formula P₀−P=2.303P₀εbc, which is valid for dilute solutions. Determination of iron in a reference material, using 1,10-phenanthroline as the chromogenic reagent, was chosen as an example to demonstrate the suitability of the proposed method and clarify several important statistical questions. Also discussed is why and to what extent molecular fluorescence methods are more sensitive than molecular absorption methods.     

Reaction of carboxamide with Cu2Oisonitrile complex; formation of a new chelated copper(I) complex

Reaction of carboxamides with Cu₂O in the presence of t-butyl isocyanide gave new chelated copper(I) complexes, which probably are formed by the insertion of t-butyl isocyanide into the coppernitrogen bond of copper(I) amide isonitrile complexes, which were initially produced from the carboxamides and Cu₂Ot-butyl isocyanide complex. The same chelated copper(I) complexes were prepared more readily by the reaction of the corresponding N-trimethylsilyl-carboxamides with Cu₂Ot-butyl isocyanide complex. Reactions of the copper(I) complexes thus obtained with alkylating agents, such as alkyl halides, alkyl tosylates and triethyloxonium tetrafluoroborate, also were described.     

The third law of thermodynamics and the degeneracy of the ground state for lattice systems

The third law of thermodynamics, in the sense that the entropy per unit volume goes to zero as the temperature goes to zero, is investigated within the framework of statistical mechanics for quantum and classical lattice models. We present two main results: (i) For all models the question of whether the third law is satisfied can be decided completely in terms of ground-state degeneracies alone, provided these are computed for all possible boundary conditions. In principle, there is no need to investigate possible entropy contributions from low-lying excited states, (ii) The third law is shown to hold for ferromagnetic models by an analysis of the ground states.Dedicated to Pierre Résibois. Work supported in part by NSF grant PHY-7825390 A01.     

关于分布函数极大值位置的讨论

将关于某个变量的连续分布函数进行变数变换,除非新老变数为线性关系,否则变换前后的分布函数的极大值之间的关系一般会不同于新老变数之间的关系。