Josiah Willard Gibbs and the Foundations of Statistical Mechanics

In this study, I discuss the development of the ideas of Josiah Willard Gibbs' Elementary Principles in Statistical Mechanics and the fundamental role they played in forming the modern concepts in that field. Gibbs' book on statistical mechanics became an instant classic and has remained so for almost a century.     

Non-linear couette flow with heat transfer using the B-G-K model

Zusammenfassung Die Wärmeübertragung in der ebenen Couette-Strömung eines verdünnten Gases ist mit Hilfe der Momenten-Methode, angewendet auf das nicht lineare B-G-K-Modell, untersucht worden. Im Falle der isothermen Strömung reduziert sich die Geschwindigkeitsverteilung auf die Resultate der linearisierten B-G-K-Gleichung. Die Übereinstimmung der Resultate für die Temperaturverteilung und den Wärmefluss mit den Ergebnissen von früheren Arbeiten ist befriedigend.     

Integration of Auditor Preferences and Sampling Objectives: A Polynomial Goal-Programming Perspective

The choice of an audit sample involves integration of diverse goals. Such integration must consider the preferences of the auditor towards costs as well as risks. Traditionally this problem has been formulated to determine minimal sample size and its allocation such that each of the goals is satisfied simultaneously or to the extent possible. However, these formulations do not consider trade-offs between goals, so that the sample may not reflect the auditor's preferences regarding sampling costs and risks. In this paper, we model such trade-offs by utilizing a polynomial goal-programming framework and utilize a practical case problem to illustrate the framework. Computational experience shows the technique to be feasible and inexpensive.     

Erwin Schrödinger and the rise of wave mechanics. III. Early response and applications

This article (Part III) deals with the early applications of wave mechanics to atomic problems—including the demonstration of the formal mathematical equivalence of wave mechanics with the quantum mechanics of Born, Heisenberg, and Jordan, and that of Dirac—by Schrödinger himself and others. The new theory was immediately accepted by the scientific community.This article (in three parts) is an expanded version of the Schrödinger Centenary Lecture delivered by me at CERN (Organisation Européenne pour la Recherche Nucléaire), 1211 Geneva 23, Switzerland, on July 30, 1987.     

On the matched-asymptotic solution of elastodynamic problems: Loading over a semi-infinite rectangular boundary

The paper discusses the solution to an elastodynamic problem of an infinite medium excited by loads acting over a semi-infinite rectangular boundary whose height 2a is assumed small compared to the wavelengths of interest. The solution is developed using the method of matched-asymptotics in conjunction with an application of the Wiener-Hopf technique for the outer problems and the Muskhelishvili-Kolosov complex functions for the inner problems. The solutions are matched mutually and the resulting stress behaviour, as far as it is described by the inner limit to the outer solution, is also derived.     

Bergman cyclopolymerization within the channels of functional hybrid nanocomposites formed by co-assembly of silica and polymerizable surfactant monomer

The Bergman cyclopolymerization of polymerizable surfactant monomer was carried out within the hexagonal channels of functional hybrid nanocomposite formed by co-assembly with silica.     

Improvement in electrical and magnetic properties of mixed Mg-Al-Mn ferrite system synthesized by citrate precursor technique

In the present work, mixed magnesium-manganese ferrites of composition Mg_0.9Mn_0.1Al_0.3Co_zFe_1.7−zO₄ where z=0.3, 0.5 and 0.7 have been synthesized by the citrate precursor technique. X-ray diffraction patterns of the samples confirmed the formation of single-phase spinel structure. The ferrites have been investigated for their electric and magnetic properties such as dc resistivity, Curie temperature, saturation magnetization, initial permeability and relative loss factor (RLF). Fairly constant value of initial permeability over a wide frequency range (0.1-20 MHz) and low values of the relative loss factor of the order of 10⁻⁴-10⁻⁵, in the frequency range 0.1-30 MHz, are the cardinal achievements of the present investigation. In addition to this, initial permeability was found to increase with an increase in temperature while RLF was observed to be low at these temperatures. The dc resistivity and Curie temperature were found to increase with an increase in cobalt content. The mechanisms contributing to these results are discussed in detail in this paper.     

Significance of plaque morphology in modifying flow characteristics in a diseased coronary artery: Numerical simulation using plaque measurements from intravascular ultrasound imaging

The paper deals with numerical investigation of the effect of plaque morphology on the flow characteristics in a diseased coronary artery using realistic plaque morphology. The morphological information of the lumen and the plaque is obtained from intravascular ultrasound imaging measurements of 42 patients performed at Cleveland Clinic Foundation, Ohio. For this data, study of Bhaganagar et al. (2010) [1] has revealed the stenosis for 42 patients can be categorized into four types – type I (peak-valley), type II (ascending), type III (descending), and type IV (diffuse). The aim of the present study is to isolate the effect of shape of the stenosis on the flow characteristics for a given degree of the stenosis. In this study, we conduct fluid dynamic simulations for the four stenosis types (type I–IV) and analyze the differences in the flow characteristics between these types. Finely refined tetrahedral mesh for the 3-D solid model of the artery with plaques has been generated. The 3-D steady flow simulations were performed using the turbulence (k–ε) model in a finite volume based computational fluid dynamics solver. The axial velocity, the radial velocity, turbulence kinetic energy and wall shear stress profiles of the plaque have been analyzed. From the axial and radial velocity profiles results the differences in the velocity patterns are significantly visible at proximal as well as distal to the throat, region of maximum stenosis. Turbulent kinetic energy and wall shear stress profiles have revealed significant differences in the vicinity of the plaque. Additional unsteady flow simulations have been performed to validate the hypothesis of the significance of plaque morphology in flow alterations in diseased coronary artery. The results revealed the importance of accounting for plaque morphology in addition to plaque height to accurately characterize the turbulent flow in a diseased coronary artery.