Experimental studies on the microstructure and hardness of laser-treated steel specimens

An experimental investigation with 5 kW CW CO₂ laser system was carried out to study the effects of different laser and process parameters on the microstructure and hardness of carbon steel specimen with varying carbon percentage. The laser beam is allowed to scan on the surface of the work piece varying the power (1.1–2.5 kW) and traverse speed (6–15 mm/s) at two different spot sizes using TEM_01* mode laser beam. The most hardenable microstructure achieved in case of three grades of carbon steel and the most influencing parameter on the value of hardness are reported. Besides the above study, some multipass operations are also carried out to recommend an appropriate gap between consecutive passes.     

Simulation of two‐phase flow–body interaction problems using direct forcing/fictitious domain–level set method

In the present paper, a direct forcing/fictitious domain (DF/FD)–level set method is proposed to simulate the twophase flow–body interaction. The DF/FD does not sacrifice accuracy and robustness by employing a discrete δ (Dirac delta) function to transfer quantities between the Eulerian nodes and Lagrangian points explicitly as the immersed boundary method. The advantages of this approach are the simple concept, the easy implementation and the utilization of original governing equation without modification. The main idea is to combine DF/FD method with the level set method in the Cartesian coordinates. We present the results of a number of test cases to illustrate the effectiveness of the proposed method for single‐phase flow–body interaction problem and the two‐phase flows with a stationary body. Eventually, the simulations of various water entry problems have been conducted to validate the capability and the accuracy of the present method on solving the twophase flow–body interaction. Consequently, the present results are found to be in good agreement with those of previous studies. Copyright © 2013 John Wiley & Sons, Ltd.     

A note on the disjunctive index of joined a-perfect graphs

In this paper we present a lower bound of the disjunctive rank of the facets describing the stable set polytope of joined a-perfect graphs. This class contains near-bipartite, t-perfect, h-perfect and complement of fuzzy interval graphs, among others. The stable set polytope of joined a-perfect graphs is described by means of full rank constraints of its node induced prime antiwebs. As a first step, we completely determine the disjunctive rank of all these constraints. Using this result we obtain a lower bound of the disjunctive index of joined a-perfect graphs and prove that this bound can be achieved. In addition, we completely determine the disjunctive index of every antiweb and observe that it does not always coincide with the disjunctive rank of its full rank constraint.     

Syndetically proximal pairs

For continuous self-maps of compact metric spaces, we study the syndetically proximal relation, and in particular we identify certain sufficient conditions for the syndetically proximal cell of each point to be small. We show that any interval map f with positive topological entropy has a syndetically scrambled Cantor set, and an uncountable syndetically scrambled set invariant under some power of f. In the process of proving this, we improve a classical result about interval maps and establish that if f is an interval map with positive topological entropy and m?2, then there is n∈N such that the one-sided full shift on m symbols is topologically conjugate to a subsystem of fn² (the classical result gives only semi-conjugacy).     

On the paper “Symmetry analysis of wave equation on sphere” by H. Azad and M.T. Mustafa

Using the scalar curvature of the product manifold S²×R and the complete group classification of nonlinear Poisson equation on (pseudo) Riemannian manifolds, we extend the previous results on symmetry analysis of homogeneous wave equation obtained by H. Azad and M.T. Mustafa [H. Azad, M.T. Mustafa, Symmetry analysis of wave equation on sphere, J. Math. Anal. Appl. 333 (2007) 1180-1188] to nonlinear Klein-Gordon equations on the two-dimensional sphere.     

Simultaneous Determination of Caffeine and Theophylline in Human Plasma with a Weak Cation Monolithic SPE-column

A simple reversed‐phase high performance liquid chromatography (RP‐HPLC) method was developed to determine the level of caffeine and theophylline in human plasma samples. The sample clean‐up step involved the on‐line solid‐phase extraction (SPE) of the analytes from plasma samples into a weak cation monolithic column using a column switching system. Separation was performed on a C₁₈ column (5 µm, 150 mm×4.6 mm) with ultraviolet detection at 274 nm. The mobile phase consisted of methanol‐water (32/68, V/V) under isocratic conditions at a flow rate of 0.6 mL·min⁻¹. The measured concentration of caffeine and theophylline showed a good linear relationship over the concentrations range, 0.1–80.0 µg·mL⁻¹. The absolute recoveries ranged from 77.10% to 85.39%, and the inter‐day and intra‐day relative standard deviations (RSD) were all less than 5%. This method avoids a tedious pretreatment and provides an economic, repeatable and effective method for assaying trace drugs in biological samples.     

Conduction of Strongly Coupled Electrons Through Narrow Channels on Liquid Helium Surface: Simulation

The conduction of electrons through narrow channels formed on the surface of liquid helium is analyzed by numerical simulations. It is shown that, when electrons are strongly coupled, we have nonlinear and even negative dependence of conductance on the width of the constriction which is controlled by the gate voltage (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On surface tension modelling using the level set method

The paper describes and compares the performance of two options for numerically representing the surface tension force in combination with the level set interface‐tracking method. In both models, the surface tension is represented as a body force, concentrated near the interface, but the technical implementation is different: the first model is based on a traditional level set approach in which the force is distributed in a band around the interface using a regularized delta function, whereas in the second, the force is partly distributed in a band around the interface and partly localized to the actual computational cells containing the interface. A comparative study, involving analysis of several two‐phase flows with moving interfaces, shows that in general the two surface tension models produce results of similar accuracy. However, in the particular case of merging and pinching‐off of interfaces, the traditional level set model of surface tension produces an error that results in non‐converging solutions for film‐like interfaces (i.e. ones involving large contact areas). In contrast, the second model, based on the localized representation of the surface tension force, displays consistent first‐order convergence. Copyright © 2008 John Wiley & Sons, Ltd.     

The thermodynamic limit of quantum Coulomb systems Part I. General theory

This article is the first in a series dealing with the thermodynamic properties of quantum Coulomb systems.In this first part, we consider a general real-valued function E defined on all bounded open sets of R³. Our aim is to give sufficient conditions such that E has a thermodynamic limit. This means that the limit E(Ωn)|Ωn|⁻¹ exists for all ‘regular enough’ sequence Ωn with growing volume, |Ωn|→∞, and is independent of the considered sequence.The sufficient conditions presented in our work all have a clear physical interpretation. In the next paper, we show that the free energies of many different quantum Coulomb systems satisfy these assumptions, hence have a thermodynamic limit.