[Book review] Mathematics and Culture II

Review of Mathematics and Culture II. Visual Perfection: Mathematics and Creativity, Michele Emmer (Ed.), Springer, 2005 ISBN: 978-3-540-21368-0

Investigation into the performance of turbulence models for fluid flow and heat transfer phenomena in electronic applications

Heat is extracted away from an electronic package by convection, conduction, and/or radiation. The amount of heat extracted by forced convection using air is highly dependent on the characteristics of the airflow around the package which includes its velocity and direction. Turbulence in the air is also important and is required to be modeled accurately in thermal design codes that use computational fluid dynamics (CFD). During air cooling the flow can be classified as laminar, transitional, or turbulent. In electronics systems, the flow around the packages is usually in the transition region, which lies between laminar and turbulent flow. This requires a low-Reynolds number numerical model to fully capture the impact of turbulence on the fluid flow calculations. This paper provides comparisons between a number of turbulence models with experimental data. These models included the distance from the nearest wall and the local velocity (LVEL), Wolfshtein, Norris and Reynolds, k-ε, k-ω, shear-stress transport (SST), and kε/kl models. Results show that in terms of the fluid flow calculations most of the models capture the difficult wake recirculation region behind the package reasonably well, although for packages whose heights cause a high degree of recirculation behind the package the SST model appears to struggle. The paper also demonstrates the sensitivity of the models to changes in the mesh density; this study is aimed specifically at thermal design engineers as mesh independent simulations are rarely conducted in an industrial environment.

A Generic Framework for Describing Study Plans for Networked Universities using Meta-Data

This paper presents a generic framework that can be used to describe study plans using meta-data. The context of this research and associated technologies and standards is presented. The approach adopted here has been developed within the mENU project that aims to provide a model for a European Networked University. The methodology for the design of the generic Framework is discussed and the main design requirements are presented. The approach adopted was based on a set of templates containing meta-data required for the description of programs of study and consisting of generic building elements annotated appropriately. The process followed to develop the templates is presented together with a set of evaluation criteria to test the suitability of the approach. The templates structure is presented and example templates are shown. A first evaluation of the approach has shown that the proposed framework can provide a flexible and competent means for the generic description of study plans for the purposes of a networked university.

Beer, (Anthony) Stafford (1926-2002)

Biography of (Anthony) Stafford Beer (1926-2002), management cybernetician.

Guidance on interviewing child witnesses in Scotland

The guidance was commissioned from Dr Amina Memon and Lynn Hulse at Aberdeen University. Their work was overseen by a steering group with representatives from the Scottish Executive Justice Department, the Crown Office and Procurator Fiscal Service, NCH Scotland, the Association of Chief Police Officers in Scotland, the Association of Directors of Social Work, the Law Society for Scotland, the Scottish Association of Community Child Health and the Scottish Children’s Reporter Administration. A full list of those involved is given in the Appendix C. pt. 1. Guidance on interviewing child witnesses in Scotland -- pt. 2. Guidance on the questioning of children in court -- pt. 3. Lord Justice-General's memorandum on child witnesses: appendix to Guidance on the questioning of children in court -- pt. 4. Guidance on child witness court familiarisation visits -- pt. 5. Information about child, young and vulnerable adult witnesses to inform decision-making in the legal process: good practice guide -- pt. 6. Code of practice to facilitate the provision of therapeutic support to child witnesses in court proceedings -- pt. 7. Guidance on the conduct of identity parades with child witnesses.

[Book review] "Memory and Suggestibility in the Forensic Interview"

Book review of: Eisen, M.L., Quas, J.A. & Goodman, G.S. (Eds.) (2002). Memory and suggestibility in the forensic interview. Mahwah, NJ: Lawrence Erlbaum Associates. ISBN: 0-8058-3080-4/$55.00 Special Prepaid Price

A distributed algorithm for European options with nonlinear volatility

A distributed algorithm is developed to solve nonlinear Black-Scholes equations in the hedging of portfolios. The algorithm is based on an approximate inverse Laplace transform and is particularly suitable for problems that do not require detailed knowledge of each intermediate time steps.

[Review] M. Feistauer, J. Felcman, I. Straskbraba, Mathematical and Computational Methods for Compressible Flow, Oxford Science Publication, Oxford, ISBN 0198505884, 2004 (535pp.)

The growth of computer power allows the solution of complex problems related to compressible flow, which is an important class of problems in modern day CFD. Over the last 15 years or so, many review works on CFD have been published. This book concerns both mathematical and numerical methods for compressible flow. In particular, it provides a clear cut introduction as well as in depth treatment of modern numerical methods in CFD. This book is organised in two parts. The first part consists of Chapters 1 and 2, and is mainly devoted to theoretical discussions and results. Chapter 1 concerns fundamental physical concepts and theoretical results in gas dynamics. Chapter 2 describes the basic mathematical theory of compressible flow using the inviscid Euler equations and the viscous Navier–Stokes equations. Existence and uniqueness results are also included. The second part consists of modern numerical methods for the Euler and Navier–Stokes equations. Chapter 3 is devoted entirely to the finite volume method for the numerical solution of the Euler equations and covers fundamental concepts such as order of numerical schemes, stability and high-order schemes. The finite volume method is illustrated for 1-D as well as multidimensional Euler equations. Chapter 4 covers the theory of the finite element method and its application to compressible flow. A section is devoted to the combined finite volume–finite element method, and its background theory is also included. Throughout the book numerous examples have been included to demonstrate the numerical methods. The book provides a good insight into the numerical schemes, theoretical analysis, and validation of test problems. It is a very useful reference for applied mathematicians, numerical analysts, and practice engineers. It is also an important reference for postgraduate researchers in the field of scientific computing and CFD.

Study of Anisotropic Conductive Adhesive Joint Behaviour under 3-Point Bending

Flip chip interconnections using anisotropic conductive film (ACF) are now a very attractive technique for electronic packaging assembly. Although ACF is environmentally friendly, many factors may influence the reliability of the final ACF joint. External mechanical loading is one of these factors. Finite element analysis (FEA) was carried out to understand the effect of mechanical loading on the ACF joint. A 3-dimensional model of adhesively bonded flip chip assembly was built and simulations were performed for the 3-point bending test. The results show that the stress at its highest value at the corners, where the chip and ACF were connected together. The ACF thickness was increased at these corner regions. It was found that higher mechanical loading results in higher stress that causes a greater gap between the chip and the substrate at the corner position. Experimental work was also carried out to study the electrical reliability of the ACF joint with the applied bending load. As per the prediction from FEA, it was found that at first the corner joint failed. Successive open joints from the corner towards the middle were also noticed with the increase of the applied load.

Dynamic analysis of Flip-Chip Self-Alignment

Self-alignment of soldered electronic components such as flip-chips (FC), ball grid arrays (BGA) and optoelectronic devices during solder reflow is important as it ensures good alignment between components and substrates. Two uncoupled analytical models are presented which provide estimates of the dynamic time scales of both the chip and the solder in the self-alignment process. These predicted time scales can be used to decide whether a coupled dynamic analysis is required for the analysis of the chip motion. In this paper, we will show that for flip-chips, the alignment dynamics can be described accurately only when the chip motion is coupled with the solder motion because the two have similar time-scale values. To study this coupled phenomenon, a dynamic modeling method has been developed. The modeling results show that the uncoupled and coupled calculations result in significantly different predictions. The calculations based on the coupled model predict much faster rates of alignment than those predicted using the uncoupled approach.

Wetting and Reaction of Sn-2.8Ag-0.5Cu-1.0Bi Solder with Cu and Ni Substrates

The wettability of newly developed Sn-2.8Ag-0.5Cu-1.0Bi lead-free solder on Cu and Ni substrates was assessed through the wetting balance tests. The wettability assessment parameters such as contact angle (ϑc) and maximum wetting force (Fw) were documented for three solder bath temperatures with three commercial fluxes, namely, no-clean (NC), nonactivated (R), and water-soluble organic acid flux (WS). It was found that the lead-free Sn-2.8Ag-0.5Cu-1.0Bi solder exhibited less wetting force, i.e., poorer wettability, than the conventional Sn-37Pb solder for all flux types and solder bath temperatures. The wettability of Sn-2.8Ag-0.5Cu-1.0Bi lead-free solder on Cu substrate was much higher than that on Ni substrate. Nonwetting for Sn-2.8Ag-0.5Cu-1.0Bi and Sn-Pb solders on Ni substrate occurred when R-type flux was used. A model was built and simulations were performed for the wetting balance test. The simulation results were found very close to the experimental results. It was also observed that larger values of immersion depth resulted in a decrease of the wetting force and corresponding meniscus height, whereas the increase in substrate perimeter enhanced the wettability. The wetting reactions between the solder and Cu/Ni substrates were also investigated, and it was found that Cu atoms diffused into the solder through the intermetallic compounds (IMCs) much faster than did the Ni atoms. Rapid formation of IMCs inhibited the wettability of Sn-2.8Ag-0.5Cu-1.0Bi solder compared to the Sn-Pb solder.

The effect of curing on the performance of ACF bonded chip-on-flex assemblies after thermal ageing

Purpose – Anisotropic conductive film (ACF) is now an attractive technology for direct mounting of chips onto the substrate as an alternative to lead-free solders. However, despite its various advantages over other technologies, it also has many unresolved reliability issues. For instance, the performance of ACF assembly in high temperature applications is questionable. The purpose of this paper is to study the effect of bonding temperatures on the curing of ACFs, and their mechanical and electrical performance after high temperature ageing. Design/methodology/approach – In the work presented in this paper, the curing degree of an ACF at different bonding temperatures was measured using a differential scanning calorimeter. The adhesion strength and the contact resistance of ACF bonded chip-on-flex assembly were measured before and after thermal ageing and the results were correlated with the curing degree of ACF. The ACF was an epoxy-based adhesive in which Au-Ni coated polymer particles were randomly dispersed. Findings – The results showed that higher bonding temperatures had resulted in better ACF curing and stronger adhesion. After ageing, the adhesion strength increased for the samples bonded at lower temperatures and decreased for the samples bonded at higher temperatures. ACF assemblies with higher degrees of curing showed smaller increases in contact resistance after ageing. Conduction gaps at the bump-particle and/or particle-pad interfaces were found with the help of scanning electron microscopy and are thought to be the root cause of the increase in contact resistance. Originality/value – The present study focuses on the effect of bonding temperatures on the curing of ACFs, and their adhesion strength and electrical performances after high temperature ageing. The results of this study may help the development of ACFs with higher heat resistance, so that ACFs can be considered as an alternative to lead-free solders.

Turbulence modelling for electronic cooling: A review

This paper is intended to provide a general review of the current capabilities of turbulence models within the specific area of electronic cooling. The work discussed in this paper is aimed at examining currently available turbulence models and the formulation of a new two-layer hybrid kElki model which is specifically designed for electronic application areas. A classic backward facing step configuration will be used to evaluate the performance of the turbulence models in the prediction of separated flows. The preliminary results suggest that the hybrid ke/kl turbulence model is a promising zonal model to pursue.

Modelling the Performance of Flexible Substrates for Lead-Free Applications

In this paper, the performance of flexible substrates for lead-free applications was studied using finite element method (FEM). Firstly, the thermal induced stress in the flex substrate during the lead free solder reflow process was predicted. The shear stress at the interface between the copper track and flex was plotted. This shear stress increases with the thickness of the copper track. Secondly, an ACF flip chip was taken as a typical lead-free application of the flex substrate. The reflow effect on the reliability of ACF interconnections was analyzed. Higher stress was identified along the interface between the conductive particle and the metallization, and the interfacial stress increases with the reflow peak temperature and the coefficient of thermal expansion (CTE) of the adhesive. The moisture effect on the reliability of ACF joints were studied using a macro-micro modeling technique, the predominantly tensile stress found at the interface between the conductive particle and metallization could reduce the contact area and even cause the electrical failure. Modeling results are consistent with the findings in the experimental work