Crystallography of carbide-free bainite in a hard bainitic steel

The convergent beam Kikuchi line diffraction technique has been used to accurately determine the orientation relationships between bainitic ferrite and retained austenite in a hard bainitic steel. A reproducible orientation relationship has been uniquely observed for both the upper and lower bainite. It is [GRAPHICS] However, the habit plane of upper bainite is different from that of lower bainite. The former has habit plane that is either within 5 degrees of (221)(A) or of (259)(A). The latter only corresponds with a habit plane that is within 5 degrees of (259)(A). The determined orientation relationship is completely consistent with reported results determined using the same technique with an accuracy of +/- 0.5 degrees in lath martensite in an Fe-20 wt.% Ni-6 wt.% Mn alloy and in a low carbon low alloy steel. It also agrees well with the orientation relationship between granular bainite and austenite in an Fe-19 wt.% Ni-3.5 wt.% Mn-0.15 wt.% C steel. Hence it is believed that, at least from a crystallographic point view, the bainite transformation has the characteristics of martensitic transformation. (c) 2006 Elsevier B.V. All rights reserved.

Robustness of mathematical models for biological systems

The robustness of mathematical models for biological systems is studied by sensitivity analysis and stochastic simulations. Using a neural network model with three genes as the test problem, we study robustness properties of synthesis and degradation processes. For single parameter robustness, sensitivity analysis techniques are applied for studying parameter variations and stochastic simulations are used for investigating the impact of external noise. Results of sensitivity analysis are consistent with those obtained by stochastic simulations. Stochastic models with external noise can be used for studying the robustness not only to external noise but also to parameter variations. For external noise we also use stochastic models to study the robustness of the function of each gene and that of the system.

A mathematical modelling technique for the analysis of the dynamics of a simple continuous EDA

This paper presents some initial attempts to mathematically model the dynamics of a continuous estimation of distribution algorithm (EDA) based on a Gaussian distribution and truncation selection. Case studies are conducted on both unimodal and multimodal problems to highlight the effectiveness of the proposed technique and explore some important properties of the EDA. With some general assumptions, we show that, for ID unimodal problems and with the (mu, lambda) scheme: (1). The behaviour of the EDA is dependent only on the general shape of the test function, rather than its specific form; (2). When initialized far from the global optimum, the EDA has a tendency to converge prematurely; (3). Given a certain selection pressure, there is a unique value for the proposed amplification parameter that could help the EDA achieve desirable performance; for ID multimodal problems: (1). The EDA could get stuck with the (mu, lambda) scheme; (2). The EDA will never get stuck with the (mu, lambda) scheme.