A mathematical model of crevice and pitting corrosion—I. The physical model

A predictive and self-consistent mathematical model incorporating the electrochemical, chemical and ionic migration processes characterizing the propagation stage of crevice and pitting corrosion in metals is described. The model predicts the steady-state solution chemistry and electrode kinetics (and hence metal penetration rates) within an active corrosion cavity as a function of the many parameters on which these depend, such as external electrode potential and crevice dimensions. The crevice is modelled as a parallel-sided slot filled with a dilute sodium chloride solution. The cavity propagation rates are found to be faster in the case of a crevice with passive walls than one with active walls. The distribution of current over the internal surface of a crevice with corroding walls can be assessed using this model, giving an indication of the future shape of the cavity. The model is extended to include a solid hydroxide precipitation reaction and considers the effect of consequent changes in the chemical and physical environment within the crevice on the predicted corrosion rates. In this paper, the model is applied to crevice and pitting corrosion in carbon steel.

Radiation effects on the immiscible polymer blend of nylon1010 and high-impact polystyrene (HIPS) I: Gel/dose curves, mathematical expectation theorem and thermal behaviour

This paper studies the radiation properties of the immiscible blend of nylon1010 and HIPS. The gel fraction increased with increasing radiation dose. The network was found mostly in nylon1010, the networks were also found in both nylon1010 and HIPS when the dose reaches 0.85 MGy or more. We used the Charleby-Pinner equation and the modified Zhang-Sun-Qian equation to simulate the relationship with the dose and the sol fraction. The latter equation fits well with these polymer blends and the relationship used by it showed better linearity than the one by the Charleby-Pinner equation. We also studied the conditions of formation of the network by the mathematical expectation theorem for the binary system. Thermal properties of polymer blend were observed by DSC curves. The crystallization temperature decreases with increasing dose because the cross-linking reaction inhibited the crystallization procession and destroyed the crystals. The melting temperature also reduced with increasing radiation dose. The dual melting peak gradually shifted to single peak and the high melting peak disappeared at high radiation dose. However, the radiation-induced crystallization was observed by the heat of fusion increasing at low radiation dose. On the other hand, the crystal will be damaged by radiation. A similar conclusion may be drawn by the DSC traces when the polymer blends were crystallized. When the radiation dose increases, the heat of fusion reduces dramatically and so does the heat of crystallization. (C) 1999 Elsevier Science Ltd. All rights reserved.

非均质储层叠前地震反演技术研究及应用

(1) I research on the relationship between elastic parameters, lithology and liquid. It is a physical base for pre-stack seismic inversion. I research all kinds of approximate expressions of Zoeppritz function. Then the relation of all kinds of approximate expressions can be confirmed. The geological model of water sand and gas sand in different depth was designed. Moreover I research on precision of all kinds of approximate expressions. (2) In process of seismic data which aim at amplitude recovery and apply in pre-stack seismic inversion, I advance to adopt double flow chart for different aim. Pre-stack noise elimination, real amplitude recovery and NMO correction of long offset are the key taches. (3) I made a systemic expatiate for the thinking and applicability about all kinds of expressions of elastic impedance. And mathematical model was applied to compare the precision with all kinds of expressions of elastic impedance. I propose a new pre-stack simultaneous inversion which is based on the Zoppritz function and simulated annealing algorithm. This method can ensure calculation precision of reflection coefficient from different incident angle and get a global optimum solution. Therefore this method improves the precision of pre-stack seismic inversion. (4) The object function of P-S wave pre-stack simultaneous inversion was established. I compared the precision and convergence between simultaneous inversion and P-wave inversion. And the results show that simultaneous inversion is superior to P-wave inversion. Through the study of AVO event of transformed wave, AVO characters of different kinds of gas sand were analyzed. (5) I carried out the study work of pre-stack seismic inversion for carbonate reservoir in middle of Tarim basin and sand shale reservoir in Sulige Area of Erdos Basin. The method and technology in this paper was applied to practical work. And I made a prediction for heterogeneous reservoir. Moreover it acquires a good application effect. Key Word: reflection coefficient， amplitude recovery， pre-stack seismic inversion， Heterogeneous reservoir，prediction.

Symbolic Mathematical Laboratory

A large computer program has been developed to aid applied mathematicians in the solution of problems in non-numerical analysis which involve tedious manipulations of mathematical expressions. The mathematician uses typed commands and a light pen to direct the computer in the application of mathematical transformations; the intermediate results are displayed in standard text-book format so that the system user can decide the next step in the problem solution. Three problems selected from the literature have been solved to illustrate the use of the system. A detailed analysis of the problems of input, transformation, and display of mathematical expressions is also presented.

The Structure of Mathematical Knowledge

This report develops a conceptual framework in which to talk about mathematical knowledge. There are several broad categories of mathematical knowledge: results which contain the traditional logical aspects of mathematics; examples which contain illustrative material; and concepts which include formal and informal ideas, that is, definitions and heuristics.

Evaluation of nonlinear chromatographic performance by frontal analysis using a simple multi-plate mathematical model

A multi-plate (NIP) mathematical model was proposed by frontal analysis to evaluate nonlinear chromatographic performance. One of its advantages is that the parameters may be easily calculated from experimental data. Moreover, there is a good correlation between it and the equilibrium-dispersive (E-D) or Thomas models. This shows that it can well accommodate both types of band broadening that is comprised of either diffusion-dominated processes or kinetic sorption processes. The MP model can well describe experimental breakthrough curves that were obtained from membrane affinity chromatography and column reversed-phase liquid chromatography. Furthermore, the coefficients of mass transfer may be calculated according to the relationship between the MP model and the E-D or Thomas models. (C) 2004 Elsevier B.V. All rights reserved.

Design thinking - a critical analysis.

The latest buzz phrase to enter the world of design research is “Design Thinking”. But is this anything new and does it really have any practical or theoretical relevance to the design world? Many sceptics believe the term has more to do with business strategy and little to do with the complex process of designing products, services and systems. Moreover, many view the term as misleading and a cheap attempt to piggyback the world of business management onto design. This paper seeks to ask is design thinking anything new? Several authors have explicitly or implicitly articulated the term “Design Thinking” before, such as Peter Rowe’s seminal book “Design Thinking” [1] first published in 1987 and Herbert Simon’s “The Sciences of the Artificial” [2] first published in 1969. In Tim Brown’s “Change by Design” [3], design thinking is thought of as a system of three overlapping spaces rather than a sequence of orderly steps namely inspiration – the problem or opportunity that motivates the search for solutions; ideation – the process of generating, developing and testing ideas; and implementation – the path that leads from the design studio, lab and factory to the market. This paper seeks to examine and critically analyse the tenets of this new design thinking manifesto set against three case studies of modern design practice. As such, the paper will compare design thinking theory with the reality of design in practice.

Thinking with and outside the box: developing computer support for evidence teaching

B. Schafer, J. Keppens and Q. Shen. Thinking with and outside the Box: Developing Computer Support for Evidence Teaching. P. Robert and M. Redmayne (Eds.), Innovations in Evidence and Proof: Integrating Theory, Research and Teaching, pp. 139-158, 2007.

Corporate Responsibility for Crimes - Thinking Outside the Box

Emeseh, Engobo, 'Corporate Responsibility for Crime: Thinking outside the Box' I University of Botswana Law Journal (2005) 28-49 RAE2008

Re-thinking missions ; a laymen's inquiry after one hundred years, by the Commission of appraisal, William Ernest Hocking, chairman.

http://www.archive.org/details/rethinkingmissio011901mbp

Mathematical modelling and optimisation of the formulation and manufacture of aggregate food products

In this PhD study, mathematical modelling and optimisation of granola production has been carried out. Granola is an aggregated food product used in breakfast cereals and cereal bars. It is a baked crispy food product typically incorporating oats, other cereals and nuts bound together with a binder, such as honey, water and oil, to form a structured unit aggregate. In this work, the design and operation of two parallel processes to produce aggregate granola products were incorporated: i) a high shear mixing granulation stage (in a designated granulator) followed by drying/toasting in an oven. ii) a continuous fluidised bed followed by drying/toasting in an oven. In addition, the particle breakage of granola during pneumatic conveying produced by both a high shear granulator (HSG) and fluidised bed granulator (FBG) process were examined. Products were pneumatically conveyed in a purpose built conveying rig designed to mimic product conveying and packaging. Three different conveying rig configurations were employed; a straight pipe, a rig consisting two 45° bends and one with 90° bend. It was observed that the least amount of breakage occurred in the straight pipe while the most breakage occurred at 90° bend pipe. Moreover, lower levels of breakage were observed in two 45° bend pipe than the 90° bend vi pipe configuration. In general, increasing the impact angle increases the degree of breakage. Additionally for the granules produced in the HSG, those produced at 300 rpm have the lowest breakage rates while the granules produced at 150 rpm have the highest breakage rates. This effect clearly the importance of shear history (during granule production) on breakage rates during subsequent processing. In terms of the FBG there was no single operating parameter that was deemed to have a significant effect on breakage during subsequent conveying. A population balance model was developed to analyse the particle breakage occurring during pneumatic conveying. The population balance equations that govern this breakage process are solved using discretization. The Markov chain method was used for the solution of PBEs for this process. This study found that increasing the air velocity (by increasing the air pressure to the rig), results in increased breakage among granola aggregates. Furthermore, the analysis carried out in this work provides that a greater degree of breakage of granola aggregates occur in line with an increase in bend angle.