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.

Performance-Driven Microfabrication-Oriented Methodology for MEMS Conceptual Design with Application in Microfluidic Device Design

Performance and manufacturability are two important issues that must be taken into account during MEMS design. Existing MEMS design models or systems follow a process-driven design paradigm, that is, design starts from the specification of process sequence or the customization of foundry-ready process template. There has been essentially no methodology or model that supports generic, high-level design synthesis for MEMS conceptual design. As a result, there lacks a basis for specifying the initial process sequences. To address this problem, this paper proposes a performance-driven, microfabrication-oriented methodology for MEMS conceptual design. A unified behaviour representation method is proposed which incorporates information of both physical interactions and chemical/biological/other reactions. Based on this method, a behavioural process based design synthesis model is proposed, which exploits multidisciplinary phenomena for design solutions, including both the structural components and their configuration for the MEMS device, as well as the necessary substances for the chemical/biological/other reactions. The model supports both forward and backward synthetic search for suitable phenomena. To ensure manufacturability, a strategy of using microfabrication-oriented phenomena as design knowledge is proposed, where the phenomena are developed from existing MEMS devices that have associated MEMS-specific microfabrication processes or foundry-ready process templates. To test the applicability of the proposed methodology, the paper also studies microfluidic device design and uses a micro-pump design for the case study.