Heegaard diagrams and surgery descriptions for twisted face-pairing 3-manifolds

The twisted face-pairing construction of our earlier papers gives an efficient way of generating, mechanically and with little effort, myriads of relatively simple face-pairing descriptions of interesting closed 3-manifolds. The corresponding description in terms of surgery, or Dehn-filling, reveals the twist construction as a carefully organized surgery on a link. In this paper, we work out the relationship between the twisted face-pairing description of closed 3-manifolds and the more common descriptions by surgery and Heegaard diagrams. We show that all Heegaard diagrams have a natural decomposition into subdiagrams called Heegaard cylinders, each of which has a natural shape given by the ratio of two positive integers. We characterize the Heegaard diagrams arising naturally from a twisted face-pairing description as those whose Heegaard cylinders all have integral shape. This characterization allows us to use the Kirby calculus and standard tools of Heegaard theory to attack the problem of finding which closed, orientable 3-manifolds have a twisted face-pairing description.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-10.abs.htm

Precise control of flexible manipulators

Experimental apparatus were developed for physically testing control systems for pointing flexible structures, such as limber spacecraft, for the case that control actuators cannot be collocated with sensors. Structural damping ratios are less than 0.003, each basic configuration of sensor/actuator noncollocation is available, and inertias can be halved or doubled abruptly during control maneuvers, thereby imposing, in particular, a sudden reversal in the plant's pole-zero sequence. First experimental results are presented, including stable control with both collocation and noncollocation

Control of a flexible robot arm

Exact equations of motion of an arm with known parameters were developed and analyzed preparatory to designing control systems for robotic manipulators. The design of an experimental one-link arm for testing control designs is presented

Rethinking the normative content of critical theory: Marx, Habermas and beyond

This thesis criticizes Marx's labour theory of value in terms of Habermas's critique of subject-centred thinking, before going on to criticize Habermas's subject-centred approach to the economic system in terms of an intersubjectively re-formulated conception of labour, for while Habermas restores normative content to the principle of self-constitution he restricts it to communicative action. This places the economic system (and its bureaucratic state apparatus) beyond the normative content of modernity. Drawing upon Honneth's writings on struggles for recognition, the thesis seeks to re-normatize labour on the basis of worker's own struggles to re-normatize the economic system. The first half of the thesis explores the tensions that arise from Marx's attempt to locate his critique of capitalism in a subject-centred conception of self-constitution. Although Marx seeks to historicize the categories of political economy (in line with capitalist exchange relations), he also seeks to preserve a transhistorical conception of labour as the subject of self-objectification (as the standpoint from which to criticize capitalism). However, this leaves Marx vulnerable to his own historical critique of political economy. It is then argued that it is only possible to redeem the latter by re-grounding critical theory in the labour movement's social and historical struggles to oppose capital. This requires a re-formulation of Marx's labour theory of value. In place of Marx's notion that 'value' is an expression of self-objectifying labour we substitute Simmel's intersubjective approach to money-value. Marx's account of value is then understood as arising from the diremption of intersubjectivity into an 'objective' economic system and its 'subjective' agents. This generates a bifurcation of selfconstitution with the intersubjective form of normative social-constitution, on the one side, and the dirempted objective and subjective forms of economic-constitution on the other. The second half of the thesis critically analyzes Habermas' s contention that modern sociality is divided into a normative lifeworld and a non-normative system. This takes the form of an empirical critique of Habermas' s restriction of normativity to communicative action, and a theoretical critique of his restriction of the charge of reification to the economic system's encroachment upon the latter. In keeping with the theory of discourse ethics, it is argued that Habermas cannot legitimately withdraw normative content from labour and claim universal scope for the former. Consequently, not only is the economic system's capacity to suppress the normativity of labour invalid from the standpoint of 'practical reason', but so is Habermas's attempt to legitimate the system on the basis of 'functional reason'. The thesis draws on Honneth's work to extend the realm of intersubjectivity into the economy on the basis of the struggles of the labour movement to sublate its diremption of self-regulating system and self-interested actors. We conclude by arguing that trade unions and the welfare state may be understood to comprise normative vehicles for subjecting 'market-value' to an intersubjectively accountable form of 'social-value'

MONTAGE: AGB nucleosynthesis with full s-process calculations

We present MONTAGE, a post-processing nucleosynthesis code that combines a traditional network for isotopes lighter than calcium with a rapid algorithm for calculating the s-process nucleosynthesis of the heavier isotopes. The separation of those parts of the network where only neutron-capture and beta-decay reactions are significant provides a substantial advantage in computational efficiency. We present the yields for a complete set of s-process isotopes for a 3 Mo, Z = 0.02 stellar model, as a demonstration of the utility of the approach. Future work will include a large grid of models suitable for use in calculations of Galactic chemical evolution.Comment: 9 pages, 4 figures. Accepted by PAS

Self-Tuning Adaptive-Controller Using Online Frequency Identification

A real time adaptive controller was designed and tested successfully on a fourth order laboratory dynamic system which features very low structural damping and a noncolocated actuator sensor pair. The controller, implemented in a digital minicomputer, consists of a state estimator, a set of state feedback gains, and a frequency locked loop (FLL) for real time parameter identification. The FLL can detect the closed loop natural frequency of the system being controlled, calculate the mismatch between a plant parameter and its counterpart in the state estimator, and correct the estimator parameter in real time. The adaptation algorithm can correct the controller error and stabilize the system for more than 50% variation in the plant natural frequency, compared with a 10% stability margin in frequency variation for a fixed gain controller having the same performance at the nominal plant condition. After it has locked to the correct plant frequency, the adaptive controller works as well as the fixed gain controller does when there is no parameter mismatch. The very rapid convergence of this adaptive system is demonstrated experimentally, and can also be proven with simple root locus methods