The DØ experiment enjoyed a very successful data-collection run at the Fermilab Tevatron collider between 1992 and 1996. Since then, the detector has been upgraded to take advantage of improvements to the Tevatron and to enhance its physics capabilities. We describe the new elements of the detector, including the silicon microstrip tracker, central fiber tracker, solenoidal magnet, preshower detectors, forward muon detector, and forward proton detector. The uranium/liquid-argon calorimeters and central muon detector, remaining from Run I, are discussed briefly. We also present the associated electronics, triggering, and data acquisition systems, along with the design and implementation of software specific to DØ.

This paper presents a comprehensive model for piezoceramic actuators (PAs), which accounts for hysteresis, non-linear electric field and dynamic effects. The hysteresis model is based on the widely used general Maxwell slip model, while an enhanced electro-mechanical non-linear model replaces the linear constitutive equations commonly used. Further on, a linear second order model compensates the frequency response of the actuator. Each individual model is fully characterized from experimental data yielded by a specific PA, then incorporated into a comprehensive 'direct' model able to determine the output strain based on the applied input voltage, fully compensating the aforementioned effects, where the term 'direct' represents an electrical-to-mechanical operating path. The 'direct' model was implemented in a Matlab/Simulink environment and successfully validated via experimental results, exhibiting higher accuracy and simplicity than many published models. This simplicity would allow a straightforward inclusion of other behaviour such as creep, ageing, material non-linearity, etc, if such parameters are important for a particular application.Based on the same formulation, two other models are also presented: the first is an 'alternate' model intended to operate within a force-controlled scheme (instead of a displacement/position control), thus able to capture the complex mechanical interactions occurring between a PA and its host structure. The second development is an 'inverse' model, able to operate within an open-loop control scheme, that is, yielding a 'linearized' PA behaviour. The performance of the developed models is demonstrated via a numerical sample case simulated in Matlab/Simulink, consisting of a PA coupled to a simple mechanical system, aimed at shifting the natural frequency of the latter.

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A genuine gauge theory for the Poincaré, de Sitter or anti-de Sitter algebras can be constructed in (2n − 1)-dimensional spacetime by means of the Chern-Simons form, yielding a gravitational theory that differs from General Relativity but shares many of its properties, such as second order field equations for the metric. The particular form of the Lagrangian is determined by a rank n, symmetric tensor invariant under the relevant algebra. In practice, the calculation of this invariant tensor can be reduced to the computation of the trace of the symmetrized product of n Dirac Gamma matrices Γ ab in 2n-dimensional spacetime. While straightforward in principle, this calculation can become extremely cumbersome in practice. For large enough n, existing computer algebra packages take an inordinate long time to produce the answer or plainly fail having used up all available memory. In this talk we show that the general formula for the trace of the symmetrized product of 2n Gamma matrices Γ ab can be written as a certain sum over the integer partitions s of n, with every term being multiplied by a numerical coefficient αs. We then give a general algorithm that computes the α-coefficients as the solution of a linear system of equations generated by evaluating the general formula for different sets of tensors B ab with random numerical entries. A recurrence relation between different coefficients is shown to hold and is used in a second, "minimal" algorithm to greatly speed up the computations. Runtime of the minimal algorithm stays below 1 min on a typical desktop computer for up to n = 25, which easily covers all foreseeable applications of the trace formula.

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