The recursion hierarchy for PCF is strict

We consider the sublanguages of Plotkin's PCF obtained by imposing some bound k on the levels of types for which fixed point operators are admitted. We show that these languages form a strict hierarchy, in the sense that a fixed point operator for a type of level k can never be defined (up to observational equivalence) using fixed point operators for lower types. This answers a question posed by Berger. Our proof makes substantial use of the theory of nested sequential procedures (also called PCF B\"ohm trees) as expounded in the recent book of Longley and Normann

Convergence Criteria for Axial Compressor Flow Calculations

Computational fluid dynamics is routinely used in the turbomachinery industry to aid in the design of axial flow compressors. The predictive capability of such codes is related to the quality of the numerical convergence of the flow solutions they produce. In certain cases convergence cannot be attained and various publications have linked this to the boundary conditions used within the code. In this paper an investigation in to how common types of boundary conditions affect the numerical convergence is described. The point at which steady-state calculations fail to predict the increasing non-axisymmetric flowfield at off-design, part speed operation is identified. The analysis of the convergence process is combined with numerical experiments to show that the rate of convergence of steady-state mixing-plane multi-stage axial compressor calculations depends upon the operating point on the pressure-rise versus mass flow rate characteristic. Intrinsically, as the calculated overall characteristic reaches its peak the rate of convergence decreases to zero. Ways to enhance the rate of convergence, for example the technique of adding a downstream nozzle, and conditions under which such techniques are likely to be successful are discussed.Siemens Turbomachinery, Lincol

EFFECTS OF STATOR PLATFORM GEOMETRY FEATURES ON BLADE ROW PERFORMANCE

Real geometry features such as shroud cavities, interplatform and vane-pack gaps can affect the hub endwall flow through compressor blade rows. Additionally, misalignment of the platform endwalls due to manufacturing tolerances can be important. This paper details an experimental and computational investigation of these effects. To ensure that the measurements were representative a novel experimental technique was developed to generate end-wall skew in the linear cascade. Without the presence of the endwall boundary layer skew the cascade flow did not capture the flow features typically observed in multi-stage compressor operation. The skew generation method involves injecting flow along the endwall in such a manner as to control both the displacement thickness and tangential momentum thickness of the resulting boundary layer. The study reveals that real geometry features can have a significant impact on the flowfield within a blade passage. For stator shrouds, increasing leakage flow rates increases the stagnation pressure loss coefficient however, increasing the level of whirl pickup of the leakage flow can offset the natural secondary flow and thus reduce the loss. All of the steps and gaps that were found to be present in real compressors were found to increase the losses relative to a smooth endwall. It is also shown that CFD simulations are capable in capturing the trends observed in the experiments.Rolls-Royce pl

Report of the Citizens\u27 Dickey-Lincoln Project Impact Review Committee to Governor James B. Longley

The construction of the Dickey-Lincoln Hydroelectric Project. To examine, in depth, the proposal and its impact as seen by various segments of our society. The report will identify the factors that must carry the main weight in making a final determination

On the ubiquity of certain total type structures

It is a fact of experience from the study of higher type computability that a wide range of approaches to defining a class of (hereditarily) total functionals over N leads in practice to a relatively small handful of distinct type structures. Among these are the type structure C of Kleene-Kreisel continuous functionals, its effective substructure C eff, and the type structure HEO of the hereditarily effective operations. However, the proofs of the relevant equivalences are often non-trivial, and it is not immediately clear why these particular type structures should arise so ubiquitously. In this paper we present some new results which go some way towards explaining this phenomenon. Our results show that a large class of extensional collapse constructions always give rise to C, C eff or HEO (as appropriate). We obtain versions of our results for both the “standard” and “modified” extensional collapse constructions. The proofs make essential use of a technique due to Normann. Many new results, as well as some previously known ones, can be obtained as instances of our theorems, but more importantly, the proofs apply uniformly to a whole family of constructions, and provide strong evidence that the above three type structures are highly canonical mathematical objects

Computability structures, simulations and realizability

We generalize the standard construction of realizability models (specifically, of categories of assemblies) to a wide class of computability structures, broad enough to embrace models of computation such as labelled transition systems and process algebras. We consider a general notion of simulation between such computability structures, and show how these simulations correspond precisely to certain functors between the realizability models. Furthermore, we show that our class of computability structures has good closure properties — in particular, it is ‘cartesian closed ’ in a slightly relaxed sense. Finally, we investigate some important subclasses of computability structures and of simulations between them. We suggest that our 2-category of computability structures and simulations may offer a useful framework for investigating questions of computational power, abstraction and simulability for a wide range of models.

Some Programming Languages Suggested by Game Models (Extended Abstract)

AbstractWe consider a simple and well-known category of alternating games (also known as sequential data structures) and several categories derived from it. In each case, we present an extension of Plotkin's language FPC (or a suitable linearization thereof) which defines all computable strategies of appropriate types. The quest for such languages results in a novel selection of language primitives for state encapsulation, coroutining and backtracking