Set-Theoretic Types for Polymorphic Variants

Polymorphic variants are a useful feature of the OCaml language whose current definition and implementation rely on kinding constraints to simulate a subtyping relation via unification. This yields an awkward formalization and results in a type system whose behaviour is in some cases unintuitive and/or unduly restrictive. In this work, we present an alternative formalization of poly-morphic variants, based on set-theoretic types and subtyping, that yields a cleaner and more streamlined system. Our formalization is more expressive than the current one (it types more programs while preserving type safety), it can internalize some meta-theoretic properties, and it removes some pathological cases of the current implementation resulting in a more intuitive and, thus, predictable type system. More generally, this work shows how to add full-fledged union types to functional languages of the ML family that usually rely on the Hindley-Milner type system. As an aside, our system also improves the theory of semantic subtyping, notably by proving completeness for the type reconstruction algorithm.Comment: ACM SIGPLAN International Conference on Functional Programming, Sep 2016, Nara, Japan. ICFP 16, 21st ACM SIGPLAN International Conference on Functional Programming, 201

On the aeroacoustic and flow structures developed on a flat plate with a serrated sawtooth trailing edge

Open Access funded by Engineering and Physical Sciences Research Council.Results of an experimental study on turbulent flow over a flat plate with a serrated sawtooth trailing edge are presented in this paper. After tripping the boundary layer to become turbulent, the broadband noise sources at the sawtooth serrated trailing edge is studied by several experimental techniques. Broadband noise reduction by the serrated sawtooth trailing edge can be realistically achieved in the flat plate configuration. The variations of wall pressure power spectral density and the spanwise coherence (which relates to the spanwise correlation length) in a sawtooth trailing edge play a minor role in the mechanisms underpinning the reduction of self noise radiation. Conditional-averaging technique was applied in the boundary layer data where a pair of pressure-driven oblique vortical structures near the sawtooth side edges is identified. In the current flat plate configuration, the interaction between the vortical structures and the local turbulent boundary layer results in a redistribution of the momentum transport and turbulent shear stress near the sawtooth side edges as well as the sawtooth tip, thus affecting the efficiency of self noise radiation.The authors are grateful for the support from the EPSRC Doctoral Training Grants in the United Kingdom

Aging effects on airflow dynamics and lung function in human bronchioles

Background and objective The mortality rate for patients requiring mechanical ventilation is about 35% and this rate increases to about 53% for the elderly. In general, with increasing age, the dynamic lung function and respiratory mechanics are compromised, and several experiments are being conducted to estimate these changes and understand the underlying mechanisms to better treat elderly patients. Materials and methods Human tracheobronchial (G1 ~ G9), bronchioles (G10 ~ G22) and alveolar sacs (G23) geometric models were developed based on reported anatomical dimensions for a 50 and an 80-year-old subject. The aged model was developed by altering the geometry and material properties of the model developed for the 50-year-old. Computational simulations using coupled fluid-solid analysis were performed for geometric models of bronchioles and alveolar sacs under mechanical ventilation to estimate the airflow and lung function characteristics. Findings The airway mechanical characteristics decreased with aging, specifically a 38% pressure drop was observed for the 80-year-old as compared to the 50-year-old. The shear stress on airway walls increased with aging and the highest shear stress was observed in the 80-year-old during inhalation. A 50% increase in peak strain was observed for the 80-year-old as compared to the 50-year-old during exhalation. The simulation results indicate that there is a 41% increase in lung compliance and a 35%-50% change in airway mechanical characteristics for the 80-year-old in comparison to the 50-year-old. Overall, the airway mechanical characteristics as well as lung function are compromised due to aging. Conclusion Our study demonstrates and quantifies the effects of aging on the airflow dynamics and lung capacity. These changes in the aging lung are important considerations for mechanical ventilation parameters in elderly patients. Realistic geometry and material properties need to be included in the computational models in future studies

Optimization-based Constrained Funnel Synthesis for Systems with Lipschitz Nonlinearities via Numerical Optimal Control

This paper presents a funnel synthesis algorithm for computing controlled invariant sets and feedback control gains around a given nominal trajectory for dynamical systems with locally Lipschitz nonlinearities and bounded disturbances. The resulting funnel synthesis problem involves a differential linear matrix inequality (DLMI) whose solution satisfies a Lyapunov condition that implies invariance and attractivity properties. Due to these properties, the proposed method can balance maximization of initial invariant funnel size, i.e., size of the funnel entry, and minimization of the size of the attractive funnel for attenuating the effect of disturbance. To solve the resulting funnel synthesis problem with the DLMI as constraints, we employ a numerical optimal control approach that uses a multiple shooting method to convert the problem into a finite dimensional semidefinite programming problem. This framework does not require piecewise linear system matrices and funnel parameters, which is typically assumed in recent related work. We illustrate the proposed funnel synthesis method with a numerical example.Comment: 6 pages, 3 figures, accepted to LCS

Effect of Plasma Composition on the Interpretation of Faraday Rotation

Faraday rotation (FR) is widely used to infer the orientation and strength of magnetic fields in astrophysical plasmas. Although the absence of electron-positron pairs is a plausible assumption in many astrophysical environments, the magnetospheres of pulsars and black holes and their associated jets may involve a significant pair plasma fraction. This motivates being mindful of the effect of positrons on FR. Here we derive and interpret exact expressions of FR for a neutral plasma of arbitrary composition. We focus on electron-ion-positron plasmas in which charge neutrality is maintained by an arbitrary combination of ions and positrons. Because a pure electron-positron plasma has zero FR, the greater the fraction of positrons the higher the field strength required to account for the same FR. We first obtain general formulae and then specifically consider parameters relevant to active galctic nuclei (AGN) jets to illustrate the significant differences in field strengths that FR measurements from radio frequency measurements. Complementarily, using galaxy cluster core plasmas as examples, we discuss how plasma composition can be constrained if independent measurements of the field strength and number density are available and combined with FR.Comment: Submitted to MNRA