Problem-driven scenario generation: an analytical approach for stochastic programs with tail risk measure

Mathematical Programming - Scenario generation is the construction of a discrete random vector to represent parameters of uncertain values in a stochastic program. Most approaches to scenario...     

Simulating bubble dynamics in a buoyant system

Multiphase flows are critical components of many physical systems; however, numerical models of multiphase flows with large parameter gradients can be challenging. Here, two different numerical methods, volume of fluid (VOF) and smoothed particle hydrodynamics (SPH), are used to model the buoyant rise of isolated gas bubbles through quiescent fluids for a range of Bond and Reynolds numbers. The VOF is an Eulerian grid–based method, whereas the SPH is Lagrangian and mesh free. Each method has unique strengths and weaknesses, and a comparison of the two approaches as applied to multiphase phenomena has not previously been performed. The VOF and SPH simulations are compared, verified, and validated. Results using two-dimensional VOF and SPH simulations are similar to each other and are able to reproduce numerical benchmarks and experimental results for sufficiently large Morton and Reynolds numbers. It is also shown that at low Reynolds numbers, the two methods, SPH and VOF, diverge in the transient regime of the bubble rise. Regimes that require simulations capable of representing three-dimensional drag are identified as well as regimes in which results from VOF and SPH diverge.     

Continuum versus discrete networks,graph Laplacians,and reproducing kernel Hilbert spaces

Motivated by applications to machine learning, we construct a reversible and irreducible Markov chain whose state space is a certain collection of measurable sets of a chosen l.c.h. space $\mathfrak{X}$. We study the resulting network (connected undirected graph), including transience, Royden and Riesz decompositions, and kernel factorization. We describe a construction for Hilbert spaces of signed measures which comes equipped with a new notion of reproducing kernels and there is a unique solution to a regularized optimization problem involving the approximation of $L^2$ functions by functions of finite energy. The latter has applications to machine learning (for Markov random fields, for example).     

Novel parameter estimation techniques for a multi-term fractional dynamical epidemic model of dengue fever

Numerical Algorithms - An inverse problem to identify parameters for the single-term (and multi-term) fractional-order system of an outbreak of dengue fever is considered. Firstly, we propose a...     

Validation of an analytical method to quantify the permeation and penetration of flurbiprofen into human pharynx tissue

The aim of this investigation was to develop receiver and extraction fluids, and subsequently validate an analytical method to quantify the permeation and penetration of flurbiprofen into human pharynx tissue using a Franz diffusion cell. The solubility and stability of flurbiprofen in a suitable receiver fluid, and a suitable extraction method and fluid to recover and quantitate flurbiprofen from human pharynx tissue, were investigated using high‐performance liquid chromatography (HPLC). The potential interference of human pharynx tissue in the receiver fluid was also investigated. The HPLC analytical method was successfully validated according to current guidelines. The final receiver fluid demonstrated sufficient solubility and stability, and the extraction method and fluid resulted in >95% recovery of flurbiprofen following exposure to human pharynx tissue. The lower limit of quantitation of flurbiprofen was 0.045 μg/mL in both the receiver and extraction fluids. There was no interference of the human pharynx tissue with the HPLC method. This investigation validated an analytical method for quantitating flurbiprofen, and determined a suitable receiver fluid and extraction method and fluid, which can be used to investigate the permeation and penetration of flurbiprofen through human pharynx tissue using the Franz diffusion cell method.     

A Photoionization Reflectron Time-of-Flight Mass Spectrometric Study on the Detection of Ethynamine (HCCNH2) and 2H-Azirine (c-H2CCHN)

Ices of acetylene (C₂H₂) and ammonia (NH₃) were irradiated with energetic electrons to simulate interstellar ices processed by galactic cosmic rays in order to investigate the formation of C₂H₃N isomers. Supported by quantum chemical calculations, experiments detected product molecules as they sublime from the ices using photoionization reflectron time-of-flight mass spectrometry (PI-ReTOF-MS). Isotopically-labeled ices confirmed the C₂H₃N assignments while photon energies of 8.81 eV, 9.80 eV, and 10.49 eV were utilized to discriminate isomers based on their known ionization energies. Results indicate the formation of ethynamine (HCCNH₂) and 2H-azirine (c-H₂CCHN) in the irradiated C₂H₂:NH₃ ices, and the energetics of their formation mechanisms are discussed. These findings suggest that these two isomers can form in interstellar ices and, upon sublimation during the hot core phase, could be detected using radio astronomy.     

Evaluation of the Long‐term Cumulative UVA Facial Exposure of Queensland School Teachers derived for an Extended Period from the OMI Satellite Irradiance

This research presents a novel methodology for deriving the total daily broadband solar UVA (320–400 nm) received by school teachers during their working day from Ozone Monitoring Instrument (OMI) satellite solar noon UVA irradiance measurements for a Queensland subtropical site (27.5°S, 152°E). Daily UVA exposures are weighted to the anatomical human cheek (anterior infra‐orbital region) for teachers wearing and not wearing broad‐brimmed hats. The method utilizes the OMI UVA irradiance data collected daily at high temporal resolution over 2005 to 2016 to derive the total daily UVA exposure to a horizontal plane. These horizontal plane exposures are scaled by factors to take into account the timing of outdoor activity. The relationship between exposures to a horizontal plane and those to a vertical plane and the protection provided by a broad‐brimmed hat was assessed to evaluate the total daily UVA exposures to the cheek for classroom and physical education teaching staff expected to be outside at different periods of the day. The developed method enables the total daily UVA exposure to specific anatomical sites to be evaluated from the satellite solar noon irradiance at locations that do not have access to surface‐based instrumentation capable of recording in the solar UVA waveband.