Toward assessing the effects of aerosols on deep convection: a numerical study using the WRF-Chemistry model

As the formative agents of cloud droplets, aerosols play an undeniably important role in the development of clouds and precipitation. Few meteorological models have been developed or adapted to simulate aerosols and their contribution to cloud and precipitation processes. The Weather Research and Forecasting model (WRF) has recently been coupled with an atmospheric chemistry suite and is jointly referred to as WRF-Chem, allowing atmospheric chemistry and meteorology to influence each other’s evolution within a mesoscale modeling framework. Provided that the model physics are robust, this framework allows the feedbacks between aerosol chemistry, cloud physics, and dynamics to be investigated. This study focuses on the effects of aerosols on meteorology, specifically, the interaction of aerosol chemical species with microphysical processes represented within the framework of the WRF-Chem. Aerosols are represented by eight size bins using the Model for Simulating Aerosol Interactions and Chemistry (MOSAIC) sectional parameterization, which is linked to the Purdue Lin bulk microphysics scheme. The aim of this study is to examine the sensitivity of deep convective precipitation modeled by the 2D WRF-Chem to varying aerosol number concentration and aerosol type. A systematic study has been performed regarding the effects of aerosols on parameters such as total precipitation, updraft/downdraft speed, distribution of hydrometeor species, and organizational features, within idealized maritime and continental thermodynamic environments. Initial results were obtained using WRFv3.0.1, and a second series of tests were run using WRFv3.2 after several changes to the activation, autoconversion, and Lin et al. microphysics schemes added by the WRF community, as well as the implementation of prescribed vertical levels by the author. The results of WRFv3.2 runs contrasted starkly with WRFv3.0.1 runs. The WRFv3.0.1 runs produced a propagating system resembling a developing squall line, whereas the WRFv3.2 runs did not. The response of total precipitation, updraft/downdraft speeds, and system organization to increasing aerosol concentrations were opposite between runs with different versions of WRF. Results of the WRFv3.2 runs, however, were in better agreement in timing and magnitude of vertical velocity and hydrometeor content with a WRFv3.0.1 run using single-moment Lin et al. microphysics, than WRFv3.0.1 runs with chemistry. One result consistent throughout all simulations was an inhibition in warm-rain processes due to enhanced aerosol concentrations, which resulted in a delay of precipitation onset that ranged from 2-3 minutes in WRFv3.2 runs, and up to 15 minutes in WRFv.3.0.1 runs. This result was not observed in a previous study by Ntelekos et al. (2009) using the WRF-Chem, perhaps due to their use of coarser horizontal and vertical resolution within their experiment. The changes to microphysical processes such as activation and autoconversion from WRFv3.0.1 to WRFv3.2, along with changes in the packing of vertical levels, had more impact than the varying aerosol concentrations even though the range of aerosol tested was greater than that observed in field studies. In order to take full advantage of the input of aerosols now offered by the chemistry module in WRF, the author recommends that a fully double-moment microphysics scheme be linked, rather than the limited double-moment Lin et al. scheme that currently exists. With this modification, the WRF-Chem will be a powerful tool for studying aerosol-cloud interactions and allow comparison of results with other studies using more modern and complex microphysical parameterizations.

Coordinated pricing and inventory management

This dissertation mainly focuses on coordinated pricing and inventory management problems, where the related background is provided in Chapter 1. Several periodic-review models are then discussed in Chapters 2,3,4 and 5, respectively. Chapter 2 analyzes a deterministic single-product model, where a price adjustment cost incurs if the current selling price is changed from the previous period. We develop exact algorithms for the problem under different conditions and find out that computation complexity varies significantly associated with the cost structure. %Moreover, our numerical study indicates that dynamic pricing strategies may outperform static pricing strategies even when price adjustment cost accounts for a significant portion of the total profit. Chapter 3 develops a single-product model in which demand of a period depends not only on the current selling price but also on past prices through the so-called reference price. Strongly polynomial time algorithms are designed for the case without no fixed ordering cost, and a heuristic is proposed for the general case together with an error bound estimation. Moreover, our illustrates through numerical studies that incorporating reference price effect into coordinated pricing and inventory models can have a significant impact on firms' profits. Chapter 4 discusses the stochastic version of the model in Chapter 3 when customers are loss averse. It extends the associated results developed in literature and proves that the reference price dependent base-stock policy is proved to be optimal under a certain conditions. Instead of dealing with specific problems, Chapter 5 establishes the preservation of supermodularity in a class of optimization problems. This property and its extensions include several existing results in the literature as special cases, and provide powerful tools as we illustrate their applications to several operations problems: the stochastic two-product model with cross-price effects, the two-stage inventory control model, and the self-financing model.

Examining the growth and evolution of magnetic fields in clusters of galaxies: a numerical perspective

Magnetic fields are ubiquitous in galaxy cluster atmospheres and have a variety of astrophysical and cosmological consequences. Magnetic fields can contribute to the pressure support of clusters, affect thermal conduction, and modify the evolution of bubbles driven by active galactic nuclei. However, we currently do not fully understand the origin and evolution of these fields throughout cosmic time. Furthermore, we do not have a general understanding of the relationship between magnetic field strength and topology and other cluster properties, such as mass and X-ray luminosity. We can now begin to answer some of these questions using large-scale cosmological magnetohydrodynamic (MHD) simulations of the formation of galaxy clusters including the seeding and growth of magnetic fields. Using large-scale cosmological simulations with the FLASH code combined with a simplified model of the acceleration of cosmic rays responsible for the generation of radio halos, we find that the galaxy cluster frequency distribution and expected number counts of radio halos from upcoming low-frequency sur- veys are strongly dependent on the strength of magnetic fields. Thus, a more complete understanding of the origin and evolution of magnetic fields is necessary to understand and constrain models of diffuse synchrotron emission from clusters. One favored model for generating magnetic fields is through the amplification of weak seed fields in active galactic nuclei (AGN) accretion disks and their subsequent injection into cluster atmospheres via AGN-driven jets and bubbles. However, current large-scale cosmological simulations cannot directly include the physical processes associated with the accretion and feedback processes of AGN or the seeding and merging of the associated SMBHs. Thus, we must include these effects as subgrid models. In order to carefully study the growth of magnetic fields in clusters via AGN-driven outflows, we present a systematic study of SMBH and AGN subgrid models. Using dark-matter only cosmological simulations, we find that many important quantities, such as the relationship between SMBH mass and galactic bulge velocity dispersion and the merger rate of black holes, are highly sensitive to the subgrid model assumptions of SMBHs. In addition, using MHD calculations of an isolated cluster, we find that magnetic field strengths, extent, topology, and relationship to other gas quantities such as temperature and density are also highly dependent on the chosen model of accretion and feedback. We use these systematic studies of SMBHs and AGN inform and constrain our choice of subgrid models, and we use those results to outline a fully cosmological MHD simulation to study the injection and growth of magnetic fields in clusters of galaxies. This simulation will be the first to study the birth and evolution of magnetic fields using a fully closed accretion-feedback cycle, with as few assumptions as possible and a clearer understanding of the effects of the various parameter choices.

A study of electrochemical transport and diffuse charge dynamics using a Langevin equation

This thesis aims to develop new numerical and computational tools to study electrochemical transport and diffuse charge dynamics at small scales. Previous efforts at modeling electrokinetic phenomena at scales where the noncontinuum effects become significant have included continuum models based on the Poisson-Nernst-Planck equations and atomic simulations using molecular dynamics algorithms. Neither of them is easy to use or conducive to electrokinetic transport modeling in strong confinement or over long time scales. This work introduces a new approach based on a Langevin equation for diffuse charge dynamics in nanofluidic devices, which incorporates features from both continuum and atomistic methods. The model is then extended to include steric effects resulting from finite ion size, and applied to the phenomenon of double layer charging in a symmetric binary electrolyte between parallel-plate blocking electrodes, between which a voltage is applied. Finally, the results of this approach are compared to those of the continuum model based on the Poisson-Nernst-Planck equations.

A pilot study on the productivity and behavior of the gestating sow housed in a flex stall

Animal welfare is a controversial topic in modern animal agriculture, partly because it generates interest from both the scientific community and the general public. The housing of gestating sows, particularly individual housing, is one of the most critical concerns in farm animal welfare. We hypothesize that the physical size of the standard gestation stall may limit movement and evoke demands and challenges on the sow to affect the physiological and psychological well-being of the individually housed sow. Thus, improvements in the design of the individual gestation stall system that allow more freedom to move, such as increasing stall width or designing a stall that could accommodate the changing size of the pregnant sow, may improve sow welfare. The objective of this pilot study was to evaluate the effects of a width adjustable stall (FLEX) on productivity and behavior of dry sows. The experiment consisted of 3 replications (block 1, n=4 sows; block 2, n=4 sows; block 3, n=8 sows), and multi-parious sows were allotted to either a FLEX stall or standard gestation stall for 1 gestation period. Sow mid-girth (top of the back to bottom of the udder) was measured 5-6 times throughout gestation to determine the best time points for FLEX stall width expansions. FLEX stall width was adjusted according to mid-girth measurements, and expanded to achieve an additional 2 cm of space between the bottom of the sow’s udder and floor of the stall so that sows could lie in full lateral recumbency without touching the sides of the stall. Productivity data recorded included: sow body weight (BW) and BW gain, number of piglets born and born alive, proportions of piglets stillborn, mummified, lost between birth and weaning, and weaned, and litter and mean piglet birth BW, weaning BW, and average BW gain from birth-to-weaning. Lesions were recorded on d 21 and d 111 of gestation. Sub-pilot behavior data were observed and registered for replicate 1 sows using continuous video-records for the l2 hour lights on period (period 1, 0600-1000; period 2, 1000-1400; period 3, 1400-1800) prior FLEX stall adjustment and 12 hour lights on period post adjustment on d 21, 22, 23, 43, 44, 45, 93, 94, 95. A randomized complete block design with a 2 × 2 factorial arrangement for treatments was used to analyze sow productivity and performance traits. Data were analyzed using the Mixed Models procedure of SAS. A preliminary analysis of data means and numerical trends was used to analyze sow behavior measurements. Sows housed in a FLEX stall had more (P < 0.05) total born and a tendency for more piglets born alive (P = 0.06) than sows housed in a standard stall. Sow body weight also tended to be higher (P = 0.06) for sows housed in a FLEX stall compared to sows housed in a standard stall. There were numerical trends for mean durations of sit, lay, lay (OUT), and eat behaviors to be greater for sows housed in a FLEX stall compared with sows housed in a standard stall. The mean duration of lay (IN) behavior tended to be numerically less for sows housed in a FLEX stall compared with sows housed in a standard stall. There were numerical trends for the mean durations of stand and drink behaviors to be greater for sows housed in a standard stall compared with sows housed in a FLEX stall. The mean frequencies of postural changes and mean durations of oral-nasal-facial and sham-chew behaviors were numerically similar between types of gestation stall. Mean durations and numerical trends indicate that time of day influenced all of the behaviors assessed in this study. The results of this pilot study indicate that the adjustable FLEX stall may affect sow productivity and behavior differently than the standard gestation stall, and thus potentially improve sow well-being. Future research should continue to compare the new FLEX stall design to current housing systems in use and examine physiological traits and immune status in addition to behavioral and productivity traits to assess the effects that this housing system has on the overall welfare of the gestating sow.