On starting and stopping criteria for nested primal-dual iterations

The importance of an adequate inner loop starting point (as opposed to a sufficient inner loop stopping rule) is discussed in the context of a numerical optimization algorithm consisting of nested primal-dual proximal-gradient iterations. While the number of inner iterations is fixed in advance, convergence of the whole algorithm is still guaranteed by virtue of a warm-start strategy for the inner loop, showing that inner loop "starting rules" can be just as effective as "stopping rules" for guaranteeing convergence. The algorithm itself is applicable to the numerical solution of convex optimization problems defined by the sum of a differentiable term and two possibly non-differentiable terms. One of the latter terms should take the form of the composition of a linear map and a proximable function, while the differentiable term needs an accessible gradient. The algorithm reduces to the classical proximal gradient algorithm in certain special cases and it also generalizes other existing algorithms. In addition, under some conditions of strong convexity, we show a linear rate of convergence.Comment: 18 pages, no figure

Experimental study on the performance of a 10-cell proton exchange membrane (PEM) fuel cell stack

In this study, the steady state performance and dynamic behavior of a commercial 10-cell PEM fuel cell stack was experimentally investigated using a self-designed and developed PEM Fuel Cell Testing Stand. The start-up characteristics of the stack to different current load and dynamic responses after current step-up were studied. The stack voltage was observed to experience oscillation at air excess coefficient of 2 owing to the flooding and recovery of part of cells. To correlate the stack voltage with the pressure drop across the cathode/anode, fast Fourier transform was performed to obtain the dominant frequency of pressure drop signal, which indicated the water behavior in cathode/anode thereby predicting the stack voltage change. It is potentially possible to utilize pressure drop signal as a diagnosis tool for stack voltage at a fixed current load

Constructing Wavefunctions for One-Body and Two-Body Gravitational Orbits in Classical Mechanics

The circular orbits and elliptical orbits of moving objects in a gravitational field are essential information in astronomy. There have been many methods developed in the literature and textbooks to describe these orbits. In this report, I propose to use the vis-viva equation to construct a complex function to store the state of a moving object in elliptical orbits such that one can calculate its near future numerically. This state function is constructed by splitting its momentum into real and imaginary parts with one perpendicular to the radius of the mass center and the other parallel. The wavefunctions of electrons of hydrogen atoms in quantum mechanics inspire this idea. The equations are derived for one-body problems. Two-body problems can be constructed with subsets of one-body problems with the same center of mass, but different effective mass pinned there, significantly different from existing methods and providing the same results.Comment: 8 pages, 3 figure

Experimental validation of equilibria in fuel cells with dead-ended anodes

This paper investigates the nitrogen blanketing front during the dead-ended anode (DEA) operation of a PEM fuel cell. Surprisingly the dynamic evolution of nitrogen and water accumulation in the dead-ended anode (DEA) of a PEM fuel cell arrives to a steady-state suggesting the existence of equilibrium behavior. We use a multi-component model of the two-phase one-dimensional (along-the-channel) system behavior to analyze and exploit this phenomenon. Specifically, the model is first verified with experimental observations, and then utilized for showing the evolution towards equilibrium. The full order model is reduced to a second-order ordinary differential equation (ODE) with one state, which can be used to predict and amalyse the surprising but experimentally observed steady state DEA behavior

Degradation, Efficiency, and Equilibrium of a Dead-Ended Anode Fuel Cell.

The dead-ended anode (DEA) operation of a proton exchange membrane (PEM) fuel cell is a promising solution for applications with mild power density requirements. The hydrogen recirculation hardware can be simplified while maintaining high fuel utilization. The simplified system architecture for DEA operation reduces the cost. However, nitrogen and water accumulate in the anode, leading to decreasing voltage in galvanostatic operation due to local hydrogen depletion or starvation. Anode purging is thus necessary to release the accumulated nitrogen and water, and recover the voltage. The thesis aims to optimize a DEA fuel cell by overcoming the disadvantages while maintaining the benefits. One of the major issues with local fuel starvation in DEA operation is the corrosion of the carbon that supports the platinum in the cathode catalyst layer, which dramatically reduces the durability. An along-channel and transient model has been developed to predict the carbon corrosion and associate irreversible voltage degradation in DEA operation. The carbon corrosion rate and voltage degradation were identified quantitatively after model tuning. Simulation results suggest that purge interval and cycle duration affect the spatiotemporal distribution of anode species and, therefore, the carbon corrosion rate in the opposite cathode; consequently, a model-based optimization of these two design variables were performed to achieve high lifetime efficiency of a DEA cell. There are three interrelated objectives in this optimization: the hydrogen loss during the purge, the average voltage output between the purges, and the voltage degradation due to the carbon corrosion. The simulation results show that the durability concern with DEA operation can be reduced when a systematic engineering optimization is performed. The highest lifetime efficiency is achieved with medium cycle duration and short purge interval. Finally, the focus was turned to DEA operation without purging, in which system equilibrium is observed under certain operating conditions. The criteria for achieving such a nitrogen-blanketing based equilibrium with reasonable power output were analyzed by solving the reduced-order model numerically and comparing with the full-order model simulation. The results suggest another way of operating a DEA cell with minimum requirements on power regulation and purge optimization.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/99948/1/jixinc_1.pd

Inhibitory Effect on Cerebral Inflammatory Response following Traumatic Brain Injury in Rats: A Potential Neuroprotective Mechanism of N-Acetylcysteine

Although N-acetylcysteine (NAC) has been shown to be neuroprotective for traumatic brain injury (TBI), the mechanisms for this beneficial effect are still poorly understood. Cerebral inflammation plays an important role in the pathogenesis of secondary brain injury after TBI. However, it has not been investigated whether NAC modulates TBI-induced cerebral inflammatory response. In this work, we investigated the effect of NAC administration on cortical expressions of nuclear factor kappa B (NF-κB) and inflammatory proteins such as interleukin-1β (IL-1β), tumor necrosis factor-α (TNF-α), interleukin-6 (IL-6), and intercellular adhesion molecule-1 (ICAM-1) after TBI. As a result, we found that NF-κB, proinflammatory cytokines, and ICAM-1 were increased in all injured animals. In animals given NAC post-TBI, NF-κB, IL-1β, TNF-α, and ICAM-1 were decreased in comparison to vehicle-treated animals. Measures of IL-6 showed no change after NAC treatment. NAC administration reduced brain edema, BBB permeability, and apoptotic index in the injured brain. The results suggest that post-TBI NAC administration may attenuate inflammatory response in the injured rat brain, and this may be one mechanism by which NAC ameliorates secondary brain damage following TBI

Nanofabrication, Plasmon Enhanced Fluorescence and Photo-oxidation Kinetics of CdSe Nanoparticles

Unconventional nanofabrication techniques; both those which have been newly developed and those under development, had brought inexpensive, facile, yet high quality means to fabricate nanostructures that have feature sizes of less than 100 nm in industry and academia. This dissertation focuses on developing unconventional fabrication techniques, building studying platforms, and studying the mechanisms behind them. The studies are divided into two main facets and four chapters. The first facet, in Chapter II and Chapter III, deals with the research and development of different nanofabrication techniques and nanostructures. These techniques include litho-synthesis, colloidal lithography, and photolithography. The nanostructures that were fabricated by these techniques include the metal nanoparticle arrays, and the self-assembled CdSe nanoring arrays. At the same time, the dissertation provides mechanisms and models to describe the physical and chemical nature of these techniques. The second area of this study, in Chapter III to Chapter V, presents the applications of these nanostructures in fundamental studies, i.e. the mechanisms of plasmon enhanced fluorescence and photo-oxidation kinetics of CdSe quantum dots, and applications such as molecular sensing and material fabrication. More specifically, these applications include tuning the optical properties of CdSe quantum dots, biomodification of CdSe quantum dots, and copper ion detection using plasmon and photo enhanced CdSe quantum dots. We have successfully accomplished our research goals in this dissertation. Firstly, we were able to tune the emission wavelength of quantum dots, blue-shifted for up to 45 nm, and their surface functionalization with photo-oxidation. A kinetic model to calculate the photo-oxidation rates was established. Secondly, we established a simple mathematical model to explain the mechanism of plasmon enhanced fluoresce of quantum dots. Our calculation and experimental data support the fluorescence resonance energy transfer (FRET) mechanism between quantum dots and the metal nanoparticles. Thirdly, we successfully pattered the CdSe quantum dots (diameter ~4 nm) into nanorings with tunable diameters and annular sizes on different substrates. We also established a physical model to quantitatively explain the mechanism with the forces that involved in the formation of the nanorings

Vegetation Changes in Alberta Oil Sands, Canada, Based on Remotely Sensed Data from 1995 to 2020

There are rich oil and gas resources in Alberta oil sand mining area in Canada. Since the 1960s, the Canadian government decided to increase the mining intensity. However, the exploitation will bring many adverse effects. In recent years, more people pay attention to the environmental protection and ecological restoration of mining area, such as issues related with changes of vegetated lands. Thus, the authors used the Landsat-5 TM and Landsat-8 OLI remote sensing images as the basic data sources, and obtained the land cover classification maps from 1995 to 2020 by ENVI. Based on the NDVI, NDMI and RVI, three images in each period are processed and output to explore the long-term impact of exploitation. The results show that from 1995 to 2020, the proportion of vegetation around mining areas decreased sharply, the scale of construction land in the mining area increased, and the vegetated land was changed to land types such as tailings pond, oil sand mine and other land types. In addition, three vegetation indexes decreased from 1995 to 2020. Although the exploitation of oil sand mining area brings great economic benefits, the environmental protection (especially vegetation) in oil sand mining areas should be paid more attention