published_or_final_version / abstract / Mechanical Engineering / Doctoral / Doctor of Philosophy

The expansion of supply chains into global networks has drastically increased the distance travelled along shipping lanes in a logistics system. Inherently, the increase in travel distances produces increased carbon emissions from transport vehicles. When increased emissions are combined with a carbon tax or emissions trading system, the result is a supply chain with increased costs attributable to the emission generated on the transportation routes. Most traditional supply chain design models do not take emissions and carbon costs into account. Hence, there is a need to incorporate emission costs into a supply chain optimization model to see how the optimal supply chain configuration may be affected by the additional expenses. This thesis presents a mathematical programming model for the design of green supply chains. The costs of carbon dioxide (CO2) emissions were incorporated in the objective function, along with the fixed and transportation costs that are typically modeled in traditional facility location models. The model also determined the unit flows between the various nodes of the supply chain, with the objective of minimizing the total cost of the system by strategically locating warehouses throughout the network. The literature shows that CO2 emissions produced by a truck are dependent on the weight of the vehicle and can be modeled using a concave function. Hence, the carbon emissions produced along a shipping lane are dependent upon the number of units and the weight of each unit travelling between the two nodes. Due to the concave nature of the emissions, the addition of the emission costs to the problem formulation created a nonlinear mixed integer programming (MIP) model. A solution algorithm was developed to evaluate the new problem formulation. Lagrangian relaxation was used to decompose the problem by echelon and by potential warehouse site, resulting in a problem that required less computational effort to solve and allowed for much larger problems to be evaluated. A method was then suggested to exploit a property of the relaxed formulation and transform the problem into a linear MIP problem. The solution method computed the minimum cost for a complete network that would satisfy all the needs of the customers. A primal heuristic was introduced into the Lagrangian algorithm to generate feasible solutions. The heuristic utilized data from the Lagrangian subproblems to produce good feasible solutions. Due to the many characteristics of the original problem that were carried through to the subproblems, the heuristic produced very good feasible solutions that were typically within 1% of the Lagrangian bound. The proposed algorithm was evaluated through a number of tests. The rigidity of the problem and cost breakdown were varied to assess the performance of the solution method in many situations. The test results indicated that the addition of emission costs to a network can change the optimal configuration of the supply chain. As such, this study concluded that emission costs should be considered when designing supply chains in jurisdictions with carbon costs. Furthermore, the tests revealed that in regions without carbon costs it may be possible to significantly reduce the emissions produced by the supply chain with only a small increase in the cost to operate the system.

Studies of trace gas fluxes have advanced the understanding of bulk interactions between the atmosphere and ecosystems. Micrometeorological instrumentation is currently unable to resolve vertical scalar sources and sinks within plant canopies. Inverted analytical Lagrangian equations provide a non-intrusive method to calculate source distributions. These equations are based on Taylor's (1921) description of scalar dispersion, which requires a measure of the degree of correlation between turbulent motions, defined by the Lagrangian length scale (L). Inverse Lagrangian (IL) analyses can be unstable, and the uncertainty in L leads to uncertainty in source predictions. A review of the literature on studies using IL analysis with various scalars in a multitude of canopy types found that parameterizations where L reduces to zero at the ground produce better results in the IL analysis than those that increase closer to the ground, but no individual L parameterization gives better results than any other does. The review also found that the relationship between L and the measurable Eulerian length scale (Le) may be more complex in plant canopies than the linear scaling investigated in boundary layer flows. The magnitude and profile shape of L was investigated within a corn and a forest canopy using field measurements to constrain an analytical Lagrangian equation. Measurements of net CO2 flux, soil-to-atmosphere CO2 flux, and in-canopy profiles of CO2 concentrations provided the information required to solve for L in a global optimization algorithm for half hour intervals. For dates when the corn was a strong CO2 sink, and for the majority of dates for the forest, the optimization frequently located L profiles that follow a convex shape. A constrained optimization then smoothed the profile shape to a sigmoidal equation. Inputting the optimized L profiles in the forward and inverse Lagrangian equations leads to strong correlations between measured and calculated concentrations (corn canopy: C_{calc} = 1.00C_{meas} +52.41 mumol m^{-3}, r^2 = 0.996; forest canopy: C_{calc} = 0.98C_{meas} +276.5 mumol m^{-3}, r^2 = 0.99) and fluxes (corn canopy: F_{soil} = 0.67F_{calc} - 0.12 mumol m^{-2}s^{-1}, r^2 = 0.71, F_{net} = 1.17F_{calc} + 1.97mumol m^{-2}s^{-1}, r^2 = 0.85; forest canopy: F_{soil} = 0.72F_{calc} - 1.92 mumol m^{-2}s^{-1}, r^2 = 0.18, F_{net} = 1.24F_{calc} + 0.65 mumol m^{-2}s^{-1}, r^2 = 0.88). In the corn canopy, coefficients of the sigmoidal equation were specific to each half hour and did not scale with any measured variable. Coefficients of the optimized L equation in the forest canopy scaled weakly with variables related to the stability above the canopy. Plausible L profiles for both canopies were associated with negative bulk Richardson number values. / Funding from NSERC.

This thesis presents several ways to understand transports of air and water masses in the atmosphere and ocean, and the transports of energy that they imply. It presents work using various kinds of observations as well as computer simulations of the atmosphere and oceans. One of the main focuses is to identify similarities and differences between models and observations, as well as between different models. The first half of the thesis applies Lagrangian methods to study flows in the atmosphere and oceans. Part of the work focuses on understanding how particles follow the currents in the Baltic Sea and how they disperse. It is suggested that the commonly used regional ocean model for the Baltic Sea, RCO, underestimates the transport and the dispersion of the particles, which can have consequences for studies of e.g. biogeochemistry as well as for operational use. A similar methodology is used to study how particles are transported between the tropics and mid-latitudes by the large-scale atmospheric circulation. It is found that the mass transport associated with northbound and southbound particles can cancel in the zonally averaged circulation, and we propose that the degree of cancellation depends on the method of averaging. The latter half of the thesis focuses on Eulerian stream functions and specifically a thermodynamic stream function that combines the zonal and meridional circulations of the atmosphere into a single circulation. The results are used to study the inter-annual variability of the intensity and thermodynamic properties of the global atmospheric circulation. A significant correlation to ENSO variability is found both in reanalysis and the EC-Earth coupled climate model. It is also shown that a set of models from the CMIP5 project show a slowdown of the atmospheric circulation as a result of global warming and associated changes in near-surface moisture content and upper-level radiative cooling. / Denna avhandling presenterar olika metoder för att studera datormodeller av atmosfä- ren, haven, och klimatsystemet. Metoderna använder såväl Lagrangeska synsätt dvs att betrakta atmosfären eller haven som individuella partiklar i rörelse, som Eulerska synsätt där atmosfären och haven ses som gas eller vätska i rörelse. I artikel 1 sjö- sätts ett antal “surface drifters” i Östersjön som driver fritt med havsströmmarna och vars hastighet mäts av satelliter. Genom att modellera Lagrangeska partiklars rörelser i Östersjön och jämföra med dessa “surface drifters” kan det visas att datormodeller kan underskatta både medelhastigheten av partiklarna samt deras utbredning. I ar- tikel 2 simuleras luftmassornas rörelser mellan tropikerna och mellanbreddgraderna (∼ 45◦N/S). Ett medelvärde över all longituder tenderar att ignorera betydande mass- och energitransporter mellan tropikerna och mellanbredderna, och dessa kvantifieras i detalj i artikel 2. Artiklarna 3 och 4 presenterar en metod för att studera atmosfärens storskaliga rörelser utifrån ett termodynamiskt perspektiv där luftmassornas värme och fukt studeras. Det visas att variationer ytvattentemperatur vid ekvatorn i Stilla havet kan få atmosfären att, i ett globalt medelvärde, bli fuktigare och varmare samtidigt som masstransporter- na saktar ner. På samma sätt visas att en global uppvärmning till följd av ökade utsläpp av växthusgaser kan få atmosfären att bli varmare, fuktigare och att masstransporterna kan sakta ner. / <p>At the time of the doctoral defence the following papers were unpublished and had a status as follows: Paper 3: In press; Paper 4: Manuscript.</p> / BalticWay

No description available.

Submesoscale processes, characterized by O(1km) horizontal scale and O(1) Rossby number, are ubiquitous in the world ocean and play an important role in the vertical flux of mass, buoyancy and tracers in the upper ocean. However, they have not been intensively studied due to the requirement of uniquely high spatial and temporal resolution in the observation and computer modeling. In this thesis, using a suite of high-resolution numerical experiments in the northwestern Gulf of Mexico, where rich submesoscale structures are accompanied by the strong mesoscale Loop Current eddies, the impact of resolving submesoscales on the tracer distribution and 3-D transport was extensively examined. It was concluded that, submesoscale dynamics aggregated the surface tracers and formed characteristic patterns at scales of kilometers near the ocean surface by enhanced convergence/divergence zones associated with strong ageostrophic processes. This distinctive phenomenon was evident in recent ocean color satellite images which showed similar extensive lines and spirals of floating Sargassum in the western Gulf of Mexico. In addition, better-resolved submesoscale activities increased the horizontal resolution dramatically and elevated local vertical velocity both within and below the mixed layer while leaving the horizontal component almost unaltered. The vertical dispersion increased by several fold with the largest difference close to the surface. Considering the pervasive presence of submesoscale structures at the surface ocean, these models predict that submesoscale processes may serve as an important nutrient supply mechanism in the upper ocean and potentially make a significant contribution on balancing the global biogeochemical tracer budget.

<p>In response to the differential heating of the earth, atmospheric and oceanic flows constantly act to carry surplus energy from low to high latitudes. In the ocean, this poleward energy flux occurs as part of the large scale meridional overturning circulation: warm, shallow waters are transported to high latitudes where they cool and sink, then follow subsurface pathways equatorward until they are once again upwelled to the surface and reheated. In the North Atlantic, the upper limb of this circulation has always been explained in simplistic terms: the Gulf Stream/North Atlantic Current system carries surface waters directly to high latitudes, resulting in elevated sea surface temperatures in the eastern subpolar gyre, and, because the prevailing winds sweeping across the Atlantic are warmed by these waters, anomalously warm temperatures in Western Europe. This view has long been supported by Eulerian measurements of North Atlantic sea surface temperature and surface velocities, which imply a direct and continuous transport of surface waters between the two gyres. However, though the importance of this redistribution of heat from low to high latitudes has been broadly recognized, few studies have focused on this transport within the Lagrangian frame. </p><p>The three studies included in this dissertation use data from the observational record and from a high resolution model of ocean circulation to re-examine our understanding of upper limb transport between the subtropical and subpolar gyres. Specifically, each chapter explores intergyre Lagrangian pathways and investigates the impact of those pathways on subpolar property fields. The findings from the studies suggest that intergyre transport pathways are primarily located beneath the surface and that subtropical surface waters are largely absent from the intergyre exchange process, a very different image of intergyre transport than that compiled from Eulerian data alone. As such, these studies also highlight the importance of including 3d Lagrangian information in examinations of transport pathways.</p> / Dissertation

In this thesis, we consider the massive field theories in 1+1 dimensions known as affine Toda quantum field theories. These have the special property that they possess an infinite number of conserved quantities, a feature which greatly simplifies their study, and makes extracting exact information about them a tractable problem. We consider these theories both in the full space (the bulk) and in the half space bounded by an impenetrable boundary at x = 0. In particular, we consider their fundamental objects: the scattering matrices in the bulk, and the reflection factors at the boundary, both of which can be found in a closed form. In Chapter 1, we provide a general introduction to the topic before going on, in Chapter 2, to consider the simplest ATFT—the sine-Gordon model—with a boundary. We begin by studying the classical limit, finding quite a clear picture of the boundary structure we can expect in the quantum case, which is introduced in Chapter 3. We obtain the bound-state structure for all integrable boundary conditions, as well as the corresponding reflection factors. This structure turns out to be much richer than had hitherto been imagined. We then consider more general ATFTs in the bulk. The sine-Gordon model is based on a(^(1))(_1), but there is an ATFT for any semi-simple Lie algebra. This underlying structure is known to show up in their S-matrices, but the path back to the parameters in the Lagrangian is still unclear. We investigate this, our main result being the discovery of a "generalised bootstrap" equation which explicitly encodes the Lie algebra into the S-matrix. This leads to a number of new S-matrix identities, as well as a generalisation of the idea that the conserved charges of the theory form an eigenvector of the Cartan matrix. Finally our results are summarised in Chapter 5, and possible directions for further study are highlighted.

There is an increasing interest in sustainability and a growing debate about environmental policy measures aiming at the reduction of green house gas emissions across di erent economic sectors worldwide. The transportation sector is one major greenhouse gas emitter which is heavily regulated to reduce its dependance on oil. These regulations along with the growing customer awareness about global warming has led vehicle manufacturers to seek di erent technologies to improve vehicle e ciencies and reduce the green house gases emissions while at the same time meeting customer's expectation of mobility and exibility. Plug-in hybrid electric vehicles (PHEV) is one major promising solution for a smooth transition from oil dependent transportation sector to a clean electric based sector while not compromising the mobility and exibility of the drivers. In the medium term, plug-in hybrid electric vehicles (PHEV) can lead to signi cant reductions in transportation emissions. These vehicles are equipped with a larger battery than regular hybrid electric vehicles which can be recharged from the grid. For short trips, the PHEV can depend solely on the electric engine while for longer journeys the alternative fuel can assist the electric engine to achieve extended ranges. This is bene cial when the use pattern is mixed such that and short long distances needs to be covered. The plug-in hybrid electric vehicles are well-suited for logistics since they can avoid the possible disruption caused by charge depletion in case of all-electric vehicles with tight time schedules. The use of electricity and fuel gives rise to a new variant of the classical vehicle routing with time windows which we call the plug-in hybrid electric vehicle routing problem with time windows (PHEVRPTW). The objective of the PHEVRPTW is to minimize the routing costs of a eet of PHEVs by minimizing the time they run on gasoline while meeting the demand during the available time windows. As a result, the driver of the PHEV has two decisions to make at each node: (1) recharge the vehicle battery to achieve a longer range using electricity, or (2) continue to the next open time window with the option of using the alternative fuel. In this thesis, we present a mathematical formulation for the plug-in hybrid-electric vehicle routing problem with time windows. We solve this problem using a Lagrangian relaxation and we propose a new tabu search algorithm. We also present the rst results for the full adapted Solomon instances.

We obtain explicit formulae for Lagrangian representations of the (p, q, r)-triangle group into the group of direct isometries of the complex hyperbolic plane in the case where p=q=r. Numerically approximated matrix generators of representations of the (p, p, p)-triangle group are obtained using a special basis. The numerical approximations are then used to guess the exact generators by a process utilizing the LLL algorithm. The matrices are proved rigorously to generate Lagrangian representations of the (p, p, p)-triangle group and are applied to the problem of deciding whether or not an interval contains representations of the (p, p, p)-triangle group which are not discrete.