q-Heat Operator and q-Poisson’s Operator

2000 Mathematics Subject Classification: 33D15, 33D90, 39A13

Theory and Practice in Sustainability Science: Influence of Urban Form on the Urban Heat Island and Implications for Urban Systems

As the world population continues to grow past seven billion people and global challenges continue to persist including resource availability, biodiversity loss, climate change and human well-being, a new science is required that can address the integrated nature of these challenges and the multiple scales on which they are manifest. Sustainability science has emerged to fill this role. In the fifteen years since it was first called for in the pages of Science, it has rapidly matured, however its place in the history of science and the way it is practiced today must be continually evaluated. In Part I, two chapters address this theoretical and practical grounding. Part II transitions to the applied practice of sustainability science in addressing the urban heat island (UHI) challenge wherein the climate of urban areas are warmer than their surrounding rural environs. The UHI has become increasingly important within the study of earth sciences given the increased focus on climate change and as the balance of humans now live in urban areas.

In Chapter 2 a novel contribution to the historical context of sustainability is argued. Sustainability as a concept characterizing the relationship between humans and nature emerged in the mid to late 20th century as a response to findings used to also characterize the Anthropocene. Emerging from the human-nature relationships that came before it, evidence is provided that suggests Sustainability was enabled by technology and a reorientation of world-view and is unique in its global boundary, systematic approach and ambition for both well being and the continued availability of resources and Earth system function. Sustainability is further an ambition that has wide appeal, making it one of the first normative concepts of the Anthropocene.

Despite its widespread emergence and adoption, sustainability science continues to suffer from definitional ambiguity within the academe. In Chapter 3, a review of efforts to provide direction and structure to the science reveals a continuum of approaches anchored at either end by differing visions of how the science interfaces with practice (solutions). At one end, basic science of societally defined problems informs decisions about possible solutions and their application. At the other end, applied research directly affects the options available to decision makers. While clear from the literature, survey data further suggests that the dichotomy does not appear to be as apparent in the minds of practitioners.

In Chapter 4, the UHI is first addressed at the synoptic, mesoscale. Urban climate is the most immediate manifestation of the warming global climate for the majority of people on earth. Nearly half of those people live in small to medium sized cities, an understudied scale in urban climate research. Widespread characterization would be useful to decision makers in planning and design. Using a multi-method approach, the mesoscale UHI in the study region is characterized and the secular trend over the last sixty years evaluated. Under isolated ideal conditions the findings indicate a UHI of 5.3 ± 0.97 °C to be present in the study area, the magnitude of which is growing over time.

Although urban heat islands (UHI) are well studied, there remain no panaceas for local scale mitigation and adaptation methods, therefore continued attention to characterization of the phenomenon in urban centers of different scales around the globe is required. In Chapter 5, a local scale analysis of the canopy layer and surface UHI in a medium sized city in North Carolina, USA is conducted using multiple methods including stationary urban sensors, mobile transects and remote sensing. Focusing on the ideal conditions for UHI development during an anticyclonic summer heat event, the study observes a range of UHI intensity depending on the method of observation: 8.7 °C from the stationary urban sensors; 6.9 °C from mobile transects; and, 2.2 °C from remote sensing. Additional attention is paid to the diurnal dynamics of the UHI and its correlation with vegetation indices, dewpoint and albedo. Evapotranspiration is shown to drive dynamics in the study region.

Finally, recognizing that a bridge must be established between the physical science community studying the Urban Heat Island (UHI) effect, and the planning community and decision makers implementing urban form and development policies, Chapter 6 evaluates multiple urban form characterization methods. Methods evaluated include local climate zones (LCZ), national land cover database (NCLD) classes and urban cluster analysis (UCA) to determine their utility in describing the distribution of the UHI based on three standard observation types 1) fixed urban temperature sensors, 2) mobile transects and, 3) remote sensing. Bivariate, regression and ANOVA tests are used to conduct the analyses. Findings indicate that the NLCD classes are best correlated to the UHI intensity and distribution in the study area. Further, while the UCA method is not useful directly, the variables included in the method are predictive based on regression analysis so the potential for better model design exists. Land cover variables including albedo, impervious surface fraction and pervious surface fraction are found to dominate the distribution of the UHI in the study area regardless of observation method.

Chapter 7 provides a summary of findings, and offers a brief analysis of their implications for both the scientific discourse generally, and the study area specifically. In general, the work undertaken does not achieve the full ambition of sustainability science, additional work is required to translate findings to practice and more fully evaluate adoption. The implications for planning and development in the local region are addressed in the context of a major light-rail infrastructure project including several systems level considerations like human health and development. Finally, several avenues for future work are outlined. Within the theoretical development of sustainability science, these pathways include more robust evaluations of the theoretical and actual practice. Within the UHI context, these include development of an integrated urban form characterization model, application of study methodology in other geographic areas and at different scales, and use of novel experimental methods including distributed sensor networks and citizen science.

Heat fluxes and surface radiation measurements from Samoylov Island, Lena Delta, Siberia, October 2007 to March 2008

In this study, we present the winter time surface energy balance at a polygonal tundra site in northern Siberia based on independent measurements of the net radiation, the sensible heat flux and the ground heat flux from two winter seasons. The latent heat flux is inferred from measurements of the atmospheric turbulence characteristics and a model approach. The long-wave radiation is found to be the dominant factor in the surface energy balance. The radiative losses are balanced to about 60 % by the ground heat flux and almost 40 % by the sensible heat fluxes, whereas the contribution of the latent heat flux is small. The main controlling factors of the surface energy budget are the snow cover, the cloudiness and the soil temperature gradient. Large spatial differences in the surface energy balance are observed between tundra soils and a small pond. The ground heat flux released at a freezing pond is by a factor of two higher compared to the freezing soil, whereas large differences in net radiation between the pond and soil are only observed at the end of the winter period. Differences in the surface energy balance between the two winter seasons are found to be related to differences in snow depth and cloud cover which strongly affect the temperature evolution and the freeze-up at the investigated pond.

PHYSICA: A multiphysics computational framework and its application to casting simulations

Metal casting is a process governed by the interaction of a range of physical phenomena. Most computational models of this process address only what are conventionally regarded as the primary phenomena – heat conduction and solidification. However, to predict other phenomena, such as porosity formation, requires modelling the interaction of the fluid flow, heat transfer, solidification and the development of stressdeformation in the solidified part of the casting. This paper will describe a modelling framework called PHYSICA[1] which has the capability to stimulate such multiphysical phenomena.

A Distributed algorithm for 1-D non-linear heat conduction with an unknown point source

Abstract not available

A three dimensional finite volume approach to the thermo-mechanical modelling of the shape casting of metals

This paper presents a three dimensional, thermos-mechanical modelling approach to the cooling and solidification phases associated with the shape casting of metals ei. Die, sand and investment casting. Novel vortex-based Finite Volume (FV) methods are described and employed with regard to the small strain, non-linear Computational Solid Mechanics (CSM) capabilities required to model shape casting. The CSM capabilities include the non-linear material phenomena of creep and thermo-elasto-visco-plasticity at high temperatures and thermo-elasto-visco-plasticity at low temperatures and also multi body deformable contact with which can occur between the metal casting of the mould. The vortex-based FV methods, which can be readily applied to unstructured meshes, are included within a comprehensive FV modelling framework, PHYSICA. The additional heat transfer, by conduction and convection, filling, porosity and solidification algorithms existing within PHYSICA for the complete modelling of all shape casting process employ cell-centred FV methods. The termo-mechanical coupling is performed in a staggered incremental fashion, which addresses the possible gap formation between the component and the mould, and is ultimately validated against a variety of shape casting benchmarks.

EXPOSURE TO EXTREME HEAT EVENTS AND CHRONIC RESPIRATORY DISEASES AMONG A NATIONALLY REPRESENTATIVE SAMPLE OF THE UNITED STATES POPULATION

Previous studies have shown that extreme weather events are on the rise in response to our changing climate. Such events are projected to become more frequent, more intense, and longer lasting. A consistent exposure metric for measuring these extreme events as well as information regarding how these events lead to ill health are needed to inform meaningful adaptation strategies that are specific to the needs of local communities. Using federal meteorological data corresponding to 17 years (1997-2013) of the National Health Interview Survey, this research: 1) developed a location-specific exposure metric that captures individuals’ “exposure” at a spatial scale that is consistent with publicly available county-level health outcome data; 2) characterized the United States’ population in counties that have experienced higher numbers of extreme heat events and thus identified population groups likely to experience future events; and 3) developed an empirical model describing the association between exposure to extreme heat events and hay fever. This research confirmed that the natural modes of forcing (e.g., El Niño-Southern Oscillation), seasonality, urban-rural classification, and division of country have an impact on the number extreme heat events recorded. Also, many of the areas affected by extreme heat events are shown to have a variety of vulnerable populations including women of childbearing age, people who are poor, and older adults. Lastly, this research showed that adults in the highest quartile of exposure to extreme heat events had a 7% increased odds of hay fever compared to those in the lowest quartile, suggesting that exposure to extreme heat events increases risk of hay fever among US adults.

In-situ based reanalysis of the global ocean temperature and salinity with ISAS: variability of the heat content and steric height

The In Situ Analysis System (ISAS) was developed to produce gridded fields of temperature and salinity that preserve as much as possible the time and space sampling capabilities of the Argo network of profiling floats. Since the first global re-analysis performed in 2009, the system has evolved and a careful delayed mode processing of the 2002-2012 dataset has been carried out using version 6 of ISAS and updating the statistics to produce the ISAS13 analysis. This last version is now implemented as the operational analysis tool at the Coriolis data centre. The robustness of the results with respect to the system evolution is explored through global quantities of climatological interest: the Ocean Heat Content and the Steric Height. Estimates of errors consistent with the methodology are computed. This study shows that building reliable statistics on the fields is fundamental to improve the monthly estimates and to determine the absolute error bars. The new mean fields and variances deduced from the ISAS13 re-analysis and dataset show significant changes relative to the previous ISAS estimates, in particular in the southern ocean, justifying the iterative procedure. During the decade covered by Argo, the intermediate waters appear warmer and saltier in the North Atlantic and fresher in the Southern Ocean than in WOA05 long term mean. At inter-annual scale, the impact of ENSO on the Ocean Heat Content and Steric Height is observed during the 2006-2007 and 2009-2010 events captured by the network.

Lithosphere Thickness, Heat Flow and Moho Depth in the South of Portugal

Abstract In the last years, several models have been presented trying to obtain lithosphere and Moho thickness in the Iberian Peninsula, using data related to geoid elevation and topography, gravity, seismicity and thermal analysis. The results obtained show a decrease in the thickness of the crust and the lithosphere in the SW part of the Iberian Peninsula. Density anomalies in the crust are also referred. Data obtained in the region was collected and deviations from average values used were detected. In this work, models were made taking into account the specific characteristics of the region. Heat flow, thermal conductivity, heat production, topography, gravity, seismic and geological data available for the region, were used to adjust the model. The results show that this region is different from other parts of the Iberian Peninsula and a special attention must be given to it. This work shows the importance of trying to know and understand the thermal structure of the region.

Lithosphere Thickness, Heat Flow and Moho Depth in the South of Portugal

ABSTRACT In the last years, several models were presented trying to obtain lithosphere and Moho thickness in the Iberian Peninsula, using data related to geoid elevation and topography, gravity, seismicity and thermal analysis. The results obtained show a decrease in the thickness of the crust and the lithosphere in the SW part of the Iberian Peninsula. Density anomalies in the crust are also referred. The work I intend to present is related with the south of the Ossa Morena Zone, the South Portuguese Zone and the Algarve, in the south of Portugal. Data obtained in the region was collected and deviations from average values used were detected. Models were made taking into account the specific characteristics of the region. Heat flow, thermal conductivity, heat production, topography, gravity, seismic and geological data available for the region, are used to adapt the models. A special attention will be given to the spatial variation of heat flow values and to Moho depth in the region. The results show that this region is different from other parts of the Iberian Peninsula and a special attention must be given to it. The different values obtained using seismic, gravity, and geoid height data, and the results obtained with models using thermal data shows the importance of trying to know and understand the thermal structure of the regions. Problems related with the use of average values will be focused.

Crystal growth from undercooling melts under strong gradients of temperatures generating in short-duration microgravity

Crystal growth of bulk CdTe in short-duration microgravity is performed by the unidirectional cooling method. The largest growth grains in microgravity samples are 4X2mm. The cooling profiles indicate undercooling melts in microgravity. Cooling melt samples in microgravity generate strong gradient of temperature due to stop thermal convections. Temperature distribution in the melt is calculated by the one-dimensional equation of heat conduction, and about 100 K-undercooling is considered to occur at the cooling surface.

Catalytic probes with nanostructured surface for gas/discharge diagnostics : a study of a probe signal behaviour

Catalytic probes are used for plasma diagnostics in order to quantify the density of neutral atoms. The probe response primarily depends on the probe material and its surface morphology. Here we report on the design, operation and modelling of the response of niobium pentoxide sensors with a flat and nanowire (NW) surfaces. These sensors were used to detect neutral oxygen atoms in the afterglow region of an inductively coupled rf discharge in oxygen. A very different response of the flat-surface and NW probes to the varying densities of oxygen atoms was explained by modelling heat conduction and taking into account the associated temperature gradients. It was found that the nanostructure probe can measure in a broader range than the flat oxide probe due to an increase in the surface to volume ratio, and the presence of nanostructures which act as a thermal barrier against sensor overheating. These results can be used for the development of the new generation of catalytic probes for gas/discharge diagnostics in a range of industrial and environmental applications.

Multiphysics modelling of the metals casting process

Metals casting is a process governed by the interaction of a range of physical phenomena. Most computational models of this process address only what are conventionally regarded as the primary phenomena-heat conduction and solidification. However, to predict the formation of porosity (a factor of key importance in cast quality) requires the modelling of the interaction of the fluid flow, heat transfer, solidification and the development of stress-deformation in the solidified part of a component. In this paper, a model of the casting process is described which addresses all the main continuum phenomena involved in a coupled manner. The model is solved numerically using novel finite volume unstructured mesh techniques, and then applied to both the prediction of shape deformation (plus the subsequent formation of a gap at the metal-mould interface and its impact on the heat transfer behaviour) and porosity formation in solidifying metal components. Although the porosity prediction model is phenomenologically simplistic it is based on the interaction of the continuum phenomena and yields good comparisons with available experimental results. This work represents the first of the next generation of casting simulation tools to predict aspects of the structure of cast components.

Thermal transport in out-of-equilibrium quantum harmonic chains

We address the problem of heat transport in a chain of coupled quantum harmonic oscillators, exposed to the influences of local environments of various nature, stressing the effects that the specific nature of the environment has on the phenomenology of the transport process. We study in detail the behavior of thermodynamically relevant quantities such as heat currents and mean energies of the oscillators, establishing rigorous analytical conditions for the existence of a steady state, whose features we analyze carefully. In particular, we assess the conditions that should be faced to recover trends reminiscent of the classical Fourier law of heat conduction and highlight how such a possibility depends on the environment linked to our system.