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Many geometric and analytic properties of sets hinge on the properties of elliptic measure, notoriously missing for sets of higher co-dimension. The aim of this manuscript is to develop a version of elliptic theory, associated to a linear PDE, which ultimately yields a notion analogous to that of the harmonic measure, for sets of codimension higher than 1. To this end, we turn to degenerate elliptic equations. Let In another article to appear, we will prove that when

The existence and uniqueness of solutions to the Yang-Mills heat equation is proven over

PurposeThe purpose of this study is to perform the life cycle inventory (LCI) to continuous casting of steel (CCS) process in integrated steel plant (ISP) in Krakow, Poland. The present LCI is representative for year 2015 by application of PN-EN ISO 14040 (2009). The system boundary was labeled as gate to gate. The background input and output data from the CCS has been inventoried as follows: consumption of energy and fuels, materials inputs, and waste.MethodsIn this paper, LCI CCS process on integrated permit (secondary data), literature information, and expert consultations was developed. The functional unit (FU) is represented by 1 t of steel slabs produced by CCS. Operating parameters as well as air emissions associated with the CCS process were presented. The production data (slabs) was given. The emissions of dust, Fe, PM10 and PM2.5, and waste (iron dust, iron particles, the others) are outcomes of the CCS processes.Results and discussionAnnually production of steel slabs in CCS plant amounted to 200,000 t. Coke oven gas, natural gas, steam, air, oxygen, casting powders for crystallizer and for intermediate tundish, refractory material, oil, lubricant, argon, and industrial water amounts were in the order of 2,750,000 Nm3/year, 770,000 Nm3/year, 2000 t/year, 90,000,000 Nm3/year, 970 t/year, 1300 t/year, 810 t/year, 30 t/year, 45 t/year, 330 t/year, and 13,175,300 m3/year, respectively. The average heat and electric energy consumptions were about 0.023 to 0.068 GJ/t and 12.0 to 17.2 kWh/t, respectively. Emissions in air of dust, Fe, PM10, and PM2.5 were in the order of 1.3, 0.1, 0.5, and 0.44 kg/h, respectively. The amounts of iron dust and the other waste were 200 t/year and 240 t, respectively. No information is available on CO2 emission.ConclusionsThe LCI study resulted in the development of a database with an inventory of secondary data regarding CCS process referring to the year 2015. The scope of this study considered input items needed in CCS production (entry gate) to the final delivery of steel slabs (exit gate). The raw materials, supplies, and equipment to the CCS plant and infrastructure are not taken into consideration in the analysis. The FU is 1 t of steel slabs.Recommendations and outlookThe LCI offers environmental information consisting of the list of environmental loads. The impact assessment phase aims to present more understandable results from the inventory analysis, and life cycle impact assessment will be the direction for future research.

Life cycle carbon emissions (LCO2), made up of operational and embodied carbon, have become a major metric of building environmental performance and energy efficiency. Whilst there are now standard methods for operational carbon assessment due to its significance in LCO2, there is still less emphasis on embodied carbon counting. However, the relative contribution of embodied carbon is on the rise as buildings become increasingly energy efficient. Following the rule that only something which is measurable is manageable, it is essential that we are able to accurately count embodied carbon. This study therefore reviews the concept of LCO2 in buildings and further investigates the open source UK tools for embodied carbon counting. A comparative evaluation case study, which validates an earlier review, showed that there is no logic and consistency in the carbon figures produced by embodied carbon counting tools. This is mainly due to different system boundaries, varying underlying assumptions and methodological differences in calculation. The findings suggest that an industry-agreed data structure and common methodology is needed for embodied carbon counting. Generally, the study provides insights into the use and capabilities of the identified open source UK embodied carbon counting tools and is relevant to the on-going debate about carbon regulation.

To assess the potential environmental impact of human/industrial systems, life cycle assessment (LCA) is a very common method. There are two prominent types of LCA, namely attributional (ALCA) and consequential (CLCA). A lot of literature covers these approaches, but a general consensus on what they represent and an overview of all their differences seems lacking, nor has every prominent feature been fully explored. The two main objectives of this article are: (1) to argue for and select definitions for each concept and (2) specify all conceptual characteristics (including translation into modelling restrictions), re-evaluating and going beyond findings in the state of the art. For the first objective, mainly because the validity of interpretation of a term is also a matter of consensus, we argue the selection of definitions present in the 2011 UNEP-SETAC report. ALCA attributes a share of the potential environmental impact of the world to a product life cycle, while CLCA assesses the environmental consequences of a decision (e.g., increase of product demand). Regarding the second objective, the product system in ALCA constitutes all processes that are linked by physical, energy flows or services. Because of the requirement of additivity for ALCA, a double-counting check needs to be executed, modelling is restricted (e.g., guaranteed through linearity) and partitioning of multifunctional processes is systematically needed (for evaluation per single product). The latter matters also hold in a similar manner for the impact assessment, which is commonly overlooked. CLCA, is completely consequential and there is no limitation regarding what a modelling framework should entail, with the coverage of co-products through substitution being just one approach and not the only one (e.g., additional consumption is possible). Both ALCA and CLCA can be considered over any time span (past, present & future) and either using a reference environment or different scenarios. Furthermore, both ALCA and CLCA could be specific for average or marginal (small) products or decisions, and further datasets. These findings also hold for life cycle sustainability assessment.

Ocean boundary current systems are key components of the climate system, are home to highly productive ecosystems, and have numerous societal impacts. Establishment of a global network of boundary current observing systems is a critical part of ongoing development of the Global Ocean Observing System. The characteristics of boundary current systems are reviewed, focusing on scientific and societal motivations for sustained observing. Techniques currently used to observe boundary current systems are reviewed, followed by a census of the current state of boundary current observing systems globally. Next steps in the development of boundary current observing systems are considered, leading to several specific recommendations.

This paper is dedicated to a free boundary system arising in the study of a class of shape optimization problems. The problem involves three variables: two functions u and v , and a domain ; with u and v being both positive in , vanishing simultaneously on , and satisfying an overdetermined boundary value problem involving the product of their normal derivatives on . Precisely, we consider solutions u, v ın C(B_1) of - u= f \\ and \\ - v=g =\\u>0\\=\\v>0\\, u n v n=Q B_1. Our main result is an epsilon-regularity theorem for viscosity solutions of this free boundary system. We prove a partial Harnack inequality near flat points for the couple of auxiliary functions uv and 12(u+v) . Then, we use the gained space near the free boundary to transfer the improved flatness to the original solutions. Finally, using the partial Harnack inequality, we obtain an improvement-of-flatness result, which allows to conclude that flatness implies C^1, regularity.

Purpose A large proportion of the environmental impacts of a technology is determined by decisions made at the early development stages. Therefore, effective approaches to grasp the potential environmental performance of a technology early in development are needed. This paper reflects on the usefulness of ex ante application of LCA using a case study on the appraisal of the potential environmental impacts of a lab-scale novel process for bioleaching of e-waste for metal recovery. Methods The LCA framework was applied at an early stage to the novel bioleaching process to embed it in a life cycle context, linking it to upstream and downstream flows. Then, a short-term future scaled-up scenario was defined using a proxy technology and estimated data. Environmental hotspots of this scenario were identified, and its environmental impacts were compared with those of a current industrial pyrometallurgical technique, involving an integrated smelter refinery. Results and discussion LCA displays potential environmental hotspots related to energy and material inputs for the bioleaching process and solvents for copper recovery, despite uncertainties. Comparison with an existing integrated smelter refinery technology returned an inferior environmental performance. These results could not be considered accurate given the early-stage application, yet they served as valuable preliminary information. The uncertainties also prompted further enquiry about the chosen product system boundary, the role of the emerging technology and the comparability of the technologies. Conclusions The ex ante application of life cycle assessment on an emerging technology brings a systematic rigour and discipline to an ambiguous situation at the start of technological development. Applying the LCA framework broadens the scope of the research, introducing a systems approach and long-term view. Environmental aspects and alternative perspectives on the novel technology are also brought into the research domain. The approach creates new knowledge on the novel technology’s potential development, and developmental challenges are given definition at an early stage. The LCA outcomes should not be regarded as a final result but have a signalling purpose as a contribution to technological development. Though imprecise with much conjecture involved, such an approach gives a valid mock-up of a plausible future providing useful provisional insights to be built upon. Applying ex ante LCA and an exploratory scenario to an emerging technology is of great service as a developmental design tool and can be further refined in later development stages.

PurposeTransition to bioeconomy requires all actors and stakeholders to measure the impact of systems that use bioresources and technologies to provision society. There are however some challenges with integrating LCA into business development and management, which have important implications for bioeconomy. There have been many LCA studies published in the twenty-first century, but the question must be answered: how useful are these LCA studies to help understand and manage transition to sustainable bioeconomy?MethodThis research used a structured literature review to identify 83 bioeconomy LCA studies published from January 2006 to June 2021 (excluding bioenergy). The studies were analysed for compliance with the ISO 14044 standard, with specific reference to the goal, commissioning perspective, system boundary, function and functional unit, impact methods and categories.Results and discussionsIt was found that more than 85% of the studies reviewed failed to present the required goal statement and a description of the function of the system. Nearly 13% of the studies did not define the system boundary, and only 17% included a full life cycle including raw material extraction, production, use and end-of-life stages. The majority of the LCA studies surveyed from 2006 to 2021 were either (i) not in compliance with the ISO standards or (ii) space and style limitations of the publication process prevented competent practitioners from properly conveying their work. This suggests that the value and integrity of the literature are undermined by not rigorously addressing the first and most important stage of an LCA study.ConclusionWhen interpreting the results, a major shortcoming noted was that most studies did not consider the industrial symbiosis needed between feedstock, technology, primary products, side streams, downstream valorisation and long-term circularity in order to properly understand the transition pathways required. Bioeconomy technologies were imagined as displacers for feedstocks and processes to adapt business as usual, rather than as transformers of the system to a sustainable footing.RecommendationIf LCA studies are going to provide meaningful information for actors and stakeholders to assess whether a system will be able to operate sustainably, studies should include a full, integrated system, standards should be adhered to and approaches should perhaps go beyond mere eco-efficiency, or doing less harm, as these are not necessarily indicative of sustainability. Historical bioeconomy LCA studies do not provide great insight into the transition to sustainable bioeconomy.