Gross direct and embodied carbon sinks for urban inventories

Cities and urban regions are undertaking efforts to quantify greenhouse (GHG) emissions from their jurisdictional boundaries. Although inventorying methodologies are beginning to standardize for GHG sources, carbon sequestration is generally not quantified. This article describes the methodology and quantification of gross urban carbon sinks. Sinks are categorized into direct and embodied sinks. Direct sinks generally incorporate natural process, such as humification in soils and photosynthetic biomass growth (in urban trees, perennial crops, and regional forests). Embodied sinks include activities associated with consumptive behavior that result in the import and/or storage of carbon, such as landfilling of waste, concrete construction, and utilization of durable wood products. Using methodologies based on the Intergovernmental Panel on Climate Change 2006 guidelines (for direct sinks) and peer-reviewed literature (for embodied sinks), carbon sequestration for 2005 is calculated for the Greater Toronto Area. Direct sinks are found to be 317 kilotons of carbon (kt C), and are dominated by regional forest biomass. Embodied sinks are calculated to be 234 kt C based on one year's consumption, though a complete life cycle accounting of emissions would likely transform this sum from a carbon sink to a source. There is considerable uncertainty associated with the methodologies used, which could be addressed with city-specific stock-change measurements. Further options for enhancing carbon sink capacity within urban environments are explored, such as urban biomass growth and carbon capture and storage.

Greenhouse gas emissions from waste management—assessment of quantification methods

Of the many sources of urban greenhouse gas (GHG) emissions, solid waste is the only one for which management decisions are undertaken primarily by municipal governments themselves and is hence often the largest component of cities’ corporate inventories. It is essential that decision-makers select an appropriate quantification methodology and have an appreciation of methodological strengths and shortcomings. This work compares four different waste emissions quantification methods, including Intergovernmental Panel on Climate Change (IPCC) 1996 guidelines, IPCC 2006 guidelines, U.S. Environmental Protection Agency (EPA) Waste Reduction Model (WARM), and the Federation of Canadian Municipalities- Partners for Climate Protection (FCM-PCP) quantification tool. Waste disposal data for the greater Toronto area (GTA) in 2005 are used for all methodologies; treatment options (including landfill, incineration, compost, and anaerobic digestion) are examined where available in methodologies. Landfill was shown to be the greatest source of GHG emissions, contributing more than three-quarters of total emissions associated with waste management. Results from the different landfill gas (LFG) quantification approaches ranged from an emissions source of 557 kt carbon dioxide equivalents (CO2e) (FCM-PCP) to a carbon sink of −53 kt CO2e (EPA WARM). Similar values were obtained between IPCC approaches. The IPCC 2006 method was found to be more appropriate for inventorying applications because it uses a waste-in-place (WIP) approach, rather than a methane commitment (MC) approach, despite perceived onerous data requirements for WIP. MC approaches were found to be useful from a planning standpoint; however, uncertainty associated with their projections of future parameter values limits their applicability for GHG inventorying. MC and WIP methods provided similar results in this case study; however, this is case specific because of similarity in assumptions of present and future landfill parameters and quantities of annual waste deposited in recent years being relatively consistent.

Reduced relative entropy techniques for a posteriori analysis of multiphase problems in elastodynamics

We give an a posteriori analysis of a semidiscrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics, which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (2014, SIAM J. Math. Anal., 46, 3518–3539). This framework allows energy-type arguments to be applied to continuous functions. Since we advocate the use of discontinuous Galerkin methods we make use of two families of reconstructions, one set of discrete reconstructions and a set of elliptic reconstructions to apply the reduced relative entropy framework in this setting.

Reduced relative entropy techniques for a priori analysis of multiphase problems in elastodynamics

We give an a priori analysis of a semi-discrete discontinuous Galerkin scheme approximating solutions to a model of multiphase elastodynamics which involves an energy density depending not only on the strain but also the strain gradient. A key component in the analysis is the reduced relative entropy stability framework developed in Giesselmann (SIAM J Math Anal 46(5):3518–3539, 2014). The estimate we derive is optimal in the L∞(0,T;dG) norm for the strain and the L2(0,T;dG) norm for the velocity, where dG is an appropriate mesh dependent H1-like space.

Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

Long-term positive effects of repeating a year in school: Six-year longitudinal study of self-beliefs, anxiety, social relations, school grades, and test scores

Consistently with a priori predictions, school retention (repeating a year in school) had largely positive effects for a diverse range of 10 outcomes (e.g., math self-concept, self-efficacy, anxiety, relations with teachers, parents and peers, school grades, and standardized achievement test scores). The design, based on a large, representative sample of German students (N = 1,325, M age = 11.75 years) measured each year during the first five years of secondary school, was particularly strong. It featured four independent retention groups (different groups of students, each repeating one of the four first years of secondary school, total N = 103), with multiple post-test waves to evaluate short- and long-term effects, controlling for covariates (gender, age, SES, primary school grades, IQ) and one or more sets of 10 outcomes realised prior to retention. Tests of developmental invariance demonstrated that the effects of retention (controlling for covariates and pre-retention outcomes) were highly consistent across this potentially volatile early-to-middle adolescent period; largely positive effects in the first year following retention were maintained in subsequent school years following retention. Particularly considering that these results are contrary to at least some of the accepted wisdom about school retention, the findings have important implications for educational researchers, policymakers and parents.