Modular graph forms from equivariant iterated Eisenstein integrals

The low-energy expansion of closed-string scattering amplitudes at genus one introduces infinite families of non-holomorphic modular forms called modular graph forms. Their differential and number-theoretic properties motivated Brown’s alternative construction of non-holomorphic modular forms in the recent mathematics literature from so-called equivariant iterated Eisenstein integrals. In this work, we provide the first validations beyond depth one of Brown’s conjecture that equivariant iterated Eisenstein integrals contain modular graph forms. Apart from a variety of examples at depth two and three, we spell out the systematics of the dictionary and make certain elements of Brown’s construction fully explicit to all orders

Microcellular wood-fibre thermoplastic composites, processing-structure-properties

grantor: University of TorontoIn this study, processing-structure-property relationships in foamed wood-fibre plastic composites made with a physical blowing agent were investigated. For the polymers studied, it was found that the crystallinity and morphology have a critical effect on the foaming process. Therefore, an investigation of both semicrystalline and amorphous polymers was conducted. Several amorphous and semicrystalline polymers were selected, based on preliminary experimental results. By non-isothermal crystallisation of the semicrystalline polymers at various cooling rates, specimens with different crystallinities and crystal morphologies were made. The microstructures and sorption properties of these specimens were studied. All the specimens were foamed in a batch process using carbon dioxide as blowing agent and their structures were, investigated. The results showed a great influence of crystallinity and morphology on the solubility and diffusivity of the blowing agent in and through the polymer and especially on the cellular structure of the resulting foams. In contrast to the work of Colton (1989), who suggested that the foaming process should be conducted at a temperature above the melting point, it was shown that by controlling the crystallinity and crystal morphology it is feasible to produce microcellular foams from semicrystalline polymers in the solid state. In the second phase of the study, high density polyethylene and polystyrene were used as the matrices in a foamed wood-fibre composite. Sheets of composites were produced by compounding polymers and fibre. These samples were saturated with carbon dioxide at high pressure and the saturated specimens were foamed at elevated temperatures. Structural analysis and characterisation were performed on both foamed and unfoamed samples. The experimental results showed that the addition of wood fibre had very different effects on the mechanical properties of polystyrene (a glassy polymer) and polyethylene (a semicrystalline ductile polymer). Fibres acted as nucleating agents in the crystallisation of the matrix, and drastically changed the morphology. The impact strength of PS increased when wood fibres were added, while wood fibre diminished the impact strength of PE. The presence of wood fibres significantly changed the microstructure of the composite in the foaming process. Overall, while diminishing the tensile properties (strength and modulus), foaming caused a significant improvement of impact strength of the wood-fibre composites.Ph.D

Integrated Lighting Efficiency Analysis in Large Industrial Buildings to Enhance Indoor Environmental Quality

We present observations from evaluation of internal environmental quality of industrial halls with priority on daylighting in combination with the integral lighting. The physical parameters related to indoor lighting in large industrial halls in winter and summer periods were analyzed using in situ measurements and computational methods. These are part of a comprehensive research on indoor environmental quality of industrial halls with the aims of saving energy and providing a comfortable environment for the workers while improving the productivity. The results showed that the procedures used for evaluation of residential or office buildings may not be used for industrial buildings. We also observed that the criteria of occupants’ comforts for indoor industrial buildings may differ from those of other kinds of buildings. Based on these results, an adequate attention is required for designing the industrial buildings. For this reason, appropriate evaluation methods and criteria should be created. We found the measured values of daylight factor very close to the skylight component of the total illumination. The skylight component was observed on average 30% that of the measured daylight factor values. Although the daylight is not emphasized when designing the industrial buildings and its contribution is small, but it is very important for the workers psychology and physiology. The workers must feel a connection with the exterior environment; otherwise, their productivity decreases