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We consider the probabilities of transmission pT and reflection pR of a quantum particle incident upon potential drops with significant qualitative differences. We look at a smooth potential drop for which the potential and the derivative of the potential are continuous. We also consider a potential drop which is continuous but has discontinuities in its derivative. The two cases give markedly different results for the limiting values of pT and pR with increasing values of the total potential drop V0. We explore the difference in the results using potentials that can be adjusted to go from continuous to discontinuous first derivatives. We also investigate potentials with more severe discontinuities in the derivative of the potential.

This article examines resonant tunnelling of multi-atomic systems, extending the body of work on resonant tunnelling in this area beyond diatomic homo-nuclear systems. We consider diatomic molecules with distinct atoms having different masses, and linear triatomic molecules with indistinguishable atoms. The molecule is incident in the bound state upon a step potential with an energy increase of V0 for each atom. We calculate the probabilities of reflection pR and transmission pT in the bound state and the dependence on the energy of the molecule. We find that, as was the case for the homo-nuclear molecule, resonant transmission for diatomic molecules with distinguishable atoms occurs for arbitrarily weak binding, and pT is close to one for finite binding energy. We also find resonant transmission for linear triatomic molecules. We show results for the time-dependent Schrödinger equation which agree with resonant transmission. We also consider the transmission of an N-atom one-dimensional molecule.

A mixture of waste-wood biomass and municipal biosolids waste was composted in a plastic container inside of an insulated chamber. The mixture of biomass and biosolids was approximately 50:50 and weighed 82.6 kg. The peak temperature of the compost was 32.4◦C. The small scale of the compost system allowed the lower limit of the compost decomposition rate to be studied. A model was successfully developed to predict the core temperature of the compost using the ambient temperature in the insulated chamber. A literature review was conducted to determine literature values for the overall convective and conductive heat transfer coefficient, the dry mass fraction, and heat of combustion for both biomass and biosolids. The model used an optimization algorithm to calculate the rate constant for the experimental setup. The calculated decomposition rate constant was 0.0525 Day−1.