Rigorous scaling law for the heat current in disordered harmonic chain

We study the energy current in a model of heat conduction, first considered in detail by Casher and Lebowitz. The model consists of a one-dimensional disordered harmonic chain of n i.i.d. random masses, connected to their nearest neighbors via identical springs, and coupled at the boundaries to Langevin heat baths, with respective temperatures T_1 and T_n. Let EJ_n be the steady-state energy current across the chain, averaged over the masses. We prove that EJ_n \sim (T_1 - T_n)n^{-3/2} in the limit n \to \infty, as has been conjectured by various authors over the time. The proof relies on a new explicit representation for the elements of the product of associated transfer matrices.

Harvesting undelimbed Scots pine (Pinus sylvestris L.) from first thinnings for integrated production of kraft pulp and energy

The present study evaluates the feasibility of undelimbed Scots pine (Pinus sylvestris L.) for integrated production of pulp and energy in a kraft pulp mill from the technical, economic and environmental points of view, focusing on the potential of bundle harvesting. The feasibility of tree sections for pulp production was tested by conducting an industrial wood-handling experiment, laboratory cooking and bleaching trials, using conventional small-diameter Scots pine pulpwood as a reference. These trials showed that undelimbed Scots pine sections can be processed in favourable conditions as a blend with conventional small-diameter pulpwood without reducing the pulp quality. However, fibre losses at various phases of the process may increase when using undelimbed material. In the economic evaluation, both pulp production and wood procurement costs were considered, using the relative wood paying capability of a kraft pulp mill as a determinant. The calculations were made for three Scots pine first-thinning stands with the breast-height diameter of the removal (6 12 cm) as the main distinctive factor. The supply chains included in the comparison were based on cut-to-length harvesting, whole-tree harvesting and bundle harvesting (whole-tree bundling). With the current ratio of pulp and energy prices, the wood paying capability declines with an increase in the proportion of the energy fraction of the raw material. The supply system based on the cut-to-length method was the most efficient option, resulting in the highest residual value at stump in most cases. A decline in the pulp price and an increase in the energy price improved the competitiveness of the whole-tree systems. With short truck transportation distances and low pulp prices, however, the harvesting of loose whole trees can result in higher residual value at stump in small-diameter stands. While savings in transportation costs did not compensate for the high cutting and compaction costs by the second prototype of the bundle harvester, an increase in transportation distances improved its competitiveness. Since harvesting undelimbed assortments increases nutrient export from the site, which can affect soil productivity, the whole-tree alternatives included in the present study cannot be recommended on infertile peatlands and mineral soils. The harvesting of loose whole trees or bundled whole trees implies a reduction in protective logging residues and an increase in site traffic or payloads. These factors increase the risk of soil damage, especially on peat soils with poor bearing capacity. Within the wood procurement parameters which were examined, the CO2 emissions of the supply systems varied from 13 27 kg m3. Compaction of whole trees into bundles reduced emissions from transportation by 30 39%, but these reductions were insufficient to compensate for the increased emissions from cutting and compaction.