Digital Forestry: A white paper

Digital Forestry has been proposed as “the science, technology, and art of systematically acquiring, integrating, analyzing, and applying digital information to support sustainable forests.” Although rooted in traditional forestry disciplines, Digital Forestry draws from a host of other fields that, in the past few decades, have become important for implementing the concept of forest ecosystem management and the principle of sustainable forestry. Digital Forestry is a framework that links all facets of forestry information at local, national, and global levels through an organized digital network. It is anticipated that a new set of principles will be established when practicing Digital Forestry concept for the evolution of forestry education, research, and practices as the 21st century unfolds.

The collision branching process

We consider a branching model, which we call the collision branching process (CBP), that accounts for the effect of collisions, or interactions, between particles or individuals. We establish that there is a unique CBP, and derive necessary and sufficient conditions for it to be nonexplosive. We review results on extinction probabilities, and obtain explicit expressions for the probability of explosion and the expected hitting times. The upwardly skip-free case is studied in some detail.

[Book review] The Oxford Murders

Review of the book 'The Oxford Murders' by Guillermo Martínez (trans. by Sonia Soto), Abacus, 2005, £9.99, pp 208, ISBN 0-349-11721-7

Two-machine shop scheduling: Compromise between flexibility and makespan value

In this paper, we consider the problem of providing flexibility to solutions of two-machine shop scheduling problems. We use the concept of group-scheduling to characterize a whole set of schedules so as to provide more choice to the decision-maker at any decision point. A group-schedule is a sequence of groups of permutable operations defined on each machine where each group is such that any permutation of the operations inside the group leads to a feasible schedule. Flexibility of a solution and its makespan are often conflicting, thus we search for a compromise between a low number of groups and a small value of makespan. We resolve the complexity status of the relevant problems for the two-machine flow shop, job shop and open shop. A number of approximation algorithms are developed and their worst-case performance is analyzed. For the flow shop, an effective heuristic algorithm is proposed and the results of computational experiments are reported.

Two-machine flow shop scheduling problems with no-wait jobs

In this paper we provide a fairly complete complexity classification of various versions of the two-machine permutation flow shop scheduling problem to minimize the makespan in which some of the jobs have to be processed with no-wait in process. For some version, we offer a fully polynomial-time approximation scheme and a 43-approximation algorithm.

Pre-emptive scheduling problems with controllable processing times

We consider a range of single machine and identical parallel machine pre-emptive scheduling models with controllable processing times. For each model we study a single criterion problem to minimize the compression cost of the processing times subject to the constraint that all due dates should be met. We demonstrate that each single criterion problem can be formulated in terms of minimizing a linear function over a polymatroid, and this justifies the greedy approach to its solution. A unified technique allows us to develop fast algorithms for solving both single criterion problems and bicriteria counterparts.

Comparison between weight loss of bends in a pneumatic conveyor and erosion rate obtained in a centrifugal erosion tester for the same materials

In order to find a link between results obtained from a laboratory erosion tester and tests carried out on a pneumatic conveyor, a comparison has been made between weight loss from bends on an industrial-scale pneumatic conveyor and erosion rates obtained in a small centrifugal erosion tester, for the same materials. Identical test conditions have been applied to both experiments so that comparable test results have been obtained. The erosion rate of mild steel commonly used as the wall material of conveyor pipes and pipe bends was determined individually on both test rigs. A relationship between weight loss from the bends and erosion rate determined from the tester has been developed. A discussion based on the results and their applicability to the prediction of wear in pneumatic conveyors concludes the paper.

Effect of particle concentration on erosion rate of mild steel bends in a pneumatic conveyor

Particle concentration is known as a main factor that affects erosion rate of pipe bends in pneumatic conveyors. With consideration of different bend radii, the effect of particle concentration on weight loss of mild steel bends has been investigated in an industrial scale test rig. Experimental results show that there was a significant reduction of the specific erosion rate for high particle concentrations. This reduction was considered to be as a result of the shielding effect during the particle impacts. An empirical model is given. Also a theoretical study of scaling on the shielding effect, and comparisons with some existing models, are presented. It is found that the reduction in specific erosion rate (relative to particle concentration) has a stronger relationship in conveying pipelines than has been found in the erosion tester.

Effect of bend orientation on life and puncture point location due to solid particle erosion of a high concentration flow in pneumatic conveyors

An investigation into predicting failure of pneumatic conveyor pipe bends due to hard solid particle impact erosion has been carried out on an industrial scale test rig. The bend puncture point locations may vary with many factors. However, bend orientation was suspected of being a main factor due to the biased particle distribution pattern of a high concentration flow. In this paper, puncture point locations have been studied with different pipe bend orientations and geometry (a solids loading ratio of 10 being used for the high concentration flow). Test results confirmed that the puncture point location is indeed most significantly influenced by the bend orientation (especially for a high concentration flow) due to the biased particle distribution and biased particle flux distribution.

Spatial variability of air pollution in the vicinity of a permanent monitoring station in central Paris

The strong spatial and temporal variability of traffic-related air pollution detected at roadside locations in a number of European cities has raised the question of how representative the site and time period of air quality measurements actually can be. To address this question, a 7-month sampling campaign was carried out on a major road axis (Avenue Leclerc) leading to a very busy intersection (Place Basch) in central Paris, covering the surroundings of a permanent air quality monitoring station. This station has recorded the highest CO and NOx concentrations during recent years in the region of Paris. Diffusive BTX samplers as well as a mobile monitoring unit equipped with real-time CO, NOx and O3 analysers and meteorological instruments were used to reveal the small-scale pollution gradients and their temporal trends near the permanent monitoring station. The diffusive measurements provided 7-day averages of benzene, toluene, xylene and other hydrocarbons at different heights above the ground and distances from the kerb covering summer and winter periods. Relevant traffic and meteorological data were also obtained on an hourly basis. Furthermore, three semiempirical dispersion models (STREET-SRI, OSPM and AEOLIUS) were tested for an asymmetric canyon location in Av. Leclerc. The analysis of this comprehensive data set has helped to assess the representativeness of air quality monitoring information.

Maximising heat transfer efficiency in the cold crucible induction melting process

Induction heating is an efficient method used to melt electrically conductive materials, particularly if melting takes place in a ceramic crucible. This form of melting is particularly good for alloys, as electromagnetic forces set up by the induction coil lead to vigorous stirring of the melt ensuring homogeneity and uniformity in temperature. However, for certain reactive alloys, or where high purity is required, ceramic crucibles cannot be used, but a water-cooled segmented copper crucible is employed instead. Water cooling prevents meltdown or distortion of the metal wall, but much of the energy goes into the coolant. To reduce this loss, the electromagnetic force generated by the coil is used to push the melt away from the walls and so minimise contact with water-cooled surfaces. Even then, heat is lost through the crucible base where contact is inevitable. In a collaborative programme between Greenwich and Birmingham Universities, computer modelling has been used in conjunction with experiments to improve the superheat attainable in the melt for a,number of alloys, especially for y-TiAl intermetallics to cast aeroengine turbine blades. The model solves the discretised form of the turbulent Navier-Stokes, thermal energy conservation and Maxwell equations using a Spectral Collocation technique. The time-varying melt envelope is followed explicitly during the computation using an adaptive mesh. This paper briefly describes the mathematical model used to represent the interaction between the magnetic field, fluid flow, heat transfer and change of phase in the crucible and identifies the proportions of energy used in the melt, lost in the crucible base and in the crucible walls. The role of turbulence is highlighted as important in controlling heat losses and turbulence damping is introduced as a means of improving superheat. Model validation is against experimental results and shows good agreement with measured temperatures and energy losses in the cooling fluid throughout the melting cycle.

[Book review] Piero della Francesca: A Mathematician's art by J.V. Field, Yale University Press.

Review of the book 'Piero della Francesca: A Mathematician’s Art' by J.V. Field, Yale University Press, 420 pp, £35 ISBN 0300103425.

Multilevel refinement for the vehicle routing problem

Multilevel approaches to computational problems are pervasive across many areas of applied mathematics and scientific computing. The multilevel paradigm uses recursive coarsening to create a hierarchy of approximations to the original problem, then an initial solution is found for the coarsest problem and iteratively refined and improved at each level, coarsest to finest. The solution process is aided by the global perspective (or `global view') imparted to the optimisation by the coarsening. This paper looks at their application to the Vehicle Routing Problem.

Popular lectures report

This is a report of two lectures held by the London Mathematical Society: a) What Computers Cannot Do by Dr Alan Slomson; b) The Mathematics of Shrek by Dr Joan Lazenby.