Approximate Euclidean Steiner trees

An approximate Steiner tree is a Steiner tree on a given set of terminals in Euclidean space such that the angles at the Steiner points are within a specified error e from 120 degrees. This notion arises in numerical approximations of minimum Steiner trees (W. D. Smith, Algorithmica, 7 (1992), 137–177). We investigate the worst-case relative error of the length of an approximate Steiner tree compared to the shortest tree with the same topology. Rubinstein, Weng and Wormald (J. Global Optim. 35 (2006), 573–592) conjectured that this relative error is at most linear in e, independent of the number of terminals. We verify their conjecture for the two-dimensional case as long as the error e is sufficiently small in terms of the number of terminals. We derive a lower bound linear in e for the relative error in the two-dimensional case when e is sufficiently small in terms of the number of terminals. We find improved estimates of the relative error for larger values of e, and calculate exact values in the plane for three and four terminals

IPEM code of practice for high-energy photon therapy dosimetry based on the NPL absorbed dose calibration service

The 1990 code of practice (COP), produced by the IPSM (now the Institute of Physics and Engineering in Medicine, IPEM) and the UK National Physical Laboratory (NPL), gave instructions for determining absorbed dose to water for megavoltage photon (MV) radiotherapy beams (Lillicrap et al 1990). The simplicity and clarity of the 1990 COP led to widespread uptake and high levels of consistency in external dosimetry audits. An addendum was published in 2014 to include the non-conventional conditions in Tomotherapy units. However, the 1990 COP lacked detailed recommendations for calibration conditions, and the corresponding nomenclature, to account for modern treatment units with different reference fields, including small fields as described in IAEA TRS483 (International Atomic Energy Agency (IAEA) 2017, Vienna). This updated COP recommends the irradiation geometries, the choice of ionisation chambers, appropriate correction factors and the derivation of absorbed dose to water calibration coefficients, for carrying out reference dosimetry measurements on MV external beam radiotherapy machines. It also includes worked examples of application to different conditions. The strengths of the 1990 COP are retained: recommending the NPL2611 chamber type as secondary standard; the use of tissue phantom ratio (TPR) as the beam quality specifier; and NPL-provided direct calibration coefficients for the user's chamber in a range of beam qualities similar to those in clinical use. In addition, the formalism is now extended to units that cannot achieve the standard reference field size of 10 cm × 10 cm, and recommendations are given for measuring dose in non-reference conditions. This COP is designed around the service that NPL provides and thus it does not require the range of different options presented in TRS483, such as generic correction factors for beam quality. This approach results in a significantly simpler, more concise and easier to follow protocol

A combined modeling and experimental study on low- and high-temperature oxidation chemistry of OME3 as novel fuel additive

International audienceThe present research focuses on combined modeling and experimental work on the com-bustion of oxymethylene ethers (OMEs). OMEs are promising synthetic fuels which can beproduced in a carbon-neutral manner starting from captured CO2 and renewable energy.Moreover, blending them with conventional diesel reduces soot emissions because of the ab-sence of carbon-carbon bonds. This results in less harmful emissions and contributes to amore sustainable transport sector as aimed by the Paris climate agreement objectives. Topromote the use of these kind of molecules as fuel additive, it is important to understand theirlow- and high-temperature combustion kinetics. The development of detailed microkineticmodels provides this fundamental insight and enables predictive simulations for combustionapplications.During the last decade, great progress has been made in the construction of reliable kineticmodels for numerous technologically important radical chemistry processes. The resultingmodels typically contain hundreds of species, and several thousands of associated reactions.The manual generation of microkinetic models would be a tedious, error prone and oftenincomplete process. To prevent this, automatic kinetic model generation routines have beendeveloped to systematically develop models, such as Genesys at the Laboratory for Chemi-cal Technology (Ghent University). A kinetic model for both oxidation and pyrolysis hasbeen developed for OME3 based on first principles using Genesys.A prerequisite for the generation of detailed kinetic models is the availability of accuratethermodynamic and kinetic data for species and reactions respectively. Ideally, these pa-rameters are available from experiments or high-level quantum chemical calculations. Sincethese methods are expensive and time-consuming, Genesys instead often relies on approxi-mation methods such as group additivity and rate rules. In this work, thermodynamic andkinetic parameters are obtained from quantum chemical calculations at the CBS-QB3 levelof theory for important reaction pathways for both low- and high- temperature oxidation ofOME3. The results of these calculations are extrapolated to be valid for long-chain OMEsby regression of new group additive values and rate rules.Within Genesys, the possible reactions are generally defined in terms of reaction families,e.g. hydrogen abstraction by molecular oxygen from a secondary carbon atom. Reactionfamilies from earlier studies on smaller oxymethylene ethers such as dimethoxy methaneare taken over and applied for the OME3 model. The outcome is a model containing thechemistry for OME3. To include the chemistry of smaller (oxygenated) hydrocarbons in thefinal model, the Genesys model is merged with the AramcoMech 1.3 base model.Both at ame burner and rapid compression machine experiments have been performedwith OME3 for validation of the combustion model. The ame experiments are performedat 0.053 bara and with a fuel composition of 20 mol% OME3 and 80 mol% CH4. Some mea-sured concentration profiles in function of the height above burner (HAB) of small species(i.e. OME3, CH2O, CH3OH, H2, CO2 and CO) are shown in Figure 1. Other impor-tant species which are observed include ethane, ethylene, dimethyl ether, methyl formate,dimethoxy methane and methoxymethyl formate.Ignition delay times have been measured via rapid compression at 5 bara for and to ad-ditionally validate the low-temperature section of the model. Samples were taken to identifythe reactants and products, including OME3, methyl formate, methoxymethyl formate andmethoxymethoxymethyl formate. Similarly, pyrolysis experiments are performed for OME3in a bench-scale steam cracker setup over a broad range of temperatures (723 K - 1073 K)to validate both the primary and secondary chemistry of the pyrolysis model