A distributional approach to the geometry of dislocations at the mesoscale

We develop a theory to represent dislocated single crystals at the mesoscopic scale by considering concentrated effects, governed by the distribution theory combined with multiple-valued kinematic fields. Our approach gives a new understanding of the continuum theory of defects as developed by Kroener (1980) and other authors. Fundamental 2D identities relating the incompatibility tensor to the Frank and Burgers vectors are proved under global strain assumptions relying on the geometric measure theory, thereby giving rise to rigorous homogenisation from mesoscopic to macroscopic scale.Comment: article soumi

Multi-Granular Trend Detection for Time-Series Analysis

Time series (such as stock prices) and ensembles (such as model runs for weather forecasts) are two important types of one-dimensional time-varying data. Such data is readily available in large quantities but visual analysis of the raw data quickly becomes infeasible, even for moderately sized data sets. Trend detection is an effective way to simplify time-varying data and to summarize salient information for visual display and interactive analysis. We propose a geometric model for trend-detection in one-dimensional time-varying data, inspired by topological grouping structures for moving objects in two- or higher-dimensional space. Our model gives provable guarantees on the trends detected and uses three natural parameters: granularity, support-size, and duration. These parameters can be changed on-demand. Our system also supports a variety of selection brushes and a time-sweep to facilitate refined searches and interactive visualization of (sub-)trends. We explore different visual styles and interactions through which trends, their persistence, and evolution can be explored

Corrigendum: Short-lived positron emitters in beam-on PET imaging during proton therapy (2015 Phys. Med. Biol. 60 8923)

Because of strong indications of multiple counting by the multi-channel scaler (MCS) during most of the experiments described in Dendooven et al (2015 Phys. Med. Biol. 60 8923–47), the production of short-lived positron emitters in the stopping of 55 MeV protons in water, carbon, phosphorus and calcium was remeasured. The new results are reported here. With proper single counting of the MCS, the new production rates are 1.1 to 2.9 times smaller than reported in Dendooven et al (2015 Phys. Med. Biol. 60 8923–47). The omission of the conversion from MCS time bin to time unit in the previous data analysis was corrected, leading to an increase of the production rate by a factor of 2.5 or 10 for some nuclides. The most copiously produced short-lived nuclides and their production rates relative to the relevant long-lived nuclides are: 12N (T 1/2  =  11 ms) on carbon (5.3% of 11C), 29P (T 1/2  =  4.1 s) on phosphorus (23% of 30P) and 38mK (T 1/2  =  0.92 s) on calcium (173% of 38gK). The number of decays integrated from the start of an irradiation as a function of time during the irradiation of PMMA and 4 tissue materials has been determined. For (carbon-rich) adipose tissue, 12N dominates up to 70 s. On bone tissue, 38mK dominates the beam-on PET counts from 0.2–0.7 s until about 80–110 s. Considering nuclides created on phosphorus and calcium, the short-lived ones provide 8 times more decays than the long-lived ones during a 70 s irradiation. Bone tissue will thus be much better visible in beam-on PET compared to PET imaging after an irradiation. From the estimated number of 12N PET counts, we conclude that, for any tissue, except carbon-poor ones, 12N PET imaging potentially provides equal quality proton range information as prompt gamma imaging with an optimized knife-edge slit camera

Synthesis–Structure–Activity Relations in Fe-CHA for C–H Activation: Control of Al Distribution by Interzeolite Conversion

The search for structurally relevant Al-arrangements in zeolites is an important endeavor for single site catalysis. Little is known about the mechanisms and zeolite dynamics during synthesis that are responsible for creating those Al-ensembles. Here, new synthetic strategies for creating Al-hosts in small-pore zeolites suitable for divalent cation catalysis are uncovered, leading to a mechanistic proposal for Al-organization during crystallization. As such, unique synthesis-structure-activity relations are demonstrated for the partial oxidation of methane on Fe-exchanged CHA-zeolites. With modified interzeolite conversions, the divalent cation capacity of the resulting high Si SSZ-13 zeolites (Si/Al ~ 35) can be reproducibly controlled in a range between 0.04 and 0.34 Co²⁺/Al. This capacity is a proxy for the distribution of framework aluminum in pairs and correlates with the methanol production per Al when these zeolites host the α-Fe^(II) redox active site. The uncovered IZC synthesis-structure relations paint an Al-distribution hypothesis, where incongruent dissolution of the starting USY zeolite and fast synthesis kinetics with atypical growth modes allow assembling specific Al-arrangements, resulting in a high divalent cation capacity. Prolonged synthesis times and high temperatures overcome the energetic barriers for T-atom reshuffling favoring Al-isolation. These mechanisms and the relations uncovered in this work will guide the search for relevant Al-ensembles in a range of zeolite catalysts where controlling the environment for a single active site is crucial