A Fast Algorithm for Computing the p-Curvature

We design an algorithm for computing the $p$-curvature of a differential system in positive characteristic $p$. For a system of dimension $r$ with coefficients of degree at most $d$, its complexity is \softO (p d r^\omega) operations in the ground field (where $\omega$ denotes the exponent of matrix multiplication), whereas the size of the output is about $p d r^2$. Our algorithm is then quasi-optimal assuming that matrix multiplication is (\emph{i.e.} $\omega = 2$). The main theoretical input we are using is the existence of a well-suited ring of series with divided powers for which an analogue of the Cauchy--Lipschitz Theorem holds.Comment: ISSAC 2015, Jul 2015, Bath, United Kingdo

Inhibited aluminization of an ODS FeCr alloy

Aluminide coatings are of interest for fusion energy applications both for compatibility with liquid Pb-Li and to form an alumina layer that acts as a tritium permeation barrier. Oxide dispersion strengthened (ODS) ferritic steels are a structural material candidate for commercial reactor concepts expected to operate above 600 °C. Aluminizing was conducted in a laboratory scale chemical vapor deposition reactor using accepted conditions for coating Fe- and Ni base alloys. However, the measured mass gains on the current batch of ODS Fe-14Cr were extremely low compared to other conventional and ODS alloys. After aluminizing at two different Al activities at 900 °C and at 1100 °C, characterization showed that the ODS Fe-14Cr specimens formed a dense, primarily AlN layer that prevented Al uptake. This alloy batch contained a higher (> 5000 ppma) N content than the other alloys coated and this is the most likely reason for the inhibited aluminization. Other factors such as the high O content, small (~ 140 nm) grain size and Y-Ti oxide nano-clusters in ODS Fe-14Cr also could have contributed to the observed behavior. Examples of typical aluminide coatings formed on conventional and ODS Fe- and Ni-base alloys are shown for comparison

On the reduction of the degree of linear differential operators

Let L be a linear differential operator with coefficients in some differential field k of characteristic zero with algebraically closed field of constants. Let k^a be the algebraic closure of k. For a solution y, Ly=0, we determine the linear differential operator of minimal degree M and coefficients in k^a, such that My=0. This result is then applied to some Picard-Fuchs equations which appear in the study of perturbations of plane polynomial vector fields of Lotka-Volterra type

Mechanistic-Based Lifetime Predictions for High-Temperature Alloys and Coatings

Increasing efficiency is a continuing goal for all forms of power generation from conventional fossil fuels to new renewable sources. However, increasing the process temperature to increase efficiency leads to faster degradation rates and more components with corrosion-limited lifetimes. At the highest temperatures, oxidation-resistant alumina-forming alloys and coatings are needed for maximum lifetimes. However, lifetime models accurate over the extended application durations are not currently available for a wide range of candidates and conditions. Increased mechanistic understanding and relevant long-term data sets will assist in model development and validation. Current progress is outlined for applying a reservoir-type model to Fe-base alloys and coatings. However, more work is needed to understand environmental effects, such as the presence of H2O, and to extend the current model to NiCrAl and NiCr alloys. As the critical performance factors are better understood, it will be easier to evaluate new materials in laboratory screening experiments

Tannakian duality for Anderson-Drinfeld motives and algebraic independence of Carlitz logarithms

We develop a theory of Tannakian Galois groups for t-motives and relate this to the theory of Frobenius semilinear difference equations. We show that the transcendence degree of the period matrix associated to a given t-motive is equal to the dimension of its Galois group. Using this result we prove that Carlitz logarithms of algebraic functions that are linearly independent over the rational function field are algebraically independent.Comment: 39 page