A class of well-posed parabolic final value problems

This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the solutions. The data space is the graph normed domain of an unbounded operator that maps final states to the corresponding initial states. It induces a new compatibility condition, depending crucially on the fact that analytic semigroups always are invertible in the class of closed operators. Lax--Milgram operators in vector distribution spaces constitute the main framework. The final value heat conduction problem on a smooth open set is also proved to be well posed, and non-zero Dirichlet data are shown to require an extended compatibility condition obtained by adding an improper Bochner integral.Comment: 16 pages. To appear in "Applied and numerical harmonic analysis"; a reference update. Conference contribution, based on arXiv:1707.02136, with some further development

Unchanged thermopower enhancement at the semiconductor-metal transition in correlated FeSb2−x_{2-x}Tex_x

Substitution of Sb in FeSb$_2$ by less than 0.5% of Te induces a transition from a correlated semiconductor to an unconventional metal with large effective charge carrier mass $m^*$. Spanning the entire range of the semiconductor-metal crossover, we observed an almost constant enhancement of the measured thermopower compared to that estimated by the classical theory of electron diffusion. Using the latter for a quantitative description one has to employ an enhancement factor of 10-30. Our observations point to the importance of electron-electron correlations in the thermal transport of FeSb$_2$, and suggest a route to design thermoelectric materials for cryogenic applications.Comment: 3 pages, 3 figures, accepted for publication in Appl. Phys. Lett. (2011

Short- and long-term mortality following primary total hip replacement for osteoarthritis: a Danish nationwide epidemiological study

We evaluated the short-term of 0 to 90 days and the longer term, up to 12.7 years, mortality for patients undergoing primary total hip replacement (THR) in Denmark in comparison to the general population. Through the Danish Hip Arthroplasty Registry we identified all primary THRs undertaken for osteoarthritis between 1 January 1995 and 31 December 2006. Each patient (n = 44 558) was matched at the time of surgery with three people from the general population (n = 133 674). We estimated mortality rates and mortality rate ratios with 95% confidence intervals for THR patients compared with the general population. There was a one-month period of increased mortality immediately after surgery among THR patients, but overall short-term mortality (0 to 90 days) was significantly lower (mortality rate ratio 0.8; 95% confidence interval 0.7 to 0.9). However, THR surgery was associated with increased short-term mortality in subjects under 60 years old, and among THR patients without comorbidity. Long-term mortality was lower among THR patients than in controls (mortality rate ratio 0.7; 95% confidence interval 0.7 to 0.7). Overall, THR was associated with lower short- and long-term mortality among patients with osteoarthritis. Younger patients and patients without comorbidity before surgery may also experience increased mortality after THR surgery, although the absolute risk of death is small. </jats:p

Spin-dynamic field coupling in strongly THz driven semiconductors : local inversion symmetry breaking

We study theoretically the optics in undoped direct gap semiconductors which are strongly driven in the THz regime. We calculate the optical sideband generation due to nonlinear mixing of the THz field and the near infrared probe. Starting with an inversion symmetric microscopic Hamiltonian we include the THz field nonperturbatively using non-equilibrium Green function techniques. We find that a self induced relativistic spin-THz field coupling locally breaks the inversion symmetry, resulting in the formation of odd sidebands which otherwise are absent.Comment: 8 pages, 6 figure

A Graph-Based Semantics Workbench for Concurrent Asynchronous Programs

A number of novel programming languages and libraries have been proposed that offer simpler-to-use models of concurrency than threads. It is challenging, however, to devise execution models that successfully realise their abstractions without forfeiting performance or introducing unintended behaviours. This is exemplified by SCOOP---a concurrent object-oriented message-passing language---which has seen multiple semantics proposed and implemented over its evolution. We propose a "semantics workbench" with fully and semi-automatic tools for SCOOP, that can be used to analyse and compare programs with respect to different execution models. We demonstrate its use in checking the consistency of semantics by applying it to a set of representative programs, and highlighting a deadlock-related discrepancy between the principal execution models of the language. Our workbench is based on a modular and parameterisable graph transformation semantics implemented in the GROOVE tool. We discuss how graph transformations are leveraged to atomically model intricate language abstractions, and how the visual yet algebraic nature of the model can be used to ascertain soundness.Comment: Accepted for publication in the proceedings of FASE 2016 (to appear

Binary pattern tile set synthesis is NP-hard

In the field of algorithmic self-assembly, a long-standing unproven conjecture has been that of the NP-hardness of binary pattern tile set synthesis (2-PATS). The $k$-PATS problem is that of designing a tile assembly system with the smallest number of tile types which will self-assemble an input pattern of $k$ colors. Of both theoretical and practical significance, $k$-PATS has been studied in a series of papers which have shown $k$-PATS to be NP-hard for $k = 60$, $k = 29$, and then $k = 11$. In this paper, we close the fundamental conjecture that 2-PATS is NP-hard, concluding this line of study. While most of our proof relies on standard mathematical proof techniques, one crucial lemma makes use of a computer-assisted proof, which is a relatively novel but increasingly utilized paradigm for deriving proofs for complex mathematical problems. This tool is especially powerful for attacking combinatorial problems, as exemplified by the proof of the four color theorem by Appel and Haken (simplified later by Robertson, Sanders, Seymour, and Thomas) or the recent important advance on the Erd\H{o}s discrepancy problem by Konev and Lisitsa using computer programs. We utilize a massively parallel algorithm and thus turn an otherwise intractable portion of our proof into a program which requires approximately a year of computation time, bringing the use of computer-assisted proofs to a new scale. We fully detail the algorithm employed by our code, and make the code freely available online

Toughening mechanisms in novel nano-silica epoxy polymers

A crosslinked epoxy polymer has been modified by the addition of nano-silica particles. The particles were introduced via a sol-gel technique which gave a very well dispersed phase of nanosilica particles which were about 20 nm in diameter. The glass transition temperature was unchanged by the addition of the nano-particles, but both the modulus and toughness were increased. The fracture energy increased from 100 J/m2 for the unmodified epoxy to 460 J/m2 for the epoxy with 13 vol% of nano-silica. The microscopy studies showed evidence of debonding of the nano-particles and subsequent plastic void growth of the epoxy polymer. A theoretical model of plastic void growth was used to confirm this mechanism