Surface energy and boundary layers for a chain of atoms at low temperature

We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard-Jones type. The pressure (stress) is assumed small but positive and bounded away from zero, while the temperature $\beta^{-1}$ goes to zero. Our main results are: (1) As $\beta \to \infty$ at fixed positive pressure $p>0$, the Gibbs measures $\mu_\beta$ and $\nu_\beta$ for infinite chains and semi-infinite chains satisfy path large deviations principles. The rate functions are bulk and surface energy functionals $\overline{\mathcal{E}}_{\mathrm{bulk}}$ and $\overline{\mathcal{E}}_\mathrm{surf}$. The minimizer of the surface functional corresponds to zero temperature boundary layers. (2) The surface correction to the Gibbs free energy converges to the zero temperature surface energy, characterized with the help of the minimum of $\overline{\mathcal{E}}_\mathrm{surf}$. (3) The bulk Gibbs measure and Gibbs free energy can be approximated by their Gaussian counterparts. (4) Bounds on the decay of correlations are provided, some of them uniform in $\beta$

Leading-order hadronic contributions to the electron and tau anomalous magnetic moments

The leading hadronic contributions to the anomalous magnetic moments of the electron and the $\tau$-lepton are determined by a four-flavour lattice QCD computation with twisted mass fermions. The continuum limit is taken and systematic uncertainties are quantified. Full agreement with results obtained by phenomenological analyses is found.Comment: 13 pages, 10 figures, 5 tables; version accepted for publication in EPJ

Leading hadronic contributions to the running of the electroweak coupling constants from lattice QCD

The quark-connected leading-order hadronic contributions to the running of the electromagnetic fine structure constant, $\alpha_{\rm QED}$, and the weak mixing angle, $\theta_W$, are determined by a four-flavour lattice QCD computation with twisted mass fermions. Full agreement of the results with a phenomenological analysis is observed with an even comparable statistical uncertainty. We show that the uncertainty of the lattice calculation is dominated by systematic effects which then leads to significantly larger errors than obtained by the phenomenological analysis.Comment: 15 pages, 13 figures, 6 tables; matches the published versio

Lepton anomalous magnetic moments from twisted mass fermions

We present our results for the leading-order hadronic quark-connected contributions to the electron, the muon, and the tau anomalous magnetic moments obtained with four dynamical quarks. Performing the continuum limit and an analysis of systematic effects, full agreement with phenomenological results is found. To estimate the impact of omitting the quark-disconnected contributions to the hadronic vacuum polarisation we investigate them on one of the four-flavour ensembles. Additionally, the light quark contributions on the four-flavour sea are compared to the values obtained for $N_f=2$ physically light quarks. In the latter case different methods to fit the hadronic vacuum polarisation function are tested.Comment: 7 pages, 3 figures, Contribution to the 32nd International Symposium on Lattice Field Theory (Lattice 2014), 23-28 June 2014, Columbia University, New York, NY, US

Tight Approximation Algorithms for Scheduling with Fixed Jobs and Non-Availability

We study two closely related problems in non-preemptive scheduling of sequential jobs on identical parallel machines. In these two settings there are either fixed jobs or non-availability intervals during which the machines are not available; in both cases, the objective is to minimize the makespan. Both formulations have different applications, e.g. in turnaround scheduling or overlay computing. For both problems we contribute approximation algorithms with an improved ratio of $3/2+\epsilon$, respectively, which we refine to approximation algorithms with ratio $3/2$. For scheduling with fixed jobs, a lower bound of $3/2$ on the approximation ratio has been obtained by Scharbrodt, Steger & Weisser: for scheduling with non-availability we provide the same lower bound. In total, our approximation ratio for both problems is tight via suitable inapproximability results. We use dual approximation, creation of a gap structure and job configurations, and a PTAS for the multiple subset sum problem. However, the main feature of our algorithms is a new technique for the assignment of large jobs via flexible rounding. Our new technique is based on an interesting cyclic shifting argument in combination with a network flow model for the assignment of jobs to large gaps

Leading-order hadronic contribution to the anomalous magnetic moment of the muon from N_f=2+1+1 twisted mass fermions

We present results for the leading order QCD correction to the anomalous magnetic moment of the muon including the first two generations of quarks as dynamical degrees of freedom. Several light quark masses are examined in order to yield a controlled extrapolation to the physical pion mass. We analyse ensembles for three different lattice spacings and several volumes in order to investigate lattice artefacts and finite-size effects, respectively. We also provide preliminary results for this quantity for two flavours of mass-degenerate quarks at the physical value of the pion mass.Comment: 7 pages, 7 figures, presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Heuristic Approaches to Minimize Tour Duration for the TSP with Multiple Time Windows

We present heuristics to handle practical travelling salesman problems with multiple time windows per node, where the optimization goal is minimal tour duration, which is the time spent outside the depot node. We propose a dynamic programming approach which combines state labels by encoding intervals to handle the larger state space needed for this objective function. Our implementation is able to solve many practical instances in real-time and is used for heuristic search of near-optimal solutions for hard instances. In addition, we outline a hybrid genetic algorithm we implemented to cope with hard or unknown instances. Experimental evaluation proves the efficiency and suitability for practical use of our algorithms and even leads to improved upper bounds for yet unsolved instances from the literature

Effect of different mechanical seed scarification methods on germination and emergence dynamics of baobab (Adansonia digitata L.)

The African baobab (Adansonia digitata L.) is a multipurpose fruit-producing tree that is indigenous to the African savannahs. Commercial interest in the species has grown in recent years. The major obstacle of seed-based propagation of baobab is its inherent seed dormancy. Therefore, in this study the effects of different mechanical seed scarification methods on seed germination parameters and seedling development of A. digitata were tested. The results show that mechanical scarification had a significant effect on germination and emergence dynamics of A. digitata. The highest total emergence percentage with 61.7% was achieved by scarifying the seeds with a saw on the hilum side. Cotyledon damage due to mechanical scarification occurred in all treatments. Proportions of damage categories depended significantly on treatment. The largest proportion of undamaged cotyledons was with 63.6% achieved by scarifying the seeds with a saw on the hilum side. This precise technique may be suitable for mass propagation of baobab in a rural setting but the effects of scarification methods on seedling emergence should be further investigated

Recent developments in the tmLQCD software suite

We present an overview of recent developments in the tmLQCD software suite. We summarise the features of the code, including actions and operators implemented. In particular, we discuss the optimisation efforts for modern architectures using the Blue Gene/Q system as an example.Comment: presented at the 31st International Symposium on Lattice Field Theory (Lattice 2013), 29 July - 3 August 2013, Mainz, German

Accelerating Parametric Probabilistic Verification

We present a novel method for computing reachability probabilities of parametric discrete-time Markov chains whose transition probabilities are fractions of polynomials over a set of parameters. Our algorithm is based on two key ingredients: a graph decomposition into strongly connected subgraphs combined with a novel factorization strategy for polynomials. Experimental evaluations show that these approaches can lead to a speed-up of up to several orders of magnitude in comparison to existing approache