QCD Thermodynamics with Improved Actions

The thermodynamics of the SU(3) gauge theory has been analyzed with tree level and tadpole improved Symanzik actions. A comparison with the continuum extrapolated results for the standard Wilson action shows that improved actions lead to a drastic reduction of finite cut-off effects already on lattices with temporal extent $N_\tau=4$. Results for the pressure, the critical temperature, surface tension and latent heat are presented. First results for the thermodynamics of four-flavour QCD with an improved staggered action are also presented. They indicate similarly large improvement factors for bulk thermodynamics.Comment: Talk presented at LATTICE96(finite temperature) 4 pages, LaTeX2e file, 6 eps-file

Validation of Different Approaches to Coupled Electrodynamic-Structural Mechanical Simulation of Electromagnetic Forming

Electromagnetic forming (EF) is a high speed forming process in which strain rates of over 103 s^(-1) are achieved. The workpiece is deformed by the Lorentz force resulting from the interaction of a fast varying electro magnetic field with the eddy currents induced by the field in the workpiece. Within a research group (FOR 443) funded by the German Research Foundation (DFG) an object oriented simulation tool for this multi physical process has been developed (SOFAR), that can handle the fully coupled simulation in a single software environment. In this contribution, details of the algorithmic implementation of the electromagnetic side of the coupled model are discussed and validated. Basis of this validation are benchmark simulations developed for this purpose. In particular, the implementation of transient field computation for coupled problems within SOFAR is compared with an experienced FD-code (FELMEC) developed at the Institute of Electrical Machines, Drives and Power Electronics

Minimal half-spaces and external representation of tropical polyhedra

We give a characterization of the minimal tropical half-spaces containing a given tropical polyhedron, from which we derive a counter example showing that the number of such minimal half-spaces can be infinite, contradicting some statements which appeared in the tropical literature, and disproving a conjecture of F. Block and J. Yu. We also establish an analogue of the Minkowski-Weyl theorem, showing that a tropical polyhedron can be equivalently represented internally (in terms of extreme points and rays) or externally (in terms of half-spaces containing it). A canonical external representation of a polyhedron turns out to be provided by the extreme elements of its tropical polar. We characterize these extreme elements, showing in particular that they are determined by support vectors.Comment: 19 pages, 4 figures, example added with a new figure, figures improved, references update

Algorithms for Highly Symmetric Linear and Integer Programs

This paper deals with exploiting symmetry for solving linear and integer programming problems. Basic properties of linear representations of finite groups can be used to reduce symmetric linear programming to solving linear programs of lower dimension. Combining this approach with knowledge of the geometry of feasible integer solutions yields an algorithm for solving highly symmetric integer linear programs which only takes time which is linear in the number of constraints and quadratic in the dimension.Comment: 21 pages, 1 figure; some references and further comments added, title slightly change

Non-perturbative renormalisation and improvement of non-singlet tensor currents in Nf=3N_\mathrm{f}=3 QCD

Hadronic matrix elements involving tensor currents play an important r\^ole in decays that allow to probe the consistency of the Standard Model via precision lattice QCD calculations. The non-singlet tensor current is a scale-dependent (anomalous) quantity. We fully resolve its renormalisation group (RG) running in the continuum by carrying out a recursive finite-size scaling technique. In this way ambiguities due to a perturbative RG running and matching to lattice data at low energies are eliminated. We provide the total renormalisation factor at a hadronic scale of 233 MeV, which converts the bare current into its RG-invariant form. Our calculation features three flavours of O(a) improved Wilson fermions and tree-level Symanzik-improved gauge action. We employ the (massless) Schr\"odinger functional renormalisation scheme throughout and present the first non-perturbative determination of the Symanzik counterterm $c_\mathrm{T}$ derived from an axial Ward identity. We elaborate on various details of our calculations, including two different renormalisation conditions.Comment: 39 pages, 10 figures, 11 tables

Thermodynamics of Four-Flavour QCD with Improved Staggered Fermions

We have calculated the pressure and energy density in four-flavour QCD using improved fermion and gauge actions. We observe a strong reduction of finite cut-off effects in the high temperature regime, similar to what has been noted before for the SU(3) gauge theory. Calculations have been performed on $16^3\times 4$ and 16^4 lattices for two values of the quark mass, $ma = 0.05$ and 0.1. A calculation of the string tension at zero temperature yields a critical temperature $T_c/\sqrt{\sigma} = 0.407 \pm 0.010$ for the smaller quark mass value.Comment: 12 pages, LaTeX2e File, 11 encapsulated postscript file

Computing the vertices of tropical polyhedra using directed hypergraphs

We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a directed hypergraph, constructed from the subdifferentials of the active constraints at this point, admits a unique strongly connected component that is maximal with respect to the reachability relation (all the other strongly connected components have access to it). This property can be checked in almost linear-time. This allows us to develop a tropical analogue of the classical double description method, which computes a minimal internal representation (in terms of vertices) of a polyhedron defined externally (by half-spaces or hyperplanes). We provide theoretical worst case complexity bounds and report extensive experimental tests performed using the library TPLib, showing that this method outperforms the other existing approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section 5 (using directed hypergraphs), detailed appendix; v3: major revision of the article (adding tropical hyperplanes, alternative method by arrangements, etc); v4: minor revisio

Climatic and soil factors explain the two-dimensional spectrum of global plant trait variation

Plant functional traits can predict community assembly and ecosystem functioning and are thus widely used in global models of vegetation dynamics and land–climate feedbacks. Still, we lack a global understanding of how land and climate affect plant traits. A previous global analysis of six traits observed two main axes of variation: (1) size variation at the organ and plant level and (2) leaf economics balancing leaf persistence against plant growth potential. The orthogonality of these two axes suggests they are differently influenced by environmental drivers. We find that these axes persist in a global dataset of 17 traits across more than 20,000 species. We find a dominant joint effect of climate and soil on trait variation. Additional independent climate effects are also observed across most traits, whereas independent soil effects are almost exclusively observed for economics traits. Variation in size traits correlates well with a latitudinal gradient related to water or energy limitation. In contrast, variation in economics traits is better explained by interactions of climate with soil fertility. These findings have the potential to improve our understanding of biodiversity patterns and our predictions of climate change impacts on biogeochemical cycles