421 research outputs found
TiGL - An Open Source Computational Geometry Library for Parametric Aircraft Design
This paper introduces the software TiGL: TiGL is an open source high-fidelity
geometry modeler that is used in the conceptual and preliminary aircraft and
helicopter design phase. It creates full three-dimensional models of aircraft
from their parametric CPACS description. Due to its parametric nature, it is
typically used for aircraft design analysis and optimization. First, we present
the use-case and architecture of TiGL. Then, we discuss it's geometry module,
which is used to generate the B-spline based surfaces of the aircraft. The
backbone of TiGL is its surface generator for curve network interpolation,
based on Gordon surfaces. One major part of this paper explains the
mathematical foundation of Gordon surfaces on B-splines and how we achieve the
required curve network compatibility. Finally, TiGL's aircraft component module
is introduced, which is used to create the external and internal parts of
aircraft, such as wings, flaps, fuselages, engines or structural elements
Recursive Graphical Solution of Closed Schwinger-Dyson Equations in phi^4-Theory -- Part1: Generation of Connected and One-Particle Irreducible Feynman Diagrams
Using functional derivatives with respect to the free correlation function we
derive a closed set of Schwinger-Dyson equations in phi^4-theory. Its
conversion to graphical recursion relations allows us to systematically
generate all connected and one-particle irreducible Feynman diagrams for the
two- and four-point function together with their weights.Comment: Author Information under http://www.physik.fu-berlin.de/~pelster
Parallel implementation of the non-smooth contact dynamics method for large particle systems
In numerous industrial applications there is the need to realistically model granular material. For instance, simulating the interaction of vehicles and tools with soil is of great importance for the design of earth moving machinery. The Discrete Element Method (DEM) has been successfully applied to this task [1, 2]. Large scale problems require a lot of computational resources. Hence, for the application in the industrial engineering process, the computational eïŹort is an issue. In DEM parallelization is straight forward, since each contact between adjacent particles is resolved locally without regard of the other contacts. However, modelling a contact as a stiïŹ spring imposes strong limitations on the time step size to maintain a stable simulation. The NonâSmooth Contact Dynamics Method (NSCD), on the other hand, models contacts globally as a set of inequality constraints on a system of perfectly rigid bodies [3]. At the end of every time step, all inequality constraints must be satisïŹed simultaneously, which can be achieved by solving a complementarity problem. This leads to a numerically stable method that is robust with respect to much larger time steps in comparison to DEM. Since a global problem must be solved, parallelization now strongly depends on the numerical solver that is used for the complementarity problem. We present our ïŹrst massively parallel implementation of NSCD based on the projected GauĂ-Jacobi (PGJ) iterative scheme presented in [4]. Focusing on one-sided asynchronous communication patterns with double buïŹering for data exchange, global synchronizations can be avoided. Only weak synchronization due to data dependencies of neighboring domains remains. The implementation is based on the Global address space Programming Interface (GPI), supplemented by the Multi Core Threading Package (MCTP) [5] on the processor level. This allows to eïŹciently overlap calculation and communication between processors
On convex lower-level black-box constraints in bilevel optimization with an application to gas market models with chance constraints
Bilevel optimization is an increasingly important tool to model hierarchical decision making. However, the ability of modeling such settings makes bilevel problems hard to solve in theory and practice. In this paper, we add on the general difficulty of this class of problems by further incorporating convex black-box constraints in the lower level. For this setup, we develop a cutting-plane algorithm that computes approximate bilevel-feasible points. We apply this method to a bilevel model of the European gas market in which we use a joint chance constraint to model uncertain loads. Since the chance constraint is not available in closed form, this fits into the black-box setting studied before. For the applied model, we use further problem-specific insights to derive bounds on the objective value of the bilevel problem. By doing so, we are able to show that we solve the application problem to approximate global optimality. In our numerical case study we are thus able to evaluate the welfare sensitivity in dependence of the achieved safety level of uncertain load coverage
Was macht die "Frische" von Brot aus?
Die Frische von Brot lĂ€sst sich nicht mit einheitlichen Kriterien beurteilen. Vielmehr hĂ€ngt die Wahl der jeweiligen Kritereien von den Anforderungen ab, die an das Produkt gestellt werden. Sensorische Eigenschaften spielen dabei eine bedeutende Rolle. An der ZĂŒrcher Hochschule fĂŒr Angewandte Wissenschaften (ZHAW) in WĂ€denswil wurde im Rahmen einer studentischen Arbeit eine Studie zum Thema âDefinition der Frische von Brot aus Konsumentensichtâ durchgefĂŒhrt
Orientational order and glassy states in networks of semiflexible polymers
Motivated by the structure of networks of cross-linked cytoskeletal
biopolymers, we study the orientationally ordered phases in two-dimensional
networks of randomly cross-linked semiflexible polymers. We consider permanent
cross-links which prescribe a finite angle and treat them as quenched disorder
in a semi-microscopic replica field theory. Starting from a fluid of
un-cross-linked polymers and small polymer clusters (sol) and increasing the
cross-link density, a continuous gelation transition occurs. In the resulting
gel, the semiflexible chains either display long range orientational order or
are frozen in random directions depending on the value of the crossing angle,
the crosslink concentration and the stiffness of the polymers. A crossing angle
leads to long range -fold orientational order, e.g.,
"hexatic" or "tetratic" for or , respectively.
The transition is discontinuous and the critical cross-link density depends on
the bending stiffness of the polymers and the cross-link geometry: the higher
the stiffness and the lower , the lower the critical number of cross-links.
In between the sol and the long range ordered state, we always observe a gel
which is a statistically isotropic amorphous solid (SIAS) with random
positional and random orientational localization of the participating polymers.Comment: 20 pages, added references, minor changes, final version as published
in PR
The critical exponents of the superfluid transition in He4
We improve the theoretical estimates of the critical exponents for the
three-dimensional XY universality class, which apply to the superfluid
transition in He4 along the lambda-line of its phase diagram. We obtain the
estimates alpha=-0.0151(3), nu=0.6717(1), eta=0.0381(2), gamma=1.3178(2),
beta=0.3486(1), and delta=4.780(1). Our results are obtained by finite-size
scaling analyses of high-statistics Monte Carlo simulations up to lattice size
L=128 and resummations of 22nd-order high-temperature expansions of two
improved models with suppressed leading scaling corrections. We note that our
result for the specific-heat exponent alpha disagrees with the most recent
experimental estimate alpha=-0.0127(3) at the superfluid transition of He4 in
microgravity environment.Comment: 45 pages, 16 fig
Mixed-integer programming techniques for the minimum sum-of-squares clustering problem
The minimum sum-of-squares clustering problem is a very important problem in data mining and machine learning with very many applications in, e.g., medicine or social sciences. However, it is known to be NP-hard in all relevant cases and to be notoriously hard to be solved to global optimality in practice. In this paper, we develop and test different tailored mixed-integer programming techniques to improve the performance of state-of-the-art MINLP solvers when applied to the problemâamong them are cutting planes, propagation techniques, branching rules, or primal heuristics. Our extensive numerical study shows that our techniques significantly improve the performance of the open-source MINLP solver SCIP. Consequently, using our novel techniques, we can solve many instances that are not solvable with SCIP without our techniques and we obtain much smaller gaps for those instances that can still not be solved to global optimality
Instability of the O(5) multicritical behavior in the SO(5) theory of high-Tc superconductors
We study the nature of the multicritical point in the three-dimensional
O(3)+O(2) symmetric Landau-Ginzburg-Wilson theory, which describes the
competition of two order parameters that are O(3) and O(2) symmetric,
respectively. This study is relevant for the SO(5) theory of high-Tc
superconductors, which predicts the existence of a multicritical point in the
temperature-doping phase diagram, where the antiferromagnetic and
superconducting transition lines meet.
We investigate whether the O(3)+O(2) symmetry gets effectively enlarged to
O(5) approaching the multicritical point. For this purpose, we study the
stability of the O(5) fixed point. By means of a Monte Carlo simulation, we
show that the O(5) fixed point is unstable with respect to the spin-4 quartic
perturbation with the crossover exponent , in substantial
agreement with recent field-theoretical results. This estimate is much larger
than the one-loop -expansion estimate , which has
often been used in the literature to discuss the multicritical behavior within
the SO(5) theory. Therefore, no symmetry enlargement is generically expected at
the multicritical transition.
We also perform a five-loop field-theoretical analysis of the
renormalization-group flow. It shows that bicritical systems are not in the
attraction domain of the stable decoupled fixed point. Thus, in these
systems--high-Tc cuprates should belong to this class--the multicritical point
corresponds to a first-order transition.Comment: 18 page
- âŠ