An improvement in partial order reduction using behavioral analysis

pre-printEfficacy of partial order reduction in reducing state space relies on adequate extraction of the independence relation among possible behaviors. However, traditional approaches by statically analyzing system model structures are often not able to reveal enough independence for reduction. To address such a problem, this paper presents a behavioral analysis approach that uses a compositional reachability analysis method to generate the over-approximate local state spaces for all modules in a system where a much more precise independence relation can be extracted for partial order reduction. Compared to the static analysis approaches, significantly higher reduction on complexity can be seen in a number of non-trivial examples, and as a consequence, dramatically less time and memory are required to finish these examples

Soft-gluon and Coulomb corrections to hadronic top-quark pair production beyond NNLO

We construct a resummation at partial next-to-next-to-next-to-leading logarithmic accuracy for hadronic top-quark pair production near partonic threshold, including simultaneously soft-gluon and Coulomb corrections, and use this result to obtain approximate next-to-next-to-next-to-leading order predictions for the total top-quark pair-production cross section at the LHC. We generalize a required one-loop potential in non-relativistic QCD to the colour-octet case and estimate the remaining unknown two-loop potentials and three-loop anomalous dimensions. We obtain a moderate correction of $1.5\%$ relative to the next-to-next-to-leading order prediction and observe a reduction of the perturbative uncertainty below $\pm 5\%$.Comment: 47 pages, 5 figures, v2: published version, typos corrected (including scale uncertainties in Eqs. (4.16)-(4.20)), references added; v3: see added note on p.30 for changes; the results of this work are implemented in the program TOPIXS, which can be found at http://users.ph.tum.de/t31software/topixs

Generation of linear dynamic models from a digital nonlinear simulation

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models

Adaptive Low-Rank Methods for Problems on Sobolev Spaces with Error Control in L2L_2

Low-rank tensor methods for the approximate solution of second-order elliptic partial differential equations in high dimensions have recently attracted significant attention. A critical issue is to rigorously bound the error of such approximations, not with respect to a fixed finite dimensional discrete background problem, but with respect to the exact solution of the continuous problem. While the energy norm offers a natural error measure corresponding to the underlying operator considered as an isomorphism from the energy space onto its dual, this norm requires a careful treatment in its interplay with the tensor structure of the problem. In this paper we build on our previous work on energy norm-convergent subspace-based tensor schemes contriving, however, a modified formulation which now enforces convergence only in $L_2$. In order to still be able to exploit the mapping properties of elliptic operators, a crucial ingredient of our approach is the development and analysis of a suitable asymmetric preconditioning scheme. We provide estimates for the computational complexity of the resulting method in terms of the solution error and study the practical performance of the scheme in numerical experiments. In both regards, we find that controlling solution errors in this weaker norm leads to substantial simplifications and to a reduction of the actual numerical work required for a certain error tolerance.Comment: 26 pages, 7 figure

A modeling framework for efficient reduced order simulations of parametrized lithium-ion battery cells

In this contribution we present a new modeling and simulation framework for parametrized Lithium-ion battery cells. We first derive a new continuum model for a rather general intercalation battery cell on the basis of non-equilibrium thermodynamics. In order to efficiently evaluate the resulting parameterized non-linear system of partial differential equations the reduced basis method is employed. The reduced basis method is a model order reduction technique on the basis of an incremental hierarchical approximate proper orthogonal decomposition approach and empirical operator interpolation. The modeling framework is particularly well suited to investigate and quantify degradation effects of battery cells. Several numerical experiments are given to demonstrate the scope and efficiency of the modeling framework

Nonclassical Approximate Symmetries of Evolution Equations with a Small Parameter

We introduce a method of approximate nonclassical Lie-B\"acklund symmetries for partial differential equations with a small parameter and discuss applications of this method to finding of approximate solutions both integrable and nonintegrable equations.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA