DepQBF 6.0: A Search-Based QBF Solver Beyond Traditional QCDCL

We present the latest major release version 6.0 of the quantified Boolean formula (QBF) solver DepQBF, which is based on QCDCL. QCDCL is an extension of the conflict-driven clause learning (CDCL) paradigm implemented in state of the art propositional satisfiability (SAT) solvers. The Q-resolution calculus (QRES) is a QBF proof system which underlies QCDCL. QCDCL solvers can produce QRES proofs of QBFs in prenex conjunctive normal form (PCNF) as a byproduct of the solving process. In contrast to traditional QCDCL based on QRES, DepQBF 6.0 implements a variant of QCDCL which is based on a generalization of QRES. This generalization is due to a set of additional axioms and leaves the original Q-resolution rules unchanged. The generalization of QRES enables QCDCL to potentially produce exponentially shorter proofs than the traditional variant. We present an overview of the features implemented in DepQBF and report on experimental results which demonstrate the effectiveness of generalized QRES in QCDCL.Comment: 12 pages + appendix; to appear in the proceedings of CADE-26, LNCS, Springer, 201

Systematic Study of Accuracy of Wall-Modeled Large Eddy Simulation using Uncertainty Quantification Techniques

The predictive accuracy of wall-modeled large eddy simulation is studied by systematic simulation campaigns of turbulent channel flow. The effect of wall model, grid resolution and anisotropy, numerical convective scheme and subgrid-scale modeling is investigated. All of these factors affect the resulting accuracy, and their action is to a large extent intertwined. The wall model is of the wall-stress type, and its sensitivity to location of velocity sampling, as well as law of the wall's parameters is assessed. For efficient exploration of the model parameter space (anisotropic grid resolution and wall model parameter values), generalized polynomial chaos expansions are used to construct metamodels for the responses which are taken to be measures of the predictive error in quantities of interest (QoIs). The QoIs include the mean wall shear stress and profiles of the mean velocity, the turbulent kinetic energy, and the Reynolds shear stress. DNS data is used as reference. Within the tested framework, a particular second-order accurate CFD code (OpenFOAM), the results provide ample support for grid and method parameters recommendations which are proposed in the present paper, and which provide good results for the QoIs. Notably, good results are obtained with a grid with isotropic (cubic) hexahedral cells, with $15\, 000$ cells per $\delta^3$, where $\delta$ is the channel half-height (or thickness of the turbulent boundary layer). The importance of providing enough numerical dissipation to obtain accurate QoIs is demonstrated. The main channel flow case investigated is ${\rm Re}_\tau=5200$, but extension to a wide range of ${\rm Re}$-numbers is considered. Use of other numerical methods and software would likely modify these recommendations, at least slightly, but the proposed framework is fully applicable to investigate this as well

Dependency Schemes in QBF Calculi: Semantics and Soundness

We study the parametrisation of QBF resolution calculi by dependency schemes. One of the main problems in this area is to understand for which dependency schemes the resulting calculi are sound. Towards this end we propose a semantic framework for variable independence based on ‘exhibition’ by QBF models, and use it to express a property of dependency schemes called full exhibition that is known to be sufficient for soundness in Q-resolution. Introducing a generalised form of the long-distance resolution rule, we propose a complete parametrisation of classical long-distance Q-resolution, and show that full exhibition remains sufficient for soundness. We demonstrate that our approach applies to the current research frontiers by proving that the reflexive resolution path dependency scheme is fully exhibited

Background reduction and sensitivity for germanium double beta decay experiments

Germanium detectors have very good capabilities for the investigation of rare phenomena like the neutrinoless double beta decay. Rejection of the background entangling the expected signal is one primary goal in this kind of experiments. Here, the attainable background reduction in the energy region where the neutrinoless double beta decay signal of 76Ge is expected to appear has been evaluated for experiments using germanium detectors, taking into consideration different strategies like the granularity of the detector system, the segmentation of each individual germanium detector and the application of Pulse Shape Analysis techniques to discriminate signal from background events. Detection efficiency to the signal is affected by background rejection techniques, and therefore it has been estimated for each of the background rejection scenarios considered. Finally, conditions regarding crystal mass, radiopurity, exposure to cosmic rays, shielding and rejection capabilities are discussed with the aim to achieve a background level of 10-3 c keV-1 kg-1 y-1 in the region of interest, which would allow to explore neutrino effective masses around 40 meV.Comment: 13 pages, 19 figures. Accepted by Astroparticle Physic