Running Neutrino Mass Parameters in See-Saw Scenarios

We systematically analyze quantum corrections in see-saw scenarios, including effects from above the see-saw scales. We derive approximate renormalization group equations for neutrino masses, lepton mixings and CP phases, yielding an analytic understanding and a simple estimate of the size of the effects. Even for hierarchical masses, they often exceed the precision of future experiments. Furthermore, we provide a software package allowing for a convenient numerical renormalization group analysis, with heavy singlets being integrated out successively at their mass thresholds. We also discuss applications to model building and related topics.Comment: 49 pages, 9 figures; minor corrections in Sec. 6.5.1; the accompanying software packages REAP/MPT can be downloaded from http://www.ph.tum.de/~rg

XSAT and NAE-SAT of linear CNF classes

XSAT and NAE-SAT are important variants of the propositional satisfiability problem (SAT). Both are studied here regarding their computational complexity of linear CNF formulas. We prove that both variants remain NP-complete for (monotone) linear formulas yielding the conclusion that also bicolorability of linear hypergraphs is NP-complete. The reduction used gives rise to the complexity investigation of both variants for several monotone linear subclasses that are parameterized by the size of clauses or by the number of occurrences of variables. In particular cases of these parameter values we are able to verify the NP-completeness of XSAT respectively NAE-SAT; though we cannot provide a complete treatment. Finally we focus on exact linear formulas where clauses intersect pairwise, and for which SAT is known to be polynomial-time solvable. We verify the same assertion for NAE-SAT relying on some well-known result; whereas we obtain NP-completeness for XSAT of exact linear formulas. The case of uniform clause size k remains open for the latter problem. However, we can provide its polynomial-time behavior for k at most 6

XSAT and NAE-SAT of linear CNF classes

XSAT and NAE-SAT are important variants of the propositional satisfiability problem (SAT). Both are studied here regarding their computational complexity of linear CNF formulas. We prove that both variants remain NP-complete for (monotone) linear formulas yielding the conclusion that also bicolorability of linear hypergraphs is NP-complete. The reduction used gives rise to the complexity investigation of both variants for several monotone linear subclasses that are parameterized by the size of clauses or by the number of occurrences of variables. In particular cases of these parameter values we are able to verify the NP-completeness of XSAT respectively NAE-SAT; though we cannot provide a complete treatment. Finally we focus on exact linear formulas where clauses intersect pairwise, and for which SAT is known to be polynomial-time solvable. We verify the same assertion for NAE-SAT relying on some well-known result; whereas we obtain NP-completeness for XSAT of exact linear formulas. The case of uniform clause size k remains open for the latter problem. However, we can provide its polynomial-time behavior for k at most 6

Testing procedure for fatigue characterization of steel-CFRP hybrid laminate considering material dependent self-heating

Combining carbon fiber reinforced polymers (CFRP) with steel offers the potential of utilizing the desired characteristics of both materials, such as specific strength/stiffness and fatigue strength of fiber reinforced polymers (FRP) and impact resistance of metals. Since in such hybrid laminates multiple material layers are combined, a gradual failure is likely that can lead to changes in mechanical properties. A failure of the metal partner leads to an increase in stress on the FRP, which under fatigue load results in increased self-heating of the FRP. Therefore, a suitable testing procedure is required and developed in this study, to enable a reproducible characterization of the mechanical properties under fatigue load. The resulting testing procedure, containing multiple frequency tests as well as load increase and constant amplitude tests, enabled characterization of the fatigue performance while never exceeding a testing induced change in temperature of 4 K. In addition to the development of the testing procedure, an insight into the manufacturing induced residual stresses occurring in such hybrid laminates, which impacts the load-bearing capacity, was established using finite element simulation. The gathered data and knowledge represents a basis for future in-depth investigations in the area of residual stress influence on the performance of hybrid laminates and highlights its importance, since not only the used testing procedure determines the measured fatigue performance