Quantitative temporal logics over the reals: PSpace and below

AbstractIn many cases, the addition of metric operators to qualitative temporal logics (TLs) increases the complexity of satisfiability by at least one exponential: while common qualitative TLs are complete for NP or PSpace, their metric extensions are often ExpSpace-complete or even undecidable. In this paper, we exhibit several metric extensions of qualitative TLs of the real line that are at most PSpace-complete, and analyze the transition from NP to PSpace for such logics. Our first result is that the logic obtained by extending since-until logic of the real line with the operators ‘sometime within n time units in the past/future’ is still PSpace-complete. In contrast to existing results, we also capture the case where n is coded in binary and the finite variability assumption is not made. To establish containment in PSpace, we use a novel reduction technique that can also be used to prove tight upper complexity bounds for many other metric TLs in which the numerical parameters to metric operators are coded in binary. We then consider metric TLs of the reals that do not offer any qualitative temporal operators. In such languages, the complexity turns out to depend on whether binary or unary coding of parameters is assumed: satisfiability is still PSpace-complete under binary coding, but only NP-complete under unary coding

Quantitative Temporal Logics: PSpace and below

Often the addition of metric operators to qualitative temporal logics leads to an increase of the complexity of satisfiability by at least one exponential. In this paper, we exhibit a number of metric extensions of qualitative temporal logics of the real line that do not lead to an increase in computational complexity. The main result states that the language obtained by extending since/until logic of the real line with the operators 'sometime within n time units', n coded in binary, is PSpace-complete even without the finite variability assumption. Without qualitative temporal operators the complexity of this language turns out to depend on whether binary or unary coding of parameters is assumed: it is still PSpace-hard under binary coding but in NP under unary coding

Criticality of porosity defects on the fatigue performance of wire + arc additive manufactured titanium alloy

This study was aimed at investigating the effect of internal porosity on the fatigue strength of wire + arc additive manufactured titanium alloy (WAAM Ti-6Al-4V). Unlike similar titanium alloys built by the powder bed fusion processes, WAAM Ti-6Al-4V seldom contains gas pores. However, feedstock may get contaminated that may cause pores of considerable size in the built materials. Two types of specimens were tested: (1) control group without porosity referred to as reference specimens; (2) designed porosity group using contaminated wires to build the specimen gauge section, referred to as porosity specimens. Test results have shown that static strength of the two groups was comparable, but the elongation in porosity group was reduced by 60% and its fatigue strength was 33% lower than the control group. The stress intensity factor range of the crack initiating pore calculated by Murakami’s approach has provided good correlation with the fatigue life. The kink point on the data fitting curve corresponds well with the threshold value of the stress intensity factor range found in the literature. For predicting the fatigue limit, a modified Kitagawa-Takahashi diagram was proposed consisting of three regions depending on porosity size. Critical pore diameter was found to be about 100 µm

A single ion as a shot noise limited magnetic field gradient probe

It is expected that ion trap quantum computing can be made scalable through protocols that make use of transport of ion qubits between sub-regions within the ion trap. In this scenario, any magnetic field inhomogeneity the ion experiences during the transport, may lead to dephasing and loss of fidelity. Here we demonstrate how to measure, and compensate for, magnetic field gradients inside a segmented ion trap, by transporting a single ion over variable distances. We attain a relative magnetic field sensitivity of \Delta B/B_0 ~ 5*10^{-7} over a test distance of 140 \micro m, which can be extended to the mm range, still with sub \micro m resolution. A fast experimental sequence is presented, facilitating its use as a magnetic field gradient calibration routine, and it is demonstrated that the main limitation is the quantum shot noise.Comment: 5 pages, 3 figure

In situ characterization of damage development in Cottonid due to quasi-static tensile loading

Cottonid is a layered material based 100% on cellulose that holds excellent material properties by being completely sustainable. The finite nature of petroleum-based resources nowadays makes these properties significant for technical applications again. To understand how Cottonid reacts to application-oriented mechanical loads and how it fails, development of microstructural damage on the surface and in the volume of Cottonid was studied using innovative in situ testing techniques for the first time. Quasi-static tensile tests were comparatively performed in a scanning electron microscope as well as a microfocus computer tomograph, and the development of defects present in the initial condition of the material was investigated. In the elastic region, no visible damage initiation on the surface and a decrease of overall void volume within the gauge length could be detected. When reaching the yield strength, crack initiation on the surface starts at critical areas, like pores and microcracks, which propagation and assembly could be visualized via scanning electron micrographs. In the plastic region, an increase in void volume could be shown in the gauge length until final failure of the specimen. Innovative material testing techniques presented in this study support lifetime estimation in technical applications and understanding of process–structure–property relations. Particularly, characterization of microstructural damage development due to a mechanical load, which leads to final failure of the specimen, is essential to be able to create material models for lifetime prediction in respect to variable manufacturing or application parameters

Speciation of uranium: Compilation of a thermodynamic database and its experimental evaluation using different analytical techniques

Environmental hazards are caused by uranium mining legacies and enhanced radioactivity in utilized groundwater and surface water resources. Knowledge of uranium speciation in these waters is essential for predicting radionuclide migration and for installing effective water purification technology. The validity of the thermodynamic data for the environmental media affected by uranium mining legacies is of utmost importance. Therefore, a comprehensive and consistent database was established according to current knowledge. The uranium data included in the database is based on the NEA TDB (Guillaumont et al., 2003) and is modified or supplemented as necessary e.g. for calcium and magnesium uranyl carbonates. The specific ion interaction theory (Brönsted, 1922) is used to estimate activity constants, which is sufficient for the considered low ionic strengths. The success of this approach was evaluated by comparative experimental investigations and model calculations (PHREEQC (Parkhurst and Appelo, 1999)) for several model systems. The waters differ in pH (2.7–9.8), uranium concentration (10−9-10−4 mol/L) and ionic strength (0.002–0.2 mol/L). We used chemical extraction experiments, ESI-Orbitrap-MS and time-resolved laser-induced fluorescence spectroscopy (TRLFS) to measure the uranium speciation. The latter method is nonintrusive and therefore does not change the chemical composition of the investigated waters. This is very important, because any change of the system under study may also change the speciation