Phase-Amplitude Relations for a Particle with a Superposition of Two Energy Levels in a Double Potential Well

We study the connection between the phase and the amplitude of the wave function and the conditions under which this relationship exists. For this we use model of particle in a box. We have shown that the amplitude can be calculated from the phase and vice versa if the log Analytical uncertainty relations are satisfied.

Method Validation and Characterization of the Associated Uncertainty for Malondialdehyde Quantification in Exhaled Breath Condensate

There are several methods for quantifying malondialdehyde (MDA), an oxidative stress biomarker, in exhaled breath condensate (EBC). However, due to the very diluted nature of this biological matrix, a high variability is observed at low concentrations. We aimed to optimize a 2,4-dinitrophenylhydrazine-based method using liquid chromatography coupled to tandem mass spectrometry and characterize the uncertainty associated with this method. We investigated the following parameters for the method validation: calibration linearity, limit of detection (LOD), precision, recovery, and matrix effect. The results were used to identify the main sources of uncertainty and calculating the combined uncertainty. The applicability of this method was evaluated in an ongoing epidemiological study by analyzing 164 EBC samples collected from different professional groups in subway environments. The optimized method was sensitive (LOD: 70 pg/mL), precise (inter-day variation < 19%) and accurate (recovery range: 92–106.5%). The calculated analytical uncertainty was the highest at the LOQ level and reached 23%. Although the analytical uncertainty was high at low MDA concentrations, it was significantly lower than that the observed inter-individual variability. Hence, this method performs sufficiently well and can be recommended for future use in epidemiological researches relying on between-subject differences.

ERGO: a new Robust Design Optimization Technique combining Multi-Objective Bayesian Optimization with Analytical Uncertainty Quantification

In this work, robust design optimization (RDO) is treated, motivated by the increasing desire to account for variability the design phase. The problem is formulated in a multi-objective setting with the objective of simultaneously minimizing the mean of the objective and its variance due to variability of design variables and/or parameters. This allows the designer to choose its robustness level without the need to repeat the optimization as typically encountered when formulated as a single objective. To account for the computational cost that is often encountered in RDO problems, the problem is fitted in a Bayesian optimization framework. The use of surrogate modeling techniques to efficiently solve problems under uncertainty has effectively found its way in the optimization community leading to surrogate-assisted optimization-under-uncertainty schemes. The surrogates are often considered cheap-to-sample black-boxes and are sampled to obtain the desired quantities of interest. However, since the analytical formulation of the surrogates is known, an analytical treatment of the problem is available. To obtain the quantities of interest without sampling an analytical uncertainty propagation through the surrogate is presented. The multi-objective Bayesian optimization framework and the analytical uncertainty quantification are linked together through the formulation of the robust expected improvement (REI), obtaining the novel efficient robust global optimization (ERGO) scheme. The method is tested on a series of test cases to examine its behavior for varying difficulties and validated on an aerodynamic test function which proves the effectiveness of the novel scheme.

Substantial heterogeneity of carbon and oxygen stable-isotope compositions of single layers or specimens of natural carbonate materials: New evidence from replicate sampling of continental carbonates affirms previous evidence from marine limestones

ABSTRACT The uncertainty of measurements of carbon and oxygen stable-isotope ratios of carbonate materials is commonly assumed to be the analytical uncertainty determined from replicate analyses of single samples, but this ignores the possibility that heterogeneity of the material studied is greater than the analytical uncertainty. To test this question, we took eight samples from each of 13 layers or specimens of various non-marine (“continental”) carbonates and found ranges of δ13C and δ18O of 0.3 to 5.1‰, all exceeding the range of the typical lab-reported analytical uncertainty, ± 0.1‰, placed around single samples. These results are similar to previous replicate sampling of marine limestone layers, which revealed ranges of 0.2 to 2.8‰. Both sets of results, and other published data, demonstrate that analytical uncertainty derived from replicate analysis of a single sample is not a valid estimate of the uncertainty of δ13C or δ18O values characterizing a layer or specimen, and they remind us that we should not place great credence in anomalies or events defined by single samples of layers or specimens, regardless of the replication of analysis of that single sample. Our results indicate that the required layer-level or specimen-level uncertainty can be derived only from replicate sampling at different locations in layers or specimens, and that the layer-level or specimen-level uncertainty is inevitably greater than typical lab-reported analytical uncertainty. Credibility of anomalies or events in time series would be increased by replicate sampling of a random or dispersed subset of layers to estimate the variability of all layers and/or by replicate sampling of layers at and around a potential but unconfirmed event. The significance of the variability discussed above is evident in use of δ18O data to estimate paleotemperatures, where a difference of 1‰ in δ18O implies a difference of 4°C in temperature. Use of a single sample resulting in mischaracterization of the δ18O of an ancient material by 1.5‰ relative to the true mean for that material (which our results suggest is quite possible) would lead to a corresponding misestimation of temperature of 6°C, a significant difference in paleoenvironmental studies.

Radiocarbon dating of alpine ice cores with the dissolved organic carbon (DOC) fraction

High-alpine glaciers are valuable archives of past climatic and environmental conditions. The interpretation of the preserved signal requires a precise chronology. Radiocarbon (14C) dating of the water-insoluble organic carbon (WIOC) fraction has become an important dating tool to constrain the age of ice cores from mid-latitude and low-latitude glaciers. However, in some cases this method is restricted by the low WIOC concentration in the ice. In this work, we report first 14C dating results using the dissolved organic carbon (DOC) fraction, which is present at concentrations of at least a factor of 2 higher than the WIOC fraction. We evaluated this new approach by comparison to the established WIO14C dating based on parallel ice core sample sections from four different Eurasian glaciers covering an age range of several hundred to around 20 000 years; 14C dating of the two fractions yielded comparable ages, with WIO14C revealing a slight, barely significant, systematic offset towards older ages comparable in magnitude with the analytical uncertainty. We attribute this offset to two effects of about equal size but opposite in direction: (i) in-situ-produced 14C contributing to the DOC resulting in a bias towards younger ages and (ii) incompletely removed carbonates from particulate mineral dust (14C-depleted) contributing to the WIOC fraction with a bias towards older ages. The estimated amount of in-situ-produced 14C in the DOC fraction is smaller than the analytical uncertainty for most samples. Nevertheless, under extreme conditions, such as very high altitude and/or low snow accumulation rates, DO14C dating results need to be interpreted cautiously. While during DOC extraction the removal of inorganic carbon is monitored for completeness, the removal for WIOC samples was so far only assumed to be quantitative, at least for ice samples containing average levels of mineral dust. Here we estimated an average removal efficiency of 98±2 %, resulting in a small offset of the order of the current analytical uncertainty. Future optimization of the removal procedure has the potential to improve the accuracy and precision of WIO14C dating. With this study we demonstrate that using the DOC fraction for 14C dating not only is a valuable alternative to the use of WIOC but also benefits from a reduced required ice mass of typically ∼250 g to achieve comparable precision of around ±200 years. This approach thus has the potential of pushing radiocarbon dating of ice forward even to remote regions where the carbon content in the ice is particularly low.

Supplemental Material: Curation and analysis of global sedimentary geochemical data to inform Earth history

Table of valid lithologies; map depicting sample locations; crossplot illustrating analytical uncertainty; flowchart of the proposed workflow; histograms showing the effects of progressive filtering, the distribution of spatial and age scales, and proximity and probability values; and results of parameters sensitivity tests.

Supplemental Material: Curation and analysis of global sedimentary geochemical data to inform Earth history

Table of valid lithologies; map depicting sample locations; crossplot illustrating analytical uncertainty; flowchart of the proposed workflow; histograms showing the effects of progressive filtering, the distribution of spatial and age scales, and proximity and probability values; and results of parameters sensitivity tests.

Supplemental Material: Curation and analysis of global sedimentary geochemical data to inform Earth history

(i) table of valid lithologies; (ii) map depicting sample locations; (iii) crossplot illustrating analytical uncertainty; (iv) flowchart of the proposed workflow; (v) histograms showing the effects of progressive filtering, the distribution of spatial and age scales, and proximity and probability values; and (vi) results of parameters sensitivity tests.

New age constraints on the Late Cretaceous lower Williams Fork Formation, Coal Canyon, Colorado

The precise age of terrestrial sediments in the Late Cretaceous Williams Fork Formation of western Colorado is poorly constrained due to a paucity of radiometric data. Sanidine and zircon dating of a volcanic ash encased in coal (i.e., the Coal Canyon ash) within the Cameo-Wheeler coal zone of the lower Williams Fork Formation in Coal Canyon, Colorado provides an important new age constraint for the southwestern Piceance Basin. A 10-30 cm thick, light gray, clayey mudstone encased in coal was sampled for both zircon U-Pb and sanidine 40Ar/39Ar geochronology. The presence of numerous euhedral zircon crystals, a lenticular geometry, and a clayey texture suggest that the mudstone is a minimally reworked and slightly altered volcanic ash. Analysis of the euhedral zircon crystals (n=108) in the ash produced a statistically robust U-Pb date with 93 grains yielding a weighed mean age of 74.52 ±0.11 Ma (1σ analytical uncertainty). 40Ar/39Ar sanidine analyses yielded a younger weighted mean age of 73.10 ±0.12 Ma (1σ analytical uncertainty) based on 6 of the 36 grains analyzed. Our preferred age is given by the weighted mean age of the sanidine as it is based on higher precision analyses that can better discriminate older inherited grains that are likely included in the zircon mean-age calculation. Isotopic data for the Coal Canyon ash overlap in age with a K-Ar date of 72.5 ±5.1 Ma for a widespread Williams Fork Formation tonstein, known as the Yampa Bed, found in coal-bearing outcrops and mine workings throughout the northern Piceance and Sand Wash basins and Axial Basin Uplift. Based on the similarity in isotopic age, sedimentologic context and stratigraphic position, we suggest that the Coal Canyon ash and the regionally extensive Yampa Bed are coeval. Additionally, this correlation corroborates that the Cameo-Wheeler coal zone of the Williams Fork Formation in the southwestern Piceance Basin is correlative with the Middle coal zone of the Danforth Hills and Yampa regions. Lastly, this proposed correlation may suggest that the Coal Canyon ash, like the Yampa Bed, correlates with the Baculites reesidei ammonite zone, which is associated regionally with a bentonite dated to 72.94 ±0.45 Ma. Detrital sanidine geochronology of two lower Williams Fork sandstone units that overly the Coal Canyon ash did not produce grains younger than the ash and thus do not quantitatively improve the chronostratigraphy of these specific units. Lastly, the Coal Canyon ash date serves as a basis for future evaluations of the diachroneity of non-marine strata of the Williams Fork Formation.