The g-factor of the electron bound in 28 Si 13+ : the most stringent test of bound-state quantum electrodynamics

This thesis describes the ultra-precise determination of the g-factor of the electron bound to hydrogenlike 28Si13+. The experiment is based on the simultaneous determination of the cyclotron- and Larmor frequency of a single ion, which is stored in a triple Penning-trap setup. The continuous Stern-Gerlach effect is used to couple the spin of the bound electron to the motional frequencies of the ion via a magnetic bottle, which allows the non-destructive determination of the spin state. To this end, a highly sensitive, cryogenic detection system was developed, which allowed the direct, non-destructive detection of the eigenfrequencies with the required precision.rnThe development of a novel, phase sensitive detection technique finally allowed the determination of the g-factor with a relative accuracy of 40 ppt, which was previously inconceivable. The comparison of the hereby determined value with the value predicted by quantumelectrodynamics (QED) allows the verification of the validity of this fundamental theory under the extreme conditions of the strong binding potential of a highly charged ion. The exact agreement of theory and experiment is an impressive demonstration of the exactness of QED. The experimental possibilities created in this work will allow in the near future not only further tests of theory, but also the determination of the mass of the electron with a precision that exceeds the current literature value by more than an order of magnitude.

Chiral properties of two-flavour QCD at zero and non-zero temperature

Lattice Quantum Chromodynamics (LQCD) is the preferred tool for obtaining non-perturbative results from QCD in the low-energy regime. It has by nowrnentered the era in which high precision calculations for a number of phenomenologically relevant observables at the physical point, with dynamical quark degrees of freedom and controlled systematics, become feasible. Despite these successes there are still quantities where control of systematic effects is insufficient. The subject of this thesis is the exploration of the potential of todays state-of-the-art simulation algorithms for non-perturbativelyrn$\mathcal{O}(a)$-improved Wilson fermions to produce reliable results in thernchiral regime and at the physical point both for zero and non-zero temperature. Important in this context is the control over the chiral extrapolation. Thisrnthesis is concerned with two particular topics, namely the computation of hadronic form factors at zero temperature, and the properties of the phaserntransition in the chiral limit of two-flavour QCD.rnrnThe electromagnetic iso-vector form factor of the pion provides a platform to study systematic effects and the chiral extrapolation for observables connected to the structure of mesons (and baryons). Mesonic form factors are computationally simpler than their baryonic counterparts but share most of the systematic effects. This thesis contains a comprehensive study of the form factor in the regime of low momentum transfer $q^2$, where the form factor is connected to the charge radius of the pion. A particular emphasis is on the region very close to $q^2=0$ which has not been explored so far, neither in experiment nor in LQCD. The results for the form factor close the gap between the smallest spacelike $q^2$-value available so far and $q^2=0$, and reach an unprecedented accuracy at full control over the main systematic effects. This enables the model-independent extraction of the pion charge radius. The results for the form factor and the charge radius are used to test chiral perturbation theory ($\chi$PT) and are thereby extrapolated to the physical point and the continuum. The final result in units of the hadronic radius $r_0$ is rn$$ \left\langle r_\pi^2 \right\rangle^{\rm phys}/r_0^2 = 1.87 \: \left(^{+12}_{-10}\right)\left(^{+\:4}_{-15}\right) \quad \textnormal{or} \quad \left\langle r_\pi^2 \right\rangle^{\rm phys} = 0.473 \: \left(^{+30}_{-26}\right)\left(^{+10}_{-38}\right)(10) \: \textnormal{fm} \;, $$rn which agrees well with the results from other measurements in LQCD and experiment. Note, that this is the first continuum extrapolated result for the charge radius from LQCD which has been extracted from measurements of the form factor in the region of small $q^2$.rnrnThe order of the phase transition in the chiral limit of two-flavour QCD and the associated transition temperature are the last unkown features of the phase diagram at zero chemical potential. The two possible scenarios are a second order transition in the $O(4)$-universality class or a first order transition. Since direct simulations in the chiral limit are not possible the transition can only be investigated by simulating at non-zero quark mass with a subsequent chiral extrapolation, guided by the universal scaling in the vicinity of the critical point. The thesis presents the setup and first results from a study on this topic. The study provides the ideal platform to test the potential and limits of todays simulation algorithms at finite temperature. The results from a first scan at a constant zero-temperature pion mass of about 290~MeV are promising, and it appears that simulations down to physical quark masses are feasible. Of particular relevance for the order of the chiral transition is the strength of the anomalous breaking of the $U_A(1)$ symmetry at the transition point. It can be studied by looking at the degeneracies of the correlation functions in scalar and pseudoscalar channels. For the temperature scan reported in this thesis the breaking is still pronounced in the transition region and the symmetry becomes effectively restored only above $1.16\:T_C$. The thesis also provides an extensive outline of research perspectives and includes a generalisation of the standard multi-histogram method to explicitly $\beta$-dependent fermion actions.

Vibrational spectroscopic monitoring of CO2-O energy transfer: cooling processes in atmospheres of Venus & Mars

The vibrational excitation of CO2 by a fast-moving O atom followed by infrared emission from the vibrationally excited CO2 has been shown to be an important cooling mechanism in the upper atmospheresof Venus, Earth and Mars. We are trying to determine more precisely the efficiency (rate coefficient) of the CO2-O vibrational energy transfer. For experimental ease the reverse reaction is used, i.e. collision of a vibrationally excited CO2 with atomic O, where we are able to convert to the atmospherically relevant reaction via a known equilibrium constant. The goal of this experiment was to measure the magnitudes of rate coefficients for vibrational energy states above the first excited state, a bending mode in CO2. An isotope of CO2, 13CO2, was used for experimental ease. The rate coefficients for given vibrational energy transfers in 13CO2 are not significantly different from 12CO2 at this level of precision. A slow-flowing gas mixture was flowed through a reaction cell: 13CO2 (vibrational specie of interest), O3(atomic O source), and Ar (bath gas). Transient diode laser absorption spectroscopy was used to monitor thechanging absorption of certain vibrational modes of 13CO2 after a UV pulse from a Nd:YAG laser was fired. Ozone absorbed the UV pulse in a process which vibrationally excited 13CO2 and liberated atomic O.Transient absorption signals were obtained by tuning the diode laser frequency to an appropriate ν3 transition and monitoring the population as a function of time following the Nd:YAG pulse. Transient absorption curves were obtained for various O atom concentrations to determine the rate coefficient of interest. Therotational states of the transitions used for detection were difficult to identify, though their short reequilibration timescale made the identification irrelevant for vibrational energy transfer measurements. The rate coefficient for quenching of the (1000) state was found to be (4 ± 8) x 10-12 cm3 s-1 which is the same order of magnitude as the lowest-energy bend-excited mode: (1.8 ± 0.3) x 10-12 cm3 s-1. More data is necessary before it can be certain that the numerical difference between the two is real.

Evaluating the Impact of the Number of Access Points in Mobile Robots Localization Using Artificial Neural Networks

Localization is information of fundamental importance to carry out various tasks in the mobile robotic area. The exact degree of precision required in the localization depends on the nature of the task. The GPS provides global position estimation but is restricted to outdoor environments and has an inherent imprecision of a few meters. In indoor spaces, other sensors like lasers and cameras are commonly used for position estimation, but these require landmarks (or maps) in the environment and a fair amount of computation to process complex algorithms. These sensors also have a limited field of vision. Currently, Wireless Networks (WN) are widely available in indoor environments and can allow efficient global localization that requires relatively low computing resources. However, the inherent instability in the wireless signal prevents it from being used for very accurate position estimation. The growth in the number of Access Points (AP) increases the overlap signals areas and this could be a useful means of improving the precision of the localization. In this paper we evaluate the impact of the number of Access Points in mobile nodes localization using Artificial Neural Networks (ANN). We use three to eight APs as a source signal and show how the ANNs learn and generalize the data. Added to this, we evaluate the robustness of the ANNs and evaluate a heuristic to try to decrease the error in the localization. In order to validate our approach several ANNs topologies have been evaluated in experimental tests that were conducted with a mobile node in an indoor space.

Quantitative assessment of oral orbicular muscle deformation after cleft lip reconstruction: an ultrasound elastography study

Reconstruction of a cleft lip leads inevitably to scar tissue formation. Scar tissue within the restored oral orbicular muscle might be assessed by quantification of the local contractility of this muscle. Furthermore, information about the contraction capability of the oral orbicular muscle is crucial for planning the revision surgery of an individual patient. We used ultrasound elastography to determine the local deformation (strain) of the upper lip and to differentiate contracting muscle from passive scar tissue. Raw ultrasound data (radio-frequency format; rf-) were acquired, while the lips were brought from normal state into a pout condition and back in normal state, in three patients and three normal individuals. During this movement, the oral orbicular muscle contracts and, consequently, thickens in contrast to scar tissue that will not contract, or even expand. An iterative coarse-to-fine strain estimation method was used to calculate the local tissue strain. Analysis of the raw ultrasound data allows estimation of tissue strain with a high precision. The minimum strain that can be assessed reproducibly is 0.1%. In normal individuals, strain of the orbicular oral muscle was in the order of 20%. Also, a uniform strain distribution in the oral orbicular muscle was found. However, in patients deviating values were found in the region of the reconstruction and the muscle tissue surrounding that. In two patients with a successful reconstruction, strain was reduced by 6% in the reconstructed region with respect to the normal parts of the muscle (from 22% to 16% and from 25% to 19%). In a patient with severe aesthetical and functional disability, strain decreased from 30% in the normal region to 5% in the reconstructed region. With ultrasound elastography, the strain of the oral orbicular muscle can be quantified. In healthy subjects, the strain profiles and maximum strain values in all parts of the muscle were similar. The maximum strain of the muscle during pout was 20% +/- 1%. In surgically repaired cleft lips, decreased deformation was observed.

Quantile-Based Optimization of Noisy Computer Experiments with Tunable Precision

This article addresses the issue of kriging-based optimization of stochastic simulators. Many of these simulators depend on factors that tune the level of precision of the response, the gain in accuracy being at a price of computational time. The contribution of this work is two-fold: first, we propose a quantile-based criterion for the sequential design of experiments, in the fashion of the classical expected improvement criterion, which allows an elegant treatment of heterogeneous response precisions. Second, we present a procedure for the allocation of the computational time given to each measurement, allowing a better distribution of the computational effort and increased efficiency. Finally, the optimization method is applied to an original application in nuclear criticality safety. This article has supplementary material available online. The proposed criterion is available in the R package DiceOptim.

A new application of emulsions to measure the gravitational force on antihydrogen

We propose to build and operate a detector based on the emulsion film technology for the measurement of the gravitational acceleration on antimatter, to be performed by the AEgIS experiment (AD6) at CERN. The goal of AEgIS is to test the weak equivalence principle with a precision of 1% on the gravitational acceleration g by measuring the vertical position of the annihilation vertex of antihydrogen atoms after their free fall while moving horizontally in a vacuum pipe. With the emulsion technology developed at the University of Bern we propose to improve the performance of AEgIS by exploiting the superior position resolution of emulsion films over other particle detectors. The idea is to use a new type of emulsion films, especially developed for applications in vacuum, to yield a spatial resolution of the order of one micron in the measurement of the sag of the antihydrogen atoms in the gravitational field. This is an order of magnitude better than what was planned in the original AEgIS proposal.

Measurement of angular correlations in Drell-Yan lepton pairs to probe Z/gamma* boson transverse momentum at sqrt(s)=7 TeV with the ATLAS detector

A measurement of angular correlations in Drell-Yan lepton pairs via the phi(eta)* observable is presented. This variable probes the same physics as the Z/gamma* boson transverse momentum with a better experimental resolution. The Z/gamma* -> e(+)e(-) and Z/gamma* -> mu(+)mu(-) decays produced in proton-proton collisions at a centre-of-mass energy of root s = 7 TeV are used. The data were collected with the ATLAS detector at the LHC and correspond to an integrated luminosity of 4.6 fb(-1). Normalised differential cross sections as a function of phi(eta)* are measured separately for electron and muon decay channels. These channels are then combined for improved accuracy. The cross section is also measured double differentially as a function of phi(eta)* for three independent bins of the Z boson rapidity. The results are compared to QCD calculations and to predictions from different Monte Carlo event generators. The data are reasonably well described, in all measured Z boson rapidity regions, by resummed QCD predictions combined with fixed-order perturbative QCD calculations or by some Monte Carlo event generators. The measurement precision is typically better by one order of magnitude than present theoretical uncertainties.

Dynamic computer simulation of electrophoretic enantiomer migration order and separation in presence of a neutral cyclodextrin

One-dimensional dynamic computer simulation was employed to investigate the separation and migration order change of ketoconazole enantiomers at low pH in presence of increasing amounts of (2-hydroxypropyl)-β-cyclodextrin (OHP-β-CD). The 1:1 interaction of ketoconazole with the neutral cyclodextrin was simulated under real experimental conditions and by varying input parameters for complex mobilities and complexation constants. Simulation results obtained with experimentally determined apparent ionic mobilities, complex mobilities, and complexation constants were found to compare well with the calculated separation selectivity and experimental data. Simulation data revealed that the migration order of the ketoconazole enantiomers at low (OHP-β-CD) concentrations (i.e. below migration order inversion) is essentially determined by the difference in complexation constants and at high (OHP-β-CD) concentrations (i.e. above migration order inversion) by the difference in complex mobilities. Furthermore, simulations with complex mobilities set to zero provided data that mimic migration order and separation with the chiral selector being immobilized. For the studied CEC configuration, no migration order inversion is predicted and separations are shown to be quicker and electrophoretic transport reduced in comparison to migration in free solution. The presented data illustrate that dynamic computer simulation is a valuable tool to study electrokinetic migration and separations of enantiomers in presence of a complexing agent.

Measuring localized viscoelasticity of the vitreous body using intraocular microprobes.

Vitrectomy is a standard ophthalmic procedure to remove the vitreous body from the eye. The biomechanics of the vitreous affects its duration (by changing the removal rate) and the mechanical forces transmitted via the vitreous on the surrounding tissues during the procedure. Biomechanical characterization of the vitreous is essential for optimizing the design and control of instruments that operate within the vitreous for improved precision, safety, and efficacy. The measurements are carried out using a magnetic microprobe inserted into the vitreous, a method known as magnetic microrheology. The location of the probe is tracked by a microscope/camera while magnetic forces are exerted wirelessly by applied magnetic fields. In this work, in vitro artificial vitreous, ex vivo human vitreous and ex vivo porcine vitreous were characterized. In addition, in vivo rabbit measurements were performed using a suturelessly injected probe. Measurements indicate that viscoelasticity parameters of the ex vivo human vitreous are an order of magnitude different from those of the ex vivo porcine vitreous. The in vivo intra-operative measurements show typical viscoelastic behavior of the vitreous with a lower compliance than the ex vivo measurements. The results of the magnetic microrheology measurements were validated with those obtained by a standard atomic force microscopy (AFM) method and in vitro artificial vitreous. This method allows minimally-invasive characterization of localized mechanical properties of the vitreous in vitro, ex vivo, and in vivo. A better understanding of the characteristics of the vitreous can lead to improvements in treatments concerning vitreal manipulation such as vitrectomy.

Can we constrain the interior structure of rocky exoplanets from mass and radius measurements?

Aims. We present an inversion method based on Bayesian analysis to constrain the interior structure of terrestrial exoplanets, in the form of chemical composition of the mantle and core size. Specifically, we identify what parts of the interior structure of terrestrial exoplanets can be determined from observations of mass, radius, and stellar elemental abundances. Methods. We perform a full probabilistic inverse analysis to formally account for observational and model uncertainties and obtain confidence regions of interior structure models. This enables us to characterize how model variability depends on data and associated uncertainties. Results. We test our method on terrestrial solar system planets and find that our model predictions are consistent with independent estimates. Furthermore, we apply our method to synthetic exoplanets up to 10 Earth masses and up to 1.7 Earth radii, and to exoplanet Kepler-36b. Importantly, the inversion strategy proposed here provides a framework for understanding the level of precision required to characterize the interior of exoplanets. Conclusions. Our main conclusions are (1) observations of mass and radius are sufficient to constrain core size; (2) stellar elemental abundances (Fe, Si, Mg) are principal constraints to reduce degeneracy in interior structure models and to constrain mantle composition; (3) the inherent degeneracy in determining interior structure from mass and radius observations does not only depend on measurement accuracies, but also on the actual size and density of the exoplanet. We argue that precise observations of stellar elemental abundances are central in order to place constraints on planetary bulk composition and to reduce model degeneracy. We provide a general methodology of analyzing interior structures of exoplanets that may help to understand how interior models are distributed among star systems. The methodology we propose is sufficiently general to allow its future extension to more complex internal structures including hydrogen- and water-rich exoplanets.

Geochemistry of the lower sheeted dike complex of ODP Holes 137-504B and 140-504B

Sixty-three samples representing 379 m of sheeted dikes from Deep Sea Drilling Project/Ocean Drilling Program Site 504B have been analyzed for major and selected trace elements by X-ray fluorescence. The samples range from microcrystalline aphyric basalts to moderately phyric (2%-10% phenocrysts) diabase that are typically multiply saturated with plagioclase, olivine, and clinopyroxene, in order of relative abundance. All analyzed samples are classified as Group D compositions with moderate to slightly elevated compatible elements (MgÆ-value = 0.65% ± 0.03%; Al2O3 = 15.5% ± 0.8%; CaO = 13.0% ± 0.3%; Ni = 114 ± 29 ppm), and unusually depleted levels of moderate to highly incompatible elements (Nb < 1 ppm; Zr = 44 ± 7 ppm; Rb < 0.5 ppm; Ba ~ 1 ppm; P2O5 = 0.07% ± 0.02%). These compositions are consistent with a multistage melting of a normal ocean ridge basaltic mantle source followed by extensive fractionation of olivine, plagioclase, and clinopyroxene. Leg 140 aphyric to sparsely phyric (0%-2% phenocrysts) basalts and diabases are compositionally indistinguishable from similarly phyric samples at higher levels in the hole. An examination of the entire crustal section, from the overlying volcanics through the sheeted dikes observed in Leg 140, reveals no significant trends indicating the enrichment or depletion of Costa Rica Rift Zone source magmas over time. Similarly, significant trends toward increased or decreased differentiation cannot be identified, although compositional patterns reflecting variable amounts of phenocryst addition are apparent at various depths. Below ? 1700 mbsf to the bottom of the Leg 140 section, there is a broadly systematic pattern of Zn depletion with depth, the result of high-temperature hydrothermal leaching. This zone of depletion is thought to be a significant source of Zn for the hydrothermal fluids depositing metal sulfides at ridge-crest hydrothermal vents and the sulfide-mineralization zone, located in the transition between pillow lavas and sheeted dikes. Localized zones of intense alteration (60%-95% recrystallization) are present on a centimeter to meter scale in many lithologic units. Within these zones, normally immobile elements Ti, Zr, Y, and rare-earth elements are strongly depleted compared with "fresher" samples centimeters away. The extent of compositional variability of these elements tends to obscure primary igneous trends if the highly altered samples are not identified or removed. At levels up to 40% (or possibly 60%) recrystallization, Ti, Zr, and Y retain their primary signatures. Although the mechanisms are unclear, it is possible that these intense alteration zones are a source of Y and rare-earth elements for the typically rare-earth-element-enriched hydrothermal vent fluids of mid-ocean ridges.

Distribution of deep-sea foraminifera in surface sediments east of New Zealand

Paleobathymetric assessments of fossil foraminiferal faunas play a significant role in the analysis of the paleogeographic, sedimentary, and tectonic histories of New Zealand's Neogene marine sedimentary basins. At depths >100 m, these assessments often have large uncertainties. This study, aimed at improving the precision of paleodepth assessments, documents the present-day distribution of deep-sea foraminifera (>63 µm) in 66 samples of seafloor sediment at 90-700 m water depth (outer shelf to mid-abyssal), east of New Zealand. One hundred and thirty-nine of the 465 recorded species of benthic foraminifera are new records for the New Zealand region. Characters of the foraminiferal faunas which appear to provide the most useful information for estimating paleobathymetry are, in decreasing order of reliability: relative abundance of common benthic species; benthic species associations; upper depth limits of key benthic species; and relative abundance of planktic foraminifera. R mode cluster analysis on the quantitative census data of the 58 most abundant species of benthic foraminifera produced six species associations within three higher level clusters: (1) calcareous species most abundant at mid-bathyal to outer shelf depths (<1000 m); (2) calcareous species most abundant at mid-bathyal and greater depths (>600 m); (3) agglutinated species mostly occurring at deep abyssal depths (>3000 m). A detrended correspondence analysis ordination plot exhibits a strong relationship between these species associations and bathymetry. This is manifest in the bathymetric ranges of the relative abundance peaks of many of the common benthic species (e.g., Abditodentrix pseudothalmanni 500-2800 m, Bolivina robusta 200-650 m, Bulimina marginata f. marginata 20-600 m, B. marginata f. aculeata 400-3000 m, Cassidulina norvangi 1000-4500 m, Epistominella exigua 1000-4700 m, and Trifarina angulosa 10-650 m), which should prove useful in paleobathymetric estimates. The upper depth limits of 28 benthic foraminiferal species (e.g., Fursenkoina complanata 200 m, Bulimina truncana 450 m, Melonis affinis 550 m, Eggerella bradyi 750 m, and Cassidulina norvangi 1000 m) have potential to improve the precision of paleobathymetric estimates based initially on the total faunal composition. The planktic percentage of foraminiferal tests increases from outer shelf to upper abyssal depths followed by a rapid decline within the foraminiferal lysocline (below c. 3600 m). A planktic percentage <50% is suggestive of shelf depths, and >50% is suggestive of bathyal or abyssal depths above the CCD. In the abyssal zone there is dramatic taphonomic loss of most agglutinated tests (except some textulariids) at burial depths of 0.1-0.2 m, which negates the potential usefulness of these taxa in paleobathymetric assessments.

Delta 66Zn ratios and age of carbonates from ODP Site 138-849 (Table 1)

The carbonate fraction of sediment core ODP 849, leg 138, located in the eastern equatorial Pacific, mostly consisting of coccoliths, was separated and analyzed for its Zn isotopic composition. The overall variation in Zn isotopic composition, as determined by multiple-collector, magnetic-sector, inductively coupled plasma mass spectrometry, was found to be on the order of 1? (expressed in delta66Zn, where deltaxZn=[(xZn/64Zn)sample/(xZn/64Zn)standard -1]*10**3 and x=66, 67 or 68) over the last 175 ka. The analytical precision was 0.04 per mil and the overall reproducibility was usually better than 0.07 per mil. The Zn isotopic composition signal exhibits several marked peaks and a high-frequency variability. A periodogram of the delta66Zn signal showed two periodicities of 35.2 and 21.2 ka. We suggest that the latter is caused by the precession of the Earth's axis of rotation. The periodogram exhibits a minimum at 41.1 ka, thus showing that the Zn isotopic composition is independent of the obliquity in the eastern equatorial Pacific. The range of delta66Zn values observed for the carbonate fraction of ODP 849 overlaps with the range observed for Fe-Mn nodules in the world's oceans, which suggests that seawater/carbonate Zn isotope fractionation is weak. We therefore assume that most of the Zn isotope variability is a result of the selective entrainment of the light isotopes by organic matter in the surface ocean. The ODP 849 delta66Zn record seems to follow the changes in the insolation cycles. Changes in the late summer/fall equatorial insolation modulate the intensity of the equatorial upwelling, hence the mixing between deep and surface waters. We propose that during decreased summer/fall equatorial insolation, when a steep thermocline can develop (El Niño-like conditions), the surface waters cannot be replenished by deep waters and become depleted in the lighter Zn isotopes by biological activity, thus resulting in the progressive increase of the delta66Zn values of the carbonate shells presumably in equilibrium with surface seawater.

(Table 6) Selenium isotopic composition of sediment samples from ODP Site 185-1149

Multiple-collector inductively coupled plasma mass spectrometry has been used for the precise measurement of the isotopic composition of Se in geological samples. Se is chemically purified before analysis by using cotton impregnated with thioglycollic acid. This preconcentration step is required for the removal of matrix-interfering elements for hydride generation, such as transitional metals, and also for the quantitative separation of other hydride-forming elements, such as Ge, Sb, and As. The analyte is introduced in the plasma torch with a continuous-flow hydride generation system. Instrumental mass fractionation is corrected with a "standard-sample bracketing" approach. By use of this new technique, the minimum Se required per analysis is lowered to 10 ng, which is one order of magnitude less than the amount needed for the N-TIMS technique. The estimated external precision calculated for the 82Se/76Se isotope ratio is 0.25? (2 sigma), and the data are reported as delta notation (?) relative to our internal standard (MERCK elemental standard solution). Measurements of Se isotopes are presented for samples of standard solutions and geological reference materials, such as silicate rocks, soils, and sediments. The Se isotopic composition of selected terrestrial and extraterrestrial materials are also presented. An overall Se isotope variation of 8? has been observed, suggesting that Se isotopes fractionate readily and are extremely useful tracers of natural processes.