Modulus method and radial stretch map in the Heisenberg group

We develop a modulus method for surface families inside a domain in the Heisenberg group and we prove that the stretch map between two Heisenberg spherical rings is a minimiser for the mean distortion among the class of contact quasiconformal maps between these rings which satisfy certain boundary conditions.

Modulus and Poincaré Inequalities on Non-Self-Similar Sierpiński Carpets

A carpet is a metric space homeomorphic to the Sierpiński carpet. We characterize, within a certain class of examples, non-self-similar carpets supporting curve families of nontrivial modulus and supporting Poincaré inequalities. Our results yield new examples of compact doubling metric measure spaces supporting Poincaré inequalities: these examples have no manifold points, yet embed isometrically as subsets of Euclidean space.

Change of the condyle-position in maximum intercuspidation during digital, clinical occlusal analysis

Digital analysis of the occlusal contacts can be performed with the T-scan device (T Scan III, TekScan, Boston, USA). However, the thickness of the interocclusal T-scan sheet (100 μm) may lead to a displacement of the mandible. Thus, the aim of this study was to investigate the impact of the T-scan sheet on the position of the mandibular condyles in maximum intercuspidation. Twenty dentate subjects with healthy jaw function were enrolled in the study. An ultrasonic axiography device was used to measure the position of the condyles. Ten 3D condyle positions in maximum intercuspidation of the teeth were recorded: first the reference position without the sheet, then 3 times without the sheet, 3 times with the sheet, and finally again 3 times without the sheet. There was a statistically significant difference (Wilcoxon matched pairs test) between the condyle positions with and without the interocclusally positioned T-scan sheet (P < 0.0005). The T-scan device lead to a displacement of the condyles of about 1 mm mainly in ventral direction (P = 0.005). Thus, occlusal analysis is not performed in physiological, maximum intercuspidation. This has to be considered when interpreting the measured contact points.

Computational and experimental methodology for site-matched investigations of the influence of mineral mass fraction and collagen orientation on the axial indentation modulus of lamellar bone

Relationships between mineralization, collagen orientation and indentation modulus were investigated in bone structural units from the mid-shaft of human femora using a site-matched design. Mineral mass fraction, collagen fibril angle and indentation moduli were measured in registered anatomical sites using backscattered electron imaging, polarized light microscopy and nano-indentation, respectively. Theoretical indentation moduli were calculated with a homogenization model from the quantified mineral densities and mean collagen fibril orientations. The average indentation moduli predicted based on local mineralization and collagen fibers arrangement were not significantly different from the average measured experimentally with nanoindentation (p=0.9). Surprisingly, no substantial correlation of the measured indentation moduli with tissue mineralization and/or collagen fiber arrangement was found. Nano-porosity, micro-damage, collagen cross-links, non-collagenous proteins or other parameters affect the indentation measurements. Additional testing/simulation methods need to be considered to properly understand the variability of indentation moduli, beyond the mineralization and collagen arrangement in bone structural units.

Tissue properties of the human vertebral body sub-structures evaluated by means of microindentation

Purpose The better understanding of vertebral mechanical properties can help to improve the diagnosis of vertebral fractures. As the bone mechanical competence depends not only from bone mineral density (BMD) but also from bone quality, the goal of the present study was to investigate the anisotropic indentation moduli of the different sub-structures of the healthy human vertebral body and spondylophytes by means of microindentation. Methods Six human vertebral bodies and five osteophytes (spondylophytes) were collected and prepared for microindentation test. In particular, indentations were performed on bone structural units of the cortical shell (along axial, circumferential and radial directions), of the endplates (along the anterio-posterior and lateral directions), of the trabecular bone (along the axial and transverse directions) and of the spondylophytes (along the axial direction). A total of 3164 indentations down to a maximum depth of 2.5 µm were performed and the indentation modulus was computed for each measurement. Results The cortical shell showed an orthotropic behavior (indentation modulus, Ei, higher if measured along the axial direction, 14.6±2.8 GPa, compared to the circumferential one, 12.3±3.5 GPa, and radial one, 8.3±3.1 GPa). Moreover, the cortical endplates (similar Ei along the antero-posterior, 13.0±2.9 GPa, and along the lateral, 12.0±3.0 GPa, directions) and the trabecular bone (Ei= 13.7±3.4 GPa along the axial direction versus Ei=10.9±3.7 GPa along the transverse one) showed transversal isotropy behavior. Furthermore, the spondylophytes showed the lower mechanical properties measured along the axial direction (Ei=10.5±3.3 GPa). Conclusions The original results presented in this study improve our understanding of vertebral biomechanics and can be helpful to define the material properties of the vertebral substructures in computational models such as FE analysis.

Glacier response to the change in atmospheric circulation in the eastern Mediterranean during the Last Glacial Maximum

In this study, we document glacial deposits and reconstruct the glacial history in the Karagöl valley system in the eastern Uludağ in northwestern Turkey based on 42 cosmogenic 10Be exposure ages from boulders and bedrock. Our results suggest the Last Glacial Maximum (LGM) advance prior to 20.4 ± 1.2 ka and at least three re-advances until 18.6 ± 1.2 ka during the global LGM within Marine Isotope Stage-2. In addition, two older advances of unknown age are geomorphologically well constrained, but not dated due to the absence of suitable boulders. Glaciers advanced again two times during the Lateglacial. The older is exposure dated to not later than 15.9 ± 1.1 ka and the younger is attributed to the Younger Dryas (YD) based on field evidence. The timing of the glaciations in the Karagöl valley correlates well with documented archives in the Anatolian and Mediterranean mountains and the Alps. These glacier fluctuations may be explained by the change in the atmospheric circulation pattern during the different phases of North Atlantic Oscillation (NAO) winter indices.

Transient simulations of the carbon and nitrogen dynamics in northern peatlands: from the Last Glacial Maximum to the 21st century

The development of northern high-latitude peatlands played an important role in the carbon (C) balance of the land biosphere since the Last Glacial Maximum (LGM). At present, carbon storage in northern peatlands is substantial and estimated to be 500 ± 100 Pg C (1 Pg C = 1015 g C). Here, we develop and apply a peatland module embedded in a dynamic global vegetation and land surface process model (LPX-Bern 1.0). The peatland module features a dynamic nitrogen cycle, a dynamic C transfer between peatland acrotelm (upper oxic layer) and catotelm (deep anoxic layer), hydrology- and temperature-dependent respiration rates, and peatland specific plant functional types. Nitrogen limitation down-regulates average modern net primary productivity over peatlands by about half. Decadal acrotelm-to-catotelm C fluxes vary between −20 and +50 g C m−2 yr−1 over the Holocene. Key model parameters are calibrated with reconstructed peat accumulation rates from peat-core data. The model reproduces the major features of the peat core data and of the observation-based modern circumpolar soil carbon distribution. Results from a set of simulations for possible evolutions of northern peat development and areal extent show that soil C stocks in modern peatlands increased by 365–550 Pg C since the LGM, of which 175–272 Pg C accumulated between 11 and 5 kyr BP. Furthermore, our simulations suggest a persistent C sequestration rate of 35–50 Pg C per 1000 yr in present-day peatlands under current climate conditions, and that this C sink could either sustain or turn towards a source by 2100 AD depending on climate trajectories as projected for different representative greenhouse gas concentration pathways.

A reconstruction of atmospheric carbon dioxide and its stable carbon isotopic composition from the penultimate glacial maximum to the last glacial inception

The reconstruction of the stable carbon isotope evolution in atmospheric CO2 (δ13Catm), as archived in Antarctic ice cores, bears the potential to disentangle the contributions of the different carbon cycle fluxes causing past CO2 variations. Here we present a new record of δ13Catm before, during and after the Marine Isotope Stage 5.5 (155 000 to 105 000 yr BP). The dataset is archived on the data repository PANGEA® (www.pangea.de) under 10.1594/PANGAEA.817041. The record was derived with a well established sublimation method using ice from the EPICA Dome C (EDC) and the Talos Dome ice cores in East Antarctica. We find a 0.4‰ shift to heavier values between the mean δ13Catm level in the Penultimate (~ 140 000 yr BP) and Last Glacial Maximum (~ 22 000 yr BP), which can be explained by either (i) changes in the isotopic composition or (ii) intensity of the carbon input fluxes to the combined ocean/atmosphere carbon reservoir or (iii) by long-term peat buildup. Our isotopic data suggest that the carbon cycle evolution along Termination II and the subsequent interglacial was controlled by essentially the same processes as during the last 24 000 yr, but with different phasing and magnitudes. Furthermore, a 5000 yr lag in the CO2 decline relative to EDC temperatures is confirmed during the glacial inception at the end of MIS5.5 (120 000 yr BP). Based on our isotopic data this lag can be explained by terrestrial carbon release and carbonate compensation.

Resin composites: Modulus of elasticity and marginal quality

OBJECTIVE To investigate how the modulus of elasticity of resin composites influences marginal quality in restorations submitted to thermocyclic and mechanical loading. METHODS Charisma, Filtek Supreme XTE and Grandio were selected as they were found to possess different moduli of elasticity but quite similar polymerization contraction. MOD cavities (n=30) were prepared in extracted premolars, restored and then subjected to thermocyclic and mechanical loading. Marginal quality of the restorations before and after loading was analyzed on epoxy replicas under a scanning electron microscope. The percentage of gap-free margins and occurrence of paramarginal fractures were registered. Modulus of elasticity and polymerization contraction were analyzed with parametric and margins with nonparametric ANOVA and post hoc Tukey HSD or Wilcoxon rank-sum tests, respectively. The number of paramarginal fractures was analyzed with exact Fisher tests (α=0.05). RESULTS Grandio demonstrated significantly more gap-free enamel margins than Charisma and Filtek Supreme XTE, before and after loading (p<0.01), whereas there was no difference between Charisma and Filtek Supreme XTE (p>0.05). No significant effect of resin composite (p=0.81) on the quality of dentine margins was observed, before or after loading. Deterioration of all margins was evident after loading (p<0.0001). More paramarginal enamel fractures were observed after loading in teeth restored with Grandio when compared to Charisma (p=0.008). CONCLUSIONS The resin composite with the highest modulus of elasticity resulted in the highest number of gap-free enamel margins but with an increased incidence of paramarginal enamel fractures. CLINICAL SIGNIFICANCE The results from this study suggest that the marginal quality of restorations can be improved by the selection of a resin composite with modulus of elasticity close to that of dentine, although an increase in paramarginal enamel fractures can result as a consequence.

Terrestrial and submarine evidence for the extent and timing of the Last Glacial Maximum and the onset of deglaciation on the maritime-Antarctic and sub-Antarctic islands

This paper is the maritime and sub–Antarctic contribution to the Scientific Committee for Antarctic Research (SCAR) Past Antarctic Ice Sheet Dynamics (PAIS) community Antarctic Ice Sheet reconstruction. The overarching aim for all sectors of Antarctica was to reconstruct the Last Glacial Maximum (LGM) ice sheet extent and thickness, and map the subsequent deglaciation in a series of 5000 year time slices. However, our review of the literature found surprisingly few high quality chronological constraints on changing glacier extents on these timescales in the maritime and sub–Antarctic sector. Therefore, in this paper we focus on an assessment of the terrestrial and offshore evidence for the LGM ice extent, establishing minimum ages for the onset of deglaciation, and separating evidence of deglaciation from LGM limits from those associated with later Holocene glacier fluctuations. Evidence included geomorphological descriptions of glacial landscapes, radiocarbon dated basal peat and lake sediment deposits, cosmogenic isotope ages of glacial features and molecular biological data. We propose a classification of the glacial history of the maritime and sub–Antarctic islands based on this assembled evidence. These include: (Type I) islands which accumulated little or no LGM ice; (Type II) islands with a limited LGM ice extent but evidence of extensive earlier continental shelf glaciations; (Type III) seamounts and volcanoes unlikely to have accumulated significant LGM ice cover; (Type IV) islands on shallow shelves with both terrestrial and submarine evidence of LGM (and/or earlier) ice expansion; (Type V) Islands north of the Antarctic Polar Front with terrestrial evidence of LGM ice expansion; and (Type VI) islands with no data. Finally, we review the climatological and geomorphological settings that separate the glaciological history of the islands within this classification scheme.

A community-based geological reconstruction of Antarctic Ice Sheet deglaciation since the Last Glacial Maximum

A robust understanding of Antarctic Ice Sheet deglacial history since the Last Glacial Maximum is important in order to constrain ice sheet and glacial-isostatic adjustment models, and to explore the forcing mechanisms responsible for ice sheet retreat. Such understanding can be derived from a broad range of geological and glaciological datasets and recent decades have seen an upsurge in such data gathering around the continent and Sub-Antarctic islands. Here, we report a new synthesis of those datasets, based on an accompanying series of reviews of the geological data, organised by sector. We present a series of timeslice maps for 20 ka, 15 ka, 10 ka and 5 ka, including grounding line position and ice sheet thickness changes, along with a clear assessment of levels of confidence. The reconstruction shows that the Antarctic Ice sheet did not everywhere reach the continental shelf edge at its maximum, that initial retreat was asynchronous, and that the spatial pattern of deglaciation was highly variable, particularly on the inner shelf. The deglacial reconstruction is consistent with a moderate overall excess ice volume and with a relatively small Antarctic contribution to meltwater pulse 1a. We discuss key areas of uncertainty both around the continent and by time interval, and we highlight potential priorities for future work. The synthesis is intended to be a resource for the modelling and glacial geological community.