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Notizen: The half-space problem of rarefied gas flow (the Kramers problem) is considered and use of the SN algorithm is outlined. Accurate numerical results for the velocity slip coefficient and velocity defect are obtained for a hard sphere gas and are compared with previously reported results and experimental data.

Notizen: In the Littleton Formation, garnet porphyroblasts preserve three generations of growth that occurred before formation of the Bolton Syncline. Inclusion trails of foliations overgrown by these porphyroblasts are always truncated by the matrix foliation suggesting that garnet growth predated the matrix foliation. In contrast, many staurolite porphyroblasts grew synchronously with formation of the Bolton Syncline. However, local rim overgrowths of the matrix foliation suggest that some staurolite porphyroblasts continued to grow after development of the fold during younger crenulation producing deformations. The axes of curvature or intersection of foliations defined by inclusion trails inside the garnet porphyroblasts lie oblique to the axial plane of the Bolton Syncline but do not change orientation across it. This suggests the garnets were not rotated during the subsequent deformation associated with fold development or during even younger crenulation events. Three samples also contain a different set of axes defined by curvature of inclusion trails in the cores of garnet porphyroblasts suggesting a protracted history of garnet growth. Foliation intersection axes in staurolite porphyroblasts are consistently orientated close to the trend of the axial plane of the Bolton Syncline on both limbs of the fold. In contrast, axes defined by curvature or intersection of foliations in the rims of staurolite porphyroblasts in two samples exhibit a different trend. This phase of staurolite growth is associated with a crenulation producing deformation that postdated formation of the Bolton Syncline. Measurement of foliation intersection axes defined by inclusion trails in both garnet and staurolite porphyroblasts has enabled the timing of growth relative to one another and to the development of the Bolton Syncline to be distinguished in rocks where other approaches have not been successful. Consistent orientation of foliation intersection axes across a range of younger structures suggests that the porphyroblasts did not rotate relative to geographical coordinates during subsequent ductile deformation. Foliation intersection axes in porphyroblasts are thus useful for correlating phases of porphyroblastic growth in this region.

Notizen: Recent studies have used the relative rotation axis of sigmoidal and spiral-shaped inclusion trails, known as Foliation Inflexion/Intersection Axis (FIA), to investigate geological processes such as fold mechanisms and porphyroblast growth. The geological usefulness of this method depends upon the accurate measurement of FIA orientations and correct correlation of temporally related FIAs. This paper uses new data from the Canton Schist to assess the variation in FIA orientations within and between samples, and evaluates criteria for correlating FIAs. For the first time, an entire data set of FIA measurements is published, and data are presented in a way that reflects the variation in FIA orientations within individual samples and provides an indication of the reliability of the data. Analysis of 61 FIA trends determined from the Canton Schist indicate a minimum intrasample range in FIA orientations of 30°. Three competing models are presented for correlation of these FIAs, and each of the models employ different correlation criteria. Correlation of FIAs in Model 1 is based on relative timing and textural criteria, while Model 2 uses relative timing, orientation and patterns of changing FIA orientations, and Model 3 uses relative timing and FIA orientation as correlation criteria. Importantly, the three models differ in the spread of FIA orientations within individual sets, and the number of sets distinguished in the data. Relative timing is the most reliable criterion for correlation, followed by textural criteria and patterns of changing FIA orientations from core to rim of porphyroblasts. It is proposed that within a set of temporally related FIAs, the typical spread of orientations involves clustering of data in a 60° range, but outliers occur at other orientations including near-normal to the peak distribution. Consequently, in populations of FIA data that contain a wide range of orientations, correlation on the basis of orientation is unreliable in the absence of additional criteria. The results of this study suggest that FIAs are best used as semiquantitative indicators of bulk trends rather than an exact measurement for the purpose of quantitative analyses.

Notizen: Schists from the Appalachian Orogen in south-east Vermont have undergone multiple phases of garnet growth. These phases can be distinguished by the trend and relative timing of foliation inflexion or intersection axes (FIAs) of foliations preserved as inclusion trails in garnet porphyroblasts. The relative timing of different generations of FIAs is determined from samples containing porphyroblasts with two or three differently trending FIAs developed outwards from core to rim (multi-FIA porphyroblasts). Schists from south-east Vermont show a consistent pattern of relative clockwise rotation of FIA trends from oldest to youngest. Four populations or sets of FIAs can be distinguished on the basis of their relative timings and trends. From oldest to youngest, the four sets have modal peaks trending SW–NE, W–E, NNW–SSE and SSW–NNE. These peaks show that each of the four FIA sets has a statistically consistent trend at all scales across a 35×125 km area containing numerous mesoscopic and macroscopic folds. The FIAs of Set 4 are defined by inclusion trails that are continuous with matrix foliations, have trends subparallel to most folds and are inferred to have developed contemporaneously with these structures. Conversely, Sets 1 to 3 are oblique to and pre-date most matrix foliations and folds. All four FIA sets occur in Siluro-Devonian rocks and must have formed in the Acadian Orogeny. The lack of statistically significant differences in the distribution of FIA trends across the study area and their consistent relative timings in multi-FIA porphyroblasts, despite a complex regional deformation history involving numerous phases of folding at all scales, suggest the porphyroblasts have not rotated relative to one another. The change in FIA trend with time resulted from rotation of the kinematic reference frame of bulk flow, possibly as a consequence of the reorganization of lithospheric plates responsible for Acadian orogenesis.Recognition of distinct generations of FIAs provides a means of distinguishing different phases of porphyroblast growth. Four periods of garnet porphyroblast growth occurred in the schists of south-east Vermont. This growth was heterogeneously distributed on the cm2–m2 scale. No single porphyroblast records all stages of growth, and adjacent samples from the same or dissimilar rock types commonly contain porphyroblasts that preserve different sequences of growth. Factors that may have been responsible for switching porphyroblast growth on and off at this scale include: (i) subtle differences in bulk chemical composition; (ii) oscillating levels of heat, owing to the buffering effect of endothermic garnet-forming reactions; (iii) channelized infiltration of fluids with localized fluid buffering of bulk composition; and (iv) cyclic controls on the rates of diffusion and material transport of reactants, either by channelized fluid flow or by a changing pattern of microfracturing during foliation development.Consistency in FIA trend and relative timing provide a new method for potentially distinguishing and correlating successive metamorphic events, or even phases of metamorphism within a progressive tectonothermal event, along and across orogens. Using a consistent pattern of core to rim changes in FIA trend, multiple phases of growth of a single porphyroblastic mineral can be quantitatively distinguished, allowing correlation of different phases of growth around and across macroscopic folds. The relative timing of growth of different porphyroblastic minerals can also be quantitatively determined using FIA data and correlated around and across macroscopic folds. Conceptually, the paragenetic history preserved in each generation of porphyroblast growth, in the form of chemical zoning and the minerals in inclusion trails, could be combined to produce a more detailed P–T–t–deformation path than previously determined.

Notizen: Abstract The half-space problem of rarefied gas flow (the Kramers problem) is considered for the linearized Boltzmann equation and arbitrary gas-surface interaction. Accurate numerical results for the velocity slip coefficient and velocity defect are obtained for the rigid sphere interaction and Maxwellian boundary condition.