Tectonic evolution of the Karakoram metamorphic complex (NW Himalayas) reflected in the 3D structures of spiral garnets: Insights from X-ray computed micro-tomography

We thank Pentti Hölttä and Syed Zahid Shah for many useful discussions. We thank the referees, F. George and an anonymous reviewer, for their constructive comments.Spiral garnet porphyroblasts are known to record lengthy periods of deformation and metamorphism by preserving single or multiple FIAs (Foliation Intersection Axis) formed normal to tectonic shortening directions. Thanks to technological advances in X-ray computed micro-tomography (XCMT), FIAs can now be readily determined in relatively large samples in contrast to previous methods that require the preparation of a set of radial vertical and horizontal thin sections of samples. XCMT scanning not only alleviates tedious thin section based procedures but also illuminates the complete internal architecture of a rock sample allowing three-dimensional (3D) quantitative shape analysis of an individual porphyroblast as well as precise measurement of FIAs. We applied the technique to a sample from the Hunza Valley in the Karakoram metamorphic complex (KMC), NW Himalayas, containing numerous garnet porphyroblasts with spiral-shaped inclusion trails. The XCMT imaging reveals an E-Wtrending FIA within the sample, which is consistent with orthogonal N-S collision of the India-Kohistan Island Arc with Asia. Garnet long axes (X-GT) have variable plunges that define a broad sub-vertical maximumand a small sub-horizontalmaximum. The X-GT principle maxima lie at N-090 and N-120. Smaller maxima lie at N-020 and N- 340. Geometric relationships between X-GT axes and FIA orientation in the sample suggest that porphyroblast shapes are controlled by the geometry of the lens-shaped microlithons in which they tend to nucleate and grow. The orientation of inclusion trails and matrix foliations in the sample are correlated with three discrete tectono-metamorphic events that respectively produced andalusite, sillimanite and kyanite in the KMC. Late staurolite growth in the sample reveals howthe rocks extruded to the surface via a significant role of roll-on tectonics, which can be correlated with the Central Himalayas

Modeling mass transfer in fracture flows with the time domain-random walk method

The time domain-random walk method was developed further for simulating mass transfer in fracture flows together with matrix diffusion in surrounding porous media. Specifically, a time domain-random walk scheme was developed for numerically approximating solutions of the advection-diffusion equation when the diffusion coefficient exhibits significant spatial variation or even discontinuities. The proposed scheme relies on second-order accurate, central-difference approximations of the advective and diffusive fluxes. The scheme was verified by comparing simulated results against analytical solutions in flow configurations involving a rectangular channel connected on one side with a porous matrix. Simulations with several flow rates, diffusion coefficients, and matrix porosities indicate good agreement between the numerical approximations and analytical solutions.Peer reviewe

Determining Crack Aperture Distribution in Rocks Using the C-14-PMMA Autoradiographic Method : Experiments and Simulations

Because cracks control the global mechanical and transport properties of crystalline rocks, it is of a crucial importance to suitably determine their aperture distribution, which evolves through alteration processes and rock weathering. Due to the high variability of crack networks in rocks, a multiscale approach is needed. The C-14-PMMA (polymethylmethacrylate) method was developed to determine crack apertures using a set of artificial crack samples with different controlled apertures and tilt angles and also using Monte Carlo simulations. The experiments and simulations show the same result: the estimation of apparent aperture w(A) was successful regardless of tilt angle, even if the estimates are less accurate for low tilt angles (Peer reviewe

Response of electrically coupled spiking neurons: a cellular automaton approach

Experimental data suggest that some classes of spiking neurons in the first layers of sensory systems are electrically coupled via gap junctions or ephaptic interactions. When the electrical coupling is removed, the response function (firing rate {\it vs.} stimulus intensity) of the uncoupled neurons typically shows a decrease in dynamic range and sensitivity. In order to assess the effect of electrical coupling in the sensory periphery, we calculate the response to a Poisson stimulus of a chain of excitable neurons modeled by $n$-state Greenberg-Hastings cellular automata in two approximation levels. The single-site mean field approximation is shown to give poor results, failing to predict the absorbing state of the lattice, while the results for the pair approximation are in good agreement with computer simulations in the whole stimulus range. In particular, the dynamic range is substantially enlarged due to the propagation of excitable waves, which suggests a functional role for lateral electrical coupling. For probabilistic spike propagation the Hill exponent of the response function is $\alpha=1$, while for deterministic spike propagation we obtain $\alpha=1/2$, which is close to the experimental values of the psychophysical Stevens exponents for odor and light intensities. Our calculations are in qualitative agreement with experimental response functions of ganglion cells in the mammalian retina.Comment: 11 pages, 8 figures, to appear in the Phys. Rev.