Modeling grain boundaries in solids using a combined nonlinear and geometrical method

The complex arrangements of atoms near grain boundaries are difficult to understand theoretically. We propose a phenomenological (Ginzburg-Landau-like) description of crystalline phases based on symmetries and fairly general stability arguments. This method allows a very detailed description of defects at the lattice scale with virtually no tunning parameters, unlike usual phase-field methods. The model equations are directly inspired from those used in a very different physical context, namely, the formation of periodic patterns in systems out-of-equilibrium ({\it e.g.} Rayleigh-B\'enard convection, Turing patterns). We apply the formalism to the study of symmetric tilt boundaries. Our results are in quantitative agreement with those predicted by a recent crystallographic theory of grain boundaries based on a geometrical quasicrystal-like construction. These results suggest that frustration and competition effects near defects in crystalline arrangements have some universal features, of interest in solids or other periodic phases.Comment: 10 pages, 3 figure

On the Equivalence Problem for Toric Contact Structures on S^3-bundles over S^2$

We study the contact equivalence problem for toric contact structures on $S^3$-bundles over $S^2$. That is, given two toric contact structures, one can ask the question: when are they equivalent as contact structures while inequivalent as toric contact structures? In general this appears to be a difficult problem. To find inequivalent toric contact structures that are contact equivalent, we show that the corresponding 3-tori belong to distinct conjugacy classes in the contactomorphism group. To show that two toric contact structures with the same first Chern class are contact inequivalent, we use Morse-Bott contact homology. We treat a subclass of contact structures which include the Sasaki-Einstein contact structures $Y^{p,q}$ studied by physicists. In this subcase we give a complete solution to the contact equivalence problem by showing that $Y^{p,q}$ and $Y^{p'q'}$ are inequivalent as contact structures if and only if $p\neq p'$.Comment: 61 page

Distribution of the least-squares estimators of a single Brownian trajectory diffusion coefficient

In this paper we study the distribution function $P(u_{\alpha})$ of the estimators $u_{\alpha} \sim T^{-1} \int^T_0 \, \omega(t) \, {\bf B}^2_{t} \, dt$, which optimise the least-squares fitting of the diffusion coefficient $D_f$ of a single $d$-dimensional Brownian trajectory ${\bf B}_{t}$. We pursue here the optimisation further by considering a family of weight functions of the form $\omega(t) = (t_0 + t)^{-\alpha}$, where $t_0$ is a time lag and $\alpha$ is an arbitrary real number, and seeking such values of $\alpha$ for which the estimators most efficiently filter out the fluctuations. We calculate $P(u_{\alpha})$ exactly for arbitrary $\alpha$ and arbitrary spatial dimension $d$, and show that only for $\alpha = 2$ the distribution $P(u_{\alpha})$ converges, as $\epsilon = t_0/T \to 0$, to the Dirac delta-function centered at the ensemble average value of the estimator. This allows us to conclude that only the estimators with $\alpha = 2$ possess an ergodic property, so that the ensemble averaged diffusion coefficient can be obtained with any necessary precision from a single trajectory data, but at the expense of a progressively higher experimental resolution. For any $\alpha \neq 2$ the distribution attains, as $\epsilon \to 0$, a certain limiting form with a finite variance, which signifies that such estimators are not ergodic.Comment: 27 pages, 5 figure

A Fluid Inclusion and Structural Analysis of the West Chance Vein System, Sunshine Mine, Kellogg, Idaho

The Sunshine mine, near Kellogg ID, is a mesothermal Ag-Pb vein deposit in the Coeur d’Alene mining district. Proterozoic siliciclastic rocks of the Ravalli Group, Belt Supergroup, host the ore bodies. The recently discovered West Chance ore body has been under development for the past five years. This tabular ore body strikes west and dips steeply to the south, has 300m (~1000 ft) strike length and extends approximately 914m (~3000 ft) down dip. Ore is located where the WNW-striking Chance fault changes to a predominately west-striking structure. This study consists of a fluid inclusion and structural analysis of the West Chance ore body to determine pressure, temperature, and composition parameters of mineralization, and to evaluate possible structural controls on ore deposition. Fluid inclusion analysis of over 60 primary inclusions from quartz veins within the West Chance ore body show the dominant type of fluid inclusion to be liquid-rich inclusions composed of H2O-NaCl. Homogenization temperatures, T(h), range from 190.6°C to 325.8°C, with a mean value of 270.9°C. There is no systematic variation of T(h) with respect to depth and no evidence of boiling. Salinities increase with depth through the vein system; thus range from 0.5 wt.% NaCl in the upper portions to 12.2 wt.% NaCl lower in the ore body. Increasing salinity with depth suggests that ore deposition in the West Chance is a result of mixing of two fluids of similar temperature but varying salinities or that boiling occurred higher in the system yielding the observed salinity contrast. A constructed P-V-T diagram suggests that the West Chance ore body formed at pressures in the range of 0.5-2 kbars, corresponding to depths of 1.75-7 km for fluid pressure under lithostatic load. Structural analysis consisted of mapping, petrofabric analysis, and compilation of existing data and showed that the mineralized fault system consists of an anastomosing series of smaller faults that strike WSW to WNW. Megascopic features and petrographic textures indicate that the fault has been reactivated over time. Ore shoots plunge steeply to the west with a 60-70° rake. Previous work on structural control of ore fluids has suggested mineralization took place during left-lateral or reverse motion. The present study of the West Chance ore body shows there is evidence for both types of motion and supports left-lateral, reverse, and right-lateral as a sequence of fault motions, with right lateral motion occurring after ore deposition. However, there are no constraints on the absolute timing of faulting

Changes in the Spatial Allocation of Cropland in the Ft. Cobb Watershed as a Result of Environmental Restrictions

Pollution runoff estimates from SWAT are used in a mathematical programming model to optimally model site-specific crop and conservation practices for pollution abatement in the Ft. Cobb watershed in Southwestern Oklahoma. Results indicate the tradeoffs between producer income, sediment and nutrient runoff and the spatial allocation of crops in the watershed.Environmental Economics and Policy,

Structures of fibrils formed by α-synuclein hereditary disease mutant H50Q reveal new polymorphs.

Deposits of amyloid fibrils of α-synuclein are the histological hallmarks of Parkinson's disease, dementia with Lewy bodies and multiple system atrophy, with hereditary mutations in α-synuclein linked to the first two of these conditions. Seeing the changes to the structures of amyloid fibrils bearing these mutations may help to understand these diseases. To this end, we determined the cryo-EM structures of α-synuclein fibrils containing the H50Q hereditary mutation. We find that the H50Q mutation results in two previously unobserved polymorphs of α-synuclein: narrow and wide fibrils, formed from either one or two protofilaments, respectively. These structures recapitulate conserved features of the wild-type fold but reveal new structural elements, including a previously unobserved hydrogen-bond network and surprising new protofilament arrangements. The structures of the H50Q polymorphs help to rationalize the faster aggregation kinetics, higher seeding capacity in biosensor cells and greater cytotoxicity that we observe for H50Q compared to wild-type α-synuclein

Toric self-dual Einstein metrics as quotients

We use the quaternion Kahler reduction technique to study old and new self-dual Einstein metrics of negative scalar curvature with at least a two-dimensional isometry group, and relate the quotient construction to the hyperbolic eigenfunction Ansatz. We focus in particular on the (semi-)quaternion Kahler quotients of (semi-)quaternion Kahler hyperboloids, analysing the completeness and topology, and relating them to the self-dual Einstein Hermitian metrics of Apostolov-Gauduchon and Bryant.Comment: 30 page

Finite surgeries on three-tangle pretzel knots

We classify Dehn surgeries on (p,q,r) pretzel knots that result in a manifold of finite fundamental group. The only hyperbolic pretzel knots that admit non-trivial finite surgeries are (-2,3,7) and (-2,3,9). Agol and Lackenby's 6-theorem reduces the argument to knots with small indices p,q,r. We treat these using the Culler-Shalen norm of the SL(2,C)-character variety. In particular, we introduce new techniques for demonstrating that boundary slopes are detected by the character variety.Comment: 18 pages, 15 figures v2 - minor revisions throughou