The fully residually F quotients of F*<x,y>

We describe the fully residually F; or limit groups relative to F; (where F is a free group) that arise from systems of equations in two variables over F that have coefficients in F.Comment: 64 pages, 2 figures. Following recommendations from a referee, the paper has been completely reorganized and many small mistakes have been corrected. There were also a few gaps in the earlier version of the paper that have been fixed. In particular much of the content of Section 8 in the previous version had to be replaced. This paper is to appear in Groups. Geom. Dy

Dynamic fluvial systems and gravel progradation in the Himalayan foreland

Although the large-scale stratigraphy of many terrestrial foreland basins is punctuated by major episodes of gravel progradation, the relationships of such facies to hinterland tectonism and climate change are often unclear. Structural reentrants provide windows into older and more proximal parts of the foreland than are usually exposed, and thus provide key insights to earlier phases of foreland evolution. Our magnetostratigraphic studies show that, although the major lithofacies preserved within the Himachal Pradesh structural reentrant in northwestern India resemble Neogene facies in Pakistan, they have a much greater temporal and spatial variability. From 11.5 to 7 Ma, major facies boundaries in Himachal Pradesh vary by as much as 2–3 m.y. across distances of 20–30 km and are controlled by the interference between a major southeastward-flowing axial river and a major southwestward-flow- ing transverse river. A thick but highly confined middle to late Miocene conglomerate facies includes the oldest extensive Siwalik conglomerates yet dated (10 Ma) and implies the development of significant erosional topography along the Main Boundary thrust prior to 11 Ma. Our studies document extensive syntectonic gravel progradation with conglomerates extending tens of kilometers into the undeformed foreland during a period of increased subsidence rate and within 1–2 m.y. of major thrust initiation. Overall, gravel progradation is modulated by the interplay among subsidence, sediment supply, and the proportion of gravels in rivers entering the foreland

Numerical Solution of the (1s1s) and (1s2s) Hydrogenic Pair Equations

The pair functions which determine the exact first-order wave function for the ground state of the three-electron atom have been found with the matrix finite-difference method. The second- and third-order energies for the (1s1s)^1S, (1s2s)^3S, and (1s2s)^1S states of the two-electron atom are presented along with contour and perspective plots of the pair functions

The first passage problem for diffusion through a cylindrical pore with sticky walls

We calculate the first passage time distribution for diffusion through a cylindrical pore with sticky walls. A particle diffusively explores the interior of the pore through a series of binding and unbinding events with the cylinder wall. Through a diagrammatic expansion we obtain first passage time statistics for the particle's exit from the pore. Connections between the model and nucleocytoplasmic transport in cells are discussed.Comment: v2: 13 pages, 6 figures, substantial revision

On the quasi-isometric rigidity of graphs of surface groups

Let $\Gamma$ be a word hyperbolic group with a cyclic JSJ decomposition that has only rigid vertex groups, which are all fundamental groups of closed surface groups. We show that any group $H$ quasi-isometric to $\Gamma$ is abstractly commensurable with $\Gamma$.Comment: 54 pages, 10 figures, comments welcom