Lens rigidity with trapped geodesics in two dimensions

We consider the scattering and lens rigidity of compact surfaces with boundary that have a trapped geodesic. In particular we show that the flat cylinder and the flat M\"obius strip are determined by their lens data. We also see by example that the flat M\"obius strip is not determined by it's scattering data. We then consider the case of negatively curved cylinders with convex boundary and show that they are lens rigid.Comment: 12 pages, 2 figure

Predicting hydrologic response from physio-climatic attributes: an application to ungauged sub-catchments of the Burdekin River, North Queensland

The Burdekin is a large (140,000 square kilometres) catchment located in the dry tropics of North Queensland, Australia. To assess the water resources of this catchment, we require a methodology which will allow us to determine the daily streamflow at any point within the catchment. To this end, we have utilised a simple, lumped parameter model, IHACRES. Of the five parameters in the model, three have been set to default values, while the other two have been related to the physio-climatic attributes of the sub-catchment under consideration. The parameter defining total catchment water yield was constrained using %yield, which is related to summer precipitation, while the streamflow recession time constant was related to the total length of stream reaches in the catchment. These relationships were applicable over a range of scales from 68 square kilometres to 130,000 square kilometres, however three separate relationships were required to define c in the three major regions of the Burdekin – the upper Burdekin, Bowen, and Belyando Suttor. This research has provided a valuable insight into the hydrologic behaviour of the Burdekin catchment, while also providing a useful methodology for water resources assessment. The invariance of the relationships with scale indicates that the dominant processes may be similar for a range of scales, while the fact that different relationships were required for each of the three major regions indicates the geographic limitations of this regionalisation approach

The Biophysical Toolbox: a Biophysical Modelling Tool Developed within the IWRAM-DSS

With rapid intensification of agricultural catchments in northern Thailand a suite of environmental issues have surfaced. The Integrated Water Resources Assessment and Management (IWRAM) project was instigated in response to these issues. The project developed a Decision Support System for the exploration of biophysical and socio-economic impacts of water resources use option. The IWRAM-DSS is comprised of a 'Biophysical Toolbox' that can be implemented alone or an 'Integrated Toolbox' that links socioeconomic models with the biophysical toolbox to explore economic trade-offs and impacts of various scenarios. The Biophysical Toolbox is comprised of three modules - the CATCHCROP crop model, a hydrologic module based upon the IHACRES rainfall-runoff model, and a Universal Soil Loss Equation (USLE) approach modified to suit conditions in northern Thailand. This working paper describes and implements the Fortran 77 version of the Biophysical Toolkit developed jointly by Dr. Barry Croke and Wendy Merritt. A Java version of the model has been coded by Dr. Claude Dietrich and Nick Ardlie, however this version has not been linked with the economic model as part of the fully integrated IWRAM-DSS

Conjugacy and rigidity for nonpositively curved manifolds of higher rank

Let M and N be compact Riemannian manifolds with sectional curvature K ⩽ 0 such that M has dimension ⩾ 3 and rank ⩾ 2. If there exists a C0 conjugacy F between the geodesic flows of the unit tangent bundles of M and N, then there exists an isometry G: M → N that induces the same isomorphism as F between the fundamental groups of M and N