Structured Linearization of Discrete Mechanical Systems for Analysis and Optimal Control

Variational integrators are well-suited for simulation of mechanical systems because they preserve mechanical quantities about a system such as momentum, or its change if external forcing is involved, and holonomic constraints. While they are not energy-preserving they do exhibit long-time stable energy behavior. However, variational integrators often simulate mechanical system dynamics by solving an implicit difference equation at each time step, one that is moreover expressed purely in terms of configurations at different time steps. This paper formulates the first- and second-order linearizations of a variational integrator in a manner that is amenable to control analysis and synthesis, creating a bridge between existing analysis and optimal control tools for discrete dynamic systems and variational integrators for mechanical systems in generalized coordinates with forcing and holonomic constraints. The forced pendulum is used to illustrate the technique. A second example solves the discrete LQR problem to find a locally stabilizing controller for a 40 DOF system with 6 constraints.Comment: 13 page

Transboundary groundwater : geopolitical consequences, commons sense, and the law of the hidden sea

With 97% of the world’s freshwater resources stored underground, the connection between groundwater resources to the metrics of space, scale and time common to the geographic study of natural resources has not been extensively investigated by geographers. While nearly 240 transboundary aquifers are mapped across the world, a potential “tragedy” is brewing due to the poorly structured institutional capacity built within river basin treaties and agreements and River Basin Organizations to accommodate the management and governance of these transboundary aquifers. Regimes to manage or govern groundwater remain weak. On the basis of a survey of 400 freshwater treaties and agreements completed as part of this study, about 15% include provisions for groundwater. Very few of the treaties and agreements address transboundary aquifers, the coastal aquifer systems which serve as the water supplies to an increasing number of mega cities with populations exceeding 10 million people, the types of aquifers that store groundwater and respond differently to intensive exploitation, or the three dimensional boundaries of the resource or user domains. Recognized as a common pool resource, groundwater resources serve as an example of a “pure” common pool resource. This is because of the difficulty in excluding users and because of the subtractability of the resource as groundwater is pumped or artificially drained from the subsurface. Yet the management and governance of groundwater resources is challenging and increasingly conflictive not only due to its hidden nature, but also because of the difficulty in placing boundaries around the groundwater resources and user domains. These domain boundaries are three dimensional and change with time. Drawing these domain boundaries is supremely political and morph with changing social and cultural values. The present work incorporates an interdisciplinarity and broad systems approach to explore the geography of groundwater to provide context to an inventory of global groundwater resources and user domains. On the basis of surveys of international law and national policies focusing on groundwater, a previously unrecognized typology was derived for the boundaries for groundwater resources and user domains. This work found that (1) traditional approaches to defining groundwater domains focus on predevelopment conditions, referred to herein as a bona-fide “commons” boundary; (2) groundwater development creates human-caused or fiat “hydrocommons” boundary where hydrology and hydraulics are meshed, and (3) the social and cultural values of groundwater users define a fiat “commons heritage” boundary acknowledging that groundwater resources are part of the “common heritage of humankind”. The significance of this typology is that it is difficult to aggregate demographic, social, and economic data within specific boundaries for groundwater resources for detailed geographic analyses, much less develop international regimes, without agreement on the fundamental unit of analysis. Given the complexity of the geologic and political setting of global groundwater resources, a new paradigm of “post-sovereign governance” was examined as part of this study to assess the applicability of global groundwater governance as opposed to international regimes, including the recognition of the geographic overlap between groundwater and ocean resources through an evaluation of the applicability of a law of the sea model for multilateral collaboration regarding groundwater resources through the Law of the Hidden Sea

Parallel block structured adaptive mesh refinement on graphics processing units.

Block-structured adaptive mesh refinement is a technique that can be used when solving partial differential equations to reduce the number of zones necessary to achieve the required accuracy in areas of interest. These areas (shock fronts, material interfaces, etc.) are recursively covered with finer mesh patches that are grouped into a hierarchy of refinement levels. Despite the potential for large savings in computational requirements and memory usage without a corresponding reduction in accuracy, AMR adds overhead in managing the mesh hierarchy, adding complex communication and data movement requirements to a simulation. In this paper, we describe the design and implementation of a native GPU-based AMR library, including: the classes used to manage data on a mesh patch, the routines used for transferring data between GPUs on different nodes, and the data-parallel operators developed to coarsen and refine mesh data. We validate the performance and accuracy of our implementation using three test problems and two architectures: an eight-node cluster, and over four thousand nodes of Oak Ridge National Laboratory’s Titan supercomputer. Our GPU-based AMR hydrodynamics code performs up to 4.87x faster than the CPU-based implementation, and has been scaled to over four thousand GPUs using a combination of MPI and CUDA

Polyhedral Analysis using Parametric Objectives

The abstract domain of polyhedra lies at the heart of many program analysis techniques. However, its operations can be expensive, precluding their application to polyhedra that involve many variables. This paper describes a new approach to computing polyhedral domain operations. The core of this approach is an algorithm to calculate variable elimination (projection) based on parametric linear programming. The algorithm enumerates only non-redundant inequalities of the projection space, hence permits anytime approximation of the output

Projected climate adaptation benefits of One CGIAR

In the present analysis, we first create a projection of the number of beneficiaries (rural individuals and households) in climate hazard areas using geospatial datasets on climate hazards and rural population. We find that: (1) By 2030, CGIAR’s work on climate adaptation is projected to benefit 234 million rural people in 59 million rural households in regions facing significant climate hazards. (2) Some 66% of the projected individual beneficiaries are in SA (34%) and SEA (32%). India (26%) and China (24%) alone account for about 50% of beneficiaries globally. Approximately 15% are in SSA, equally divided between ESA and WCA; the remaining beneficiaries are in LAC (7%) and CWANA (11%). (3) Adoption of climate-smart agricultural practices, climate-adapted varieties, and climate-related advisory services will increase productivity by an average of 24 % and, in at least 62% of cases, will also reduce interannual yield variability. Despite these significant potential upside gains, changing farming practices also carries production risk. (4) Scaling up both improved varieties and improved agronomy could more than double economic benefits as compared to improved varities alone; this suggests that integrative programs that bundle several innovations have the potential to amplify impact

Complete Genome Sequence of Streptococcus pneumoniae Strain BVJ1JL, a Serotype 1 Carriage Isolate from Malawi.

Streptococcus pneumoniae is a leading cause of pneumonia, meningitis, and bacteremia. Serotype 1 is rarely carried but is commonly associated with invasive pneumococcal disease, and in the African "meningitis belt," it is prone to cause cyclical epidemics. We report the complete genome sequence of S. pneumoniae serotype 1 strain BVJ1JL, isolated in Malawi