Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices

Geophysical monitoring and reactive transport modeling of ureolytically-driven calcium carbonate precipitation

Ureolytically-driven calcium carbonate precipitation is the basis for a promising in-situ remediation method for sequestration of divalent radionuclide and trace metal ions. It has also been proposed for use in geotechnical engineering for soil strengthening applications. Monitoring the occurrence, spatial distribution, and temporal evolution of calcium carbonate precipitation in the subsurface is critical for evaluating the performance of this technology and for developing the predictive models needed for engineering application. In this study, we conducted laboratory column experiments using natural sediment and groundwater to evaluate the utility of geophysical (complex resistivity and seismic) sensing methods, dynamic synchrotron x-ray computed tomography (micro-CT), and reactive transport modeling for tracking ureolytically-driven calcium carbonate precipitation processes under site relevant conditions. Reactive transport modeling with TOUGHREACT successfully simulated the changes of the major chemical components during urea hydrolysis. Even at the relatively low level of urea hydrolysis observed in the experiments, the simulations predicted an enhanced calcium carbonate precipitation rate that was 3-4 times greater than the baseline level. Reactive transport modeling results, geophysical monitoring data and micro-CT imaging correlated well with reaction processes validated by geochemical data. In particular, increases in ionic strength of the pore fluid during urea hydrolysis predicted by geochemical modeling were successfully captured by electrical conductivity measurements and confirmed by geochemical data. The low level of urea hydrolysis and calcium carbonate precipitation suggested by the model and geochemical data was corroborated by minor changes in seismic P-wave velocity measurements and micro-CT imaging; the latter provided direct evidence of sparsely distributed calcium carbonate precipitation. Ion exchange processes promoted through NH4+ production during urea hydrolysis were incorporated in the model and captured critical changes in the major metal species. The electrical phase increases were potentially due to ion exchange processes that modified charge structure at mineral/water interfaces. Our study revealed the potential of geophysical monitoring for geochemical changes during urea hydrolysis and the advantages of combining multiple approaches to understand complex biogeochemical processes in the subsurface

Soil engineering in vivo: harnessing natural biogeochemical systems for sustainable, multi-functional engineering solutions

Carbon sequestration, infrastructure rehabilitation, brownfields clean-up, hazardous waste disposal, water resources protection and global warming—these twenty-first century challenges can neither be solved by the high-energy consumptive practices that hallmark industry today, nor by minor tweaking or optimization of these processes. A more radical, holistic approach is required to develop the sustainable solutions society needs. Most of the above challenges occur within, are supported on, are enabled by or grown from soil. Soil, contrary to conventional civil engineering thought, is a living system host to multiple simultaneous processes. It is proposed herein that ‘soil engineering in vivo’, wherein the natural capacity of soil as a living ecosystem is used to provide multiple solutions simultaneously, may provide new, innovative, sustainable solutions to some of these great challenges of the twenty-first century. This requires a multi-disciplinary perspective that embraces the science of biology, chemistry and physics and applies this knowledge to provide multi-functional civil and environmental engineering designs for the soil environment. For example, can native soil bacterial species moderate the carbonate cycle in soils to simultaneously solidify liquefiable soil, immobilize reactive heavy metals and sequester carbon—effectively providing civil engineering functionality while clarifying the ground water and removing carbon from the atmosphere? Exploration of these ideas has begun in earnest in recent years. This paper explores the potential, challenges and opportunities of this new field, and highlights one biogeochemical function of soil that has shown promise and is developing rapidly as a new technology. The example is used to propose a generalized approach in which the potential of this new field can be fully realized