Assimilation of Historical Head Data to Estimate Spatial Distributions of Stream Bed and Aquifer Hydraulic Conductivity Fields

Management of water resources in alluvial aquifers relies mainly on understanding interactions between hydraulically connected streams and aquifers. Numerical models that simulate this interaction often are used as decision support tools in water resource management. However, the accuracy of numerical predictions relies heavily on the unknown system parameters (i.e. stream bed conductivity and aquifer hydraulic conductivity) which are spatially heterogeneous and difficult to measure directly. This paper employs an Ensemble Smoother to invert groundwater level measurements to jointly estimate spatially-varying streambed and alluvial aquifer hydraulic conductivity along a 35.6 km segment of the South Platte River in northeastern Colorado. The accuracy of the inversion procedure is evaluated using a synthetic experiment and historical groundwater level measurements, with the latter constituting the novelty of this study in the inversion and validation of high resolution fields of streambed and aquifer conductivities. Results show that the estimated streambed conductivity field and aquifer conductivity field produce an acceptable agreement between observed and simulated groundwater levels and stream flow rates. The estimated parameter fields are also used to simulate the spatially varying flow exchange between the alluvial aquifer and the stream, which exhibit high spatial variability along the river reach with a maximum average monthly aquifer gain of about 2.3 m3/day and a maximum average monthly aquifer loss of 2.8 m3/day, per unit area of streambed (m2). These results demonstrate that data assimilation inversion provides a reliable and computationally affordable tool to estimate the spatial variability of streambed and aquifer conductivities at high resolution in real-world systems

Effects of selective dilution on the magnetic properties of La_{0.7}Sr_{0.3}Mn_{1-x}M'_xO_3 (M' = Al, Ti)

The magnetic lattice of mixed-valence Mn ions in La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ is selectively diluted by partial substitution of Al or Ti for Mn. The ferromagnetic transition temperature $T_\mathrm{c}$ and the saturation magnetization $M_\mathrm{s}$ both decrease with substitution. By presenting the data in terms of selective dilution, $T_\mathrm{c}$ in the low-doping region is found to follow the relation $T_\mathrm{c}=T_\mathrm{c0}(1-n_\mathrm{p})$, where $T_\mathrm{c0}$ refers to the undiluted system and $n_\mathrm{p}$ is the dilution concentration defined as $n_\mathrm{p}=x/0.7$ or $n_\mathrm{p}=x/0.3$ for $M^\prime=$ Al or Ti, respectively. The scaling behavior of $T_\mathrm{c}(n_\mathrm{p})$ can be analyzed in the framework of the molecular-field theory and still valid when Mn is substituted by both Al and Ti. The results are discussed with respect to the contributions from ferromagnetic double exchange and other possible antiferromagnetic superexchange interactions coexisting in the material.Comment: Revtex4, 4 pages, 4 figures, 2006 Halong Conference Repor

Selective dilution and magnetic properties of La_{0.7}Sr_{0.3}Mn_{1-x}M'_xO_3 (M' = Al, Ti)

The magnetic lattice of mixed-valence Mn ions in La$_{0.7}$Sr$_{0.3}$MnO$_3$ is selectively diluted by partial substitution of Mn by Al or Ti. The ferromagnetic transition temperature and the saturation moment decreases with substitution in both series. The volume fraction of the non-ferromagnetic phases evolves non-linearly with the substitution concentration and faster than theoretically expected. By presenting the data in terms of selective dilutions, the reduction of $T_\mathrm{c}$ is found to be scaled by the relative ionic concentrations and is consistent with a prediction derived from molecular-field theory.Comment: 6 pages, 5 figures, REVTex4.0. Submitted to PR

Smooth analysis of the condition number and the least singular value

Let \a be a complex random variable with mean zero and bounded variance. Let $N_{n}$ be the random matrix of size $n$ whose entries are iid copies of \a and $M$ be a fixed matrix of the same size. The goal of this paper is to give a general estimate for the condition number and least singular value of the matrix $M + N_{n}$, generalizing an earlier result of Spielman and Teng for the case when \a is gaussian. Our investigation reveals an interesting fact that the "core" matrix $M$ does play a role on tail bounds for the least singular value of $M+N_{n}$. This does not occur in Spielman-Teng studies when \a is gaussian. Consequently, our general estimate involves the norm $\|M\|$. In the special case when $\|M\|$ is relatively small, this estimate is nearly optimal and extends or refines existing results.Comment: 20 pages. An erratum to the published version has been adde

Using Resonances to Control Chaotic Mixing within a Translating and Rotating Droplet

Enhancing and controlling chaotic advection or chaotic mixing within liquid droplets is crucial for a variety of applications including digital microfluidic devices which use microscopic ``discrete'' fluid volumes (droplets) as microreactors. In this work, we consider the Stokes flow of a translating spherical liquid droplet which we perturb by imposing a time-periodic rigid-body rotation. Using the tools of dynamical systems, we have shown in previous work that the rotation not only leads to one or more three-dimensional chaotic mixing regions, in which mixing occurs through the stretching and folding of material lines, but also offers the possibility of controlling both the size and the location of chaotic mixing within the drop. Such a control was achieved through appropriate tuning of the amplitude and frequency of the rotation in order to use resonances between the natural frequencies of the system and those of the external forcing. In this paper, we study the influence of the orientation of the rotation axis on the chaotic mixing zones as a third parameter, as well as propose an experimental set up to implement the techniques discussed.Comment: 15 pages, 6 figure