Publications

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In gas chromatography, a chemical sample separates into its constituent components as it travels along a long thin column. As the component chemicals exit the column they are detected and identified, allowing the chemical makeup of the sample to be determined. For correct identification of the component chemicals, the distribution of the concentration of each chemical along the length of the column must be nearly symmetric. The prediction and control of asymmetries in gas chromatography has been an active research area since the advent of the technique. In this paper, we develop from first principles a general model for isothermal linear chromatography. We use this model to develop closed-form expressions for terms related to the first, second, and third moments of the distribution of the concentration, which determines the velocity, diffusion rate, and asymmetry of the distribution. We show that for all practical experimental situations, only fronting peaks are predicted by this model, suggesting that a nonlinear chromatography model is required to predict tailing peaks. For situations where asymmetries arise, we analyze the rate at which the concentration distribution returns to a normal distribution. Numerical examples are also provided.

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The approximate solution of optimization and control problems for systems governed by linear, elliptic partial differential equations is considered. Such problems are most often solved using methods based on the application of the Lagrange multiplier rule followed by discretization through, e.g., a Galerkin finite element method. As an alternative, we show how least-squares finite element methods can be used for this purpose. Penalty-based formulations, another approach widely used in other settings, have not enjoyed the same level of popularity in the partial differential equation case perhaps because naively defined penalty-based methods can have practical deficiencies. We use methodologies associated with modern least-squares finite element methods to develop and analyze practical penalty methods for the approximate solution of optimization problems for systems governed by linear, elliptic partial differential equations. We develop an abstract theory for such problems; along the way, we introduce several methods based on least-squares notions, and compare and constrast their properties.

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The peridynamic model was introduced by Silling in 1998. In this paper, we demonstrate the application of the quasistatic peridynamic model to two-dimensional, linear elastic, plane stress and plane strain problems, with special attention to the modeling of plain and reinforced concrete structures. We consider just one deviation from linearity--that which arises due to the irreversible sudden breaking of bonds between particles. The peridynamic model starts with the assumption that Newton's second law holds true on every infinitesimally small free body (or particle) within the domain of analysis. A specified force density function, called the pairwise force function, (with units of force per unit volume per unit volume) between each pair of infinitesimally small particles is postulated to act if the particles are closer together than some finite distance, called the material horizon. The pairwise force function may be assumed to be a function of the relative position and the relative displacement between the two particles. In this paper, we assume that for two particles closer together than the specified 'material horizon' the pairwise force function increases linearly with respect to the stretch, but at some specified stretch, the pairwise force function is irreversibly reduced to zero.

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Due to advances in CMOS fabrication technology, high performance computing capabilities have continually grown. More capable hardware has allowed a range of complex scientific applications to be developed. However, these applications present a bottleneck to future performance. Entrenched 'legacy' codes - 'Dusty Decks' - demand that new hardware must remain compatible with existing software. Additionally, conventional architectures faces increasing challenges. Many of these challenges revolve around the growing disparity between processor and memory speed - the 'Memory Wall' - and difficulties scaling to large numbers of parallel processors. To a large extent, these limitations are inherent to the traditional computer architecture. As data is consumed more quickly, moving that data to the point of computation becomes more difficult. Barring any upward revision in the speed of light, this will continue to be a fundamental limitation on the speed of computation. This work focuses on these solving these problems in the context of Light Weight Processing (LWP). LWP is an innovative technique which combines Processing-In-Memory, short vector computation, multithreading, and extended memory semantics. It applies these techniques to try and answer the questions 'What will a next-generation supercomputer look like?' and 'How will we program it?' To that end, this work presents four contributions: (1) An implementation of MPI which uses features of LWP to substantially improve message processing throughput; (2) A technique leveraging extended memory semantics to improve message passing by overlapping computation and communication; (3) An OpenMP library modified to allow efficient partitioning of threads between a conventional CPU and LWPs - greatly improving cost/performance; and (4) An algorithm to extract very small 'threadlets' which can overcome the inherent disadvantages of a simple processor pipeline.

Controlled seeding of perturbations is employed to study the evolution of wire array z-pinch implosion instabilities which strongly impact x-ray production when the 3D plasma stagnates on axis. Wires modulated in radius exhibit locally enhanced magnetic field and imploding bubble formation at discontinuities in wire radius due to the perturbed current path. Wires coated with localized spectroscopic dopants are used to track turbulent material flow. Experiments and MHD modeling offer insight into the behavior of z-pinch instabilities.

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Wereportonthedesignofgeneral,flexible,consistentandefficientinterfacestodirectsolveralgorithmsforthesolutionofsystemsoflinearequations.Wesupposethatsuchalgorithmsareavailableinformofsoftwarelibraries,andweintroduceaframeworktofacilitatetheusageoftheselibraries.Thisframeworkiscomposedbytwocomponents:anabstractmatrixinterfacetoaccessthelinearsystemmatrixelements,andanabstractsolverinterfacethatcontrolsthesolutionofthelinearsystem.Wedescribeaconcreteimplementationoftheproposedframework,whichallowsahigh-levelviewandusageofmostofthecurrentlyavailablelibrariesthatimplementsdirectsolutionmethodsforlinearsystems.Wecommentontheadvantagesandlimitationoftheframework.3

Under conditions that were predicted as 'safe' by well-established TCAD packages, radiation hardness can still be significantly degraded by a few lucky arsenic ions reaching the gate oxide during self-aligned CMOS source/drain ion implantation. The most likely explanation is that both oxide traps and interface traps are created when ions penetrate and damage the gate oxide after channeling or traveling along polysilicon grain boundaries during the implantation process.

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