Development of a mathematical and computer model to assess water quality impacts of hazardous compounds from minor gasoline spills in the inter-tidal zone of the Miami River, Florida

The objective of this study was to develop a model to predict transport and fate of gasoline components of environmental concern in the Miami River by mathematically simulating the movement of dissolved benzene, toluene, xylene (BTX), and methyl-tertiary-butyl ether (MTBE) occurring from minor gasoline spills in the inter-tidal zone of the river. Computer codes were based on mathematical algorithms that acknowledge the role of advective and dispersive physical phenomena along the river and prevailing phase transformations of BTX and MTBE. Phase transformations included volatilization and settling. ^ The model used a finite-difference scheme of steady-state conditions, with a set of numerical equations that was solved by two numerical methods: Gauss-Seidel and Jacobi iterations. A numerical validation process was conducted by comparing the results from both methods with analytical and numerical reference solutions. Since similar trends were achieved after the numerical validation process, it was concluded that the computer codes algorithmically were correct. The Gauss-Seidel iteration yielded at a faster convergence rate than the Jacobi iteration. Hence, the mathematical code was selected to further develop the computer program and software. The model was then analyzed for its sensitivity. It was found that the model was very sensitive to wind speed but not to sediment settling velocity. ^ A computer software was developed with the model code embedded. The software was provided with two major user-friendly visualized forms, one to interface with the database files and the other to execute and present the graphical and tabulated results. For all predicted concentrations of BTX and MTBE, the maximum concentrations were over an order of magnitude lower than current drinking water standards. It should be pointed out, however, that smaller concentrations than the latter reported standards and values, although not harmful to humans, may be very harmful to organisms of the trophic levels of the Miami River ecosystem and associated waters. This computer model can be used for the rapid assessment and management of the effects of minor gasoline spills on inter-tidal riverine water quality. ^

Pore formation during dehydration of polycrystalline gypsum observed and quantified in a time-series synchrotron radiation based X-ray micro-tomography experiment

We conducted an in-situ X-ray micro-computed tomography heating experiment at the Advanced Photon Source (USA) to dehydrate an unconfined 2.3 mm diameter cylinder of Volterra Gypsum. We used a purpose-built X-ray transparent furnace to heat the sample to 388 K for a total of 310 min to acquire a three-dimensional time-series tomography dataset comprising nine time steps. The voxel size of 2.2 μm3 proved sufficient to pinpoint reaction initiation and the organization of drainage architecture in space and time. We observed that dehydration commences across a narrow front, which propagates from the margins to the centre of the sample in more than four hours. The advance of this front can be fitted with a square-root function, implying that the initiation of the reaction in the sample can be described as a diffusion process. Novel parallelized computer codes allow quantifying the geometry of the porosity and the drainage architecture from the very large tomographic datasets (20483 voxels) in unprecedented detail. We determined position, volume, shape and orientation of each resolvable pore and tracked these properties over the duration of the experiment. We found that the pore-size distribution follows a power law. Pores tend to be anisotropic but rarely crack-shaped and have a preferred orientation, likely controlled by a pre-existing fabric in the sample. With on-going dehydration, pores coalesce into a single interconnected pore cluster that is connected to the surface of the sample cylinder and provides an effective drainage pathway. Our observations can be summarized in a model in which gypsum is stabilized by thermal expansion stresses and locally increased pore fluid pressures until the dehydration front approaches to within about 100 μm. Then, the internal stresses are released and dehydration happens efficiently, resulting in new pore space. Pressure release, the production of pores and the advance of the front are coupled in a feedback loop.

Mechanism based emulation of dynamic simulation models : concept and application in hydrology

Many model-based investigation techniques, such as sensitivity analysis, optimization, and statistical inference, require a large number of model evaluations to be performed at different input and/or parameter values. This limits the application of these techniques to models that can be implemented in computationally efficient computer codes. Emulators, by providing efficient interpolation between outputs of deterministic simulation models, can considerably extend the field of applicability of such computationally demanding techniques. So far, the dominant techniques for developing emulators have been priors in the form of Gaussian stochastic processes (GASP) that were conditioned with a design data set of inputs and corresponding model outputs. In the context of dynamic models, this approach has two essential disadvantages: (i) these emulators do not consider our knowledge of the structure of the model, and (ii) they run into numerical difficulties if there are a large number of closely spaced input points as is often the case in the time dimension of dynamic models. To address both of these problems, a new concept of developing emulators for dynamic models is proposed. This concept is based on a prior that combines a simplified linear state space model of the temporal evolution of the dynamic model with Gaussian stochastic processes for the innovation terms as functions of model parameters and/or inputs. These innovation terms are intended to correct the error of the linear model at each output step. Conditioning this prior to the design data set is done by Kalman smoothing. This leads to an efficient emulator that, due to the consideration of our knowledge about dominant mechanisms built into the simulation model, can be expected to outperform purely statistical emulators at least in cases in which the design data set is small. The feasibility and potential difficulties of the proposed approach are demonstrated by the application to a simple hydrological model.

A Comparative Study of the Formulations for Topology Optimization of Compliant Mechanisms

The topology optimization problem for the synthesis of compliant mechanisms has been formulated in many different ways in the last 15 years, but there is not yet a definitive formulation that is universally accepted. Furthermore, there are two unresolved issues in this problem. In this paper, we present a comparative study of five distinctly different formulations that are reported in the literature. Three benchmark examples are solved with these formulations using the same input and output specifications and the same numerical optimization algorithm. A total of 35 different synthesis examples are implemented. The examples are limited to desired instantaneous output direction for prescribed input force direction. Hence, this study is limited to linear elastic modeling with small deformations. Two design parameterizations, namely, the frame element based ground structure and the density approach using continuum elements, are used. The obtained designs are evaluated with all other objective functions and are compared with each other. The checkerboard patterns, point flexures, the ability to converge from an unbiased uniform initial guess, and the computation time are analyzed. Some observations are noted based on the extensive implementation done in this study. Complete details of the benchmark problems and the results are included. The computer codes related to this study are made available on the internet for ready access.

Early Warning Signals of Ecological Transitions: Methods for Spatial Patterns

A number of ecosystems can exhibit abrupt shifts between alternative stable states. Because of their important ecological and economic consequences, recent research has focused on devising early warning signals for anticipating such abrupt ecological transitions. In particular, theoretical studies show that changes in spatial characteristics of the system could provide early warnings of approaching transitions. However, the empirical validation of these indicators lag behind their theoretical developments. Here, we summarize a range of currently available spatial early warning signals, suggest potential null models to interpret their trends, and apply them to three simulated spatial data sets of systems undergoing an abrupt transition. In addition to providing a step-by-step methodology for applying these signals to spatial data sets, we propose a statistical toolbox that may be used to help detect approaching transitions in a wide range of spatial data. We hope that our methodology together with the computer codes will stimulate the application and testing of spatial early warning signals on real spatial data.

Implementation of multi-group cross-section methodology in BGCore MC-depletion code

BGCore is a software package for comprehensive computer simulation of nuclear reactor systems and their fuel cycles. The BGCore interfaces Monte Carlo particles transport code MCNP4C with a SARAF module - an independently developed code for calculating in-core fuel composition and spent fuel emissions following discharge. In BGCore system, depletion coupling methodology is based on the multi-group approach that significantly reduces computation time and allows tracking of large number of nuclides during calculations. In this study, burnup calculation capabilities of BGCore system were validated against well established and verified, computer codes for thermal and fast spectrum lattices. Very good agreement in k eigenvalue and nuclide densities prediction was observed for all cases under consideration. In addition, decay heat prediction capabilities of the BGCore system were benchmarked against the most recent edition of ANS Standard methodology for UO2 fuel decay power prediction in LWRs. It was found that the difference between ANS standard data and that predicted by the BGCore does not exceed 5%.

Application of axial discontinuity factors for high conversion water reactors

The paper shows that generating cross sections using three-dimensional geometry and application of axial discontinuity factors are essential requirements for obtaining accurate prediction of criticality and zone average reaction rates in highly heterogeneous RBWR-type systems using computer codes based on diffusion theory approximation. The same methodology as presented here will be used to generate discontinuity factors for each axial interface between fuel assembly zones to ensure preservation of reaction rates in each zone and global multiplication factor. The use of discontinuity factors and three-dimensional cross sections may allow for a coarser energy group structure which is desirable to simplify and speed up transient calculations.

Modal stability theory

This article contains a review of modal stability theory. It covers local stability analysis of parallel flows including temporal stability, spatial stability, phase velocity, group velocity, spatio-temporal stability, the linearized Navier-Stokes equations, the Orr-Sommerfeld equation, the Rayleigh equation, the Briggs-Bers criterion, Poiseuille flow, free shear flows, and secondary modal instability. It also covers the parabolized stability equation (PSE), temporal and spatial biglobal theory, 2D eigenvalue problems, 3D eigenvalue problems, spectral collocation methods, and other numerical solution methods. Computer codes are provided for tutorials described in the article. These tutorials cover the main topics of the article and can be adapted to form the basis of research codes. Copyright © 2014 by ASME.

A general framework for aquatic biogeochemical models

One of the most of challenging steps in the development of coupled hydrodynamic-biogeochemical models is the combination of multiple, often incompatible computer codes that describe individual physical, chemical, biological and geological processes. This “coupling” is time-consuming, error-prone, and demanding in terms of scientific and programming expertise. The open source, Fortran-based Framework for Aquatic Biogeochemical Models addresses these problems by providing a consistent set of programming interfaces through which hydrodynamic and biogeochemical models communicate. Models are coded once to connect to FABM, after which arbitrary combinations of hydrodynamic and biogeochemical models can be made. Thus, a biogeochemical model code works unmodified within models of a chemostat, a vertically structured water column, and a three-dimensional basin. Moreover, complex biogeochemistry can be distributed over many compact, self-contained modules, coupled at run-time. By enabling distributed development and user-controlled coupling of biogeochemical models, FABM enables optimal use of the expertise of scientists, programmers and end-users.

R-matrix theory of electron molecule scattering

This paper presents an overview of R-matrix theory of electron scattering by diatomic and polyatomic molecules. The paper commences with a detailed discussion of the fixed-nuclei approximation which in recent years has been used as the basis of the most accurate ab initio calculations. This discussion includes an overview of the computer codes which enable electron collisions with both diatomic and polyatomic molecules to be calculated. Nuclear motion including rotational and vibrational excitation and dissociation is then discussed. In non-resonant energy regions, or when the scattered electron energy is not close to thresholds, the adiabatic-nuclei approximation can be successfully used. However, when these conditions are not applicable, non-adiabatic R-matrix theory must be used and a detailed discussion of this theory is given. Finally, recent applications of the theory to treat electron scattering by polyatomic molecules are reviewed and a detailed comparison of R-matrix calculations and experimental measurements for water is presented.

Photoionization of Cl-like Argon using the Breit-Pauli R-matrix method

Here we present the photoionization cross sections for the ground and metastable states of Cl-like Argon by exploiting the fully relativistic Breit-Pauli R-matrix computer codes to determine these transitions of interest. We compare our work with previous theoretical and experimental results and present a detailed investigation into the model of Ar III, the resonant structure and identification process.

Application of Reptation Quantum Monte Carlo and Related Methods to LiH

This work investigates mathematical details and computational aspects of Metropolis-Hastings reptation quantum Monte Carlo and its variants, in addition to the Bounce method and its variants. The issues that concern us include the sensitivity of these algorithms' target densities to the position of the trial electron density along the reptile, time-reversal symmetry of the propagators, and the length of the reptile. We calculate the ground-state energy and one-electron properties of LiH at its equilibrium geometry for all these algorithms. The importance sampling is performed with a single-determinant large Slater-type orbitals (STO) basis set. The computer codes were written to exploit the efficiencies engineered into modern, high-performance computing software. Using the Bounce method in the calculation of non-energy-related properties, those represented by operators that do not commute with the Hamiltonian, is a novel work. We found that the unmodified Bounce gives good ground state energy and very good one-electron properties. We attribute this to its favourable time-reversal symmetry in its target density's Green's functions. Breaking this symmetry gives poorer results. Use of a short reptile in the Bounce method does not alter the quality of the results. This suggests that in future applications one can use a shorter reptile to cut down the computational time dramatically.

Analytical Investigations 0n Collapse of Cylindrical Submarine Shells

Submarine hull structure is a watertight envelope, under hydrostatic pressure when in operation. Stiffened cylindrical shells constitute the major portion of these submarine hulls and these thin shells under compression are susceptible to buckling failure. Normally loss of stability occurs at the limit point rather than at the bifurcation point and the stability analysis has to consider the change in geometry at each load step. Hence geometric nonlinear analysis of the shell forms becomes. a necessity. External hydrostatic pressure will follow the deformed configuration of the shell and hence follower force effect has to be accounted for. Computer codes have been developed based on all-cubic axisymmetric cylindrical shell finite element and discrete ring stiffener element for linear elastic, linear buckling and geometric nonIinear analysis of stiffened cylindrical shells. These analysis programs have the capability to treat hydrostatic pressure as a radial load and as a follower force. Analytical investigations are carried out on two attack submarine cylindrical hull models besides standard benchmark problems. In each case, the analysis has been carried out for interstiffener, interdeepframe and interbulkhead configurations. The shell stiffener attachment in each of this configuration has been represented by the simply supported-simply supported, clamped-clamped and fixed-fixed boundary conditions in this study. The results of the analytical investigations have been discussed and the observations and conclusions are described. Rotation restraint at the ends is influential for interstiffener and interbulkhead configurations and the significance of axial restraint becomes predominant in the interbulkhead configuration. The follower force effect of hydrostatic pressure is not significant in interstiffener and interdeepframe configurations where as it has very high detrimental effect on buckling pressure on interbulkhead configuration. The geometric nonlinear interbulkhead analysis incorporating follower force effect gives the critical value of buckling pressure and this analysis is recommended for the determination of collapse pressure of stiffened cylindrical submarine shells.