@article{banks_potter_2005, title={Well-posedness results for a class of toxicokinetic models}, volume={14}, number={2}, journal={Dynamic Systems and Applications}, author={Banks, H. T. and Potter, L. K.}, year={2005}, pages={297–322} }
 @article{banks_potter_2002, title={Model predictions and comparisons for three toxicokinetic models for the systemic transport of trichloroethylene}, volume={35}, ISSN={["0895-7177"]}, DOI={10.1016/S0895-7177(02)00067-5}, abstractNote={In this paper, we present and compare three physiologically based pharmacokinetic models for the systemic transport of trichloroethylene (TCE), a common environmental toxicant. Of particular interest is the disposition of TCE in the adipose tissue, where TCE is known to accumulate. The first two systemic models utilize standard ODE-based adipose compartments that assume rapid equilibrium and uniformity. The third model includes a PDE-based axial dispersion model that is designed to capture the heterogeneous physiology of adipose tissue and the expected transport of TCE there. Using numerical methods and model simulations, we compare the predicted concentration profiles of TCE in the adipose tissue for the three systemic models. Our results suggest that the dispersion-based adipose compartmental model is best able to capture the physiological heterogeneities of adipose tissue and their expected effects on TCE adipose concentrations.}, number={9-10}, journal={MATHEMATICAL AND COMPUTER MODELLING}, author={Banks, HT and Potter, LK}, year={2002}, month={May}, pages={1007–1032} }
 @article{albanese_banks_evans_potter_2002, title={Physiologically based pharmacokinetic models for the transport of trichloroethylene in adipose tissue}, volume={64}, ISSN={["1522-9602"]}, DOI={10.1006/bulm.2001.0268}, abstractNote={In this paper we present three physiologically based pharmacokinetic (PBPK) models for the systemic transport of trichloroethylene (TCE), with a focus on the adipose, or fat tissue. TCE is a widespread environmental contaminant, and has been shown to produce toxic effects in both animals and humans. A key characteristic of TCE is its tendency to accumulate in fat tissue, which has a major impact on the overall systemic disposition of TCE.Here we use PBPK models to predict the dynamics of TCE in the various tissues and organs, including the adipose tissue. The first model utilizes the standard ‘perfusion-limited’ compartmental model for the fat tissue, while the second model uses a ‘diffusion-limited’ model to describe the transport through the adipose tissue. Both of these ODE models are based on ‘well-mixed’ and rapid equilibrium assumptions, and do not take into account the specific and largely heterogeneous physiology of adipose tissue.The third model we discuss is a PBPK hybrid model with an axial-dispersion type model for the adipose tissue. This PDE-based model is designed to capture key physiological heterogeneities of fat tissue, including widely varying fat cell sizes, lipid distribution, and blood flow properties. Model simulations demonstrate that this model may be well-suited to predict the experimental behavior of TCE in adipose tissue using parameter estimation techniques.}, number={1}, journal={BULLETIN OF MATHEMATICAL BIOLOGY}, author={Albanese, RA and Banks, HT and Evans, MV and Potter, LK}, year={2002}, month={Jan}, pages={97–131} }
 @article{banks_pinter_potter_gaitens_yanyo_1999, title={Modeling of nonlinear hysteresis in elastomers under uniaxial tension}, volume={10}, ISSN={["1045-389X"]}, DOI={10.1106/8M8M-F8DQ-GJ2V-PGK1}, abstractNote={As a fundamental component of an overall program in modeling smart material damping devices, we consider inactive host material models for moderate to highly filled rubbers undergoing uniaxial tensile deformations. Beginning from a neo-Hookean strain energy function formulation for nonlinear extension, we develop general constitutive models for both quasi-static and dynamic deformations of a viscoelastic rod. The constitutive laws are nonlinear and contain hysteresis through a Boltzmann superposition integral term. The resulting integropartial differential equations models are shown to be equivalent to the usual Lagrangian dynamic distributed parameter models coupled with linear ordinary differential equations for internal variables (internal strains). Comprehensive well-posedness results (existence, uniqueness and continuous dependence) are summarized in a discussion of theoretical aspects of the systems. The models are validated with experiments designed and carried out explicitly for this study. In particular, quasi-static Instron experimental data are used in a least squares inverse problem formulation to estimate nonlinear elastic and nonlinear viscoelastic contributions to the general stress-strain constitutive laws proposed. It is shown that the models provide an excellent prediction of nested hysteresis loops manifested in the data. These models are then used as initial estimates in determining the nonlinear hysteretic constitutive laws for the dynamic experiments. It is shown that in cases of more highly filled rubbers, multiple internal variable models lead to best fits to the data.}, number={2}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Banks, HT and Pinter, GA and Potter, LK and Gaitens, MJ and Yanyo, LC}, year={1999}, month={Feb}, pages={116–134} }
 @article{godbole_potter_sklar_1998, title={Improved upper bounds for the reliability of d-dimensional consecutive-k-out-of-n:F systems}, volume={45}, DOI={10.1002/(SICI)1520-6750(199803)45:2<219::AID-NAV6>3.0.CO;2-B}, abstractNote={Consider a 2-dimensional consecutive-k-out-of-n : F system, as described by Salvia and Lasher [9], whose components have independent, perhaps identical, failure probabilities. In this paper, we use Janson's exponential inequalities [5]; to derive improved upper bounds on such a system's reliability, and compare our results numerically to previously determined upper bounds. In the case of equal component-failure probabilities, we determine analytically, given k and n, those component-failure probabilities for which our bound betters the upper bounds found by Fu and Koutras [4] and Koutras et al. [6]. A different kind of analytic comparison is made with the upper bound of Barbour et al. [3]. We further generalize our upper bound, given identical component-failure probabilities, to suit d-dimensional systems for d ≤ 3. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 219–230, 1998}, number={2}, journal={Naval Research Logistics}, author={Godbole, A. P. and Potter, L. K. and Sklar, J. K.}, year={1998}, pages={219–230} }
 @article{godbole_potter_sandquist_1998, title={Sign-balanced covering matrices}, volume={190}, ISSN={["0012-365X"]}, DOI={10.1016/S0012-365X(98)00122-8}, abstractNote={A q × n array with entries from 0, 1,...,q − 1 is said to form a difference matrix if the vector difference (modulo q) of each pair of columns consists of a permutation of [0, 1,... q − 1]; this definition is inverted from the more standard one to be found, e.g., in Colbourn and de Launey (1996). The following idea generalizes this notion: Given an appropriate δ (-[−1, 1]t, a λq × n array will be said to form a (t, q, λ, Δ) sign-balanced matrix if for each choice C1, C2,..., Ct of t columns and for each choice ɛ = (ɛ1,...,ɛt) ∈ Δ of signs, the linear combination ∑j=1tεjCj contains (mod q) each entry of [0, 1,...,q − 1] exactly λ times. We consider the following extremal problem in this paper: How large does the number k = k(n, t, q, λ, δ) of rows have to be so that for each choice of t columns and for each choice (ɛ1, ..., ɛt) of signs in δ, the linear combination ∑j=1tεjCj contains each entry of [0, 1,..., q − 1] at least λ times? We use probabilistic methods, in particular the Lovász local lemma and the Stein-Chen method of Poisson approximation to obtain general (logarithmic) upper bounds on the numbers k(n, t, q, λ, δ), and to provide Poisson approximations for the probability distribution of the number W of deficient sets of t columns, given a random array. It is proved, in addition, that arithmetic modulo q yields the smallest array - in a sense to be described.}, number={1-3}, journal={DISCRETE MATHEMATICS}, author={Godbole, AP and Potter, LK and Sandquist, EJ}, year={1998}, month={Aug}, pages={79–93} }