Seth F. Oppenheimer

A comparison of regularizations for an ill-posed problem

We consider numerical methods for a quasi-boundary value regularization of the backward parabolic problem given by {u t +Au=0, 0<t<T {u(T)= f, where A is positive self-adjoint and unbounded. The regularization, due to Clark and Oppenheimer, perturbs the final value u(T) by adding αu(0), where α is a small parameter. We show how this leads very naturally to a reformulation of the problem as a second-kind Fredholm integral equation, which can be very easily approximated using methods previously developed by Ames and Epperson. Error estimates and examples are provided. We also compare the regularization used here with that from Ames and Epperson.

Optimal control of insects through sterile insect release and habitat modification

This paper develops an optimal control framework for an ordinary differential equation model to investigate the introduction of sterile mosquitoes to reduce the incidence of mosquito-borne diseases. Existence of a solution given an optimal strategy and the optimal control is determined in association with the negative effects of the disease on the population while minimizing the cost due to this control mechanism. Numerical simulations have shown the importance of effects of the bounds on the release of sterile mosquitoes and the bounds on the likelihood of egg maturation. The optimal strategy is to maximize the use of habitat modification or insecticide. A combination of techniques leads to a more rapid elimination of the wild mosquito population.

Tracking the Fate of Microbially Sequestered Carbon Dioxide in Soil Organic Matter

The microbial contribution to soil organic matter (SOM) has recently been shown to be much larger than previously thought and thus its role in carbon sequestration may also be underestimated. In this study we employ (13)C ((13)CO₂) to assess the potential CO₂ sequestration capacity of soil chemoautotrophic bacteria and combine nuclear magnetic resonance (NMR) with stable isotope probing (SIP), techniques that independently make use of the isotopic enrichment of soil microbial biomass. In this way molecular information generated from NMR is linked with identification of microbes responsible for carbon capture. A mathematical model is developed to determine real-time CO₂ flux so that net sequestration can be calculated. Twenty-eight groups of bacteria showing close homologies with existing species were identified. Surprisingly, Ralstonia eutropha was the dominant group. Through NMR we observed the formation of lipids, carbohydrates, and proteins produced directly from CO₂ utilized by microbial biomass. The component of SOM directly associated with CO₂ capture was calculated at 2.86 mg C (89.21 mg kg(-1)) after 48 h. This approach can differentiate between SOM derived through microbial uptake of CO₂ and other SOM constituents and represents a first step in tracking the fate and dynamics of microbial biomass in soil.

Greater Than Additive Suppression of TLR3-Induced IL-6 Responses by Administration of Dieldrin and Atrazine

Current risk assessment practices do not consider possible synergistic or antagonistic interactions of compounds to which persons may be exposed during the same period of time. This may simply reflect the minimal amount of data available on such interactions, particularly with regard to immunotoxicology. Therefore, this study was conducted to determine if such interactions occur between the most abundantly used conventional pesticide in the United States (atrazine) and a legacy pesticide that is still present in the United States food supply at levels greater than recognized as safe (dieldrin). The results provide evidence that greater than additive effects on signaling and cytokine production occur and suggest that evaluation of common mixtures for such effects may be needed. The compounds both separately and together directly inhibited cytokine production induced by polyinosinic-polycytidylic acid (poly I:C) by macrophages in cell culture. Subcutaneous administration of dieldrin (10–20 mg/kg, daily for 7 d) and atrazine (one dose on Day 7, 100–200 mg/kg) inhibited the production of IL-6 and IL-12 in the peritoneal cavity in a dose-dependent manner, but IL-10 was either increased or not affected. The suppression of IL-6 production and inhibition of NF-κ B activation was greater than additive when comparing animals given both compounds to those given either compound separately. However, at lower dosages of both compounds (10 mg/kg dieldrin and 50 mg/kg atrazine), the effect was much greater than additive on IL-6 production (adding the individual effects of atrazine and dieldrin on IL-6 production indicates 20% suppression, whereas the combination yields 80% suppression) and essentially additive for inhibition of the activation of c-JUN (a component of the transcription factor, AP-1). Previously published results indicate that atrazine induces a neuroendocrine stress response, and results reported here indicate that dieldrin at 20 mg/kg increases serum corticosterone concentrations, indicating a stress response. This and other possible mechanisms of the greater than additive effects on cytokine production are discussed. Dieldrin and atrazine administered orally (as opposed to subcutaneously as in the other experiments) also effectively suppressed IL-6 production. These results suggest that interactions other than additive effects for compounds with similar mechanisms of action should be considered in risk assessment. Finally, a molecular mechanism for the greater than additive inhibition of IL-6 production is proposed and a mathematical model incorporating that mechanism is presented.

Tau method approximation for radiative transfer problems in a slab medium

An approximate method for solving the radiative transfer equation in a slab medium with an isotropic scattering is proposed. The method is based upon constructing the double Legendre series to approximate the required solution using Legendre tau method. The differential and integral expressions which arise in the radiative transfer equation are converted into a system of linear algebraic equations which can be solved for the unknown coefficients. Numerical examples are included to demonstrate the validity and applicability of the method and a comparison is made with existing results.

The identification of a time dependent sorption parameter from soil column experiments

Soil column studies are used frequently in seeking to understand the behavior of a particular contaminant in a saturated homogeneous soil of a given type. The concentration of the contaminant is modeled by a parabolic partial differential equation. We seek to identify the sorption partitioning coefficient as a function of time from limited boundary data. We discuss an output least squares formulation of the problem with Tikhonov regularization. We explicitly characterize a source condition that determines the rate of convergence of the method. Numerical examples are presented.

A discrete bidirectional reflectance model in remote sensing

A numerical scheme is devised to develop a discrete bidirectional reflectance model. A pseudospectral method is utilized with which the discrete solution of the radiative transfer equation is made part of this development. To produce discrete bidirectional reflectance values, a set of algebraic equations is solved. Illustrative examples are given to demonstrate the performance of the developed model.

A convection-diffusion problem in a network1This work was partially supported by US Army contract DACA39-94-0018.1

In recent years, it has become increasingly clear that the standard method of modeling hydrodynamic dispersion in groundwater flow by diffusion is often unsatisfactory. In the last few years, several authors have tried to overcome this problem by modeling subsurface flow by flow in a network. This has had some success and even some agreement with experiment. This work will lay the mathematical foundations for such models which, up to this point in time, have been studied only numerically. A well-posedness result is obtained for a class of these models. Some qualitative properties of solutions, such as positivity, ordering, and boundedness are also given.

A legendre wavelet method for the radiative transfer equation in remote sensing

An approximate method for solving radiative Transfer equation in a slab medium with an isotropic scattering is presented. The method is based upon Legendre wavelets approximations. The differential and integral expressions which arise in the radiative transfer equation are converted into some linear systems of differential equations which can be solved for the unknown coefficient. Numerical examples are included to demonstrate the validity and applicability of the technique and a comparison is made with existing results.

Diffusing wild type and sterile mosquitoes in an optimal control setting

This paper develops an optimal control framework to investigate the introduction of sterile type mosquitoes to reduce the overal moquito population. As is well known, mosquitoes are vectors of disease. For instance the WHO lists, among other diseases, Malaria, Dengue Fever, Rift Valley Fever, Yellow Fever, Chikungunya Fever and Zika. [http://www.who.int/mediacentre/factsheets/fs387/en/ ] The goal is to establish the existence of a solution given an optimal sterilization protocol as well as to develop the corresponding optimal control representation to minimize the infiltrating mosquito population while minimizing fecundity and the number of sterile type mosquitoes introduced into the environment per unit time. This paper incorporates the diffusion of the mosquitoes into the controlled model and presents a number of numerical simulations.