Model Formulation Sample Clauses

Model Formulation. Hydrologic parameters will be derived from the site-scale and regional-scale models. Spatial discretization may be finer than regional-scale models for computational purposes. Hydraulic and thermal properties will be generalized within hydrostratigraphic layers. The model will use a single porosity and permeability within each model element. The model will not include any postulated repository affects and only ambient groundwater temperatures will be considered. The thermal model of the LHG will approximate to the current saturated zone regional interpretation. The thermal model will be steady state for both groundwater flow and thermal transport. The top of the model will be a prescribed hydraulic flux and temperature at the water table. The model will extend to the depth of the Paleozoic carbonate aquifer or deepest thermal log. The bottom of the model will be simulated as a prescribed hydraulic head and a spatially variable thermal flux. The upgradient and downgradient boundaries will be prescribed hydraulic fluxes or hydraulic heads based on the requirements for numerical stability. Both the hydraulic heads and groundwater temperatures will vary with depth. Hydraulic head at the water table surface and any hydraulic heads at depth will be the calibration parameters. The spatial thermal distribution between the upgradient and downgradient boundaries will be the evaluation parameters. Thermal rock properties will be extracted from the project database. Because there is less thermal data at distance from the potential repository location, generalized information will be used in the thermal model. The methodology of Rautman (1995) may be used to assign thermal conductivity unless data that are more explicit are available. DOCUMENT CHANGE NOTICE (DCN) page 4 of 5 DCN No. 1 to Document No. SIP-DRI-039, Revision 0, Effective Date: 15FEB05.

Model Formulation. This section formulates the mathematical model for deciding about the surplus inventory at the beginning of each quality period. The supermarket pays the supplier for buying product i which equals 𝑐𝑖𝐷𝑖 and anticipates to sell them during the quality period j with the price 𝑠𝑖𝑖𝑖 and the quantity 𝑃′𝑖𝑖𝑖 which leads to a revenue 𝑠𝑖𝑖𝑖 𝑃′𝑖𝑖𝑖. So, the total revenue that the supermarket anticipates for the predefined evaluation period equals the following equation. 𝑇𝑅′ = ∑ ∑𝑛𝑖 𝑠 𝑃′ − ∑ 𝑐 𝐷 (1) 𝑖𝑖=1 𝑖 𝑖 Considering equation (1) for a specific product (product i), the equation can be revised as follows. 𝑇𝑅′ = ∑𝑛𝑖 𝑠 𝑃′ − 𝑐 𝐷

Model Formulation. Our model represents the population dynamics of two bacteria, Sphingomonas sp. TFEE and Burkholderia sp. MN1, in fenitrothion-treated soil (Fig. 2 and Table 2). The variables S0, S1, and S2 denote the concentrations of fenitrothion, 3M4N, and MHQ in the soil, respectively. The population densities of Sphingomonas sp. TFEE and Burkholderia sp. MN1 are denoted by x1 and x2, respectively. The repeated application of fenitrothion is represented by λ. Although bacterial degradation is considered to be a major factor determining the fate of fenitrothion, 3M4N, and j j i a +S MHQ, these compounds naturally decompose over time, as represented by −d0S0, d1S1, and d2S2, respectively. We do not consider any possibilities that metabolite 3M4N and MHQ are produced via natural decomposition of fenitrothion and 3M4N. We assume that the uptake rate of 3M4N and MHQ follows the conventional formulation known as Xxxxxxxxx-Xxxxxx kinetics, with a half-saturation constant aj and maximum uptake rate m of the form: f (S ) := mj Si , (i, j = 1, 2). Popula- j i tion growth of the bacteria is simply proportional to the uptake of substrates with constant conversion rates (i.e., yields) of η1 for Sphingomonas sp. TFEE and η2 for Burkholderia sp. MN1, respectively. Conventionally we can assume that interaction between enzyme and substrate follows the mass action law (Xxxxxx et al., 1998). Let E(t) denote the concentration of the fenitrothion-degrading enzyme synthesized by Sphingomonas sp. TFEE. We assume that E(t) is proportional to the population density of Sphingomonas sp. TFEE, that is, E(t) = kx1(t). Hence the concentration of enzyme–substrate complex is given by β'S0E := βS0x1. Here constant β = kβ' represents the rate of decomposition of enzyme–substrate complex into 3M4N and enzyme. Following the experimental observations, we assume that a portion of MHQ is excreted from Burkholderia sp. MN1 after the metabolism of 3M4N. Let γ denote the fraction of MHQ excreted by Burkholderia sp. MN1. By definition, γ must be assigned a value between 0 and 1. Hence the total excretion of MHQ is given by γf2(S1)x2/η2. The remaining (1 γ)f2(S1)x2/η2 is exploited for the population growth of Burkholderia sp. MN1. Loss of activity for individual bacterium can oc- cur via starvation, mutation, being prey to predation, or other factors. We simply assume that the loss rates of Sphingomonas sp. TFEE and Burkholderia sp. MN1 are given by µ1x1 and µ2x2, respectively. The model, including all of the ab...

Model Formulation