Homogeneous Saturation

Suppose that J = (fv., fs) is the saturated homogeneous ideal of X, and assume that this is a minimal set of generators of degrees d i... i ds. Then =2. Moreover dj i b for j > 2 because if X is contained in a surface of degree d which does not have Q as a component, then on Q the linear system... 

Saturated homogeneous ideal, 1 -9 Schlessinger s theorem, B-14 Schubert cycle, 7-12 Section, 7-10, 10-7 Semi-homogeneous functor, B-20... 

Skaggs and Kabala studied a ID solute transport through a saturated homogeneous medium problem with a complex contaminant release history and assumed no prior knowledge of the release function. This closed form solution is similar to Eq. (50). Due to this similarity, Eq. (46) can be utilized to estimate the concentration release history (Cr). The accuracy of the TR method depends on the regularization parameter a. 

The two-dimensional transient transport of the solute originating from the dissolution of a PCE pool in saturated, homogeneous porous media under uniform interstitial groundwater flow and in the presence of dissolved humic substances is governed by [57]... 

Numerous empirical correlations for the prediction of residual NAPL dissolution have been presented in the literature and have been compiled by Khachikian and Harmon [68]. On the other hand, just a few correlations for the rate of interface mass transfer from single-component NAPL pools in saturated, homogeneous porous media have been established, and they are based on numerically determined mass transfer coefficients [69, 70]. These correlations relate a dimensionless mass transfer coefficient, i.e., Sherwood number, to appropriate Peclet numbers, as dictated by dimensional analysis with application of the Buckingham Pi theorem [71,72], and they have been developed under the assumption that the thickness of the concentration boundary layer originating from a dissolving NAPL pool is mainly controlled by the contact time of groundwater with the NAPL-water interface that is directly affected by the interstitial groundwater velocity, hydrodynamic dispersion, and pool size. For uniform... 

The nonlinear least squares regression program PEST [79] was used to fit the proposed correlation relating the time invariant Sherwood number to overall Peclet numbers for circular pools given by Eq. (91) to the seven experimentally determined Sh values presented in Fig. 12b, in order to estimate the empirical coefficients fi, y2> and y3. The experimental, overall Sherwood number correlation applicable to circular TCE pool dissolution in water saturated, homogeneous porous media can be expressed by the following relationship ... 

Darcy s law Flow rate in a saturated homogeneous porous media is directly proportional to the hydraulic gradient... 

Gain bandwidth Type, gain saturation Homogeneous saturation flux Decay lifetime (lower level) Inversion density Small signal gain coefficient Pump power density Output power density Laser size (diameter length) Excitation current/voltage Excitation current density Excitation power Output power Efficiency... 

This is a Voigt profile with a Bennet hole centered at w - (see Fig.3.18). The halfwidth 6o) of this hole is determined by the saturated homogeneous linewidth = yA + Sq and the depth 4Sq/y is also determined by the intensity of the saturating field and the Einstein coefficient B 2 transition [3.19]. 

Oostrom, M., Hofstee, C., Walker, R.C. and J.H. Dane. 1999a. Movement and remediation of trichloroethylene in a saturated homogeneous porous medium. 1. SpiU behavior and initial dissolution. Journal of Contaminant Hydrology 37 159-178. 

---