PubMed · 13205153
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G LUNDIN, L AKESSON. 1954. A new nitrogen meter model.. https://pubmed.ncbi.nlm.nih.gov/13205153/
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A mathematical model was proposed to allow the analysis of steady-state and transient behaviors of single-stage continuous aqueous two-phase systems. Since the complete system of simultaneous equations contains more equations than unknown variables, a program based on the method of least squares was developed to solve the problem. The methodology was tested using a system composed of thaumatin, sodium chloride, and a contaminant protein. A poly(ethylene-glycol)/phosphate salt/water system was selected to isolate the thaumatin. For the steady-state and transient operations, a constrained optimization procedure--from the Matlab Optimization Toolbox (MathWork, Inc.)--was implemented after recasting the system of equations as a minimization problem. Euler's method was used in the transient case to discretize the differential equations. The steady-state concentrations agreed with published data. An input-output model based on a 4% step change decrease in the inlet stream flow rate showed that output variables such as concentrations of sodium chloride and phosphate salt settled to their final values in different time periods. The proposed analysis may be helpful in the dynamic control of large-scale commercial extractor units using advanced control schemes.
Solute transport displaying mass transfer behavior (i.e., tailing) occurs in many aquifers and soils. Spatial patterns of hydraulic conductivity may play a role because of both advection and diffusion through isolated low conductivity areas. We demonstrated such processes in laboratory experiments designed to visualize solute transport through a thin chamber (40 cm x 20 cm x 0.64 cm thick) packed with glass beads and containing circular emplacements of smaller glass beads with lower conductivity. The experiments used three different contrasts of conductivity between the large-bead matrix and the emplacements, targeting three different regimes of solute transport: low contrast, targeting macrodispersion; intermediate contrast, targeting advection-dominated mass transfer between the high-conductivity regions and the emplacements; and high contrast, targeting diffusion-dominated mass transfer. Use of a strong light source, a high-resolution CCD camera, and a colorimetric dye produced images with a spatial resolution of about 400 microm and a concentration range of approximately 2 orders of magnitude. These images confirm the existence of the three different regimes, and we observed tailing driven by both advection and diffusion. Outflow concentration measured by spectrophotometer achieved 3 orders of magnitude in concentration range and showed good agreement with known models in the case of dispersion and diffusive mass transfer, with estimated parameters close to a priori predictions. Existing models for diffusive mass transfer did notfitthe breakthrough curves from the intermediate-contrast chamber, but a model of slow advection through cylinders did. Thus, both breakthrough curves and chamber images confirm that different contrasts in small-scale K lead to different regimes of solute transport and thus require different models of upscaled solute transport.
Helical tomotherapy has been developed at the University of Wisconsin, and 'Hi-Art II' clinical machines are now commercially manufactured. At the core of each machine lies a ring-gantry-mounted short linear accelerator which generates x-rays that are collimated into a fan beam of intensity-modulated radiation by a binary multileaf, the modulation being variable with gantry angle. Patients are treated lying on a couch which is translated continuously through the bore of the machine as the gantry rotates. Highly conformal dose-distributions can be delivered using this technique, which is the therapy equivalent of spiral computed tomography. The approach requires synchrony of gantry rotation, couch translation, accelerator pulsing and the opening and closing of the leaves of the binary multileaf collimator used to modulate the radiation beam. In the course of clinically implementing helical tomotherapy, we have developed a quality assurance (QA) system for our machine. The system is analogous to that recommended for conventional clinical linear accelerator QA by AAPM Task Group 40 but contains some novel components, reflecting differences between the Hi-Art devices and conventional clinical accelerators. Here the design and dosimetric characteristics of Hi-Art machines are summarized and the QA system is set out along with experimental details of its implementation. Connections between this machine-based QA work, pre-treatment patient-specific delivery QA and fraction-by-fraction dose verification are discussed.