A cellular automata model to investigate immune cell–tumor cell interactions in growing tumors in two spatial dimensions

We develop a hybrid cellular automata model to describe the effect of the immune system and chemokines on a growing tumor. The hybrid cellular automata model consists of partial differential equations to model chemokine concentrations, and discrete cellular automata to model cell–cell interactions and changes. The computational implementation overlays these two components on the same spatial region. We present representative simulations of the model and show that increasing the number of immature dendritic cells (DCs) in the domain causes a decrease in the number of tumor cells. This result strongly supports the hypothesis that DCs can be used as a cancer treatment. Furthermore, we also use the hybrid cellular automata model to investigate the growth of a tumor in a number of computational “cancer patients.” Using these virtual patients, the model can explain that increasing the number of DCs in the domain causes longer “survival.” Not surprisingly, the model also reflects the fact that the parameter related to tumor division rate plays an important role in tumor metastasis.

Two-dimensional bow and stern flows in a finite-depth fluid with constant vorticity

This thesis is concerned with two-dimensional free surface flows past semi-infinite surface-piercing bodies in a fluid of finite-depth. Throughout the study, it is assumed that the fluid in question is incompressible, and that the effects of viscosity and surface tension are negligible. The problems considered are physically important, since they can be used to model the flow of water near the bow or stern of a wide, blunt ship. Alternatively, the solutions can be interpreted as describing the flow into, or out of, a horizontal slot. In the past, all research conducted on this topic has been dedicated to the situation where the flow is irrotational. The results from such studies are extended here, by allowing the fluid to have constant vorticity throughout the flow domain. In addition, new results for irrotational flow are also presented. When studying the flow of a fluid past a surface-piercing body, it is important to stipulate in advance the nature of the free surface as it intersects the body. Three different possibilities are considered in this thesis. In the first of these possibilities, it is assumed that the free surface rises up and meets the body at a stagnation point. For this configuration, the nonlinear problem is solved numerically with the use of a boundary integral method in the physical plane. Here the semi-infinite body is assumed to be rectangular in shape, with a rounded corner. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterised by a train of waves upstream. In the limit that the height of the body above the horizontal bottom vanishes, the flow approaches that due to a submerged line sink in a $90^\circ$ corner. This limiting problem is also examined as a special case. The second configuration considered in this thesis involves the free surface attaching smoothly to the front face of the rectangular shaped body. For this configuration, nonlinear solutions are computed using a similar numerical scheme to that used in the stagnant attachment case. It is found that these solution exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Finally, the flow of a fluid emerging from beneath a semi-infinite flat plate is examined. Here the free surface is assumed to detach from the trailing edge of the plate horizontally. A linear problem is formulated under the assumption that the elevation of the plate is close to the undisturbed free surface level. This problem is solved exactly using the Wiener-Hopf technique, and subcritical solutions are found which are characterised by a train of sinusoidal waves in the far field. The nonlinear problem is also considered. Exact relations between certain parameters for supercritical flow are derived using conservation of mass and momentum arguments, and these are confirmed numerically. Nonlinear subcritical solutions are computed, and the results are compared to those predicted by the linear theory.

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

Multiple sulfur isotope analyses support a magmatic model for the volcanogenic massive sulfide deposits of the Teutonic Bore volcanic complex, Yilgarn Craton, Western Australia

We report sensitive high mass resolution ion microprobe, stable isotopes (SHRIMP SI) multiple sulfur isotope analyses (32S, 33S, 34S) to constrain the sources of sulfur in three Archean VMS deposits—Teutonic Bore, Bentley, and Jaguar—from the Teutonic Bore volcanic complex of the Yilgarn Craton, Western Australia, together with sedimentary pyrites from associated black shales and interpillow pyrites. The pyrites from VMS mineralization are dominated by mantle sulfur but include a small amount of slightly negative mass-independent fractionation (MIF) anomalies, whereas sulfur from the pyrites in the sedimentary rocks has pronounced positive MIF, with ∆33S values that lie between 0.19 and 6.20‰ (with one outlier at −1.62‰). The wall rocks to the mineralization include sedimentary rocks that have contributed no detectable positive MIF sulfur to the VMS deposits, which is difficult to reconcile with the leaching model for the formation of these deposits. The sulfur isotope data are best explained by mixing between sulfur derived from a magmatic-hydrothermal fluid and seawater sulfur as represented by the interpillow pyrites. The massive sulfide lens pyrites have a weighted mean ∆33S value of −0.27 ± 0.05‰ (MSWD = 1.6) nearly identical with −0.31 ± 0.08‰ (MSWD = 2.4) for pyrites from the stringer zone, which requires mixing to have occurred below the sea floor. We employed a two-component mixing model to estimate the contribution of seawater sulfur to the total sulfur budget of the two Teutonic Bore volcanic complex VMS deposits. The results are 15 to 18% for both Teutonic Bore and Bentley, much higher than the 3% obtained by Jamieson et al. (2013) for the giant Kidd Creek deposit. Similar calculations, carried out for other Neoarchean VMS deposits give value between 2% and 30%, which are similar to modern hydrothermal VMS deposits. We suggest that multiple sulfur isotope analyses may be used to predict the size of Archean VMS deposits and to provide a vector to ore deposit but further studies are needed to test these suggestions.

Fate and transport of bensulfuron-methyl and imazosulfuron in paddy fields: Experiments and model simulation

Experiments were conducted to determine the fate of bensulfuron-methyl (BSM) and imazosulfuron (IMS) under paddy conditions. Initially, laboratory experiments were conducted and the photolysis half-lives of the two herbicides were found to be much shorter than their hydrolysis half-lives in aqueous solutions. In the aerobic water–soil system, dissipation followed first-order kinetics with water half-lives of 9.1 and 11.0 days and soil half-lives of 12.4 and 18.5 days (first phase) and 35.0 and 44.1 days (second phase) for bensulfuron-methyl and imazosulfuron, respectively. However, the anaerobic soil half-lives were only 12.7 and 9.8 days for BSM and IMS, respectively. The values of K d were determined to be 16.0 and 13.8 for BSM and IMS, respectively. Subsequent field measurements for the two herbicides revealed that dissipation of both herbicides in paddy water involved biphasic first-order kinetics, with the dissipation rates in the first phase being much faster than those in the second phase. The dissipation of bensulfuron-methyl and imazosulfuron in the paddy surface soil were also followed biphasic first-order kinetics. These results were then used as input parameters for the PCPF-1 model to simulate the fate and transport of BSM and IMS in the paddy environment (water and 1-cm surface soil layer). The measured and simulated values agreed well and the mass balance error during the simulation period was −1.2 and 2.8% of applied pesticide, respectively, for BSM and IMS.

Improving factory performance using an integrated sugar factory model

A whole of factory model of a raw sugar factory was developed in SysCAD software to assess and improve factory operations. The integrated sugar factory model ‘Sugar-SysCAD’ includes individual models for milling, heating and clarification, evaporation, crystallisation, steam cycle, sugar dryer and process and injection water circuits. These individual unit operation models can be either used as standalone models to optimise the unit operation or in the integrated mode to provide more accurate prediction of the effects of changes in any part of the process on the outputs of the whole factory process. Using the integrated sugar factory model, the effect of specific process operations can be understood and practical solutions can be determined to address process problems. The paper presents two factory scenarios to show the capabilities of the whole of factory model.

Thin-Layer Chromatography with Ultraviolet and Mass Spectrometric Detection: From Preparative-Layer to Miniaturized Ultra-Thin-Layer Technique

The present challenge in drug discovery is to synthesize new compounds efficiently in minimal time. The trend is towards carefully designed and well-characterized compound libraries because fast and effective synthesis methods easily produce thousands of new compounds. The need for rapid and reliable analysis methods is increased at the same time. Quality assessment, including the identification and purity tests, is highly important since false (negative or positive) results, for instance in tests of biological activity or determination of early-ADME parameters in vitro (the pharmacokinetic study of drug absorption, distribution, metabolism, and excretion), must be avoided. This thesis summarizes the principles of classical planar chromatographic separation combined with ultraviolet (UV) and mass spectrometric (MS) detection, and introduces powerful, rapid, easy, low-cost, and alternative tools and techniques for qualitative and quantitative analysis of small drug or drug-like molecules. High performance thin-layer chromatography (HPTLC) was introduced and evaluated for fast semi-quantitative assessment of the purity of synthesis target compounds. HPTLC methods were compared with the liquid chromatography (LC) methods. Electrospray ionization mass spectrometry (ESI MS) and atmospheric pressure matrix-assisted laser desorption/ionization MS (AP MALDI MS) were used to identify and confirm the product zones on the plate. AP MALDI MS was rapid, and easy to carry out directly on the plate without scraping. The PLC method was used to isolate target compounds from crude synthesized products and purify them for bioactivity and preliminary ADME tests. Ultra-thin-layer chromatography (UTLC) with AP MALDI MS and desorption electrospray ionization mass spectrometry (DESI MS) was introduced and studied for the first time. Because of the thinner adsorbent layer, the monolithic UTLC plate provided 10 100 times better sensitivity in MALDI analysis than did HPTLC plates. The limits of detection (LODs) down to low picomole range were demonstrated for UTLC AP MALDI and UTLC DESI MS. In a comparison of AP and vacuum MALDI MS detection for UTLC plates, desorption from the irregular surface of the plates with the combination of an external AP MALDI ion source and an ion trap instrument provided clearly less variation in mass accuracy than the vacuum MALDI time-of-flight (TOF) instrument. The performance of the two-dimensional (2D) UTLC separation with AP MALDI MS method was studied for the first time. The influence of the urine matrix on the separation and the repeatability was evaluated with benzodiazepines as model substances in human urine. The applicability of 2D UTLC AP MALDI MS was demonstrated in the detection of metabolites in an authentic urine sample.

Testing approximate theories of first-order phase transitions on the two-dimensional Potts model

The two-dimensional,q-state (q>4) Potts model is used as a testing ground for approximate theories of first-order phase transitions. In particular, the predictions of a theory analogous to the Ramakrishnan-Yussouff theory of freezing are compared with those of ordinary mean-field (Curie-Wiess) theory. It is found that the Curie-Weiss theory is a better approximation than the Ramakrishnan-Yussouff theory, even though the former neglects all fluctuations. It is shown that the Ramakrishnan-Yussouff theory overestimates the effects of fluctuations in this system. The reasons behind the failure of the Ramakrishnan-Yussouff approximation and the suitability of using the two-dimensional Potts model as a testing ground for these theories are discussed.

Spatial model of site index based on Y-ray spectrometry and a digital elevation model for two Pinus species in Tuan Toolara State Forest, Queensland, Australia

Site index prediction models are an important aid for forest management and planning activities. This paper introduces a multiple regression model for spatially mapping and comparing site indices for two Pinus species (Pinus elliottii Engelm. and Queensland hybrid, a P. elliottii x Pinus caribaea Morelet hybrid) based on independent variables derived from two major sources: g-ray spectrometry (potassium (K), thorium (Th), and uranium (U)) and a digital elevation model (elevation, slope, curvature, hillshade, flow accumulation, and distance to streams). In addition, interpolated rainfall was tested. Species were coded as a dichotomous dummy variable; interaction effects between species and the g-ray spectrometric and geomorphologic variables were considered. The model explained up to 60% of the variance of site index and the standard error of estimate was 1.9 m. Uranium, elevation, distance to streams, thorium, and flow accumulation significantly correlate to the spatial variation of the site index of both species, and hillshade, curvature, elevation and slope accounted for the extra variability of one species over the other. The predicted site indices varied between 20.0 and 27.3 m for P. elliottii, and between 23.1 and 33.1 m for Queensland hybrid; the advantage of Queensland hybrid over P. elliottii ranged from 1.8 to 6.8 m, with the mean at 4.0 m. This compartment-based prediction and comparison study provides not only an overview of forest productivity of the whole plantation area studied but also a management tool at compartment scale.

Net radiation dynamics: performance of 20 daily net radiation models as related to model structure and intricacy in two climates.

We compared daily net radiation (Rn) estimates from 19 methods with the ASCE-EWRI Rn estimates in two climates: Clay Center, Nebraska (sub-humid) and Davis, California (semi-arid) for the calendar year. The performances of all 20 methods, including the ASCE-EWRI Rn method, were then evaluated against Rn data measured over a non-stressed maize canopy during two growing seasons in 2005 and 2006 at Clay Center. Methods differ in terms of inputs, structure, and equation intricacy. Most methods differ in estimating the cloudiness factor, emissivity (e), and calculating net longwave radiation (Rnl). All methods use albedo (a) of 0.23 for a reference grass/alfalfa surface. When comparing the performance of all 20 Rn methods with measured Rn, we hypothesized that the a values for grass/alfalfa and non-stressed maize canopy were similar enough to only cause minor differences in Rn and grass- and alfalfa-reference evapotranspiration (ETo and ETr) estimates. The measured seasonal average a for the maize canopy was 0.19 in both years. Using a = 0.19 instead of a = 0.23 resulted in 6% overestimation of Rn. Using a = 0.19 instead of a = 0.23 for ETo and ETr estimations, the 6% difference in Rn translated to only 4% and 3% differences in ETo and ETr, respectively, supporting the validity of our hypothesis. Most methods had good correlations with the ASCE-EWRI Rn (r2 > 0.95). The root mean square difference (RMSD) was less than 2 MJ m-2 d-1 between 12 methods and the ASCE-EWRI Rn at Clay Center and between 14 methods and the ASCE-EWRI Rn at Davis. The performance of some methods showed variations between the two climates. In general, r2 values were higher for the semi-arid climate than for the sub-humid climate. Methods that use dynamic e as a function of mean air temperature performed better in both climates than those that calculate e using actual vapor pressure. The ASCE-EWRI-estimated Rn values had one of the best agreements with the measured Rn (r2 = 0.93, RMSD = 1.44 MJ m-2 d-1), and estimates were within 7% of the measured Rn. The Rn estimates from six methods, including the ASCE-EWRI, were not significantly different from measured Rn. Most methods underestimated measured Rn by 6% to 23%. Some of the differences between measured and estimated Rn were attributed to the poor estimation of Rnl. We conducted sensitivity analyses to evaluate the effect of Rnl on Rn, ETo, and ETr. The Rnl effect on Rn was linear and strong, but its effect on ETo and ETr was subsidiary. Results suggest that the Rn data measured over green vegetation (e.g., irrigated maize canopy) can be an alternative Rn data source for ET estimations when measured Rn data over the reference surface are not available. In the absence of measured Rn, another alternative would be using one of the Rn models that we analyzed when all the input variables are not available to solve the ASCE-EWRI Rn equation. Our results can be used to provide practical information on which method to select based on data availability for reliable estimates of daily Rn in climates similar to Clay Center and Davis.

Thermodynamic scaling theory for the two-impurity Anderson model

We present results of a study of the two-impurity Anderson model using a thermodynamic scaling theory developed recently. The model is characterized by the Coulomb energy U, the orbital energy epsilond, the d-level width Gamma, and the separation between impurities R. If Gamma<<−epsilond<~Gamma. Here we find that the single-impurity physics dominates the low-temperature behavior, and impurity-impurity interactions are perturbative. The qualitative features of the temperature-dependent susceptibility are discussed. Journal of Applied Physics is copyrighted by The American Institute of Physics.

Gauge hierarchy in a supersymmetric model

In a globally supersymmetric gauge theory with two distinct mass scales, the possible limitation on the gauge hierarchy due to the structure of the loop-corrected Higgs potential is shown to be absent. Also it has been demonstrated that the supersymmetry forces the large corrections to the two-point Greens functions of the light fields from the quadratic divergences and the logarithmic divergences with large coefficients to be zeroseparately. This would, therefore, allow a gauge hierarchy as large as desired.

A new kinetic model for bulk polymerization of vinyl chloride based on two-phase hypothesis

A kinetic model has been developed for the bulk polymerization of vinyl chloride using Talamini's hypothesis of two-phase polymerization and a new concept of kinetic solubility which assumes that rapidly growing polymer chains have considerably greater solubility than the thermodynamic solubility of preformed polymer molecules of the same size and so can remain in solution even under thermodynamically unfavourable conditions. It is further assumed that this kinetic solubility is a function of chain length. The model yields a rate expression consistent with the experimental data for vinyl chloride bulk polymerization and moreover is able to explain several characteristic kinetic features of this system. Application of the model rate expression to the available rate data has yielded 2.36 × 108l mol−1 sec−1 for the termination rate constant in the polymer-rich phase; as expected, this value is smaller than that reported for homogenous polymerization by a factor of 10–30.

Comprehensive Two-Dimensional Gas Chromatography: Instrumental and Methodological Development

Comprehensive two-dimensional gas chromatography (GC×GC) offers enhanced separation efficiency, reliability in qualitative and quantitative analysis, capability to detect low quantities, and information on the whole sample and its components. These features are essential in the analysis of complex samples, in which the number of compounds may be large or the analytes of interest are present at trace level. This study involved the development of instrumentation, data analysis programs and methodologies for GC×GC and their application in studies on qualitative and quantitative aspects of GC×GC analysis. Environmental samples were used as model samples. Instrumental development comprised the construction of three versions of a semi-rotating cryogenic modulator in which modulation was based on two-step cryogenic trapping with continuously flowing carbon dioxide as coolant. Two-step trapping was achieved by rotating the nozzle spraying the carbon dioxide with a motor. The fastest rotation and highest modulation frequency were achieved with a permanent magnetic motor, and modulation was most accurate when the motor was controlled with a microcontroller containing a quartz crystal. Heated wire resistors were unnecessary for the desorption step when liquid carbon dioxide was used as coolant. With use of the modulators developed in this study, the narrowest peaks were 75 ms at base. Three data analysis programs were developed allowing basic, comparison and identification operations. Basic operations enabled the visualisation of two-dimensional plots and the determination of retention times, peak heights and volumes. The overlaying feature in the comparison program allowed easy comparison of 2D plots. An automated identification procedure based on mass spectra and retention parameters allowed the qualitative analysis of data obtained by GC×GC and time-of-flight mass spectrometry. In the methodological development, sample preparation (extraction and clean-up) and GC×GC methods were developed for the analysis of atmospheric aerosol and sediment samples. Dynamic sonication assisted extraction was well suited for atmospheric aerosols collected on a filter. A clean-up procedure utilising normal phase liquid chromatography with ultra violet detection worked well in the removal of aliphatic hydrocarbons from a sediment extract. GC×GC with flame ionisation detection or quadrupole mass spectrometry provided good reliability in the qualitative analysis of target analytes. However, GC×GC with time-of-flight mass spectrometry was needed in the analysis of unknowns. The automated identification procedure that was developed was efficient in the analysis of large data files, but manual search and analyst knowledge are invaluable as well. Quantitative analysis was examined in terms of calibration procedures and the effect of matrix compounds on GC×GC separation. In addition to calibration in GC×GC with summed peak areas or peak volumes, simplified area calibration based on normal GC signal can be used to quantify compounds in samples analysed by GC×GC so long as certain qualitative and quantitative prerequisites are met. In a study of the effect of matrix compounds on GC×GC separation, it was shown that quality of the separation of PAHs is not significantly disturbed by the amount of matrix and quantitativeness suffers only slightly in the presence of matrix and when the amount of target compounds is low. The benefits of GC×GC in the analysis of complex samples easily overcome some minor drawbacks of the technique. The developed instrumentation and methodologies performed well for environmental samples, but they could also be applied for other complex samples.