Academic literature on the topic 'Freshwater microbiology mathematical models'

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Journal articles on the topic "Freshwater microbiology mathematical models"

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Chiyaka, Edward T., Gesham Magombedze, and Lawrence Mutimbu. "Modelling within Host Parasite Dynamics of Schistosomiasis." Computational and Mathematical Methods in Medicine 11, no. 3 (2010): 255–80. http://dx.doi.org/10.1080/17486701003614336.

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Schistosomiasis infection is characterized by the presence of adult worms in the portal and mesenteric veins of humans as part of a complex migratory cycle initiated by cutaneous penetration of the cercariae shed by infected freshwater snails. The drug praziquantel is not always effective in the treatment against schistosomiasis at larvae stage. However, our simulations show that it is effective against mature worms and eggs. As a result, the study and understanding of immunological responses is key in understanding parasite dynamics. We therefore introduce quantitative interpretations of human immunological responses of the disease to formulate mathematical models for the within-host dynamics of schistosomiasis. We also use numerical simulations to demonstrate that it is the level of T cells that differentiates between either an effective immune response or some degree of infection. These cells are responsible for the differentiation and recruitment of eosinophils that are instrumental in clearing the parasite. From the model analysis, we conclude that control of infection is much attributed to the value of a functionf, a measure of the average number of larvae penetrating a susceptible individual having hatched from an egg released by an infected individual. This agrees with evidence that there is a close association between the ecology, the distribution of infection and the disease.
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Stelling, Jörg. "Mathematical models in microbial systems biology." Current Opinion in Microbiology 7, no. 5 (October 2004): 513–18. http://dx.doi.org/10.1016/j.mib.2004.08.004.

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Costanza, Robert, and Fred H. Sklar. "Articulation, accuracy and effectiveness of mathematical models: A review of freshwater wetland applications." Ecological Modelling 27, no. 1-2 (March 1985): 45–68. http://dx.doi.org/10.1016/0304-3800(85)90024-9.

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Tom, Eric, and Kevin A. Schulman. "Mathematical Models in Decision Analysis." Infection Control and Hospital Epidemiology 18, no. 1 (January 1997): 65–73. http://dx.doi.org/10.2307/30141966.

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Tom, Eric, and Kevin A. Schulman. "Mathematical Models in Decision Analysis." Infection Control and Hospital Epidemiology 18, no. 1 (January 1997): 65–73. http://dx.doi.org/10.1086/647503.

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Li, Hao, Guozhong Xie, and Alan S. Edmondson. "Review of Secondary Mathematical Models of Predictive Microbiology." Journal of Food Products Marketing 14, no. 2 (May 28, 2008): 57–74. http://dx.doi.org/10.1080/10454440801918283.

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Grassly, Nicholas C., and Christophe Fraser. "Mathematical models of infectious disease transmission." Nature Reviews Microbiology 6, no. 6 (May 13, 2008): 477–87. http://dx.doi.org/10.1038/nrmicro1845.

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Schneider, B., and G. I. Marchuk. "Mathematical Models in Immunology." Biometrics 42, no. 4 (December 1986): 1003. http://dx.doi.org/10.2307/2530721.

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Bao, Weijun, Songming Zhu, Shuirong Guo, Li Wang, Shixue Huang, Jingyi Fu, and Zhangying Ye. "Particle size distribution mathematical models and properties of suspended solids in a typical freshwater pond." Environmental Pollution 241 (October 2018): 164–71. http://dx.doi.org/10.1016/j.envpol.2018.05.063.

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Shang, Qian Ming. "Modeling and Simulation of Freshwater Generator Subsystem of Low Speed Engine Room Simulator Based on Visual." Advanced Materials Research 557-559 (July 2012): 2324–28. http://dx.doi.org/10.4028/www.scientific.net/amr.557-559.2324.

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3d models of the equipments of freshwater generator system are built according to the real ship. In support of a simulative sustainable system, a real-time variable database and mathematical models of the subsystem are set up. Then the precision of the models are proved to meet the demands by comparing the simulation results with the practical situation. The interfaces are available by making use of VC++6.0. Finally, the data connections between the math models and interfaces are established by means of the technology of network communications. The purpose of developing this simulation system is training, which offers students a chance to make a good knowledge of the structure and working principle of the freshwater generator subsystem.
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Dissertations / Theses on the topic "Freshwater microbiology mathematical models"

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Linke, Simon, and n/a. "River conservation planning: accounting for condition, vulnerability and connected systems." University of Canberra. Resource, Environmental & Heritage Sciences, 2006. http://erl.canberra.edu.au./public/adt-AUC20070716.155500.

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Conservation science in rivers is still lagging behind its terrestrial and marine counterparts, despite increasing threats to freshwater biodiversity and extinction rates being estimated as five times higher than in terrestrial ecosystems. Internationally, most protected rivers have been assigned reserve status in the framework of terrestrial conservation plans, neglecting catchment effects of disturbance. While freshwater conservation tools are mainly index based (e.g. richness, rarity), modern terrestrial and marine conservation planning methods use complementarity-based algorithms - proven to be most efficient at protecting a large number of taxa for the least cost. The few complementarity-based lotic conservation efforts all use broad river classifications instead of biota as targets, a method heavily disputed in the literature. They also ignore current condition and future vulnerability. It was the aim of this thesis to develop a framework for conservation planning that: a) accounts for the connected nature of rivers b) is complementarity based and uses biota as targets c) integrates current status and future vulnerability I developed two different approaches using macroinvertebrate datasets from Australia, Canada and the USA. The first new method was a site/based two-tiered approach integrating condition and conservation value, based on RIVPACS/AUSRIVAS � a modelling technique that predicts macroinvertebrate composition. The condition stage assesses biodiversity loss by estimating a site-specific expected assemblage and comparing it to the actual observed assemblage. Sites with significant biodiversity loss are flagged for restoration, or other management actions. All other sites progress to the conservation stage, in which an index of site-specific taxonomic rarity is calculated. This second index (O/E BIODIV) assesses the number of rare taxa (as defined by <50% probability of occurrence). Using this approach on a dataset near Sydney, NSW, Australia, I was able to identify three regions: 1) an area in need of restoration; 2) a region of high conservation value and 3) an area that had high conservation potential if protection and restoration measures could counteract present disturbance. However, a second trial run with three datasets from the USA and Canada highlighted problems with O/E (BIODIV). If common taxa are predicted at lower probabilities of occurrence (p<50%) because of model error, they enter the index and change O/E (BIODIV). Therefore, despite an attractive theoretical grounding, the application of O/E (BIODIV) will be restricted to datasets where strong environmental gradients explain a large quantity of variation in the data and permit accurate predictions of rare taxa. It also requires extensive knowledge of regional species pools to ensure that introduced organisms are not counted in the index. The second approach was a proper adaptation of terrestrial complementarity algorithms and an extension to the Irreplaceability-Vulnerability framework by Margules and Pressey (2000). For this large-scale method, distributions for 400 invertebrate taxa were modeled across 1854 subcatchments in Victoria, Australia using Generalised Additive Models (GAMs). The best heuristic algorithm to estimate conservation value was determined by calculating the minimum area needed to cover all 400 taxa. Solutions were restricted to include rules for the protection of whole catchments upstream of a subcatchment that contained the target taxon. A summed rarity algorithm proved to be most efficient, beating the second best solution by 100 000 hectares. To protect 90% of the taxa, only 2% of the study area need to be protected. This increases to 10% of the study area when full representation of the targets is required. Irreplaceability was calculated by running the heuristic algorithm 1000 times with 90% of the catchments randomly removed. Two statistics were then estimated: f (the frequency of selection across 1000 runs) and average c (contribution to conservation targets). Four groups of catchments were identified: a) catchments that have high contributions and are always selected; b) catchments that have high contributions and are not always selected; c) catchments that are always chosen but do not contribute many taxa; d) catchments that are rarely chosen and did not contribute many taxa. Summed c, the sum of contributions over 1000 runs was chosen as an indicator of irreplaceability, integrating the frequency of selection and the number of taxa protected. Irreplaceability (I) was then linked to condition (C) and vulnerability (V) to create the ICVframework for river conservation planning. Condition was estimated using a stressor gradient approach (SGA), in which GIS layers of disturbance were summarised to three principal axes using principal components analysis (PCA). The main stressor gradient � agriculture � classified 75% of the study area as disturbed, a value consistent with existing assessments of river condition. Vulnerability was defined as the likelihood that land use in a catchment would intensify in the future. Hereby current tenure was compared to land capability. If a catchment would support a land use that would have a stronger effect on the rivers than its current tenure, it was classified as vulnerable. 79% of catchments contained more than 50% vulnerable land. When integrating the three estimators in the ICV-framework, seven percent of catchments were identified as highly irreplaceable but in degraded condition. These were flagged for urgent restoration. Unprotected, but highly irreplaceable and highly vulnerable catchments that were still in good condition made up 2.5% of the total area. These catchments are prime candidates for river reserves. The ICV framework developed here is the first method for systematic conservation planning in rivers that is complementarity-based, biota-driven but flexible to other conservation targets and accounts for catchment effects, thus fulfilling all the gaps outlined in the aims.
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Hanson, John Mark 1955. "Patterns of animal abundance in lakes : the role of competition in the fish-macroinvertebrate relationship." Thesis, McGill University, 1985. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=71975.

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Data taken from the literature were used to develop and evaluate models predicting fish biomass and yield, crustacean zooplankton biomass, and profundal macrobenthos biomass in lakes. Total phosphorus concentration and macrobenthos biomass/mean depth were the best univariate predictors of fish biomass and yield. Phosphorus concentration was also the best predictor of zooplankton and macrobenthos biomass. In experiments testing for inter- and intraspecific competition, conducted in situ at densities based on measured natural fish densities, growth of yellow perch (Perca flavescens) and pumpkinseed (Lepomis gibbosus) reared alone was inversely related to density. Both species primarily ate macroinvertebrates when reared alone. When reared together: perch growth was significantly depressed compared to that of perch reared alone; pumpkinseed growth was equivalent to that of pumpkinseed reared alone; and the diet of perch changed to include food of inferior quality (microcrustaceans) in the presence of the superior competitor, pumpkinseed, whose diet did not change.
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Schluter, Jonas. "Competition and cooperation in host-associated microbial communities : insights from computational and mathematical models." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:f2c26005-0332-44cf-88bc-2f78548c1244.

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Our bodies contain a vast number and diversity of microbes. These microbes interact, and these interactions can define how microbes affect us. Microbial ecology and evolution, therefore, are important for both microbiology and human health. However, our understanding of microbial communities remains limited. There is a need for theory that dissects the complexity and identifies the key factors and processes affecting microbial groups. Here I develop realistic computer simulations and population models of microbial communities. My first project seeks to explain microbial communication (quorum sensing) and argues that quorum sensing is a way to infer when competing genotypes are no longer a threat. The second project proposes an evolutionary explanation for another major microbial trait: adhesion. I argue that adhesion is a weapon allowing cells to compete within microbial groups and push competitors out, particularly when growing on a host epithelium. The third project moves from microbes to the host and asks whether a host can control which microbes grow and persist inside it. I develop a model of the human gut epithelium and show that the gut architecture amplifies the ability of hosts to select helpful microbes over harmful ones using nutrient secretion. In addition to selecting particular microbial strains, a host will also benefit from stable symbiotic communities that behave in a predictable manner. But what determines whether host-associated communities are ecologically stable? My final project uses ecological network theory to show that ecological stability is likely to be a problem for gut communities that are diverse and contain species that cooperate with each other. However, I argue that the host should function as an ecosystem engineer that increases ecological stability by weakening the strong dependence of cooperating species upon one another. While host-associated communities are complex ecological systems, my thesis identifies key factors that affect their form and function.
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Wen, Yuan Hua. "Pharmacokinetic modeling of pollutant fluxes by limnoplankton." Thesis, McGill University, 1996. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=34481.

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The objective of this thesis was to construct general models to predict pollutant fluxes in limnoplankton by incorporating characteristics of the organism and the structures of the chemical. A two-compartmental pharmacokinetic model was used to quantify the pollutant uptake, depuration and intercompartmental exchanges. The model pollutants were phosphorus and 22 organic chemicals.
The rate constants of phosphorus uptake, excretion and intercompartmental changes by algae and cladocerans decreased with cell volume or body size raised to a power close to $-$0.25, except the intercompartmental exchanges for cladocerans which showed more negative slopes. In contrast, uptake, excretion and internal exchange rates per individual increased with cell size or body weight to a power similar to 0.75 with a similar exception for the cladoceran intercompartmental exchanges, which had slopes $<$0.75.
Bioconcentration factors, rate constants and flux rates of uptake and intercompartmental exchange from metabolic pool to structural pool of 22 $ sp{14}$C-labelled organic toxicants by Chlorella pyrenoidosa and Daphnia magna were positively correlated with the octanol/water partition coefficient, molecular weight, parachor, connectivity index, boiling point and melting point, and negatively with aqueous solubility. However, those of elimination and internal transfer from structural pool to metabolic pool showed opposite changes. Comparisons of pharmacokinetic parameters between Daphnia and Chlorella demonstrated that, although all kinetic parameters displayed similar patterns, the relative magnitudes of each corresponding parameters were significantly different between two species.
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Linton, Richard Howard. "Use of the Gompertz equation to model non-linear survival curves and predict temperature, pH, and sodium chloride effects for Listeria monocytogenes Scott A." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06062008-164544/.

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Huang, Fang. "Modeling patterns of small scale spatial variation in soil." Link to electronic thesis, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-011106-155345/.

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Thesis (M.S.)--Worcester Polytechnic Institute.
Keywords: spatial variations; nested random effects models; semivariogram models; kriging methods; multiple logistic regression models; missing; multiple imputation. Includes bibliographical references (p. 35-36).
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Manipura, Walappuly Mudiyanselage Janakasiri Aruna Shantha Bandara. "Bioprocess development for removal of nitrogenous compounds from precious metal refinery wastewater." Thesis, Rhodes University, 2008. http://hdl.handle.net/10962/d1007341.

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Removal of nitrogenous compounds from precious metal refinery (PMR) wastewater is important in terms of avoiding eutrophication (environmental protection), metal recovery (increased overall process efficiency and value recovery) and reuse of treated water (maximum use of natural resources). Extreme pH conditions (4 to 13 depending on the wastewater stream), high chemical oxygen demand (> 10,000 mg/I), numerous metals and high concentrations of those metals (> 20 mg/l of platinum group metals) in the wastewater are the main challenges for biological removal of nitrogenous compounds from PMR wastewater. Nitrogenous compounds such as NH₄⁺-N and N0₃-N are strong metal ligands, which make it difficult to recover metals from the wastewater. Therefore, a bioprocess was developed for removal of nitrogenous compounds from carefully simulated PMR wastewater. A preliminary investigation of metal wastewater was carried out to determine its composition and physico-chemical properties, the ability to nitrify and denitrify under different pH conditions and denitrification with different carbon Source compounds and amounts. Even at pH 4, nitrification could be carried out. A suitable hydraulic retention time was found to be 72 hours. There was no significant difference between sodium acetate and sodium lactate as carbon sources for denitrification. Based on these results, a reactor comparison study was carried out using simulated PMR wastewater in three types of reactors: continuously stirred tank reactor (CSTR), packed-bed reactor (PBR) and airlift suspension reactor (ALSR). These reactors were fed with 30 mg/l of Rh bound in an NH₄⁺ based compound (Claus salt: pentaaminechlororhodium (III) dichloride). Total nitrogen removal efficiencies of > 68 % , > 79 % and > 45 % were obtained in the CSTR, PBR and ALSR, respectively. Serially connected CSTR-PBR and PBR-CSTR reactor configurations were then studied to determine the best configuration for maximum removal of nitrogenous compounds from the wastewater. The PBR-CSTR configuration gave consistent biomass retention and automatic pH control in the CSTR. Ammonium removal efficiencies > 95 % were achieved in both reactors. As poor nitrate removal was observed a toxicity study was carried out using respirometry and the half saturation inhibition coefficients for Pt, Pd, Rh and Ru were found to be 15.81, 25.00, 33.34 and 39.25 mg/l, respectively. A mathematical model was developed to describe the nitrogen removal in PMR wastewater using activated sludge model number 1 (ASMl), two step nitrification and metal toxicity. An operational protocol was developed based on the literature review, experimental work and simulation results. The optimum reactor configuration under the set conditions (20 mg/I of Rh and < 100 mg/I of NH₄⁺-N) was found to be PBR-CSTR-PBR process, which achieved overall NH₄⁺-N and N0₃⁻-N removal efficiencies of > 90 % and 95 %, respectively. Finally, a rudimentary microbial characterisation was carried out on subsamples from the CSTR and PBRsecondary. It was found that the CSTR biomass consisted of both rods and cocci while PBRsecondary consisted of rods only. Based on these experimental works, further research needs and recommendations were made for optimisation of the developed bioprocess for removal of nitrogenous compounds from PMR wastewater.
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Poreau, Brice. "Biologie et complexité : histoire et modèles du commensalisme." Phd thesis, Université Claude Bernard - Lyon I, 2014. http://tel.archives-ouvertes.fr/tel-01063917.

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Le commensalisme est une association biologique au sein de laquelle le commensal obtient un avantage, alors que son hôte n'obtient ni avantage, ni désavantage. Ce type d'association est théorisé durant la seconde moitié du dix-neuvième siècle, notamment par Pierre-Joseph Van Beneden (1809-1894). Zoologiste belge, professeur à l'université de Louvain, il propose dans son ouvrage de 1875 intitulé Les commensaux et les parasites dans le règne animal, 264 exemples d'associations qu'il classe parmi le commensalisme. Ses travaux ont un retentissement majeur dans l'univers des zoologistes de son époque. Le concept de commensalisme perdure alors jusqu'au vingt-et-unième siècle et interroge sur les notions d'individualité, d'individuation et d'association. Notre étude porte non seulement sur le développement de ce concept au cours du dix-neuvième siècle, que nous démontrons par de nombreux documents inédits issus des archives de Pierre-Joseph Van Beneden, mais aussi sur la pérennité du concept jusqu'à nos jours. Le commensalisme est interprété comme un " marqueur " de l'émergence de nouvelles sciences du vivant : la microbiologie et l'écologie. Plus qu'un concept scientifique, le commensalisme apparaît alors comme un concept illustrant la complexité du vivant
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Wortmann, Joanne. "A modelling approach for determining the freshwater requirements of estuarine macrophytes." Thesis, 1998. http://hdl.handle.net/10413/6310.

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Increased abstraction of water in the catchment results in a reduced or altered pattern of river flow and this holds serious consequences for the downstream estuarine ecosystem. In South Africa this is a serious concern because freshwater is in limited supply and the demand for freshwater can be expected to increase in the future. A large multi-disciplinary consortium of South African scientists are working on projects to determine the freshwater requirements of estuarine ecosystems. As part of this, this thesis reports on research undertaken to develop mathematical models to determine the freshwater requirements of estuarine macrophytes. Three key macrophytes are selected. The macrophytes are Zostera capensis Setchell, Ruppia cirrhosa Grande, and Phragmites australis. They are common macrophytes in South African estuaries. Zostera and Ruppia are submerged macrophytes and Phragmites is an emergent macrophyte. They have different freshwater environments and therefore respond differently to alterations in freshwater flow. A first order differential equation model is used to determine the effect of different combinations of open and closed mouth conditions of the estuary on Zostera and Ruppia. The scenarios are selected to determine whether achieving a switch in states from a Zostera-dominated estuary to a Ruppia-dominated estuary is possible. To predict encroachment rates and colonisation patterns, a cellular automaton of the vegetative spread of existing Zostera beds is developed. After analysing various scenarios accounting for both an increase and a decrease in freshwater supply, the cellular automaton is extended to include interactions between Ruppia and Phragmites. The multi-species model is applied to the Kromme estuary, South Africa and the Great Brak estuary, South Africa. Various freshwater scenarios are examined from the natural runoff condition to the situation of no freshwater inflow. A sensitivity analysis of the spatial model with Zostera, Ruppia and Phragmites is conducted.
Thesis (Ph.D.)-University of Natal, Pietermaritzburg, 1998.
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Rockhold, Mark L. "Interactions between microbial dynamics and transport processes in soils." Thesis, 2002. http://hdl.handle.net/1957/31485.

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An experimental and numerical modeling investigation was conducted to study interactions between microbial dynamics and transport processes in variably saturated porous media. These interactions are important in a variety of applied problems such as water and wastewater treatment, bioremediation, and oil-field recovery operations. These processes and interactions also have great ecological significance, with global scale implications for carbon cycling in the environment and the related issue of climate change. Experiments were conducted under variably saturated flow conditions in columns and 2D light-transmission chambers packed with translucent quartz sand. A bioluminescent Pseudomonas fluorescens bacterium was utilized in the experiments and bioluminescence was used as a non-destructive measure of bacterial density and distribution. In the column experiments, pressure heads increased (became less negative) at all measured depths, but significant changes in apparent volumetric water contents were only observed in the upper 5 cm of the columns. Permeability was reduced by a factor of 40 within one week during growth on glucose. In the chamber experiments, aqueous-phase saturations decreased by 7-9% in the region of primary colonization and the capillary fringe dropped by 5 cm during the 6-day experiment. The colonized region expanded laterally by 15 cm and upward against the flow by about 7-8 cm. The desaturation phenomenon resulted in increased lateral spreading of solutes around the colonized region. A numerical model was developed and used to help interpret the experimental data. Water flow was modeled using the single-phase Richards equation. Solute and bacterial transport, cell growth, substrate consumption, and gas diffusion were modeled using advection-dispersion-reaction equations. Observed changes in saturations and pressure heads were reproduced approximately using fluid-media scaling to represent an apparent surface-tension lowering effect, which was assumed to be due to sorption of cells and/or biosurfactants at gas-liquid interfaces. Microbial dynamics, and substrate and oxygen consumption were represented using first-order reversible kinetics for cell attachment/detachment, and dual Monod-type kinetics for cell growth and substrate and oxygen consumption. Reasonably good matches were obtained between the observed and simulated results.
Graduation date: 2003
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Books on the topic "Freshwater microbiology mathematical models"

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Shitikov, V. K. Kolichestvennai︠a︡ gidroėkologii︠a︡: Metody, kriterii, reshenii︠a︡. Moskva: Nauka, 2005.

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Groschen, G. E. Simulated effects of projected pumping on the availability of freshwater in the Evangeline aquifer in an area southwest of Corpus Christi, Texas. Austin, Tex: U.S. Dept. of the Interior, Geological Survey, 1986.

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Groschen, G. E. Simulated effects of projected pumping on the availability of freshwater in the Evangeline aquifer in an area southwest of Corpus Christi, Texas. Austin, Tex: U.S. Dept. of the Interior, Geological Survey, 1986.

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Groschen, G. E. Simulated effects of projected pumping on the availability of freshwater in the Evangeline aquifer in an area southwest of Corpus Christi, Texas. Austin, Tex: U.S. Dept. of the Interior, Geological Survey, 1986.

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Molen, Diederik van der. The role of eutrophication models in water management. [Wageningen: s.n., 1999.

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Stanley, Jon G. Habitat suitability index models: Nonmigratory freshwater life stages of Atlantic salmon. Washington, D.C: U.S. Dept. of the Interior, National Biological Service, 1995.

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Stanley, Jon G. Habitat suitability index models: Nonmigratory freshwater life stages of Atlantic salmon. Washington, D.C: U.S. Dept. of the Interior, National Biological Service, 1995.

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Pérez-Rodríguez, Fernando. Predictive Microbiology in Foods. New York, NY: Springer New York, 2013.

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Matematicheskoe modelirovanie bioticheskikh potokov veshchestva i ėnergii v vodnykh ėkosistemakh. Sankt-Peterburg: Nauka, 1997.

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Advanced quantitative microbiology for foods and biosystems: Models for predicting growth and inactivation. Boca Raton: Taylor & Francis Group, 2006.

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Book chapters on the topic "Freshwater microbiology mathematical models"

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Hill, Alison L. "Mathematical Models of HIV Latency." In Current Topics in Microbiology and Immunology, 131–56. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/82_2017_77.

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Berg, Sergey S., James D. Forester, and Meggan E. Craft. "Infectious Disease in Wild Animal Populations: Examining Transmission and Control with Mathematical Models." In Advances in Environmental Microbiology, 239–66. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-92373-4_7.

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Pérez-Rodríguez, Fernando. "Development and application of predictive microbiology models in foods." In Mathematical and Statistical Methods in Food Science and Technology, 321–62. Chichester, UK: John Wiley & Sons, Ltd, 2013. http://dx.doi.org/10.1002/9781118434635.ch18.

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Saakian, David B., and Chin-Kun Hu. "Mathematical Models of Quasi-Species Theory and Exact Results for the Dynamics." In Current Topics in Microbiology and Immunology, 121–39. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/82_2015_471.

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Biswas, Rohit, Neha Singh, Atul Anand Mishra, and Prince Chawla. "Mathematical Models and Kinetic Studies for the Assessment of Antimicrobial Properties of Metal Nanoparticles." In Nanotechnological Approaches in Food Microbiology, 1–29. CRC Press, 2020. http://dx.doi.org/10.1201/9780429342776-1.

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