Mathematical Modeling for Studying Microbial Processes – Some Examples

Mathematical modeling may have different purposes in chemical and biochemical engineering sciences. One of them is to confirm or to reject kinetic models for certain processes, or to evaluate the importance of some transport phenomena on the net chemical or biochemical reaction rate. In the present paper different microbial processes are considered and modeled for evaluation of kinetic constants for batch and continuous processes accomplished by free and immobilized microbial cells. The practical examples are from the field of wastewater treatment and biosynthesis of products, like enzymes, lactic acid, gluconic acid, etc. By the aid of mathematical modeling the kinetics and the type of inhibition are specified for microbial wastewater denitrification and biodegradation of halogenated hydrocarbons. The importance of free and immobilized cells and their separate contribution to the overall microbial process is also evaluated for some fermentation processes: gluconic acid production, dichloroethane biodegradation, lactic acid fermentation and monochloroacetic acid biodegradation.

On the Mathematical Modelling of Microbial Growth: Some Computational Aspects

We propose a new approach to the mathematical modelling of microbial growth. Our approach differs from familiar Monod type models by considering two phases in the physiological states of the microorganisms and makes use of basic relations from enzyme kinetics. Such an approach may be useful in the modelling and control of biotechnological processes, where microorganisms are used for various biodegradation purposes and are often put under extreme inhibitory conditions. Some computational experiments are performed in support of our modelling approach.

Mathematical Modeling, Music Literacy and Their Transmission in Fine Arts Education

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2014

Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

The Influence of Phosphorus on Periphyton Mats from the Everglades and Three Tropical Karstic Wetlands

The distinctive karstic, freshwater wetlands of the northern Caribbean and Central American region support the prolific growth of calcite-rich periphyton mats. Aside from the Everglades, very little research has been conducted in these karstic wetlands, which are increasingly threatened by eutrophication. This study sought to (i) test the hypothesis that water depth and periphyton total phosphorus (TP) content are both drivers of periphyton biomass in karstic wetland habitats in Belize, Mexico and Jamaica, (ii) provide a taxonomic inventory of the periphytic diatom species in these wetlands and (iii) examine the relationship between periphyton mat TP concentration and diatom assemblage at Everglades and Caribbean locations. ^ Periphyton biomass, nutrient and diatom assemblage data were generated from periphyton mat samples collected from shallow, marl-based wetlands in Belize, Mexico and Jamaica. These data were compared to a larger dataset collected from comparable sites within Everglades National Park. A diatom taxonomic inventory was conducted on the Caribbean samples and a combination of ordination and weighted-averaging modeling techniques were used to compare relationships between periphyton TP concentration, periphyton biomass and diatom assemblage composition among the locations. ^ Within the Everglades, periphyton biomass showed a negative correlation with water depth and mat TP, while periphyton mat percent organic content was positively correlated with these two variables. These patterns were also exhibited within the Belize, Mexico and Jamaica locations, suggesting that water depth and periphyton TP content are both drivers of periphyton biomass in karstic wetland systems within the northern Caribbean region. ^ A total of 146 diatom species representing 39 genera were recorded from the three Caribbean locations, including a distinct core group of species that may be endemic to this habitat type. Weighted averaging models were produced that effectively predicted mat TP concentration from diatom assemblages for both Everglades (R2=0.56) and Caribbean (R2=0.85) locations. There were, however, significant differences among Everglades and Caribbean locations with respect to species TP optima and indicator species. This suggests that although diatoms are effective indicators of water quality in these wetlands, differences in species response to water quality changes can reduce the predictive power of these indices when applied across systems. ^

Importance of water source in controlling leaf leaching losses in a dwarf red mangrove (Rhizophora mangle L.) wetland

The southern Everglades mangrove ecotone is characterized by extensive dwarf Rhizophora mangle L. shrub forests with a seasonally variable water source (Everglades – NE Florida Bay) and residence times ranging from short to long. We conducted a leaf leaching experiment to understand the influence that water source and its corresponding water quality have on (1) the early decay of R. mangle leaves and (2) the early exchange of total organic carbon (TOC) and total phosphorus (TP) between leaves and the water column. Newly senesced leaves collected from lower Taylor River (FL) were incubated in bottles containing water from one of three sources (Everglades, ambient mangrove, and Florida Bay) that spanned a range of salinity from 0 to 32‰, [TOC] from 710 to 1400 μM, and [TP] from 0.17 to 0.33 μM. We poisoned half the bottles in order to quantify abiotic processes (i.e., leaching) and assumed that non-poisoned bottles represented both biotic (i.e., microbial) and abiotic processes. We sacrificed bottles after 1,2, 5, 10, and 21 days of incubation and quantified changes in leaf mass and changes in water column [TOC] and [TP]. We saw 10–20% loss of leaf mass after 24 h—independent of water treatment—that leveled off by Day 21. After 3 weeks, non-poisoned leaves lost more mass than poisoned leaves, and there was only an effect of salinity on mass loss in poisoned incubations—with greatest leaching-associated losses in Everglades freshwater. Normalized concentrations of TOC in the water column increased by more than two orders of magnitude after 21 days with no effect of salinity and no difference between poisoned and non-poisoned treatments. However, normalized [TP] was lower in non-poisoned incubations as a result of immobilization by epiphytic microbes. This immobilization was greatest in Everglades freshwater and reflects the high P demand in this ecosystem. Immobilization of leached P in mangrove water and Florida Bay water was delayed by several days and may indicate an initial microbial limitation by labile C during the dry season.

Tropical seagrass-associated macroalgae distributions and trends relative to water quality

Tropical coastal marine ecosystems including mangroves, seagrass beds and coral reef communities are undergoing intense degradation in response to natural and human disturbances, therefore, understanding the causes and mechanisms present challenges for scientist and managers. In order to protect our marine resources, determining the effects of nutrient loads on these coastal systems has become a key management goal. Data from monitoring programs were used to detect trends of macroalgae abundances and develop correlations with nutrient availability, as well as forecast potential responses of the communities monitored. Using eight years of data (1996–2003) from complementary but independent monitoring programs in seagrass beds and water quality of the Florida Keys National Marine Sanctuary (FKNMS), we: (1) described the distribution and abundance of macroalgae groups; (2) analyzed the status and spatiotemporal trends of macroalgae groups; and (3) explored the connection between water quality and the macroalgae distribution in the FKNMS. In the seagrass beds of the FKNMS calcareous green algae were the dominant macroalgae group followed by the red group; brown and calcareous red algae were present but in lower abundance. Spatiotemporal patterns of the macroalgae groups were analyzed with a non-linear regression model of the abundance data. For the period of record, all macroalgae groups increased in abundance (Abi) at most sites, with calcareous green algae increasing the most. Calcareous green algae and red algae exhibited seasonal pattern with peak abundances (Φi) mainly in summer for calcareous green and mainly in winter for red. Macroalgae Abi and long-term trend (mi) were correlated in a distinctive way with water quality parameters. Both the Abi and mi of calcareous green algae had positive correlations with NO3−, NO2−, total nitrogen (TN) and total organic carbon (TOC). Red algae Abi had a positive correlation with NO2−, TN, total phosphorus and TOC, and the mi in red algae was positively correlated with N:P. In contrast brown and calcareous red algae Abi had negative correlations with N:P. These results suggest that calcareous green algae and red algae are responding mainly to increases in N availability, a process that is happening in inshore sites. A combination of spatially variable factors such as local current patterns, nutrient sources, and habitat characteristics result in a complex array of the macroalgae community in the seagrass beds of the FKNMS.

Historic primary producer communities linked to water quality and hydrologic changes in the northern Everglades

The northern Everglades Water Conservation Areas have experienced recent ecological shifts in primary producer community structure involving marl periphyton mats and dense Typha-dominated macrophyte stands. Multiple investigations have identified phosphorus (P) as a driver of primary producer community structure, but effects of water impoundment beginning in the 1950s and changes in water hardness [e.g., (CaCO3)] have also been identified as a concern. In an effort to understand pre-1950, primary producer community structure and identify community shifts since 1950, we measured pigment proxies on three sediment cores collected in Water Conservation Area-2A (WCA-2A) along a phosphorus enrichment gradient. Photosynthetic pigments, sediment total phosphorus content (TP), organic matter, total organic carbon and nitrogen were used to infer historic primary producer communities and changes in water quality and hydrology regulating those communities. Excess 210Pb was used to establish historic dates for the sediment cores. Results indicate the northern area of WCA-2A increased marl deposition and increased algal abundance ca. 1920. This increase in (presumably) calcareous periphyton before intensive agriculture and impoundment suggest canal-derived calcium inputs and to some extent early drainage effects played a role in initiating this community shift. The northern area community then shifted to Typha dominance around 1965. The areas to the south in WCA-2A experienced increased marl deposition and algal abundance around or just prior to 1950s impoundment, the precise timing limited by core age resolution. Continued increases in algal abundance were evident after 1950, coinciding with impoundment and deepening of canals draining into WCA-2A, both likely increasing water mineral and nutrient concentrations. The intermediate site developed a Typha-dominated community ca. 1995 while the southern-most core site WCA-2A has yet to develop Typha dominance. Numerous studies link sediment TP >650 mg P/kg to marsh habitat degradation into Typha-dominance. The northern and intermediate cores where Typha is currently support this previous research by showing a distinct shift in the sediment record to Typha dominance corresponding to sediment TP between 600 and 700 mg P/kg. These temporal and spatial differences are consistent with modern evidence showing water-column gradients in mineral inputs (including Ca, carbonates, and phosphorus) altering primary producer community structure in WCA-2A, but also suggest hydroperiod has an effect on the mechanisms regulating periphyton development and Typha dominance.

2007 Cumulative Annual Report for the Coastal Water Quality Monitoring Network

This report summarizes the existing data from the FIU Coastal Water Quality Monitoring Network for calendar year January 1 – December 31, 2007. This includes water quality data collected from 28 stations in Florida Bay, 22 stations in Whitewater Bay, 25 stations in Ten Thousand Islands, 25 stations in Biscayne Bay, 49 stations on the Southwest Florida Shelf (Shelf), and 28 stations in the Cape Romano-Pine Island Sound area. Each of the stations in Florida Bay were monitored on a monthly basis with monitoring beginning in March 1991; Whitewater Bay monitoring began in September 1992; Biscayne Bay monthly monitoring began September 1993; the SW Florida Shelf was sampled quarterly beginning in spring 1995; and monthly sampling in the Cape Romano-Pine Island Sound area started January 1999.

2007 Cumulative Annual Report for the Coastal Water Quality Monitoring Network

This report summarizes the existing data from the FIU Coastal Water Quality Monitoring Network for calendar year January 1 – December 31, 2007. This includes water quality data collected from 28 stations in Florida Bay, 22 stations in Whitewater Bay, 25 stations in Ten Thousand Islands, 25 stations in Biscayne Bay, 49 stations on the Southwest Florida Shelf (Shelf), and 28 stations in the Cape Romano-Pine Island Sound area. Each of the stations in Florida Bay were monitored on a monthly basis with monitoring beginning in March 1991; Whitewater Bay monitoring began in September 1992; Biscayne Bay monthly monitoring began September 1993; the SW Florida Shelf was sampled quarterly beginning in spring 1995; and monthly sampling in the Cape Romano-Pine Island Sound area started January 1999.

Water Quality and Wet Season Diatom Assemblage Characteristics from the Tamiami Trail Pilot Swales Sites (Everglades National Park, Florida, USA)

A pivotal component of hydrological restoration of the Florida Everglades is the improvement of water conveyance to Everglades National Park by the degradation of the current network of canals, roadways and levees. The Tamiami Trail (L29) road/canal complex represents a major barrier to natural water flows into the park and a variety of modification options for flow improvement are currently being explored, including the installation of spreader swales immediately downstream of culverts conveying water under Tamiami Trail from the L29 canal into Everglades National Park. In this study, we evaluated water column chemistry and wet-season diatom community structure to provide baseline information for use in future monitoring activities related to the proposed Tamiami Trail modifications. Water chemistry showed pronounced fluctuations in response to precipitation and anthropogenically mediated hydrological events. Differences in water quality variables among sites were dampened during periods of inundation, and became more pronounced during periods of low canal stage, suggesting the importance of small-scale mechanisms related to isolation of habitat patches. Diatom assemblages were unexpectedly speciose (127 taxa in 40 samples) compared to typical Everglades assemblages, and spatially heterogeneous in sites associated with concentric areas of dense vegetation immediately downstream of culverts. We also observed significant compositional dissimilarities among transects, indicating that culvert pool and north transect assemblages were substantially influenced by propagule input from the canal and areas to the north, while south transect sites were compositionally similar to typical sawgrass prairie diatom communities. Central transect sites were compositionally intermediate to their north and south counterparts. We propose that the position and spatial extent of this “transitional assemblage” is a sensitive indicator of subtle environmental change related to Tamiami Trail modifications.

Relating Freshwater Flow with Estuarine Water Quality in the Southern Everglades Mangrove Ecotone

Florida Bay is more saline than it was historically, and reduced freshwater flows may lead to more phosphorus inputs to the mangrove ecotone from the marine end-member. This is important given plans to restore freshwater flow into eastern Florida Bay. We investigated the relationships between salinity, nutrients, and hydrologic variables in the mangrove ecotone of Taylor Slough. We expected that total phosphorus (TP) would increase with salinity, reflecting a downstream marine source, while total nitrogen (TN) would increase with flow in the mangrove ecotone. Despite expectations of increased flows improving the ecological health of lower Taylor Slough and Florida Bay, total nitrogen (TN) and total phosphorus (TP) dynamics may shift in response to new conditions of flow and salinity as well as organic carbon, N, and P availability. Our results showed that TP concentrations are more discharge-driven while TN is more variable and potentially derived from different sources along the flow path from the freshwater Everglades marshes to Florida Bay. Increased flow of freshwater through Taylor Slough will likely decrease TP concentrations in this historically oligotrophic and P-limited ecosystem. However, more studies along the mangrove ecotone is needed to understand how increased flows will affect nitrogen dynamics relative to phosphorus.

Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Essays in Empirical Operations Management: Bayesian Learning of Service Quality and Structural Estimation of Complementary Product Pricing and Inventory Management

This dissertation contributes to the rapidly growing empirical research area in the field of operations management. It contains two essays, tackling two different sets of operations management questions which are motivated by and built on field data sets from two very different industries --- air cargo logistics and retailing.

The first essay, based on the data set obtained from a world leading third-party logistics company, develops a novel and general Bayesian hierarchical learning framework for estimating customers' spillover learning, that is, customers' learning about the quality of a service (or product) from their previous experiences with similar yet not identical services. We then apply our model to the data set to study how customers' experiences from shipping on a particular route affect their future decisions about shipping not only on that route, but also on other routes serviced by the same logistics company. We find that customers indeed borrow experiences from similar but different services to update their quality beliefs that determine future purchase decisions. Also, service quality beliefs have a significant impact on their future purchasing decisions. Moreover, customers are risk averse; they are averse to not only experience variability but also belief uncertainty (i.e., customer's uncertainty about their beliefs). Finally, belief uncertainty affects customers' utilities more compared to experience variability.

The second essay is based on a data set obtained from a large Chinese supermarket chain, which contains sales as well as both wholesale and retail prices of un-packaged perishable vegetables. Recognizing the special characteristics of this particularly product category, we develop a structural estimation model in a discrete-continuous choice model framework. Building on this framework, we then study an optimization model for joint pricing and inventory management strategies of multiple products, which aims at improving the company's profit from direct sales and at the same time reducing food waste and thus improving social welfare.

Collectively, the studies in this dissertation provide useful modeling ideas, decision tools, insights, and guidance for firms to utilize vast sales and operations data to devise more effective business strategies.

Modeling of a Heat-Induced Buckling of Plates Using the Mesh-free Method

In the process of engineering design of structural shapes, the flat plate analysis results can be generalized to predict behaviors of complete structural shapes. In this case, the purpose of this project is to analyze a thin flat plate under conductive heat transfer and to simulate the temperature distribution, thermal stresses, total displacements, and buckling deformations. The current approach in these cases has been using the Finite Element Method (FEM), whose basis is the construction of a conforming mesh. In contrast, this project uses the mesh-free Scan Solve Method. This method eliminates the meshing limitation using a non-conforming mesh. I implemented this modeling process developing numerical algorithms and software tools to model thermally induced buckling. In addition, convergence analysis was achieved, and the results were compared with FEM. In conclusion, the results demonstrate that the method gives similar solutions to FEM in quality, but it is computationally less time consuming.