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.

Mathematical Modeling of the Weaving Structure Design

Красимир Йорджев, Христина Костадинова - В работата се разглежда една релация на еквивалентност в множеството от всички квадратни бинарни матрици. Обсъдена е комбинаторната задача за намиране мощността и елементите на фактормножеството относно тази релация. Разгледана е и възможността за получаване на някои специални елементи на това фактормножество. Предложен е алгоритъм за решаване на поставените задачи. Получените в статията резултати намират приложение при описанието топологията на различните тъкачни структури.

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

Mathematical Modeling of Perifusion Cell Culture Experiments

In perifusion cell cultures, the culture medium flows continuously through a chamber containing immobilized cells and the effluent is collected at the end. In our main applications, gonadotropin releasing hormone (GnRH) or oxytocin is introduced into the chamber as the input. They stimulate the cells to secrete luteinizing hormone (LH), which is collected in the effluent. To relate the effluent LH concentration to the cellular processes producing it, we develop and analyze a mathematical model consisting of coupled partial differential equations describing the intracellular signaling and the movement of substances in the cell chamber. We analyze three different data sets and give cellular mechanisms that explain the data. Our model indicates that two negative feedback loops, one fast and one slow, are needed to explain the data and we give their biological bases. We demonstrate that different LH outcomes in oxytocin and GnRH stimulations might originate from different receptor dynamics. We analyze the model to understand the influence of parameters, like the rate of the medium flow or the fraction collection time, on the experimental outcomes. We investigate how the rate of binding and dissociation of the input hormone to and from its receptor influence its movement down the chamber. Finally, we formulate and analyze simpler models that allow us to predict the distortion of a square pulse due to hormone-receptor interactions and to estimate parameters using perifusion data. We show that in the limit of high binding and dissociation the square pulse moves as a diffusing Gaussian and in this limit the biological parameters can be estimated.

Mathematical Modeling to Assess the Drivers of the Recent Emergence of Typhoid Fever in Blantyre, Malawi

BACKGROUND: Multiyear epidemics of Salmonella enterica serovar Typhi have been reported from countries across eastern and southern Africa in recent years. In Blantyre, Malawi, a dramatic increase in typhoid fever cases has recently occurred, and may be linked to the emergence of the H58 haplotype. Strains belonging to the H58 haplotype often exhibit multidrug resistance and may have a fitness advantage relative to other Salmonella Typhi strains.

METHODS: To explore hypotheses for the increased number of typhoid fever cases in Blantyre, we fit a mathematical model to culture-confirmed cases of Salmonella enterica infections at Queen Elizabeth Central Hospital, Blantyre. We explored 4 hypotheses: (1) an increase in the basic reproductive number (R0) in response to increasing population density; (2) a decrease in the incidence of cross-immunizing infection with Salmonella Enteritidis; (3) an increase in the duration of infectiousness due to failure to respond to first-line antibiotics; and (4) an increase in the transmission rate following the emergence of the H58 haplotype.

RESULTS: Increasing population density or decreasing cross-immunity could not fully explain the observed pattern of typhoid emergence in Blantyre, whereas models allowing for an increase in the duration of infectiousness and/or the transmission rate of typhoid following the emergence of the H58 haplotype provided a good fit to the data.

CONCLUSIONS: Our results suggest that an increase in the transmissibility of typhoid due to the emergence of drug resistance associated with the H58 haplotype may help to explain recent outbreaks of typhoid in Malawi and similar settings in Africa.

Mathematical modeling of the diffusion of magnetic particles in a ferrofluid seal under magnetic and centrifugal forces

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Dissertation, 2016

GIS-integrated mathematical modeling of social phenomena at macro- and micro- levels—a multivariate geographically-weighted regression model for identifying locations vulnerable to hosting terrorist safe-houses: France as case study

Adaptability and invisibility are hallmarks of modern terrorism, and keeping pace with its dynamic nature presents a serious challenge for societies throughout the world. Innovations in computer science have incorporated applied mathematics to develop a wide array of predictive models to support the variety of approaches to counterterrorism. Predictive models are usually designed to forecast the location of attacks. Although this may protect individual structures or locations, it does not reduce the threat—it merely changes the target. While predictive models dedicated to events or social relationships receive much attention where the mathematical and social science communities intersect, models dedicated to terrorist locations such as safe-houses (rather than their targets or training sites) are rare and possibly nonexistent. At the time of this research, there were no publically available models designed to predict locations where violent extremists are likely to reside. This research uses France as a case study to present a complex systems model that incorporates multiple quantitative, qualitative and geospatial variables that differ in terms of scale, weight, and type. Though many of these variables are recognized by specialists in security studies, there remains controversy with respect to their relative importance, degree of interaction, and interdependence. Additionally, some of the variables proposed in this research are not generally recognized as drivers, yet they warrant examination based on their potential role within a complex system. This research tested multiple regression models and determined that geographically-weighted regression analysis produced the most accurate result to accommodate non-stationary coefficient behavior, demonstrating that geographic variables are critical to understanding and predicting the phenomenon of terrorism. This dissertation presents a flexible prototypical model that can be refined and applied to other regions to inform stakeholders such as policy-makers and law enforcement in their efforts to improve national security and enhance quality-of-life.

Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.

Hydrometallurgical process modeling using advanced mathematical tools

Hydrometallurgical process modeling is the main objective of this Master’s thesis work. Three different leaching processes namely, high pressure pyrite oxidation, direct oxidation zinc concentrate (sphalerite) leaching and gold chloride leaching using rotating disc electrode (RDE) are modeled and simulated using gPROMS process simulation program in order to evaluate its model building capabilities. The leaching mechanism in each case is described in terms of a shrinking core model. The mathematical modeling carried out included process model development based on available literature, estimation of reaction kinetic parameters and assessment of the model reliability by checking the goodness fit and checking the cross correlation between the estimated parameters through the use of correlation matrices. The estimated parameter values in each case were compared with those obtained using the Modest simulation program. Further, based on the estimated reaction kinetic parameters, reactor simulation and modeling for direct oxidation zinc concentrate (sphalerite) leaching is carried out in Aspen Plus V8.6. The zinc leaching autoclave is based on Cominco reactor configuration and is modeled as a series of continuous stirred reactors (CSTRs). The sphalerite conversion is calculated and a sensitivity analysis is carried out so to determine the optimum reactor operation temperature and optimum oxygen mass flow rate. In this way, the implementation of reaction kinetic models into the process flowsheet simulation environment has been demonstrated.

Predicting active material utilisation in LiFePO4 electrodes using a multi-scale mathematical model

A mathematical model is developed to simulate the discharge of a LiFePO4 cathode. This model contains 3 size scales, which match with experimental observations present in the literature on the multi-scale nature of LiFePO4 material. A shrinking-core is used on the smallest scale to represent the phase-transition of LiFePO4 during discharge. The model is then validated against existing experimental data and this validated model is then used to investigate parameters that influence active material utilisation. Specifically the size and composition of agglomerates of LiFePO4 crystals is discussed, and we investigate and quantify the relative effects that the ionic and electronic conductivities within the oxide have on oxide utilisation. We find that agglomerates of crystals can be tolerated under low discharge rates. The role of the electrolyte in limiting (cathodic) discharge is also discussed, and we show that electrolyte transport does limit performance at high discharge rates, confirming the conclusions of recent literature.

Modeling the stepped potential discharge of primary alkaline battery cathodes

A novel model for the potentiostatic discharge of primary alkaline battery cathodes is presented. The model is used to simulate discharges resulting from the stepped potential electrochemical spectroscopy (SPECS) of primary alkaline battery cathodes cathodes, and the results are validated with experimental data. We show that a model based on a single (or mean) reaction framework can be used to simulate multi-reaction discharge behaviour and we develop a consistent functional modification to the kinetic equation of the model that allows for this to occur. The model is used to investigate the effects that the initial exchange current density, i00, and the diffusion coefficient for protons in electrolytic manganese dioxide (EMD), DH+, have on SPECS discharge. The behaviour observed is consistent with the idea that individual reduction reactions, within the multi-reaction, reduction behaviour of EMD, have distinct i00 and DH+ values.

In silico experimental modeling of cancer treatment

In silico experimental modeling of cancer involves combining findings from biological literature with computer-based models of biological systems in order to conduct investigations of hypotheses entirely in the computer laboratory. In this paper, we discuss the use of in silico modeling as a precursor to traditional clinical and laboratory research, allowing researchers to refine their experimental programs with an aim to reducing costs and increasing research efficiency. We explain the methodology of in silico experimental trials before providing an example of in silico modeling from the biomathematical literature with a view to promoting more widespread use and understanding of this research strategy.

Understanding mild acid pretreatment of sugarcane bagasse through particle scale modeling

Sugarcane bagasse is an abundant and sustainable resource, generated as a by-product of sugarcane milling. The cellulosic material within bagasse can be broken down into glucose molecules and fermented to produce ethanol, making it a promising feedstock for biofuel production. Mild acid pretreatment hydrolyses the hemicellulosic component of biomass, thus allowing enzymes greater access to the cellulosic substrate during saccharification. A particle-scale mathematical model describing the mild acid pretreatment of sugarcane bagasse has been developed, using a volume averaged framework. Discrete population-balance equations are used to characterise the polymer degradation kinetics, and diffusive effects account for mass transport within the cell wall of the bagasse. As the fibrous material hydrolyses over time, variations in the porosity of the cell wall and the downstream effects on the reaction kinetics are accounted for using conservation of volume arguments. Non-dimensionalization of the model equations reduces the number of parameters in the system to a set of four dimensionless ratios that compare the timescales of different reaction and diffusion events. Theoretical yield curves are compared to macroscopic experimental observations from the literature and inferences are made as to constraints on these “unknown” parameters. These results enable connections to be made between experimental data and the underlying thermodynamics of acid pretreatment. Consequently, the results suggest that data-fitting techniques used to obtain kinetic parameters should be carefully applied, with prudent consideration given to the chemical and physiological processes being modeled.