Oil spill environmental risk assessment of stationary sources in offshore zones (Innovating a mathematical model)

Nowadays, risks arising from the rapid development of oil and gas industries are significantly increasing. As a result, one of the main concerns of either industrial or environmental managers is the identification and assessment of such risks in order to develop and maintain appropriate proactive measures. Oil spill from stationary sources in offshore zones is one of the accidents resulting in several adverse impacts on marine ecosystems. Considering a site's current situation and relevant requirements and standards, risk assessment process is not only capable of recognizing the probable causes of accidents but also of estimating the probability of occurrence and the severity of consequences. In this way, results of risk assessment would help managers and decision makers create and employ proper control methods. Most of the represented models for risk assessment of oil spills are achieved on the basis of accurate data bases and analysis of historical data, but unfortunately such data bases are not accessible in most of the zones, especially in developing countries, or else they are newly established and not applicable yet. This issue reveals the necessity of using Expert Systems and Fuzzy Set Theory. By using such systems it will be possible to formulize the specialty and experience of several experts and specialists who have been working in petroliferous areas for several years. On the other hand, in developing countries often the damages to environment and environmental resources are not considered as risk assessment priorities and they are approximately under-estimated. For this reason, the proposed model in this research is specially addressing the environmental risk of oil spills from stationary sources in offshore zones.

A mathematical model of the early visual system and border completion via subriemannian Hamiltonian geodesics

In this thesis, we aim to discuss a simple mathematical model for the edge detection mechanism and the boundary completion problem in the human brain in a differential geometry framework. We describe the columnar structure of the primary visual cortex as the fiber bundle R2 × S1, the orientation bundle, and by introducing a first vector field on it, explain the edge detection process. Edges are detected through a lift from the domain in R2 into the manifold R2 × S1 and are horizontal to a completely non-integrable distribution. Therefore, we can construct a subriemannian structure on the manifold R2 × S1, through which we retrieve perceived smooth contours as subriemannian geodesics, solutions to Hamilton’s equations. To do so, in the first chapter, we illustrate the functioning of the most fundamental structures of the early visual system in the brain, from the retina to the primary visual cortex. We proceed with introducing the necessary concepts of differential and subriemannian geometry in chapters two and three. We finally implement our model in chapter four, where we conclude, comparing our results with the experimental findings of Heyes, Fields, and Hess on the existence of an association field.

DEA-R:ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications

We propose a new mathematical model for efficiency analysis, which combines DEA methodology with an old idea-Ratio Analysis. Our model, called DEA-R, treats all possible ratios "output/input" as outputs within the standard DEA model. Although DEA and DEA-R generate different summary measures for efficiency, the two measures are comparable. Our mathematical and empirical comparisons establish the validity of DEA-R model in its own right. The key advantage of DEA-R over DEA is that it allows effective integration of the model with experts' opinions via flexible restrictive conditions on individual "output/input" pairs. © 2007 Springer Science+Business Media, LLC.

Using Lindenmayer systems to model morphogenesis in a tropical pasture legume Stylosanthes scabra

This paper summarizes the processes involved in designing a mathematical model of a growing pasture plant, Stylosanthes scabra Vog. cv. Fitzroy. The model is based on the mathematical formalism of Lindenmayer systems and yields realistic computer-generated images of progressive plant geometry through time. The processes involved in attaining growth data, retrieving useful growth rules, and constructing a virtual plant model are outlined. Progressive output morphological data proved useful for predicting total leaf area and allowed for easier quantification of plant canopy size in terms of biomass and total leaf area.

Model for gas-liquid flow through wet porous medium

A method involving bubbling of air through a fibrous filter immersed in water has recently been investigated (Agranovski et al. [1]). Experimental results showed that the removal efficiency for ultra-fine aerosols by such filters was greatly increased compared to dry filters. Nuclear Magnetic Resonance (NMR) imaging was used to examine the wet filter and to determine the nature of the gas flow inside the filter (Agranovski et al. [2]). It was found that tortuous preferential pathways (or flow tubes) develop within the filter through which the air flows and the distribution of air and water inside the porous medium has been investigated. The aim of this paper is to investigate the geometry of the pathways and to make estimates of the flow velocities and particle removal efficiency in such pathways. A mathematical model of the flow of air along the preferred pathways has been developed and verified experimentally. Even for the highest realistic gas velocity the flow field was essentially laminar (Re approximate to 250). We solved Laplace's equation for stream function to map trajectories of particles and gas molecules to investigate the possibility of their removal from the carrier.

Mathematical models in percutaneous absorption

A number of mathematical models have been used to describe percutaneous absorption kinetics. In general, most of these models have used either diffusion-based or compartmental equations. The object of any mathematical model is to a) be able to represent the processes associated with absorption accurately, b) be able to describe/summarize experimental data with parametric equations or moments, and c) predict kinetics under varying conditions. However, in describing the processes involved, some developed models often suffer from being of too complex a form to be practically useful. In this chapter, we attempt to approach the issue of mathematical modeling in percutaneous absorption from four perspectives. These are to a) describe simple practical models, b) provide an overview of the more complex models, c) summarize some of the more important/useful models used to date, and d) examine sonic practical applications of the models. The range of processes involved in percutaneous absorption and considered in developing the mathematical models in this chapter is shown in Fig. 1. We initially address in vitro skin diffusion models and consider a) constant donor concentration and receptor conditions, b) the corresponding flux, donor, skin, and receptor amount-time profiles for solutions, and c) amount- and flux-time profiles when the donor phase is removed. More complex issues, such as finite-volume donor phase, finite-volume receptor phase, the presence of an efflux. rate constant at the membrane-receptor interphase, and two-layer diffusion, are then considered. We then look at specific models and issues concerned with a) release from topical products, b) use of compartmental models as alternatives to diffusion models, c) concentration-dependent absorption, d) modeling of skin metabolism, e) role of solute-skin-vehicle interactions, f) effects of vehicle loss, a) shunt transport, and h) in vivo diffusion, compartmental, physiological, and deconvolution models. We conclude by examining topics such as a) deep tissue penetration, b) pharmacodynamics, c) iontophoresis, d) sonophoresis, and e) pitfalls in modeling.

An optimization model for antibiotic use

There is a positive correlation between the intensity of use of a given antibiotic and the prevalence of resistant strains. The more you treat, more patients infected with resistant strains appears and, as a consequence, the higher the mortality due to the infection and the longer the hospitalization time. In contrast, the less you treat, the higher the mortality rates and the longer the hospitalization time of patients infected with sensitive strains that could be successfully treated. The hypothesis proposed in this paper is an attempt to solve such a conflict: there must be an optimum treatment intensity that minimizes both the additional mortality and hospitalization time due to the infection by both sensitive and resistant bacteria strains. In order to test this hypothesis we applied a simple mathematical model that allowed us to estimate the optimum proportion of patients to be treated in order to minimize the total number of deaths and hospitalization time due to the infection in a hospital setting. (C) 2007 Elsevier Inc. All rights reserved.

Mathematical modelling of schistosomiasis japonica: comparison of control strategies in the People's Republic of China

We present the first mathematical model on the transmission dynamics of Schistosoma japonicum. The work extends Barbour's classic model of schistosome transmission. It allows for the mammalian host heterogeneity characteristic of the S. japonicum life cycle, and solves the problem of under-specification of Barbour's model by the use of Chinese data we are collecting on human-bovine transmission in the Poyang Lake area of Jiangxi Province in China. The model predicts that in the lake/marshland areas of the Yangtze River basin: (1) once-early mass chemotherapy of humans is little better than twice-yearly mass chemotherapy in reducing human prevalence. Depending on the heterogeneity of prevalence within the population, targeted treatment of high prevalence groups, with lower overall coverage, can be more effective than mass treatment with higher overall coverage. Treatment confers a short term benefit only, with prevalence rising to endemic levels once chemotherapy programs are stopped (2) depending on the relative contributions of bovines and humans, bovine treatment can benefit humans almost as much as human treatment. Like human treatment, bovine treatment confers a short-term benefit. A combination of human and bovine treatment will dramatically reduce human prevalence and maintains the reduction for a longer period of time than treatment of a single host, although human prevalence rises once treatment ceases; (3) assuming 75% coverage of bovines, a bovine vaccine which acts on worm fecundity must have about 75% efficacy to reduce the reproduction rate below one and ensure mid-term reduction and long-term elimination of the parasite. Such a vaccination program should be accompanied by an initial period of human treatment to instigate a short-term reduction in prevalence, following which the reduction is enhanced by vaccine effects; (4) if the bovine vaccine is only 45% efficacious (the level of current prototype vaccines) it will lower the endemic prevalence, but will not result in elimination. If it is accompanied by an initial period of human treatment and by a 45% improvement in human sanitation or a 30% reduction in contaminated water contact by humans, elimination is then possible. (C) 2002 Elsevier Science B.V. All rights reserved.

A theoretical model of the evolution of virulence in sexually transmitted HIV/AIDS

INTRODUCTION: The evolution of virulence in host-parasite relationships has been the subject of several publications. In the case of HIV virulence, some authors suggest that the evolution of HIV virulence correlates with the rate of acquisition of new sexual partners. In contrast some other authors argue that the level of HIV virulence is independent of the sexual activity of the host population. METHODS: Provide a mathematical model for the study of the potential influence of human sexual behaviour on the evolution of virulence of HIV is provided. RESULTS: The results indicated that, when the probability of acquisition of infection is a function both of the sexual activity and of the virulence level of HIV strains, the evolution of HIV virulence correlates positively with the rate of acquisition of new sexual partners. CONCLUSION: It is concluded that in the case of a host population with a low (high) rate of exchange of sexual partners the evolution of HIV virulence is such that the less (more) virulent strain prevails.

Mathematical modeling of pressurized system behaviour with entrapped air

The presence of entrapped air in pressurized hydraulic systems is considered a critical condition for the infrastructure security, due to the transient pressure enhancement related with its dynamic behaviour, similar to non-linear spring action. A mathematical model for the assessment of hydraulic transients resulting from rapid pressurizations, under referred condition is presented. Water movement was modeled through the elastic column theory considering a moving liquid boundary and the entrapped air pocket as lumped gas mass, where the acoustic effects are negligible. The method of characteristics was used to obtain the numerical solution of the liquid flow. The resulting model is applied to an experimental set-up having entrapped air in the top of a vertical pipe section and the numerical results are analyzed.

Malaria transmission model for different levels of acquired immunity and temperature-dependent parameters (vector)

OBJECTIVE: Describe the overall transmission of malaria through a compartmental model, considering the human host and mosquito vector. METHODS: A mathematical model was developed based on the following parameters: human host immunity, assuming the existence of acquired immunity and immunological memory, which boosts the protective response upon reinfection; mosquito vector, taking into account that the average period of development from egg to adult mosquito and the extrinsic incubation period of parasites (transformation of infected but non-infectious mosquitoes into infectious mosquitoes) are dependent on the ambient temperature. RESULTS: The steady state equilibrium values obtained with the model allowed the calculation of the basic reproduction ratio in terms of the model's parameters. CONCLUSIONS: The model allowed the calculation of the basic reproduction ratio, one of the most important epidemiological variables.

Optimization model for medium term natural gas commitment

In this paper we study the optimal natural gas commitment for a known demand scenario. This study implies the best location of GSUs to supply all demands and the optimal allocation from sources to gas loads, through an appropriate transportation mode, in order to minimize total system costs. Our emphasis is on the formulation and use of a suitable optimization model, reflecting real-world operations and the constraints of natural gas systems. The mathematical model is based on a Lagrangean heuristic, using the Lagrangean relaxation, an efficient approach to solve the problem. Computational results are presented for Iberian and American natural gas systems, geographically organized in 65 and 88 load nodes, respectively. The location model results, supported by the computational application GasView, show the optimal location and allocation solution, system total costs and suggest a suitable gas transportation mode, presented in both numerical and graphic supports.

Fractional model for malaria transmission under control strategies

We study a fractional model for malaria transmission under control strategies.Weconsider the integer order model proposed by Chiyaka et al. (2008) in [15] and modify it to become a fractional order model. We study numerically the model for variation of the values of the fractional derivative and of the parameter that models personal protection, b. From observation of the figures we conclude that as b is increased from 0 to 1 there is a corresponding decrease in the number of infectious humans and infectious mosquitoes, for all values of α. This means that this result is invariant for variation of fractional derivative, in the values tested. These results are in agreement with those obtained in Chiyaka et al.(2008) [15] for α = 1.0 and suggest that our fractional model is epidemiologically wellposed.

A coinfection model for HIV and HCV

We study a mathematical model for the human immunodeficiency virus (HIV) and hepatites C virus (HCV) coinfection. The model predicts four distinct equilibria: the disease free, the HIV endemic, the HCV endemic, and the full endemic equilibria. The local and global stability of the disease free equilibrium was calculated for the full model and the HIV and HCV submodels. We present numerical simulations of the full model where the distinct equilibria can be observed. We show simulations of the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. From the results of the model, we infer possible measures that could be implemented in order to reduce the number of infected individuals.

Explicit series solution for a glucose-induced electrical activity model of pancreatic beta-cells

In this work, we present the explicit series solution of a specific mathematical model from the literature, the Deng bursting model, that mimics the glucose-induced electrical activity of pancreatic beta-cells (Deng, 1993). To serve to this purpose, we use a technique developed to find analytic approximate solutions for strongly nonlinear problems. This analytical algorithm involves an auxiliary parameter which provides us with an efficient way to ensure the rapid and accurate convergence to the exact solution of the bursting model. By using the homotopy solution, we investigate the dynamical effect of a biologically meaningful bifurcation parameter rho, which increases with the glucose concentration. Our analytical results are found to be in excellent agreement with the numerical ones. This work provides an illustration of how our understanding of biophysically motivated models can be directly enhanced by the application of a newly analytic method.