Iulia Martina Bulai

Biodegradation of organic pollutants in a water body

In this paper we introduce a non-linear model for the biodegradation of organic pollutants in a water body. We assume that the pollutants are removed using fungi, that need nutrients and dissolved oxygen to thrive. We show that after an initial phase the process can be rendered entirely self-sustained, even without the constant supply of fungi, thereby becoming economically very much appealing.

Shape effects on herd behavior in ecological interacting population models

Abstract In this paper, we introduce several dynamical systems modeling two-populations interactions. The main idea is to assume that the individuals of one of the populations gather together in herds, thus possess a social behavior, while individuals of the second population show a more individualistic attitude. We model the fact that the interaction between the two populations occurs mainly through the perimeter of the herd in a 2 D space or through the total surface area for populations that live in a 3 D space. This idea has already been explored earlier, but here we even accommodate the model for herds that assume fractal shapes. We account for all types of the populations intermingling: symbiosis, competition and predator–prey interactions. In the cases of obligated mutualism for the individualistic population and of competition, the stable solution attained by the populations is independent of the shape of the herd.

Two mathematical models for dissolved oxygen in a lake—CMMSE-16

In this paper two mathematical models for handling water pollution are introduced. In the first one we assume that algae and fungi are in competition for resources that come from wastewater, while in the second one we introduce explicitly the equation of nutrients. Both algae and fungi need dissolved oxygen (DO) for their biological process of growth. But there is a difference, indeed algae produce it too and in a higher quantity than the one they use. For the first model it is shown that if the coexistence equilibrium exists, it is stable without additional conditions. If the competition rate between algae and fungi is not high for a chosen set of parameters the stability of the coexistence equilibrium is reached even without an external constant input of DO in the system. For the second model we have found the matching equilibrium points with the ones of the first model, furthermore other two equilibria are found.

Hierarchical Bases Preconditioner to Enhance Convergence of CFIE With Multiscale Meshes

A hierarchical quasi-Helmholtz decomposition, originally developed to address the dense-discretization breakdowns for the electric field integral equation, is applied together with an algebraic preconditioner to improve the convergence of the combined field integral equation in multiscale problems. The effectiveness of the proposed method is studied first on some simple examples; next, tests on real-life cases up to several hundreds of wavelengths show its good performance.

The Beddington-De Angelis and the HTII product response functions: Application to polluted ecosystems biodegradation

In this paper we consider an aquatic ecosystem consisting of bacteria, organic pollutants and dissolved oxygen. By formulating two suitable mathematical models for their interactions, we investigate the sustainability in time of this ecosystem.

Modeling the Endophytic Fungus Epicoccum nigrum Action to Fight the “Olive Knot” Disease Caused by Pseudomonas savastanoi pv. savastanoi (Psv) Bacteria in Olea europaea L. Trees

In this paper, a four-populations’ nonlinear mathematical model is introduced to analyze the interactions between two different microorganisms and the olive tree on which they reside. One such microorganism infects and ultimately kills the branches while the other one has a beneficial effect on the plant. We aim at devising a control strategy of the action of the pathogenic microorganism on the plant. To this end, the equilibrium points of the ecosystem are investigated. Feasibility and stability conditions of the equilibria are derived analytically. The numerical simulations show that the infection transmission rate and the disease-related mortality can deeply affect the spread of the disease. Some conditions for the disease eradication are investigated and suggestions are given for the implementation of suitable biological controls, such as pruning of the infected leaves.

MODELING THE DIRECT AND INDIRECT EFFECTS OF POLLUTANTS ON THE SURVIVAL OF FISH IN WATER BODIES

Several sources of water pollution are causing negative consequences to marine life. The organisms that are more affected are fishes and marine mammals since they are at the top of the food chain. They are directly exposed to high levels of toxins in water and/or they feed on other fishes that are contaminated. Unfortunately, the main cause of the contaminations, and thus of the fish deaths, come from human activities, such as industry, agriculture, municipal wastewater and solid wastes. The present study is concerned with the effect of organic and inorganic pollutants on the survival of fish in water bodies. We introduce a nonlinear mathematical model by considering five interacting variables; organic pollutants, inorganic pollutants, bacteria, dissolved oxygen and fish in the water body. The model is analyzed using the stability theory of differential equations and to confirm the analytical findings, numerical simulations are performed. Our results suggest that to maintain water quality and to save fish life, the global community has to limit the release of organic and inorganic pollutants into the aquatic system.