SIMULTANEOUS EFFECT OF TWO TOXICANTS ON BIOLOGICAL SPECIES: A MATHEMATICAL MODEL

1996 ◽  
Vol 04 (01) ◽  
pp. 109-130 ◽  
Author(s):  
J.B. SHUKLA ◽  
B. DUBEY
Keyword(s):  
Mathematical Model ◽  
Emission Rate ◽  
Biological Species ◽  
The Other ◽  
Washout Rate ◽  
Extinction Rate ◽  
Growth And Survival ◽  
Simultaneous Effect ◽  
Model Study ◽  
The Stability

In this paper, a mathematical model to study the simultaneous effect of two toxicants (one is more toxic than the other) on the growth and survival of a biological species is proposed. The cases of instantaneous spill, constant and periodic emissions of each of the toxicant into the environment are considered. It is shown that in the case of an instantaneous spill of each of the toxicant into the environment, the species after its initial decrease in density may recover to its original level after a period of time, the magnitude of which depends on the toxicity and washout rate of each of the toxicant. However, if both the toxicants are emitted with constant rates, the species in the habitat is doomed to extinction sooner than the case of a single toxicant having the same influx and washout rates as one of them, the extinction rate becoming faster with the increase in toxicity and emission rate of the other toxicant. It is also shown that for a small amplitude periodic emission of the toxicant with a constant mean, the stability behavior of the system is same as that of the case of the constant emission. It is found further through the model study that if suitable efforts are made to reduce the emission rate of each of the toxicant at the source and its concentration in the environment by some removal mechanism, an appropriate level of species density can be maintained.

EXISTENCE AND SURVIVAL OF TWO COMPETING SPECIES IN A POLLUTED ENVIRONMENT: A MATHEMATICAL MODEL

2001 ◽  
Vol 09 (02) ◽  
pp. 89-103 ◽  
Author(s):  
J. B. SHUKLA ◽  
A. K. AGRAWAL ◽  
B. DUBEY ◽  
P. SINHA
Keyword(s):  
Mathematical Model ◽  
Growth Rate ◽  
Emission Rate ◽  
Biological Species ◽  
Rate Coefficients ◽  
Washout Rate ◽  
Polluted Environment ◽  
Nonlinear Mathematical Model ◽  
Model Study ◽  
External Sources

In this paper, a nonlinear mathematical model to study the effect of a toxicant emitted into the environment from external sources on two competing biological species is proposed and analyzed. The cases of constant emission and instantaneous spill of a toxicant are considered in the model study. In the case of constant emission, it is shown that four usual outcomes of competition between two species may be altered under appropriate conditions which are mainly dependent on emission rate of toxicant into the environment, uptake concentrations of toxicant by the two species and their growth rate coefficients and carrying capacities. However, in the case of instantaneous spill, it is found that if the washout rate of toxicant is large, then the four outcomes of competition exist under usual conditions. It is also pointed out that the survival of the competitors, coexisting in absence of the toxicant, may be threatened if the constant emission of toxicant into their environment continues unabatedly.

scholarly journals The effect of environmental tax on the survival of biological species in a polluted environment: a mathematical model

2010 ◽  
Vol 15 (3) ◽  
pp. 271-286 ◽  
Author(s):  
S. Agarwal ◽  
S. Devi
Keyword(s):  
Mathematical Model ◽  
Local Stability ◽  
Emission Rate ◽  
Concentration Level ◽  
Biological Species ◽  
Environmental Taxes ◽  
Environmental Tax ◽  
Polluted Environment ◽  
Nonlinear Mathematical Model ◽  
Runge Kutta Method

In this paper, a nonlinear mathematical model is proposed and analyzed for the survival of biological species affected by a pollutant present in the environment. It is considered that the emission of the pollutant into the environment is dynamic in nature and depends on the environmental tax imposed on the emitters. It is also assumed that the environmental tax is imposed to control the emission of pollutants only when the concentration level of pollutants in the environment crosses a limit over which the pollutants starts causing harm to the population under consideration. Criteria for local stability, global stability and permanence are obtained using theory of ordinary differential equations. Numerical simulations are carried out to investigate the dynamics of the system using fourth order Runge–Kutta Method. It is found that, as the emission rate of pollutants in the environment increases, the density of biological species decreases. It may also be pointed out that the biological species may even become extinct if the rate of emission of pollutants increases continuously. However, if some environmental taxes are imposed to control the rate of emission of these pollutants into the environment, the density of biological species can be maintained at a desired level.

scholarly journals A Mathematical Model to Study the Effect of Travel Between Two Regions on the Covid-19 Infections

2020 ◽  
Vol 1 (2) ◽  
pp. 75-84
Author(s):  
Mochammad Andhika Aji Pratama
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Reproduction Number ◽  
The Other ◽  
Susceptible Population ◽  
Significant Parameter ◽  
Numerous Model ◽  
Model Predictions ◽  
The Stability ◽  
The Basic Reproduction Number

COVID-19 has attracted a lot of researchers’ attention since it has emerged in Wuhan, China in December 2019. Numerous model predictions on the COVID-19 epidemic have been created in case of Wuhan and the other regions. In this paper, a new COVID-19 epidemic model between two regions is proposed. The model differentiates asymptomatic infectious compartment and symptomatic infectious compartment. It is assumed that the symptomatic population cannot infect the susceptible population due to direct isolation, but the asymptomatic population can. The symptomatic population is also assumed to be unable to travel between regions. We analyze the stability of the model using Lyapunov Function. The Basic Reproduction Number for the model is presented. The numerical simulation and sensitivity analysis are explored to determine the significant parameter of the model.

scholarly journals MODEL TESTS AHD STUDIES FOE POET EASHID, DUBAI

1970 ◽  
Vol 1 (12) ◽  
pp. 72
Author(s):  
Eric Loewy
Keyword(s):  
Mathematical Model ◽  
Deep Water ◽  
Model Tests ◽  
Entrance Channel ◽  
Construction Work ◽  
Analysis Model ◽  
Littoral Drift ◽  
Model Studies ◽  
Model Study ◽  
The Stability

This paper is a factual account of studies carried out for the design of a new deep water harbour As so often happens construction work had to be begun before many of the conclusions of the study were available so that alterations to the initial designs had to be made while work progressed The studies comprised tidal and wave recordings and analysis, model studies to determine residual wave conditions at the quays, studies to determine the extent of littoral drift, the effect of the proposed works upon this and possible measures to counter downdrift erosion In addition studies were made of the stability of the adjacent creek channel which had previously been the harbour and a mathematical model study was carried out of the effects on the creek regime of various proposed entrance works including the construction of an entirely new creek entrance channel through the new deep water harbor.

Uniformity of Magnification from Different Electron Microscopes

1967 ◽  
Vol 25 ◽  
pp. 32-33
Author(s):  
Godfrey C. Hoskins ◽  
V. Williams ◽  
V. Allison
Keyword(s):  
Diffraction Grating ◽  
The Other ◽  
Carbon Replica ◽  
Electron Microscopes ◽  
The Stability

The method demonstrated is an adaptation of a proven procedure for accurately determining the magnification of light photomicrographs. Because of the stability of modern electrical lenses, the method is shown to be directly applicable for providing precise reproducibility of magnification in various models of electron microscopes.A readily recognizable area of a carbon replica of a crossed-line diffraction grating is used as a standard. The same area of the standard was photographed in Phillips EM 200, Hitachi HU-11B2, and RCA EMU 3F electron microscopes at taps representative of the range of magnification of each. Negatives from one microscope were selected as guides and printed at convenient magnifications; then negatives from each of the other microscopes were projected to register with these prints. By deferring measurement to the print rather than comparing negatives, correspondence of magnification of the specimen in the three microscopes could be brought to within 2%.

TO THE STABILITY OF TANK VEHICLES IN THE BRAKE MODE

2019 ◽  
pp. 27-32
Author(s):  
Denys Popelysh ◽  
Yurii Seluk ◽  
Sergyi Tomchuk
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Distribution Systems ◽  
Traffic Accidents ◽  
Road Traffic ◽  
Center Of Mass ◽  
Dynamic Processes ◽  
Course Stability ◽  
The Stability ◽  
Tank Vehicles

This article discusses the question of the possibility of improving the roll stability of partially filled tank vehicles while braking. We consider the dangers associated with partially filled tank vehicles. We give examples of the severe consequences of road traffic accidents that have occurred with tank vehicles carrying dangerous goods. We conducted an analysis of the dynamic processes of fluid flow in the tank and their influence on the basic parameters of the stability of vehicle. When transporting a partially filled tank due to the comparability of the mass of the empty tank with the mass of the fluid being transported, the dynamic qualities of the vehicle change so that they differ significantly from the dynamic characteristics of other vehicles. Due to large displacements of the center of mass of cargo in the tank there are additional loads that act vehicle and significantly reduce the course stability and the drivability. We consider the dynamics of liquid sloshing in moving containers, and give examples of building a mechanical model of an oscillating fluid in a tank and a mathematical model of a vehicle with a tank. We also considered the method of improving the vehicle’s stability, which is based on the prediction of the moment of action and the nature of the dynamic processes of liquid cargo and the implementation of preventive actions by executive mechanisms. Modern automated control systems (anti-lock brake system, anti-slip control systems, stabilization systems, braking forces distribution systems, floor level systems, etc.) use a certain list of elements for collecting necessary parameters and actuators for their work. This gives the ability to influence the course stability properties without interfering with the design of the vehicle only by making changes to the software of these systems. Keywords: tank vehicle, roll stability, mathematical model, vehicle control systems.

Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

2020 ◽  
Vol 10 (6) ◽  
pp. 599-609
Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Roughness Coefficient ◽  
Computational Domain ◽  
Channel Deformations ◽  
Geological Surveys ◽  
Kuban River ◽  
The Stability ◽  
Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

scholarly journals Black Hole Algorithm for Sustainable Design of Counterfort Retaining Walls

2020 ◽  
Vol 12 (7) ◽  
pp. 2767 ◽  
Author(s):  
Víctor Yepes ◽  
José V. Martí ◽  
José García
Keyword(s):  
Black Hole ◽  
Sustainable Design ◽  
Retaining Walls ◽  
The Other ◽  
Trade Off ◽  
Construction Company ◽  
Geometric Variables ◽  
The Stability ◽  
The Cost ◽  
Black Hole Algorithm

The optimization of the cost and CO 2 emissions in earth-retaining walls is of relevance, since these structures are often used in civil engineering. The optimization of costs is essential for the competitiveness of the construction company, and the optimization of emissions is relevant in the environmental impact of construction. To address the optimization, black hole metaheuristics were used, along with a discretization mechanism based on min–max normalization. The stability of the algorithm was evaluated with respect to the solutions obtained; the steel and concrete values obtained in both optimizations were analyzed. Additionally, the geometric variables of the structure were compared. Finally, the results obtained were compared with another algorithm that solved the problem. The results show that there is a trade-off between the use of steel and concrete. The solutions that minimize CO 2 emissions prefer the use of concrete instead of those that optimize the cost. On the other hand, when comparing the geometric variables, it is seen that most remain similar in both optimizations except for the distance between buttresses. When comparing with another algorithm, the results show a good performance in optimization using the black hole algorithm.

scholarly journals On the optimal control of coronavirus (2019-nCov) mathematical model; a numerical approach

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
N. H. Sweilam ◽  
S. M. Al-Mekhlafi ◽  
A. O. Albalawi ◽  
D. Baleanu
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Weighted Average ◽  
Necessary Optimality Conditions ◽  
Numerical Approach ◽  
Population Number ◽  
Infected People ◽  
The Stability ◽  
Novel Coronavirus ◽  
Theoretical Results

Abstract In this paper, a novel coronavirus (2019-nCov) mathematical model with modified parameters is presented. This model consists of six nonlinear fractional order differential equations. Optimal control of the suggested model is the main objective of this work. Two control variables are presented in this model to minimize the population number of infected and asymptotically infected people. Necessary optimality conditions are derived. The Grünwald–Letnikov nonstandard weighted average finite difference method is constructed for simulating the proposed optimal control system. The stability of the proposed method is proved. In order to validate the theoretical results, numerical simulations and comparative studies are given.

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