scholarly journals Mathematical Modeling of Impact of Pollutants on Industries Based on Resource Biomass

2021 ◽  
Vol 33 (8) ◽  
pp. 94-105
Author(s):  
ALOK MALVIYA ◽  
◽  
MANINDER SINGH ARORA ◽  
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Stable Equilibrium ◽  
Equilibrium Analysis ◽  
Environmental Tax ◽  
Interior Equilibrium ◽  
Dependent Variables ◽  
Insight Into ◽  
Two Equilibria

Depletion of resources such as forestry, minerals etc. and resource-based industries such as wood and paper etc., due to rising pollution, is one of the biggest challenges which the humankind is facing today. In this paper, a mathematical model has been designed to give an insight into the effect of pollutants on natural resources which in turn affects the growth and stability of industries dependent on such biomass. The model is analyzed using stability theory of differential equations. Five dependent variables are considered in the model and some important assumptions are made. Two equilibria are found in the equilibrium analysis and conditions of local and global stability of interior equilibrium are obtained. Numerical simulation is also done to demonstrate the analytical findings. It is found in the study that as we impose an environmental tax on the polluters, the concentration of pollutants in the environment is controlled and the stable equilibrium shifts in such a way that the densities of resource biomass and dependent industries are close to the densities which correspond to the pollution free ecosystem.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

Mathematical Modeling of Biofilms

1997 ◽  
Vol 11 (1) ◽  
pp. 127-132 ◽  
Author(s):  
George H. Dibdin
Keyword(s):  
Mathematical Modeling ◽  
Complex System ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Mathematical Models ◽  
Diffusion Coefficients ◽  
Theoretical Basis ◽  
Reversible Reaction ◽  
Mathematical Equations ◽  
Insight Into

A set of mathematical equations constitutes a mathematical model if it aims to represent a real system and is based on some theory of that system's operation. On this definition, mathematical models, some very simple, are everywhere in science. A complex system like a biofilm requires modeling by numerical methods and, because of inevitable uncertainties in its theoretical basis, may not be able to make precise predictions. Nevertheless, such models almost always give new insight into the mechanisms involved, and stimulate further investigation. The way in which diffusion coefficients are measured for use in a model, particularly whether they include effects of reversible reaction, is a key element in the modeling. Reasons are given for separating diffusion from reversible reaction effects and dealing with them in a separate subroutine of the model.

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.

Effect of mobility conditions on the throughput of the Wireless Body Area Network

2020 ◽  
Vol 10 ◽  
Author(s):  
Shilpa Shinde ◽  
Santosh Sonavane
Keyword(s):  
Mathematical Model ◽  
Wireless Body Area Network ◽  
Data Rate ◽  
Hand Movements ◽  
Body Area Network ◽  
Area Network ◽  
Mobility Patterns ◽  
Body Area ◽  
Insight Into ◽  
Leg Movements

Background and objective: In the Wireless Body Area Network (WBAN) sensors are placed on the human body; which has various mobility patterns like seating, walking, standing and running. This mobility typically assisted with hand and leg movements on which most of the sensors are mounted. Previous studies were largely focused on simulations of WBAN mobility without focusing much on hand and leg movements. Thus for realistic studies on performance of the WBAN, it is important to consider hand and leg movements. Thus, an objective of this paper is to investigate an effect of the mobility patterns with hand movements on the throughput of the WBAN. Method: The IEEE 802.15.6 requirements are considered for WBAN design. The WBAN with star topology is used to connect three sensors and a hub. Three types of mobility viz. standing, walking and running with backward and forward hand movements is designed for simulation purpose. The throughput analysis is carried out with the three sets of simulations with standing, walking and running conditions with the speed of 0 m/s, 0.5 m/s and 3 m/s respectively. The data rate was increased from 250 Kb to 10000 Kb with AODV protocol. It is intended to investigate the effect of the hand movements and the mobility conditions on the throughput. Simulation results are analyzed with the aid of descriptive statistics. A comparative analysis between the simulated model and a mathematical model is also introduced to get more insight into the data. Results: Simulation studies showed that as the data rate is increased, throughput is also increased for all mobility conditions however, this increasing trend was discontinuous. In the standing (static) position, the throughput is found to be higher than mobility (dynamic) condition. It is found that, the throughput is better in the running condition than the walking condition. Average values of the throughput in case of the standing condition were more than that of the dynamic conditions. To validate these results, a mathematical model is created. In the mathematical model, a same trend is observed. Conclusion: Overall, it is concluded that the throughput is decreased due to mobility of the WBAN. It is understood that mathematical models have given more insight into the simulation data and confirmed the negative effect of the mobility conditions on throughput. In the future, it is proposed to investigate effect of interference on the designed network and compare the results.

On the displacements of the contours of the optic-electronic space images. Mathematical modeling of displacement

2017 ◽  
Vol 992 (4) ◽  
pp. 32-38 ◽  
Author(s):  
E.G. Voronin
Keyword(s):  
Mathematical Modeling ◽  
Remote Sensing ◽  
Mathematical Model ◽  
Point Of View ◽  
Design Features ◽  
Space Images ◽  
Electronic Imaging ◽  
Measuring Accuracy ◽  
Physical Laws

The article opens a cycle of three consecutive publications dedicated to the phenomenon of the displacement of the same points in overlapping scans obtained adjacent CCD matrices with opto-electronic imagery. This phenomenon was noticed by other authors, but the proposed explanation for the origin of displacements and the resulting estimates are insufficient, and developed their solutions seem controversial from the point of view of recovery of the measuring accuracy of opticalelectronic space images, determined by the physical laws of their formation. In the first article the mathematical modeling of the expected displacements based on the design features of a scanning opto-electronic imaging equipment. It is shown that actual bias cannot be forecast, because they include additional terms, which may be gross, systematic and random values. The proposed algorithm for computing the most probable values of the additional displacement and ways to address some of the systematic components of these displacements in a mathematical model of optical-electronic remote sensing.

Numerical Simulation on Mold Electromagnetic Eccentric Stirring and Central Segregation of Round Bloom

2013 ◽  
Vol 652-654 ◽  
pp. 2450-2454
Author(s):  
Zhi Hong Zhang ◽  
Guo Guang Cheng
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Electromagnetic Stirring ◽  
Center Line ◽  
Central Segregation

The paper describes multi-section round bloom casting using external MEMS, equipped with max section D600mm and min D280mm mold, the center line of D280mm mold not coincident with the axis of stirrer coils. it is exist eccentric electromagnetic stirring of mold which section less than max D600mm, a mathematical model of MEMS has been established, the index of central segregation of D280mm macrostructure had decreased less than 1.12 by optimized parameters of electromagnetic stirring and SEN immerse depth, in the end, the quality of round bloom had improved.

Mathematical modeling of fluid movement inside the eyeball during intravitreal injection

2021 ◽  
pp. 106-109
Author(s):  
D.V. Lipatov ◽  
◽  
S.A. Skladchikov ◽  
N.P. Savenkova ◽  
V.V. Novoderezkin ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Residence Time ◽  
Complex Structure ◽  
Posterior Vitreous Detachment ◽  
Vitreous Body ◽  
Complete Removal ◽  
Intravitreal Injections ◽  
The World

Background. The avalanche-like growth of intravitreal injections in the world has significantly increased interest in the hemodynamics of the processes that occur in the eye when a drug is injected into the vitreous cavity. Every year, the number of intravitreally used drugs and promising areas in which they can be used is growing. This also applies to the creation of new combined medicines and the development of drugs with a long-term therapeutic effect. Aims. Create mathematical model of eyeball to evaluate the movement of the drug substance in it; to estimate the time of the drug's presence in the eye cavity before its complete removal, to characterize the ways of its removal from the eye cavity; to assess the significance of posterior vitreous detachment during the time when the drug is present in the eye cavity; to evaluate the effect on the hydrodynamics of the depth of drug administration. Results. When the drug is administered closer to the center of the eyeball, its residence time increases in comparison with the parietal administration. With a complete posterior detachment of the vitreous body, the time of finding the drug in the eye is prolonged compared to its absence. The obtained results of mathematical modeling of the movement of the drug administered intravitreally cannot be mechanically transferred to the human eye, due to the more complex structure of the latter. Key words: intravitreal injections, vitreous body, mathematic computing.

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