scholarly journals Mathematical Modeling and Analysis of Eutrophication of Water Bodies Caused by Nutrients

2007 ◽  
Vol 12 (4) ◽  
pp. 511-524 ◽  
Author(s):  
A. K. Misra
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Differential Equations ◽  
Simulation Analysis ◽  
Qualitative Theory ◽  
Ecosystem Dynamics ◽  
Algal Population ◽  
Modeling And Analysis ◽  
Proposed Model ◽  
Qualitative Representation

In this paper a non-linear mathematical model is proposed for a qualitative representation of ecosystem dynamics in a eutrophied water body. The model variables are the concentration of nutrients, densities of algal population, zooplankton population, detritus and the concentration of dissolved oxygen. The model consists of five coupled ordinary differential equations. By using the qualitative theory of differential equations the model steady-state dynamics are studied. Simulation analysis is also performed to see the effect of rate of input of nutrients on different variables participating in the proposed model.

Methods of Mathematical Modeling of the Leaching Process of Cobalt-Containing Solutions

2021 ◽  
Vol 316 ◽  
pp. 661-666
Author(s):  
Nataliya V. Mokrova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Chemical Kinetics ◽  
Group Method ◽  
Data Handling ◽  
Multistage Processes ◽  
Leaching Process ◽  
Proposed Model ◽  
Simulation Results ◽  
The Mathematical Model

Current cobalt processing practices are described. This article discusses the advantages of the group argument accounting method for mathematical modeling of the leaching process of cobalt solutions. Identification of the mathematical model of the cascade of reactors of cobalt-producing is presented. Group method of data handling is allowing: to eliminate the need to calculate quantities of chemical kinetics; to get the opportunity to take into account the results of mixed experiments; to exclude the influence of random interference on the simulation results. The proposed model confirms the capabilities of the group method of data handling for describing multistage processes.

Mathematical Modeling and Analysis of Covid-19 Infection spreads in India with Restricted Optimal Treatment on Disease Incidence

BIOMATH ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2106147
Author(s):  
Debkumar Pal ◽  
D Ghosh ◽  
P K Santra ◽  
G S Mahapatra
Keyword(s):  
Mathematical Modeling ◽  
Objective Function ◽  
Reproduction Number ◽  
Disease Incidence ◽  
Treatment Control ◽  
Modeling And Analysis ◽  
Proposed Model ◽  
The Cost ◽  
Disease Free ◽  
The Basic Reproduction Number

This paper presents the current situation and how to minimize its effect in India through a mathematical model of infectious Coronavirus disease (COVID-19). This model consists of six compartments to population classes consisting of susceptible, exposed, home quarantined, government quarantined, infected individuals in treatment, and recovered class. The basic reproduction number is calculated, and the stabilities of the proposed model at the disease-free equilibrium and endemic equilibrium are observed. The next crucial treatment control of the Covid-19 epidemic model is presented in India's situation. An objective function is considered by incorporating the optimal infected individuals and the cost of necessary treatment. Finally, optimal control is achieved that minimizes our anticipated objective function. Numerical observations are presented utilizing MATLAB software to demonstrate the consistency of present-day representation from a realistic standpoint.

scholarly journals Mathematical Modeling and Analysis of Multirobot Cooperative Hunting Behaviors

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yong Song ◽  
Yibin Li ◽  
Caihong Li ◽  
Xin Ma
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Numerical Solutions ◽  
Rate Equations ◽  
Ratio Analysis ◽  
Hunting Behavior ◽  
Modeling And Analysis ◽  
Cooperative Hunting ◽  
Model Equations ◽  
The Mathematical Model

This paper presents a mathematical model of multirobot cooperative hunting behavior. Multiple robots try to search for and surround a prey. When a robot detects a prey it forms a following team. When another “searching” robot detects the same prey, the robots form a new following team. Until four robots have detected the same prey, the prey disappears from the simulation and the robots return to searching for other prey. If a following team fails to be joined by another robot within a certain time limit the team is disbanded and the robots return to searching state. The mathematical model is formulated by a set of rate equations. The evolution of robot collective hunting behaviors represents the transition between different states of robots. The complex collective hunting behavior emerges through local interaction. The paper presents numerical solutions to normalized versions of the model equations and provides both a steady state and a collaboration ratio analysis. The value of the delay time is shown through mathematical modeling to be a strong factor in the performance of the system as well as the relative numbers of the searching robots and the prey.

scholarly journals Mathematical modeling of the corpse cooling under conditions of varying ambient temperature

2021 ◽  
Vol 7 (1) ◽  
pp. 29-35
Author(s):  
German V. Nedugov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Ambient Temperature ◽  
Analytical Determination ◽  
Time Of Death ◽  
Main Condition ◽  
Proposed Model ◽  
Thermometric Determination ◽  
Early Postmortem

Background: The constancy of the ambient temperature is the main condition to correctly determine the time of death by thermometric method. However, in practice, this requirement is met only in cases of death in closed rooms. In this study, an exponential mathematical model was proposed for corpse cooling under any changes in ambient temperature. Aim: This study aimed to develop a mathematical model to determine the time of death based on the NewtonRichman cooling law in changing ambient temperature conditions. Materials and methods: Mathematical modeling of corpse cooling under changing ambient temperature is performed, focusing on problem solving of thermometric determination of the time of death. The axillary hollow was used as the diagnostic zone of the corpse, and the temperature of which at the time of death is taken is 36.6С. Results: A method of reverse reproduction of the cadaver temperature in conditions of changing ambient temperature has been developed. Results allow a relatively simple analytical determination of the time of death in the early postmortem period. Conclusions: The proposed method is advisable to be used in forensic medical practice to determine the time of death in early postmortem period. The developed mathematical model is implemented in the format of the application program Warm Bodies NRN. Use of tympanic and intraocular thermometry was recommended within the proposed model.

A NEW DISCRETIZED MODEL IN NONLINEAR KINETIC THEORY—THE SEMICONTINUOUS BOLTZMANN EQUATION

1991 ◽  
Vol 01 (01) ◽  
pp. 113-123 ◽  
Author(s):  
N. BELLOMO ◽  
E. LONGO
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Boltzmann Equation ◽  
Kinetic Theory ◽  
Continuous Dependence ◽  
Modeling And Analysis ◽  
Collision Invariants ◽  
The Mathematical Model ◽  
Nonlinear Kinetic ◽  
Discretized Model

This paper deals with the mathematical modeling and analysis of a new model of the Boltzmann equation with a finite number of velocity moduli, but with a continuous dependence on the velocity directions. The mathematical model is derived in the first part of the paper. Then the analysis of the equilibrium Maxwellian state is dealt with in the second part of the paper with the purpose of showing that the space of collision invariants is the correct one.

scholarly journals A Mathematical Model of Distributing New Information in Society

2020 ◽  
Vol 9 (1) ◽  
pp. 5-17
Author(s):  
Sergey Timofeev
Keyword(s):  
Mathematical Model ◽  
Mass Media ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Social Groups ◽  
Geometric Interpretation ◽  
Stationary Points ◽  
New Information ◽  
Proposed Model ◽  
Conceptual Meaning

Diversification of any new idea or concept in the society often begins with the emergence in the mass media of information that can win the attention of particular social groups or individuals. The author analyzes and interprets the results obtained by the means of constructing and studying a basic mathematical model of distribution of new information. The article describes factors and regularities that make the basis for the model, comments on all the relators that form the structure of the model, and describes the parameters of this structure. The proposed model is represented by a system of four ordinary differential equations. The stationary points of the system are found, and their conceptual meaning is described. The stationary points have cardinally different properties, depending on different relators. This provides for several possible scenarios of distributing new information in the society, whose description and geometric interpretation is given in the article.

scholarly journals Mathematical Modeling of the Pandemic Peak

2022 ◽  
Vol 10 (E) ◽  
pp. 22-26
Author(s):  
Nadezhda Cherkunova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Differential Equations ◽  
Time Dependence

BACKGROUND:  The article examines the history and statistics of the pandemic spread. AIM: The study aimed to  develop a mathematical model reflecting the time dependence of the parameters characterizing the spread of the pandemic. MATERIALS AND METHODS: Differential equations were used to study the spread of the pandemic. RESULTS:  The case, where the coefficients of morbidity and recovery are different is considered. The patterns of change in the number of people susceptible to the disease and the number of infectious patients are revealed as a function of time. Using the developed model, the peak of the pandemic is found, i.e., the time at which the number of infectious patients will be the maximum.

APPLICATION OF HOMOGENOUS TRANSFORMATION MATRIX TO THE MODELING OF A BALL-END CUTTER

2013 ◽  
Vol 37 (3) ◽  
pp. 775-785
Author(s):  
Jung-Fa Hsieh
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Geometric Model ◽  
Straightforward Method ◽  
Proposed Model ◽  
Cnc Grinding ◽  
Wide Range ◽  
Grinding Machine ◽  
Cnc Grinding Machine ◽  
Flank Surface

This paper presents a comprehensive and straightforward method for the mathematical modeling of a generic ball-end cutter. In the proposed approach, a mathematical model of the rake surface is developed based on a normal helix cutting edge geometric model. A mathematical model of the flank surface is then derived based on the assumption of a constant clearance angle. The proposed model is applicable to a wide range of ball-end cutters. As a result, it provides an ideal basis for the generation of the NC equations required to machine ball-end cutters on a 6-axis CNC grinding machine.

Mathematical modeling of adaptive immune response after transplantation

2020 ◽  
Vol 13 (08) ◽  
pp. 2050167
Author(s):  
Anka Markovska
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Immune Response ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Cellular Immunity ◽  
Adaptive Immune Response ◽  
Nonlinear Ordinary Differential Equations ◽  
Adaptive Immune

A mathematical model of adaptive immune response after transplantation is formulated by five nonlinear ordinary differential equations. Theorems of existence, uniqueness and nonnegativity of solution are proven. Numerical simulations of immune response after transplantation without suppression of acquired cellular immunity and after suppression were performed.

scholarly journals Some insights into an integrative mathematical model: a prototype-model for bodyweight and energy homeostasis

2016 ◽  
Vol 7 (3) ◽  
pp. 1271
Author(s):  
Jorge Guerra Pires
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Literature Review ◽  
Differential Equations ◽  
Mathematical Models ◽  
Quantitative Methods ◽  
Energy Homeostasis ◽  
State Of The Art ◽  
Prototype Model ◽  
Current State

The ambition of this document is to set in evidence the prerequisite for integrative (mathematical) models, mechanism-based models, for appetite/bodyweight control. For achieving this goal, it is provided a scrutinized literature review and it is organized them in such a way to make the point. The quantitative methods exploited by the authors are called differential equations solved numerically; they are discussed briefly since it is not our goal herein to handle details. On the current state of the art, there is no mathematical model to the best of the author’s knowledge targeting at integrating several hormones at once in mathematical descriptions: even for single hormones, the literature is either occasional or do not exist at all; it is depicted some results for simple models already built. As it can be seen, the functions and roles seem fuzzy, most hormones seem to be piloting the same undertaking. The key challenge from a mathematical modeling perspective is how to separate properly the mechanisms of each hormone. The kind of pursuit presented herein could initiate an imperative cascade of mathematical modeling applied to metabolism of bodyweight control and energy homeostasis.

Sign in / Sign up

Export Citation Format

Share Document