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.

Mathematical modelling.

2021 ◽  
Author(s):  
Ed Rutgers Durner
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Growth And Development ◽  
Fertilizer Recommendations ◽  
Mathematical Equations

Abstract Plants are studied to understand their growth and development so that their quality and productivity can be optimised. Models are developed that can be simple and descriptive, or quite complex with numerous mathematical equations; their level of complexity is linked to their purpose. This summary serves as an introduction to mathematical models in horticulture. It is not a manual for modelling itself, but rather an overview of how important mathematical models are in horticultural production. Mathematical models are used extensively in horticulture both extrinsically, i.e. when calculating chilling hour accumulations and intrinsically, i.e. when applying fertilizer to a crop. In chilling calculations, developed models are used directly. Fertilizer recommendations were probably developed using a mathematical model. The first part of this article discusses models in general and reviews general characteristics of mathematical models. The second part outlines the major uses of mathematical modelling in modern horticultural production. Presentations of specific models are limited in order to present a general discussion of models with examples that will interest most horticulturists.

scholarly journals Mathematical modeling in economics for selection of optimum investment solution

2021 ◽  
Vol 273 ◽  
pp. 08003
Author(s):  
Arthur Alukhanyan ◽  
Olga Panfilova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Linear Programming ◽  
Mathematical Models ◽  
Programming Problem ◽  
Linear Programming Problem ◽  
Target Function ◽  
Investment Portfolio ◽  
Monetary Relations ◽  
Selection Of

This work is devoted to development of economic and mathematical models for selection of the optimum investment solution. Moreover, it states the basis for development of model examples and correction of the model considering the results obtained in the examples. In the work the problem is set for selection of the investment sources and objects, which is limited to the linear programming problem. The controlled variable and basic limitations simulating real credit and monetary relations are distinguished in the provided model. The discounted profit obtained from implementation of the optimum investment portfolio is considered as a target function. The economic and mathematical model presented in the article allows finding the optimum investment solution within the limits of the credit and monetary relations taking place both at the micro- and macroeconomic level.

scholarly journals MATHEMATICAL MODELING IN SOIL BIOKINETICS

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
Mikhail Vladimirovich Glagolev
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Steady State ◽  
Numerical Methods ◽  
Computer Programs ◽  
Soil Science ◽  
State University ◽  
Moscow State University

This work is a report written at the suggestion of Ph.d. N. S. Panikov in 1985 when the author was a 2nd-year student of the Faculty of Soil Science of the M. V. Lomonosov Moscow State University. The report provides an example of a mathematical model of soil biokinetics and discusses numerical methods for solving its constituent equations. For the steady state, some useful computer programs are given, and for the non steady state, references to programs published in the literature are given.

scholarly journals Modeling algorithm of transport and technological system operation

2020 ◽  
pp. 79-85
Author(s):  
Я.Я. Эглит ◽  
К.Я. Эглите ◽  
М.А. Шаповалова ◽  
А.А. Головенко
Keyword(s):  
Mathematical Modeling ◽  
Complex System ◽  
Mathematical Model ◽  
Relevant Information ◽  
Technological System ◽  
Terminal Complex ◽  
System Operation ◽  
General Cargo ◽  
The Mathematical Model ◽  
Modeling Algorithm

Статья посвящена разработке моделирующего алгоритма работы транспортно-технологической системы. Математическое моделирование дает возможность формально описать любую сложную систему (в нашем случае специализированный терминал по перегрузке генеральных грузов) и с помощью описания исследовать различные режимы ее функционирования. Разработанная модель позволит осуществлять выбор оптимального в заданных условиях варианта функционирования перегрузочного комплекса, но, как любая математическая модель, она не учитывает неформализуемую часть релевантной информации. На специализированном терминале происходят сложные и многообразные процессы, связанные с перегрузкой различных грузов, контейнеров и других генеральных грузов, что не позволяет построить абсолютно адекватную математическую модель. Поэтому в математической модели представлены только основные, характерные для моделирующей системы, закономерности. При этом второстепенные факторы не принимаются во внимание, так как они являются несущественными. [1,3] The article is devoted to the development of a modeling algorithm for the operation of a transport and technological system. Mathematical modeling makes it possible to formally describe any complex system (in our case, a specialized terminal for transshipment of General cargo) and use the description to explore various modes of its operation. The developed model will allow you to choose the optimal option for the operation of the reloading complex under given conditions, but, like any mathematical model, it does not take into account the non-formalized part of the relevant information. At a specialized terminal, complex and diverse processes occur related to the transshipment of various cargo, containers and other General cargo, which does not allow us to build an absolutely adequate mathematical model. Therefore, the mathematical model presents only the main patterns that are characteristic of the modeling system. In this case, secondary factors are not taken into account, as they are insignificant. [1,3]

Mathematical Modeling of the Anaerobic Filter Process

1983 ◽  
Vol 15 (8-9) ◽  
pp. 197-207 ◽  
Author(s):  
M Lindgren
Keyword(s):  
Mathematical Modeling ◽  
Waste Water ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Efficient Tool ◽  
Anaerobic Filter ◽  
Filter Process

A dilute synthetic waste water was anaerobica1ly treated in a filter. A mathematical model of the anaerobic filter process was also developed and analyzed. Analysis showed that mathematical models are an efficient tool for system understanding and design.

MANAGEMENT OF COMPLEX SYSTEMS: MODELING THE BIOLOGICAL PEST CONTROL

2008 ◽  
Vol 03 (01n02) ◽  
pp. 241-256 ◽  
Author(s):  
MARAT RAFIKOV ◽  
JOSÉ MANOEL BALTHAZAR ◽  
HUBERTUS F. VON BREMEN
Keyword(s):  
Mathematical Modeling ◽  
Complex System ◽  
Mathematical Models ◽  
Pest Control ◽  
Natural Enemies ◽  
Dynamic Systems ◽  
Control Strategy ◽  
Cropping System ◽  
Systems Modeling ◽  
Biological Pest Control

The aim of this paper is to study the cropping system as complex one, applying methods from theory of dynamic systems and from the control theory to the mathematical modeling of the biological pest control. The complex system can be described by different mathematical models. Based on three models of the pest control, the various scenarios have been simulated in order to obtain the pest control strategy only through natural enemies' introduction.

scholarly journals A Mathematical Model for Top Nutation Based on Inertial Forces of Distributed Masses

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Ryspek Usubamatov ◽  
Albina Omorova
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Angular Momentum ◽  
Mathematical Models ◽  
Vibration Analysis ◽  
Analytical Approach ◽  
Main Property ◽  
Inertial Forces ◽  
Applied Torque ◽  
Dynamics And Vibration

The main property of gyroscopic devices is maintaining the axis of a spinning rotor, a mathematical model formulated on the principle of the change in the angular momentum. This principle is used for mathematical modeling of the motions of a top at known publications. Nevertheless, practical tests of gyroscopic devices do not correspond to this analytical approach. Recent investigations have demonstrated that the origin of gyroscope properties is more complex than that represented in known publications. The applied torque on a gyroscope produces internal torques of the spinning rotor based on the action of the several inertial forces. These forces are the centrifugal, Coriolis, and common inertial forces as well as the change in the angular momentum generated by the mass elements and center-mass of the spinning rotor. The action of these torques manifests itself in the resistance and precession torques of the gyroscopic devices. These inertial torques act simultaneously and interdependently around two axes and represent the fundamental principles of the gyroscope theory. The new inertial torques enable deriving mathematical models for the motions of well-known top that is the simplest form of gyroscopic devices. The novelty of the work is mathematical models for the motions of the top based on action of eight inertial forces acting around its two axes. The obtained mathematical models for the top nutation and self-stabilization are represented in terms of machine dynamics and vibration analysis. The new analytical approach for motions of the well-balanced top and top with eccentricity of the center-mass definitely responds to the practical results.

scholarly journals Mathematical Modeling to Perform an Analysis of Social Isolation Periods in the Dissemination of COVID-19

2021 ◽  
Vol 22 (4) ◽  
pp. 595-608
Author(s):  
A. Molter ◽  
R. S. Quadros ◽  
M. Rafikov ◽  
D. Buske ◽  
G. A. Gonçalves
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mathematical Models ◽  
Social Isolation ◽  
Computer Simulations ◽  
The Other ◽  
Stable Level ◽  
The Social ◽  
The World ◽  
Second Peak

The outbreak of COVID-19 has made scientists from all over the world do not measureefforts to understand the dynamics of the disease caused by this coronavirus. Several mathematical models have been proposed to describe the dynamics and make predictions. This work proposes a mathematical model that includes social isolation of susceptible individuals as a strategy of suppression and mitigation of the disease. The Susceptible-Infectious-Isolated-Recovered-Dead (SIQRD) model is proposed to analyze three important issues about the dynamics of the disease taking into account social isolation: when the isolation should begin? How long to keep the isolation? How to get out of this isolation? To get answers, computer simulations are provided and their results discussed. The results obtained show that beginning social isolation on the 10th or 15th days, after confirmation of the 50th case, and with 70% of the population in isolation, seems to be promising, since the infected curve does not grow much until it enters the isolation and remains at a stable level during the isolation. On the other hand an abrupt release of the social isolation will imply a second peak of infected individuals above the first one, which is not desired. Therefore, the release from social isolation should be gradual.

scholarly journals METHODOLOGY OF DEVELOPMENT OF MATHEMATICAL MODELS OF INFORMATION PROCESSING SYSTEMS

2021 ◽  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Information System ◽  
Information Processing ◽  
Mathematical Models ◽  
System Approach ◽  
Research Method ◽  
Literary Sources ◽  
History Of ◽  
The Mathematical Model

Modeling as a research method is a powerful cognitive tool throughout the history of human development. The article describes the methodology for the development of mathematical models of information systems, based on materials from various literary sources, author's developments on the system approach, mathematical modeling and programming. The mathematical model of the information system is described and all the characteristics of the IS are given.

scholarly journals MATHEMATICAL MODELING OF RESIDUAL STRESSES IN PLASMA COATINGS TAKING INTO ACCOUNT THE PROCESS OF INCREASING LAYERS

2020 ◽  
Vol 22 (6) ◽  
pp. 14-20
Author(s):  
V.I. Bogdanovich ◽  
◽  
M.G. Giorbelidze ◽  
I.A. Dokukina ◽  
N.V. Surkova ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Residual Stresses ◽  
Mathematical Models ◽  
Ambient Temperature ◽  
Experimental Studies ◽  
Final Temperature ◽  
Good Convergence ◽  
Plasma Coatings

Developed a mathematical model for determining residual stresses with increasing plasma coatings, taking into account the stresses arising upon cooling of the material from the final temperature to ambient temperature; tension that arises when removing the fastening devices and tension that existed in the substrate before spraying. The developed mathematical models are adapted for the most common cases of fixing the base used in the practice of coating. Experimental studies of residual stresses were carried out, which showed good convergence with the values of residual stresses obtained theoretically.

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