Mathematical modelling: transitions between the real world and the mathematical model

2004 ◽  
Vol 35 (2) ◽  
pp. 197-206 ◽  
Author(s):  
Rosalind Crouch ◽  
Christopher Haines *
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Real World ◽  
The Real ◽  
The Mathematical Model

scholarly journals When will I ever use that? Giving students opportunity to see the direct application of modelling techniques in the real world.

2016 ◽  
Vol 14 (3) ◽  
pp. 45
Author(s):  
Ros Porter ◽  
Hannah Bartholomew
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Mathematical Models ◽  
Real World ◽  
Direct Application ◽  
First Year ◽  
Thought Processes ◽  
The Real ◽  
Modelling Techniques

Mathematical modelling is unfamiliar to many young mathematicians and can be a source of anxiety for many. Although many first year mathematics undergraduates will have used mathematical models throughout GCSE and A Level most are unaware of this. Very few understand what a mathematical model is, fewer still the concept of building a model. In our experience students are reluctant to try and build their own models and fail to see the value of modelling skills in the real world. We invited 3 speakers to attend a first year modelling lecture to talk about the models they use in their jobs with the intention that this would help students see that modelling skills and analytical thought processes are valuable tools for a maths graduate. The speakers had different employment backgrounds being from banking, research (chemistry) and transport engineering. Each spoke for approximately 10 mins. giving an outline of their field. The lecture was followed by tutorials in which students were asked to reflect on what the speakers had said and how this related to their own learning. Two of the speakers also attended the tutorials and were able to have more informal conversations with the students.

Mathematical Modelling the Process of Cup Wheel Precision Grinding of Rotating Concave Paraboloid

2016 ◽  
Vol 693 ◽  
pp. 837-842
Author(s):  
Fu Yi Xia ◽  
Li Ming Xu ◽  
De Jin Hu
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Abrasive Particle ◽  
Influence Factors ◽  
Machining Process ◽  
Quadric Surface ◽  
Precision Grinding ◽  
Cup Wheel ◽  
The Mathematical Model ◽  
Trajectory Equation

A novel principle of cup wheel grinding of rotating concave quadric surface was proposed. The mathematical model of machining process was established to prove the feasibility of precision grinding of rotating concave paraboloid based on the introduced principle. The conditions of non-interference grinding of concave paraboloid were mathematically derived. The processing range and its influence factors were discussed. The trajectory equation of abrasive particle was concluded. Finally, the math expressions of numerical controlled parameters was put forward in the process of grinding of the concave paraboloid.

scholarly journals RESEARCH OF THE TENSELY-DEFORMED STATE OF ELEMENTS OF MOBILE HEAT STORAGE

2020 ◽  
Vol 42 (2) ◽  
pp. 68-75
Author(s):  
V.G. Demchenko ◽  
А.S. Тrubachev ◽  
A.V. Konyk
Keyword(s):  
Mathematical Model ◽  
Heat Storage ◽  
Quantitative Estimation ◽  
The Real ◽  
State Of The Union ◽  
Real Geometry ◽  
Deformed State ◽  
The Mathematical Model ◽  
Minimization Of Functional

Worked out methodology of determination of the tensely-deformed state of elements of mobile heat storage of capacity type, that works in the real terms of temperature and power stress on allows to estimate influence of potential energy on resilient deformation that influences on reliability of construction and to give recommendations on planning of tank (capacities) of accumulator. For determination possibly of possible tension of construction of accumulator kinematics maximum terms were certain. As a tank of accumulator shows a soba the difficult geometrical system, the mathematical model of calculation of coefficient of polynomial and decision of task of minimization of functional was improved for determination of tension for Міzеs taking into account the real geometry of equipment. Conducted quantitative estimation of the tensely-deformed state of the union coupling, corps and bottom of thermal accumulator and the resource of work of these constructions is appraised. Thus admissible tension folds 225 МРа.

scholarly journals Analysis on Present Mathematical Model for Predicting the Crop Production

2020 ◽  
Vol 9 (12) ◽  
pp. 168-170
Keyword(s):  
Mathematical Model ◽  
Mathematical Models ◽  
Real World ◽  
Crop Production ◽  
Ghg Emissions ◽  
Data Set ◽  
Factors Affecting ◽  
The Government ◽  
The Mathematical Model ◽  
Government Website

India is a worldwide agriculture business powerhouse. Future of agriculture-based products depends on the crop production. A mathematical model might be characterized as a lot of equations that speak to the conduct of a framework. By using mathematical model in agriculture field, we can predict the production of crop in particular area. There are various factors affecting crops such as Rainfall, GHG Emissions, Temperature, Urbanization, climate, humidity etc. A mathematical model is a simplified representation of a real-world system. It forms the system using mathematical principles in the form of a condition or a set of conditions. Suppose we need to increase the crop production, at that time the mathematical model plays a major role and our work can be easier, more significant by using the mathematical model. Through the mathematical model we predict the crop production in upcoming years. .AI, ML, IOT play a major role to predict the future of agriculture, but without mathematical models it is not possible to predict crop production accurately. To solve the real-world agriculture problem, mathematical models play a major role for accurate results. Correlation Analysis, Multiple Regression analysis and fuzzy logic simulation standards have been utilized for building a grain production benefit depending model from crop production. Prediction of crop is beneficiary to the farmer to analyze the crop management. By using the present agriculture data set which is available on the government website, we can build a mathematical model.

Mathematical Modelling the Power Supply-Load System for Electro-Discharge Polishing Process

2010 ◽  
Vol 159 ◽  
pp. 125-128
Author(s):  
A. Parshuta ◽  
V. Chitanov ◽  
Lilyana Kolaklieva ◽  
Roumen Kakanakov
Keyword(s):  
Mathematical Model ◽  
Mathematical Modelling ◽  
Numerical Solution ◽  
Power Supply ◽  
Equation System ◽  
Electrolyte Temperature ◽  
Polishing Process ◽  
The Real ◽  
Quadratic Interpolation ◽  
Runge Kutta

The real electro-discharge polishing (EDP) system has been presented by an equivalent electrical scheme and described by a corresponded equation system. The Runge-Kutta-Merson method with automatically changed step is used for the numerical solution the equation system. The current through the resistor equivalent to the steam gas wrapper is defined with an I-V characteristic obtained by the method of multi-interval quadratic interpolation-approximation. A mathematical model of the power supply-load system has been realized in Basic and Matlab® languages. On the base of the developed modelling conditions limiting the current and voltage overload in the EDP system have been determined depending on the maximum polished area and the electrolyte temperature.

scholarly journals Development of a subsystem for automatic protection of submersible pumps based on mathematical modeling

2018 ◽  
Vol 226 ◽  
pp. 04028
Author(s):  
Alexander V. Pilipenko ◽  
Andrei A. Tashev ◽  
Nail K. Sharifov
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Mathematical Modelling ◽  
Protection System ◽  
Piston Pump ◽  
The Mathematical Model

In this paper, the authors produce a mathematical modelling of a piston pump, develop algorithms for the operation of a protection system, taking into account the results of mathematical modelling. The authors test the mathematical model on the operation of real equipment and analyze its accuracy.

Optimal Model Selection Using MP Criterion for Uncertain Multivariable 2×2 Systems Based on IMC

2008 ◽  
Author(s):  
Inbal Shani ◽  
Neima Brauner ◽  
Coleman B. Brosilow
Keyword(s):  
Mathematical Model ◽  
Control Systems ◽  
Controller Design ◽  
Optimal Model ◽  
Time Constants ◽  
The Real ◽  
Real Process ◽  
Decoupled Control ◽  
The Mathematical Model ◽  
Performance Variations

IMC controller design for a process is based on choosing a mathematical model that describes the real process. The mathematical model describing such process is often not unique because the real variables of the process can vary within an interval. In such cases the performance of the control system varies, possibly substantially, as process parameters change. To limit such performance variations, we have developed an algorithm for choosing the model gains and the filter time constants of the IMC controller, to minimize the amount of interaction between outputs due to set point changes and disturbances for multivariable decoupled control systems. Some examples illustrate the algorithm.

scholarly journals Dynamics of an Information Spreading Model with Isolation

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xia-Xia Zhao ◽  
Jian-Zhong Wang
Keyword(s):  
Mathematical Model ◽  
Hopf Bifurcation ◽  
Limit Cycle ◽  
Real World ◽  
Modern Society ◽  
The Real ◽  
Spreading Model ◽  
Wide Range ◽  
Bistable Phenomenon ◽  
Information Spreading

Information plays an important role in modern society. In this paper, we presented a mathematical model of information spreading with isolation. It was found that such a model has rich dynamics including Hopf bifurcation. The results showed that, for a wide range of parameters, there is a bistable phenomenon in the process of information spreading and thus the information cannot be well controlled. Moreover, the model has a limit cycle which implies that the information exhibits periodic outbreak which is consistent with the observations in the real world.

scholarly journals New Thermodynamics: Inelastic Collisions and Cosmology

2020 ◽  
Vol 2 (6) ◽  
Author(s):  
Kent W. Mayhew
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Mathematical Modelling ◽  
Real World ◽  
Inelastic Collisions ◽  
Elastic Collisions ◽  
The Real ◽  
The Creation

The sciences have evolved around elastic collisions although most collisions are inelastic. Elastic collisions allow for simpler mathematical modelling, that may not be particularly suitable for cosmology. Inelastic collisions create photons. This has led to consideration of an ensemble of inelastic collisions producing CMB. This will further lead to brief discussions concerning the nature of dark matter, and dark energy. This will then be followed by a simpler analogy concerning the creation of Hawking’s radiation. A consequence of collisions being inelastic is that as a mathematical contrivance, entropy may only be an approximation when applied to the real world. And this fits well with this author’s “New Thermodynamics”.

scholarly journals Discovery of nanoscale sanal flow choking in cardiovascular system: exact prediction of the 3D boundary-layer-blockage factor in nanotubes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
V. R. Sanal Kumar ◽  
Vigneshwaran Sankar ◽  
Nichith Chandrasekaran ◽  
Sulthan Ariff Rahman Mohamed Rafic ◽  
Ajith Sukumaran ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Mathematical Model ◽  
Fluid Flow ◽  
Real World ◽  
Diastolic Pressure ◽  
Pressure Ratio ◽  
Flow Choking ◽  
The Real ◽  
Blockage Factor ◽  
Flow Systems

AbstractEvidences are escalating on the diverse neurological-disorders and asymptomatic cardiovascular-diseases associated with COVID-19 pandemic due to the Sanal-flow-choking. Herein, we established the proof of the concept of nanoscale Sanal-flow-choking in real-world fluid-flow systems using a closed-form-analytical-model. This mathematical-model is capable of predicting exactly the 3D-boundary-layer-blockage factor of nanoscale diabatic-fluid-flow systems (flow involves the transfer of heat) at the Sanal-flow-choking condition. As the pressure of the diabatic nanofluid and/or non-continuum-flows rises, average-mean-free-path diminishes and thus, the Knudsen-number lowers heading to a zero-slip wall-boundary condition with the compressible-viscous-flow regime in the nanoscale-tubes leading to Sanal-flow-choking due to the sonic-fluid-throat effect. At the Sanal-flow-choking condition the total-to-static pressure ratio (ie., systolic-to-diastolic pressure ratio) is a unique function of the heat-capacity-ratio of the real-world flows. The innovation of the nanoscale Sanal-flow-choking model is established herein through the entropy relation, as it satisfies all the conservation-laws of nature. The physical insight of the boundary-layer-blockage persuaded nanoscale Sanal-flow-choking in diabatic flows presented in this article sheds light on finding solutions to numerous unresolved scientific problems in physical, chemical and biological sciences carried forward over the centuries because the mathematical-model describing the phenomenon of Sanal-flow-choking is a unique scientific-language of the real-world-fluid flows. The 3D-boundary-layer-blockage factors presented herein for various gases are universal-benchmark-data for performing high-fidelity in silico, in vitro and in vivo experiments in nanotubes.

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