Authenticity of Mathematical Modeling

2014 ◽  
Vol 107 (9) ◽  
pp. 672-678 ◽  
Author(s):  
Dung Tran ◽  
Barbara J. Dougherty
Keyword(s):  
Mathematical Modeling ◽  
Modeling Process ◽  
Authentic Problems

The choice and context of authentic problems—such as designing a staircase or a soda can—illustrate the modeling process in several stages.

scholarly journals Engineering Students’ Perceptions of Mathematical Modeling in a Learning Module Centered on a Hydrologic Design Case Study

2021 ◽  
Author(s):  
Madeline F. Merck ◽  
Melissa A. Gallagher ◽  
Emad Habib ◽  
David Tarboton
Keyword(s):  
Mathematical Modeling ◽  
Real World ◽  
Engineering Students ◽  
Online Module ◽  
Modeling Process ◽  
Online Databases ◽  
Modeling Software ◽  
Authentic Problems ◽  
Design Case Study ◽  
Hydrologic Design

AbstractEngineering students need to spend time engaging in mathematical modeling tasks to reinforce their learning of mathematics through its application to authentic problems and real world design situations. Technological tools and resources can support this kind of learning engagement. We produced an online module that develops students’ mathematical modeling skills while developing knowledge of the fundamentals of rainfall-runoff processes and engineering design. This study examined how 251 students at two United States universities perceived mathematical modeling as implemented through the online module over a 5-year period. We found, subject to the limitation that these are perceptions from not all students, that: (a) the module allowed students to be a part of the modeling process; (b) using technology, such as modeling software and online databases, in the module helped students to understand what they were doing in mathematical modeling; (c) using the technology in the module helped students to develop their skill set; and (d) difficulties with the technology and/or the modeling decisions they had to make in the module activities were in some cases barriers that interfered with students’ ability to learn. We advocate for instructors to create modules that: (a) are situated within a real-world context, requiring students to model mathematically to solve an authentic problem; (b) take advantage of digital tools used by engineers to support students’ development of the mathematical and engineering skills needed in the workforce; and (c) use student feedback to guide module revisions.

The Implementation of Anti-Attack AES Mathematical Model in Library Network Encryption

2013 ◽  
Vol 756-759 ◽  
pp. 2944-2947
Author(s):  
Yu Fen Shen
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Advanced Encryption Standard ◽  
Safety Requirements ◽  
Model Library ◽  
Modeling Process ◽  
Encryption And Decryption ◽  
Library Network ◽  
The Mathematical Model ◽  
Replacement Operation

With the continuous improvement of university library network safety requirements, this paper studies encryption and decryption algorithm analyzing advanced encryption standard AES of the computer, substitution and replacement operation in encryption and decryption process, and key expansion mathematical model. The detailed design of the mathematical modeling process of the algorithm is given, and the whole mathematical modeling process is more thoroughly analyzed. According to the model, library network encryption application is completed. Verified by computer simulation technology, the mathematical model has a good robustness and achieved good results.

The Mathematical Modeling of the Compressive Stresses on the Cutting Tool in Machining of Inconel 718

2006 ◽  
Vol 526 ◽  
pp. 229-234 ◽  
Author(s):  
Ulvi Şeker ◽  
Adem Kurt
Keyword(s):  
Mathematical Modeling ◽  
Power Systems ◽  
Cutting Forces ◽  
Inconel 718 ◽  
Nuclear Power ◽  
Cutting Tool ◽  
Stress Distributions ◽  
Modeling Process ◽  
Compressive Stresses ◽  
Tool Stresses

In this paper, a mathematical model has been developed for the cutting tool stresses in machining of nickel-based super alloy Inconel 718 used in aircraft and spacecraft industries, nuclear power systems and steam generators etc. necessitating oxidation and corrosion resistance, high temperature and strength. The cutting forces were measured by a series of experimental measurements and stress distributions on the cutting tool were analyzed by means of the finite element method using Ansys software. The mathematical modeling process of the compressive stresses in x, y and z directions was carried out with multiple regression analysis regarding to Ansys stress results depending on the cutting forces and the chip–tool contact area. It is found that model results had good agreement with the Ansys stress results.

Based on the Mathematical Modeling Thought Method Exploration

2012 ◽  
Vol 450-451 ◽  
pp. 646-649 ◽  
Author(s):  
Zhi Bin Liu
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Method ◽  
Approximate Solution ◽  
Mathematical Thinking ◽  
Teaching Material ◽  
Mathematical Language ◽  
Actual Problem ◽  
Teaching Process ◽  
Modeling Process

Mathematical modeling is a mathematical thinking method, is using the mathematical language and means, through the abstract, simplified can approximate solution actual problem a powerful mathematical method. In this paper, according to the teaching of the specific example analyzed of mathematical modeling of understanding, base the teaching material, mathematical modeling process, strengthen the revealing of mathematical modeling consciousness training, improve the ability of mathematical modeling. Mathematical modeling thought and method of the seepage, must be run through the teaching process throughout, must have the plan, a step-by-step and destination permeates gradually.

scholarly journals Simulation emergency landing of quadrocopter

2017 ◽  
pp. 7-16
Author(s):  
Bogdan Blahitko ◽  
Yuriyi Mochulsky ◽  
Ihor Zaiachuk
Keyword(s):  
Mathematical Modeling ◽  
Modeling Process ◽  
Vertical Speed ◽  
Basic Features

The necessity of analyzing and modeling process of the emergency landing unmanned quadrocopter is described. Through mathematical modeling the basic features of landing unmanned quadrocopter are considered. The methods of safe landing of an unmanned quadrocopter in case of failure of one of four pairs of motor-screw are proposed. The basis of the proposed methods is to use a parachuting effect. Parachuting achieved by forced off the power of the motor, which is located at the opposite end of the same yoke as faulty motor As a result, quadrocopter vertical speed at the time of landing is reduced significantly and is approaching a relatively safe value.

scholarly journals Ten steps to investigate a cellular system with mathematical modeling

2021 ◽  
Vol 17 (5) ◽  
pp. e1008921
Author(s):  
Jasia King ◽  
Kerbaï Saïd Eroumé ◽  
Roman Truckenmüller ◽  
Stefan Giselbrecht ◽  
Ann E. Cowan ◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
In Silico ◽  
Membrane Lipid ◽  
Cellular System ◽  
Spatiotemporal Resolution ◽  
Number Of Components ◽  
Modeling Process ◽  
Lipid Turnover ◽  
Generic Modeling ◽  
Spatiotemporal Scales

Cellular and intracellular processes are inherently complex due to the large number of components and interactions, which are often nonlinear and occur at different spatiotemporal scales. Because of this complexity, mathematical modeling is increasingly used to simulate such systems and perform experiments in silico, many orders of magnitude faster than real experiments and often at a higher spatiotemporal resolution. In this article, we will focus on the generic modeling process and illustrate it with an example model of membrane lipid turnover.

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