• Structural Engineering and Mechanics
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• v.26 no.1
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• pp.31-42
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• 2007

The unsymmetric finite element formulation has been proposed recently to improve predictions from distorted finite elements. Studies have also shown that this special formulation using parametric functions for the test functions and metric functions for the trial functions works surprisingly well because the former satisfy the continuity conditions while the latter ensure that the stress representation during finite element computation can retrieve in a best-fit manner, the actual variation of stress in the metric space. However, a question that remained was whether the unsymmetric formulation was variationally correct. Here we determine that it is not, using the simplest possible element to amplify the principles.

• Research in Mathematical Education
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• v.26 no.3
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• pp.127-146
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• 2023

Statistical thinking has a broad definition but focuses on the context of regression modelling in the present study. To foster students' statistical thinking within the context, teaching should no longer be seen as transfer of knowledge from teacher to students but as a process of engaging with learning activities in which they develop ownership of knowledge. This study aims at collaborative learning contexts; students were divided into small groups in order to increase opportunities for peer collaboration. Each group of students was asked to do a regression project after class. Through doing the project, they learnt to organize and connect previously accrued piecemeal statistical knowledge in an integrated manner. They could also clarify misunderstandings and solve problems through verbal exchanges among themselves. They gave a clear and lucid account of the model they had built and showed collaborative interactions when presenting their projects in front of class. A survey was conducted to solicit their feedback on how peer collaboration would facilitate learning of statistics. Almost all students found their interaction with their peers productive; they focused on the development of statistical thinking with concerted effort.

• Journal of Microbiology and Biotechnology
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• v.17 no.3
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• pp.496-510
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• 2007

This paper describes the use of a discrete mathematical model to represent the basic mechanisms of regulation of the bacteria E. coli in batch fermentation. The specific phenomena studied were the changes in metabolism and genetic regulation when the bacteria use three different carbon substrates (glucose, glycerol, and acetate). The model correctly predicts the behavior of E. coli vis-a-vis substrate mixtures. In a mixture of glucose, glycerol, and acetate, it prefers glucose, then glycerol, and finally acetate. The model included 67 nodes; 28 were genes, 20 enzymes, and 19 regulators/biochemical compounds. The model represents both the genetic regulation and metabolic networks in an integrated form, which is how they function biologically. This is one of the first attempts to include both of these networks in one model. Previously, discrete mathematical models were used only to describe genetic regulation networks. The study of the network dynamics generated 8 $(2^3)$ fixed points, one for each nutrient configuration (substrate mixture) in the medium. The fixed points of the discrete model reflect the phenotypes described. Gene expression and the patterns of the metabolic fluxes generated are described accurately. The activation of the gene regulation network depends basically on the presence of glucose and glycerol. The model predicts the behavior when mixed carbon sources are utilized as well as when there is no carbon source present. Fictitious jokers (Joker1, Joker2, and Repressor SdhC) had to be created to control 12 genes whose regulation mechanism is unknown, since glycerol and glucose do not act directly on the genes. The approach presented in this paper is particularly useful to investigate potential unknown gene regulation mechanisms; such a novel approach can also be used to describe other gene regulation situations such as the comparison between non-recombinant and recombinant yeast strain, producing recombinant proteins, presently under investigation in our group.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.4
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• pp.293-305
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• 2009

In this article, we study a reduced-order modelling for distributed feedback control problem of the Burgers equations. Brief review of the centroidal Voronoi tessellation (CVT) are provided. A weighted (nonuniform density) CVT is introduced and low-order approximate solution and compensator-based control design of Burgers equation is discussed. Through weighted CVT (or CVT-nonuniform) method, obtained low-order basis is applied to low-order functional gains to design a low-order controller, and by using the low-order basis order of control modelling was reduced. Numerical experiments show that a solution of reduced-order controlled Burgers equation performs well in comparison with a solution of full order controlled Burgers equation.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.19-24
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• 2000

The objective of this study is to develope a computer simulation model and estimate theoretically the transient performance characteristics of heat exchangers in an automotive air-conditioning system. To do that, the mathematical modelling of heat exchangers, such as evaporator and condenser, is presented first of all. For detail calculation, evaporator and condenser are divided into many sub-sections. Each sub-section is an elemental volume for transient modelling. The elemental volume is assumed to consist of three components, refrigerant, tube with fin, and air, and various properties including temperatures of three components are determined step along sub-sections. The properties of refrigerant R134a and air are calculated directly in the program. The heat transfer coefficients and pressure drop in single or two phase are also calculated by suitable empirical correlations. The overall tendencies of the simulation results were agreed well with those of actual situation.

• Smart Structures and Systems
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• v.33 no.2
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• pp.133-143
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• 2024

Piezoelectric (PZT) actuators have been widely used in precision positioning fields for their excellent displacement resolution. However, due to the inherent characteristics of piezoelectric actuators, hysteresis has been proven to greatly reduce positioning performance. In this paper, five mathematical hysteretic models based on activation function are proposed to characterize the nonlinear hysteresis characteristics of piezoelectric actuators. Then the performance of the proposed models is verified by particle swarm optimization (PSO) algorithm and the experiment data. Thirdly, the fitting performance of the proposed models is compared with the classical Bouc-Wen model. Finally, the performance of the five proposed models in modelling hysteresis nonlinearity of piezoelectric drivers is compared, in terms of RMSE, MAPE, SAPE and operation efficiency, and relevant suggestions are given.

• International Journal of Air-Conditioning and Refrigeration
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• v.10 no.4
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• pp.220-228
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• 2002

The cool-down performance after soaking is very important in an automotive air-conditioning system and is considered as a key design variable. Therefore, transient characteristics of each system component are essential to the preliminary design as well as steady-state performance. The objective of this study is to develop a computer simulation model and ostinato theoretically the transient performance of an automotive air-conditioning system. To do that, the mathematical modelling of each component, such as compressor, condenser, receiver/drier, expansion valve, and evaporator, is presented first of all. The basic balance equations about mass and energy are used in modelling. For detailed calculation, condenser and evaporator are divided into many sub-sections. Each sub-section is an elemental volume for modelling. In models of expansion valve and compressor, dynamic behaviors are not considered in this analysis, but the quasisteady state ones are just considered, such as the relation between mass flow rate and pressure drop in expansion device, polytropic process in compressor, etc. Also it is assumed that there are no heat loss and no pressure drop in discharge, liquid, and suction lines. The developed simulation model is validated by comparing with the laboratory test data of an automotive air-conditioning system. The overall time-tracing properties of each component agreed well with those of test data in this case.

• KSBB Journal
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• v.14 no.5
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• pp.550-560
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• 1999

There have been many research efforts on biofilter modeling including Ottengraf et al. who derived a model equation for the concentration profile of pollutants(e.g., VOCs) in the biolayer and solved their outlet concentration of the waste gas stream through biofilter. However, for most of research works done so far, the effects to explain the effect of adsorption of organic particles to medium(i.e., adsorbent) have been ignored. In this work biofilter modeling accompanying process lumping has been proposed and the theoretical effect of adsorption property of the medium, on the biofilter performance of eliminating organic components in waste gas stream, is intensively discussed.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.09a
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• pp.131-133
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• 2005

• Structural Engineering and Mechanics
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• v.6 no.4
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• pp.467-471
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• 1998

A mathematical model is developed to predict the fatigue notch factor of butt welds subject to number of parameters such as weld geometry, residual stresses under dynamic combined loading conditions (tensile and bending). Linear elastic fracture mechanics, finite element analysis, dimensional analysis and superposition approaches are used for the modelling. The predicted results are in good agreement with the available experimental data. As a result, scatters of the fatigue data can be significantly reduced by plotting S-N curve as ($S{\cdot}K_f$) vs. N.