Pub Date : 2018-12-31DOI: 10.11113/MATEMATIKA.V34.N3.1147
Fuaada Mohd Siam, M. Nasir
In irradiation process, instead of traverse on the targeted cells, there is side effect happens to non-targeted cells. The targeted cells that had been irradiated with ionizing radiation emits damaging signal molecules to the surrounding and then, damage the bystander cells. The type of damage considered in this work is the number of double-strand breaks (DSBs) of deoxyribonucleic acid (DNA) in cell’s nucleus. By using mathematical approach, a mechanistic model that can describe this phenomenon is developed based on a structured population approach. Then, the accuracy of the model is validated by its ability to match the experimental data. The Particle Swarm (PS) optimization is employed for the data fitting procedure. PS optimization searches the parameter value that minimize the errors between the model simulation data and experimental data. It is obtained that the mathematical modelling proposed in this paper is strongly in line with the experimental data.
{"title":"Mechanistic Model of Radiation-Induced Bystander Effects to Cells using Structured Population Approach","authors":"Fuaada Mohd Siam, M. Nasir","doi":"10.11113/MATEMATIKA.V34.N3.1147","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N3.1147","url":null,"abstract":"In irradiation process, instead of traverse on the targeted cells, there is side effect happens to non-targeted cells. The targeted cells that had been irradiated with ionizing radiation emits damaging signal molecules to the surrounding and then, damage the bystander cells. The type of damage considered in this work is the number of double-strand breaks (DSBs) of deoxyribonucleic acid (DNA) in cell’s nucleus. By using mathematical approach, a mechanistic model that can describe this phenomenon is developed based on a structured population approach. Then, the accuracy of the model is validated by its ability to match the experimental data. The Particle Swarm (PS) optimization is employed for the data fitting procedure. PS optimization searches the parameter value that minimize the errors between the model simulation data and experimental data. It is obtained that the mathematical modelling proposed in this paper is strongly in line with the experimental data.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42437583","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-31DOI: 10.11113/MATEMATIKA.V34.N3.1145
M. Mardlijah, Nur Ilmayasinta, L. Hanafi, Suharmadi Sanjaya
Algae are good plants as raw materials for biodiesel. Chlorella Vulgaris is one of the most economical algae to produce biodiesel since it is rich in carbohydrates, require no special care, and easy to grow. Algae oil for biodiesel production is obtained through fairly long processes, one of which is the lipid extraction. Mathematical model can be used to obtain optimal results. The optimal control theory itself is concerned with the analysis of controlled dynamic systems, in which a system is directed from configurations given to some desire target by minimizing or maximizing some criteria. In this study, LQR formulation has the advantages of easy to analyze and implementation. In comparison, optimum control is performed using the PMP method, to obtain the best control of the dynamic system from the initial state to the end, i.e by maximizing the objective function. This method is a better method than the LQR method. Optimal control is performed in order to optimize the yield of lipid concentration in the solvent flow (Cs), in the microalgae particles (Cp), and minimizing the volume of solvent (v). From the simulation, it is found that the PMP method is more optimal in this system compared to the LQR method.
{"title":"Optimal Control of Lipid Extraction Model on Microalgae Using Linear Quadratic Regulator (LQR) and Pontryagin Maximum Principle (PMP) Methods","authors":"M. Mardlijah, Nur Ilmayasinta, L. Hanafi, Suharmadi Sanjaya","doi":"10.11113/MATEMATIKA.V34.N3.1145","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N3.1145","url":null,"abstract":"Algae are good plants as raw materials for biodiesel. Chlorella Vulgaris is one of the most economical algae to produce biodiesel since it is rich in carbohydrates, require no special care, and easy to grow. Algae oil for biodiesel production is obtained through fairly long processes, one of which is the lipid extraction. Mathematical model can be used to obtain optimal results. The optimal control theory itself is concerned with the analysis of controlled dynamic systems, in which a system is directed from configurations given to some desire target by minimizing or maximizing some criteria. In this study, LQR formulation has the advantages of easy to analyze and implementation. In comparison, optimum control is performed using the PMP method, to obtain the best control of the dynamic system from the initial state to the end, i.e by maximizing the objective function. This method is a better method than the LQR method. Optimal control is performed in order to optimize the yield of lipid concentration in the solvent flow (Cs), in the microalgae particles (Cp), and minimizing the volume of solvent (v). From the simulation, it is found that the PMP method is more optimal in this system compared to the LQR method.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48551891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-31DOI: 10.11113/MATEMATIKA.V34.N3.1149
Vincent David, A. Bahar, Z. A. Aziz
The flow of water over an obstacle is a fundamental problem in fluid mechanics. Transcritical flow means the wave phenomenon near the exact criticality. The transcritical flow cannot be handled by linear solutions as the energy is unable to propagate away from the obstacle. Thus, it is important to carry out a study to identify suitable model to analyse the transcritical flow. The aim of this study is to analyse the transcritical flow over a bump as localized obstacles where the bump consequently generates upstream and downstream flows. Nonlinear shallow water forced Korteweg-de Vries (fKdV) model is used to analyse the flow over the bump. This theoretical model, containing forcing functions represents bottom topography is considered as the simplified model to describe water flows over a bump. The effect of water dispersion over the forcing region is investigated using the fKdV model. Homotopy Analysis Method (HAM) is used to solve this theoretical fKdV model. The HAM solution which is chosen with a special choice of }-value describes the physical flow of waves and the significance of dispersion over abump is elaborated.
{"title":"Transcritical Flow Over a Bump using Forced Korteweg-de Vries Equation","authors":"Vincent David, A. Bahar, Z. A. Aziz","doi":"10.11113/MATEMATIKA.V34.N3.1149","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N3.1149","url":null,"abstract":"The flow of water over an obstacle is a fundamental problem in fluid mechanics. Transcritical flow means the wave phenomenon near the exact criticality. The transcritical flow cannot be handled by linear solutions as the energy is unable to propagate away from the obstacle. Thus, it is important to carry out a study to identify suitable model to analyse the transcritical flow. The aim of this study is to analyse the transcritical flow over a bump as localized obstacles where the bump consequently generates upstream and downstream flows. Nonlinear shallow water forced Korteweg-de Vries (fKdV) model is used to analyse the flow over the bump. This theoretical model, containing forcing functions represents bottom topography is considered as the simplified model to describe water flows over a bump. The effect of water dispersion over the forcing region is investigated using the fKdV model. Homotopy Analysis Method (HAM) is used to solve this theoretical fKdV model. The HAM solution which is chosen with a special choice of }-value describes the physical flow of waves and the significance of dispersion over abump is elaborated.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48445739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-31DOI: 10.11113/MATEMATIKA.V34.N3.1143
Ikacipta Mega Ayuputri, Nur Iriawan, P. P. Oktaviana
In distributing funds to customers as credit, multi-finance companies have two necessary risks, i.e. prepayment risk, and default risk. The default risk can be minimized by determining the factors that affect the survival of customers to make credit payment, in terms of frequency of credit payments by customers that are distributed geometry. The proposed modelling is using Bayesian Geometric Regression and Bayesian Mixture Geometric Regression. The best model of this research is modelling using Bayesian Geometric Regression method because it has lower DIC values than Bayesian Mixture Geometric Regression. Modelling using Bayesian Geometric Regression show the significant variables are marital status, down payment, installment length, length of stay, and insurance.
{"title":"Frequency Model of Credit Payment using Bayesian Geometric Regression and Bayesian Mixture Geometric Regression","authors":"Ikacipta Mega Ayuputri, Nur Iriawan, P. P. Oktaviana","doi":"10.11113/MATEMATIKA.V34.N3.1143","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N3.1143","url":null,"abstract":"In distributing funds to customers as credit, multi-finance companies have two necessary risks, i.e. prepayment risk, and default risk. The default risk can be minimized by determining the factors that affect the survival of customers to make credit payment, in terms of frequency of credit payments by customers that are distributed geometry. The proposed modelling is using Bayesian Geometric Regression and Bayesian Mixture Geometric Regression. The best model of this research is modelling using Bayesian Geometric Regression method because it has lower DIC values than Bayesian Mixture Geometric Regression. Modelling using Bayesian Geometric Regression show the significant variables are marital status, down payment, installment length, length of stay, and insurance.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42766629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-31DOI: 10.11113/MATEMATIKA.V34.N3.1135
Nurliyana Juhan, Y. Zubairi, Z. M. Khalid, A. S. M. Zuhdi
Cardiovascular disease (CVD) includes coronary heart disease, cerebrovasculardisease (stroke), peripheral artery disease, and atherosclerosis of the aorta. All femalesface the threat of CVD. But becoming aware of symptoms and signs is a great challengesince most adults at increased risk of cardiovascular disease (CVD) have no symptoms orobvious signs especially in females. The symptoms may be identified by the assessmentof their risk factors. The Bayesian approach is a specific way in dealing with this kindof problem by formalizing a priori beliefs and of combining them with the available ob-servations. This study aimed to identify associated risk factors in CVD among femalepatients presenting with ST Elevation Myocardial Infarction (STEMI) using Bayesian lo-gistic regression and obtain a feasible model to describe the data. A total of 874 STEMIfemale patients in the National Cardiovascular Disease Database-Acute Coronary Syn-drome (NCVD-ACS) registry year 2006-2013 were analysed. Bayesian Markov ChainMonte Carlo (MCMC) simulation approach was applied in the univariate and multivariateanalysis. Model performance was assessed through the model calibration and discrimina-tion. The final multivariate model of STEMI female patients consisted of six significantvariables namely smoking, dyslipidaemia, myocardial infarction (MI), renal disease, Killipclass and age group. Females aged 65 years and above have higher incidence of CVD andmortality is high among female patients with Killip class IV. Also, renal disease was astrong predictor of CVD mortality. Besides, performance measures for the model wasconsidered good. Bayesian logistic regression model provided a better understanding onthe associated risk factors of CVD for female patients which may help tailor preventionor treatment plans more effectively.
{"title":"Identifying Risk Factors for Female Cardiovascular Disease Patients in Malaysia: A Bayesian Approach","authors":"Nurliyana Juhan, Y. Zubairi, Z. M. Khalid, A. S. M. Zuhdi","doi":"10.11113/MATEMATIKA.V34.N3.1135","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N3.1135","url":null,"abstract":"Cardiovascular disease (CVD) includes coronary heart disease, cerebrovasculardisease (stroke), peripheral artery disease, and atherosclerosis of the aorta. All femalesface the threat of CVD. But becoming aware of symptoms and signs is a great challengesince most adults at increased risk of cardiovascular disease (CVD) have no symptoms orobvious signs especially in females. The symptoms may be identified by the assessmentof their risk factors. The Bayesian approach is a specific way in dealing with this kindof problem by formalizing a priori beliefs and of combining them with the available ob-servations. This study aimed to identify associated risk factors in CVD among femalepatients presenting with ST Elevation Myocardial Infarction (STEMI) using Bayesian lo-gistic regression and obtain a feasible model to describe the data. A total of 874 STEMIfemale patients in the National Cardiovascular Disease Database-Acute Coronary Syn-drome (NCVD-ACS) registry year 2006-2013 were analysed. Bayesian Markov ChainMonte Carlo (MCMC) simulation approach was applied in the univariate and multivariateanalysis. Model performance was assessed through the model calibration and discrimina-tion. The final multivariate model of STEMI female patients consisted of six significantvariables namely smoking, dyslipidaemia, myocardial infarction (MI), renal disease, Killipclass and age group. Females aged 65 years and above have higher incidence of CVD andmortality is high among female patients with Killip class IV. Also, renal disease was astrong predictor of CVD mortality. Besides, performance measures for the model wasconsidered good. Bayesian logistic regression model provided a better understanding onthe associated risk factors of CVD for female patients which may help tailor preventionor treatment plans more effectively.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47796334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-31DOI: 10.11113/MATEMATIKA.V34.N3.1150
Nur Liyana Nazari, A. Aziz, Vincent David, Zaileha Md Ali
Heat and mass transfer of MHD boundary-layer flow of a viscous incompressible fluid over an exponentially stretching sheet in the presence of radiation is investigated. The two-dimensional boundary-layer governing partial differential equations are transformed into a system of nonlinear ordinary differential equations by using similarity variables. The transformed equations of momentum, energy and concentration are solved by Homotopy Analysis Method (HAM). The validity of HAM solution is ensured by comparing the HAM solution with existing solutions. The influence of physical parameters such as magnetic parameter, Prandtl number, radiation parameter, and Schmidt number on velocity, temperature and concentration profiles are discussed. It is found that the increasing values of magnetic parameter reduces the dimensionless velocity field but enhances the dimensionless temperature and concentration field. The temperature distribution decreases with increasing values of Prandtl number. However, the temperature distribution increases when radiation parameter increases. The concentration boundary layer thickness decreases as a result of increase in Schmidt number
{"title":"Heat and Mass Transfer of Magnetohydrodynamics (MHD) Boundary Layer Flow using Homotopy Analysis Method","authors":"Nur Liyana Nazari, A. Aziz, Vincent David, Zaileha Md Ali","doi":"10.11113/MATEMATIKA.V34.N3.1150","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N3.1150","url":null,"abstract":"Heat and mass transfer of MHD boundary-layer flow of a viscous incompressible fluid over an exponentially stretching sheet in the presence of radiation is investigated. The two-dimensional boundary-layer governing partial differential equations are transformed into a system of nonlinear ordinary differential equations by using similarity variables. The transformed equations of momentum, energy and concentration are solved by Homotopy Analysis Method (HAM). The validity of HAM solution is ensured by comparing the HAM solution with existing solutions. The influence of physical parameters such as magnetic parameter, Prandtl number, radiation parameter, and Schmidt number on velocity, temperature and concentration profiles are discussed. It is found that the increasing values of magnetic parameter reduces the dimensionless velocity field but enhances the dimensionless temperature and concentration field. The temperature distribution decreases with increasing values of Prandtl number. However, the temperature distribution increases when radiation parameter increases. The concentration boundary layer thickness decreases as a result of increase in Schmidt number","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42115398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-29DOI: 10.29313/jmtm.v17i2.4368
M. Mahmudi, Salmawaty Arif, Wenny Herliana
Abstrak. Sistem koordinat kutub merupakan sistem koordinat dengan setiap titik pada bidang ditentukan oleh suatu jarak dari titik tertentu dan suatu sudut dari arah tertentu. Beberapa model grafik persamaan kutub dapat dikembangkan untuk menghasilkan bentuk-bentuk artistik yang memiliki sifat simetri. Salah satu bentuk artistik yang menarik untuk dikaji adalah Logo Dasar Universitas Syiah Kuala. Tulisan ini akan membahas bentuk Logo Dasar Universitas Syiah Kuala dengan menggunakan koordinat kutub.Kata kunci: Sistem koordinat kutub, grafik persamaan kutub, Logo Dasar Universitas Syiah KualaAbstract. The polar coordinate system is a coordinate system with each point in a field determined by a distance from a certain point and an angle from a particular direction. Several graph models of polar equations are developed to produce artistic forms that have symmetrical properties. The Original Logo of Syiah Kuala University is one of this kind of interesting artistic forms. This paper will discuss the form of Syiah Kuala University's Original Logo using polar coordinates.Keywords: The polar coordinate system, graph of polar equation, The Original Logo of Syiah Kuala University
{"title":"Logo Dasar Universitas Syiah Kuala Pada Sistem Koordinat Kutub","authors":"M. Mahmudi, Salmawaty Arif, Wenny Herliana","doi":"10.29313/jmtm.v17i2.4368","DOIUrl":"https://doi.org/10.29313/jmtm.v17i2.4368","url":null,"abstract":"Abstrak. Sistem koordinat kutub merupakan sistem koordinat dengan setiap titik pada bidang ditentukan oleh suatu jarak dari titik tertentu dan suatu sudut dari arah tertentu. Beberapa model grafik persamaan kutub dapat dikembangkan untuk menghasilkan bentuk-bentuk artistik yang memiliki sifat simetri. Salah satu bentuk artistik yang menarik untuk dikaji adalah Logo Dasar Universitas Syiah Kuala. Tulisan ini akan membahas bentuk Logo Dasar Universitas Syiah Kuala dengan menggunakan koordinat kutub.Kata kunci: Sistem koordinat kutub, grafik persamaan kutub, Logo Dasar Universitas Syiah KualaAbstract. The polar coordinate system is a coordinate system with each point in a field determined by a distance from a certain point and an angle from a particular direction. Several graph models of polar equations are developed to produce artistic forms that have symmetrical properties. The Original Logo of Syiah Kuala University is one of this kind of interesting artistic forms. This paper will discuss the form of Syiah Kuala University's Original Logo using polar coordinates.Keywords: The polar coordinate system, graph of polar equation, The Original Logo of Syiah Kuala University","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42908251","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.1038
A. Hamzah, A. H. Murid
This study presents a mathematical model examining wastewater pollutant removalthrough an oxidation pond treatment system. This model was developed to describethe reaction between microbe-based product mPHO (comprising Phototrophic bac-teria (PSB)), dissolved oxygen (DO) and pollutant namely chemical oxygen demand(COD). It consists of coupled advection-diusion-reaction equations for the microor-ganism (PSB), DO and pollutant (COD) concentrations, respectively. The couplingof these equations occurred due to the reactions between PSB, DO and COD to pro-duce harmless compounds. Since the model is nonlinear partial dierential equations(PDEs), coupled, and dynamic, computational algorithm with a specic numericalmethod, which is implicit Crank-Nicolson method, was employed to simulate the dy-namical behaviour of the system. Furthermore, numerical results revealed that theproposed model demonstrated high accuracy when compared to the experimental data.Keywords Oxidation pond; nonlinear PDEs; PSB; implicit Crank-Nicolson.
{"title":"Nonlinear Partial Dierential Equations Model Related to Oxidation Pond Treatment System: A Case Study of mPHO at Taman Timor Oxidation Pond, Johor Bahru","authors":"A. Hamzah, A. H. Murid","doi":"10.11113/MATEMATIKA.V34.N2.1038","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.1038","url":null,"abstract":"This study presents a mathematical model examining wastewater pollutant removalthrough an oxidation pond treatment system. This model was developed to describethe reaction between microbe-based product mPHO (comprising Phototrophic bac-teria (PSB)), dissolved oxygen (DO) and pollutant namely chemical oxygen demand(COD). It consists of coupled advection-diusion-reaction equations for the microor-ganism (PSB), DO and pollutant (COD) concentrations, respectively. The couplingof these equations occurred due to the reactions between PSB, DO and COD to pro-duce harmless compounds. Since the model is nonlinear partial dierential equations(PDEs), coupled, and dynamic, computational algorithm with a specic numericalmethod, which is implicit Crank-Nicolson method, was employed to simulate the dy-namical behaviour of the system. Furthermore, numerical results revealed that theproposed model demonstrated high accuracy when compared to the experimental data.Keywords Oxidation pond; nonlinear PDEs; PSB; implicit Crank-Nicolson.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44000910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.1055
Chai Jin Sian, Y. Hoe, A. H. Murid
A mathematical model is considered to determine the effectiveness of disinfectant solution for surface decontamination. The decontamination process involved the diffusion of bacteria into disinfectant solution and the reaction of the disinfectant killing effect. The mathematical model is a reaction-diffusion type. Finite difference method and method of lines with fourth-order Runge-Kutta method are utilized to solve the model numerically. To obtain stable solutions, von Neumann stability analysis is employed to evaluate the stability of finite difference method. For stiff problem, Dormand-Prince method is applied as the estimated error of fourth-order Runge-Kutta method. MATLAB programming is selected for the computation of numerical solutions. From the results obtained, fourth-order Runge-Kutta method has a larger stability region and better accuracy of solutions compared to finite difference method when solving the disinfectant solution model. Moreover, a numerical simulation is carried out to investigate the effect of different thickness of disinfectant solution on bacteria reduction. Results show that thick disinfectant solution is able to reduce the dimensionless bacteria concentration more effectively
{"title":"Some Numerical Methods and Comparisons for Solving Mathematical Model of Surface Decontamination by Disinfectant Solution","authors":"Chai Jin Sian, Y. Hoe, A. H. Murid","doi":"10.11113/MATEMATIKA.V34.N2.1055","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.1055","url":null,"abstract":"A mathematical model is considered to determine the effectiveness of disinfectant solution for surface decontamination. The decontamination process involved the diffusion of bacteria into disinfectant solution and the reaction of the disinfectant killing effect. The mathematical model is a reaction-diffusion type. Finite difference method and method of lines with fourth-order Runge-Kutta method are utilized to solve the model numerically. To obtain stable solutions, von Neumann stability analysis is employed to evaluate the stability of finite difference method. For stiff problem, Dormand-Prince method is applied as the estimated error of fourth-order Runge-Kutta method. MATLAB programming is selected for the computation of numerical solutions. From the results obtained, fourth-order Runge-Kutta method has a larger stability region and better accuracy of solutions compared to finite difference method when solving the disinfectant solution model. Moreover, a numerical simulation is carried out to investigate the effect of different thickness of disinfectant solution on bacteria reduction. Results show that thick disinfectant solution is able to reduce the dimensionless bacteria concentration more effectively","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49509113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2018-12-02DOI: 10.11113/MATEMATIKA.V34.N2.876
U. S. Rajput, G. Kumar
The present study is carried out to examine the effect of Hall current on unsteady flow of a viscous, incompressible and electrically conducting fluid past an exponentially accelerated inclined plate with variable wall temperature and mass diffusion in the presence of transversely applied uniform magnetic field. The plate temperature and the concentration level near the plate increase linearly with time. The governing equations involved in the present analysis are solved by the Laplace-transform technique. The velocity profile is discussed with the help of graphs drawn for different parameters like thermal Grashof number, mass Grashof number, Prandtl number, Hall current parameter, acceleration parameter, the magnetic field parameter and Schmidt number, and the numerical values of skin-friction have been tabulated. It is observed that the flow pattern is affected significantly with plate acceleration, Hall current. The importance of the problem can be seen in cooling of electronic components of a nuclear reactor, bed thermal storage and heat sink in the turbine blades.
{"title":"Effect of Hall Current on Unsteady Magneto Hydrodynamic Flow Past an Exponentially Accelerated Inclined Plate with Variable Temperature and Mass Diffusion","authors":"U. S. Rajput, G. Kumar","doi":"10.11113/MATEMATIKA.V34.N2.876","DOIUrl":"https://doi.org/10.11113/MATEMATIKA.V34.N2.876","url":null,"abstract":"The present study is carried out to examine the effect of Hall current on unsteady flow of a viscous, incompressible and electrically conducting fluid past an exponentially accelerated inclined plate with variable wall temperature and mass diffusion in the presence of transversely applied uniform magnetic field. The plate temperature and the concentration level near the plate increase linearly with time. The governing equations involved in the present analysis are solved by the Laplace-transform technique. The velocity profile is discussed with the help of graphs drawn for different parameters like thermal Grashof number, mass Grashof number, Prandtl number, Hall current parameter, acceleration parameter, the magnetic field parameter and Schmidt number, and the numerical values of skin-friction have been tabulated. It is observed that the flow pattern is affected significantly with plate acceleration, Hall current. The importance of the problem can be seen in cooling of electronic components of a nuclear reactor, bed thermal storage and heat sink in the turbine blades.","PeriodicalId":43733,"journal":{"name":"Matematika","volume":" ","pages":""},"PeriodicalIF":0.4,"publicationDate":"2018-12-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41333118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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