23 results
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2. Mathematical Modeling and Analysis of Transmission Dynamics and Control of Schistosomiasis.
- Author
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Kanyi, Ebrima, Afolabi, Ayodeji Sunday, and Onyango, Nelson Owuor
- Subjects
BASIC reproduction number ,SCHISTOSOMIASIS ,MATHEMATICAL analysis ,MATHEMATICAL models ,NUMERICAL analysis ,SENSITIVITY analysis - Abstract
This paper presents a mathematical model that describes the transmission dynamics of schistosomiasis for humans, snails, and the free living miracidia and cercariae. The model incorporates the treated compartment and a preventive factor due to water sanitation and hygiene (WASH) for the human subpopulation. A qualitative analysis was performed to examine the invariant regions, positivity of solutions, and disease equilibrium points together with their stabilities. The basic reproduction number, R 0 , is computed and used as a threshold value to determine the existence and stability of the equilibrium points. It is established that, under a specific condition, the disease-free equilibrium exists and there is a unique endemic equilibrium when R 0 > 1. It is shown that the disease-free equilibrium point is both locally and globally asymptotically stable provided R 0 < 1 , and the unique endemic equilibrium point is locally asymptotically stable whenever R 0 > 1 using the concept of the Center Manifold Theory. A numerical simulation carried out showed that at R 0 = 1 , the model exhibits a forward bifurcation which, thus, validates the analytic results. Numerical analyses of the control strategies were performed and discussed. Further, a sensitivity analysis of R 0 was carried out to determine the contribution of the main parameters towards the die out of the disease. Finally, the effects that these parameters have on the infected humans were numerically examined, and the results indicated that combined application of treatment and WASH will be effective in eradicating schistosomiasis. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
3. Numerical Simulation of Pollutant Transport in Fractured Vuggy Porous Karstic Aquifers.
- Author
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Xiaolin Fan, Shuyu Sun, Wei Wei, and Jisheng Kou
- Subjects
NUMERICAL analysis ,SIMULATION methods & models ,FRACTURE mechanics ,POROUS materials ,AQUIFERS ,MATHEMATICAL models ,FINITE volume method ,FINITE element method - Abstract
This paper begins with presenting a mathematical model for contaminant transport in the fractured vuggy porous media of a species of contaminant (PCP). Two phases are numerically simulated for a process of contaminant and clean water infiltrated in the fractured vuggy porous media by coupling mixed finite element (MFE) method and finite volume method (FVM), both of which are locally conservative, to approximate the model. A hybrid mixed finite element (HMFE) method is applied to approximate the velocity field for the model. The convection and diffusion terms are approached by FVM and the standard MFE, respectively. The pressure distribution and temporary evolution of the concentration profiles are obtained for two phases. The average effluent concentration on the outflow boundary is obtained at different time and shows some different features from the matrix porous media. The temporal multiscale phenomena of the effluent concentration on the outlet are observed. The results show how the different distribution of the vugs and the fractures impacts on the contaminant transport and the effluent concentration on the outlet. This paper sheds light on certain features of karstic groundwater are obtained. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
4. The Optimal Dispatch of Traffic and Patrol Police Service Platforms.
- Author
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Ke Quan Zhao, Li Luo, and Yuan Mei Xia
- Subjects
OPTIMAL control theory ,MATHEMATICAL programming ,TRAFFIC congestion ,NUMERICAL analysis ,MATHEMATICAL models ,POLICE services - Abstract
The main goal of this paper is to present a minmax programming model for the optimal dispatch of Traffic and Patrol Police Service Platforms with single traffic congestion. The objective is to minimize the longest time of the dispatch for Traffic and Patrol Police Service Platforms. Some numerical experiments are carried out, and the optimal project is given. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
5. A Selection Model to Logistic Centers Based on TOPSIS and MCGP Methods: The Case of Airline Industry.
- Author
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Kou-Huang Chen, Chin-Nung Liao, and Li-Chun Wu
- Subjects
- *
AIRLINE industry , *TOPSIS method , *MATHEMATICAL models , *FUZZY logic , *GOAL programming , *NUMERICAL analysis - Abstract
The location selection of a logistics center is a crucial decision relating to cost and benefit analysis in airline industry. However, it is difficult to be solved because there are many conflicting and multiple objectives in location problems. To solve the problem, this paper integrates fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) andmultichoice goal programming (MCGP) to obtain an appropriate logistics center from many alternative locations for airline industry. The proposed method in this paper will offer the decision makers (DMs) to set multiple aspiration levels for the decision criteria. A numerical example of application is also presented. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
6. Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems.
- Author
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Hong Shi and Guangming Xie
- Subjects
OBSERVABILITY (Control theory) ,CONTROLLABILITY in systems engineering ,PIECEWISE constant approximation ,SYSTEM analysis ,IMPULSIVE differential equations ,MATHEMATICAL models ,NUMERICAL analysis - Abstract
Impulsive differential systems are an important class of mathematical models for many practical systems in physics, chemistry, biology, engineering, and information science that exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This paper studies the controllability and observability of linear piecewise constant impulsive systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is proved that the reachability is equivalent to the controllability under some mild conditions. Then, necessary and sufficient criteria for observability and determinability of such systems are established, respectively. It is also proved that the observability is equivalent to the determinability under some mild conditions. Our criteria are of the geometric type, and they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
7. Stability of Membrane Elastodynamics with Applications to Cylindrical Aneurysms.
- Author
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Samuelson, A. and Seshaiyer, P.
- Subjects
BIOLOGICAL membranes ,ELASTODYNAMICS ,INTRACRANIAL aneurysm ruptures ,AORTIC aneurysms ,SOLID-liquid interfaces ,MATHEMATICAL models ,NUMERICAL analysis ,VISCOELASTICITY - Abstract
The enlargement and rupture of intracranial and abdominal aortic aneurysms constitutes a major medical problem. It has been suggested that enlargement and rupture are due to mechanical instabilities of the associated complex fluid-solid interaction in the lesions. In this paper, we examine a coupled fluid-structure mathematical model for a cylindrical geometry representing an idealized aneurysm using both analytical and numerical techniques. A stability analysis for this subclass of aneurysms is presented. It is shown that this subclass of aneurysms is dynamically stable both with and without a viscoelastic contribution to the arterial wall. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
8. Modeling and Simulation of a Chemical Vapor Deposition.
- Author
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Geiser, J. and Arab, M.
- Subjects
MATHEMATICAL models ,SIMULATION methods & models ,CHEMICAL vapor deposition ,BIPOLAR transistors ,MATHEMATICAL optimization ,STRUCTURAL plates ,POROUS materials ,NUMERICAL analysis - Abstract
We are motivated to model PE-CVD (plasma enhanced chemical vapor deposition) processes for metallic bipolar plates, and their optimization for depositing a heterogeneous layer on the metallic plate. Moreover a constraint to the deposition process is a very low pressure (nearly a vacuum) and a low temperature (about 400K). The contribution of this paper is to derive a multiphysics system of multiple physics problems that includes some assumptions to simplify the complicate process and allows of deriving a computable mathematical model without neglecting the real-life processes. To model the gaseous transport in the apparatus we employ mobile gas phase streams, immobile and mobile phases in a chamber that is filled with porous medium (plasma layers). Numerical methods are discussed to solve such multi-scale and multi phase models and to obtain qualitative results for the delicate multiphysical processes in the chamber. We discuss a splitting analysis to couple such multiphysical problems. The verification of such a complicated model is done with real-life experiments for single species. Such numerical simulations help to economize on expensive physical experiments and obtain control mechanisms for the delicate deposition process. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
9. Analytical Approach for Solving the Internal Waves Problems Involving the Tidal Force.
- Author
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Jaharuddin and Hermansyah, Hadi
- Subjects
- *
MATHEMATICAL models , *NUMERICAL analysis , *DIFFERENTIAL equations , *INTERNAL waves , *TIDAL forces (Mechanics) - Abstract
The mathematical model for describing internal waves of the ocean is derived from the assumption of ideal fluid; i.e., the fluid is incompressible and inviscid. These internal waves are generated through the interaction between the tidal currents and the basic topography of the fluid. Basically the mathematical model of the internal wave problem of the ocean is a system of nonlinear partial differential equations (PDEs). In this paper, the analytical approach used to solve nonlinear PDE is the Homotopy Analysis Method (HAM). HAM can be applied to determine the resolution of almost any internal wave problem involving tidal forces. The use of HAM in the solution to basic fluid equations is efficient and simple, since it involves only modest calculations using the common integral. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
10. Hesitant Fuzzy Soft Set and Its Applications in Multicriteria Decision Making.
- Author
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Fuqiang Wang, Xihua Li, and Xiaohong Chen
- Subjects
- *
FUZZY systems , *SET theory , *MULTIPLE criteria decision making , *MATHEMATICAL models , *NUMERICAL analysis - Abstract
Molodtsov's soft set theory is a newly emerging mathematical tool to handle uncertainty. However, the classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. This paper aims to extend the classical soft sets to hesitant fuzzy soft sets which are combined by the soft sets and hesitant fuzzy sets. Then, the complement, "AND", "OR", union and intersection operations are defined on hesitant fuzzy soft sets. The basic properties such as DeMorgan's laws and the relevant laws of hesitant fuzzy soft sets are proved. Finally, with the help of level soft set, the hesitant fuzzy soft sets are applied to a decision making problem and the effectiveness is proved by a numerical example. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
11. Stability Analysis of Runge-Kutta Methods for Nonlinear Functional Differential and Functional Equations.
- Author
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Yuexin Yu, Zhongyan Liu, and Liping Wen
- Subjects
- *
STABILITY theory , *RUNGE-Kutta formulas , *FUNCTIONAL differential equations , *NUMERICAL analysis , *MATHEMATICAL models - Abstract
This paper is concerned with the numerical stability of Runge-Kutta methods for a class of nonlinear functional differential and functional equations. The sufficient conditions for the stability and asymptotic stability of (k, l)-algebraically stable Runge-Kutta methods are derived. A numerical test is given to confirm the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
12. HSV-2 and Substance Abuse amongst Adolescents: Insights through Mathematical Modelling.
- Author
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Mhlanga, A., Bhunu, C. P., and Mushayabasa, S.
- Subjects
- *
SUBSTANCE use of teenagers , *HERPES simplex , *MATHEMATICAL models , *CONDOM use , *OPTIMAL control theory , *NUMERICAL analysis - Abstract
Herpes simplex virus infection is mostly spread and occurs more commonly among substance abusing adolescents as compared to the nonsubstance abusing. In this paper, amathematicalmodel for the spread of HSV-2 within a community with substance abusing adolescents is developed and analysed. The impacts of condom use and educational campaigns are examined. The study suggests that condom use is highly effective among adolescents, when we have more of them quitting than becoming substance abusers. Measures such as educational campaigns can be put in place to try and reduce adolescents from becoming substance abusers. Further, we applied optimal control theory to the proposed model. The controls represent condomuse and educational campaigns. The objective is based on maximising the susceptible nonsubstance abusing adolescents, while minimising the susceptible substance abusing adolescents, the infectious nonsubstance abusing adolescents, and the infectious substance abusing adolescents. We used Pontrygin's maximum principle to characterise the optimal levels of the two controls. The resulting optimality system is solved numerically. Overall, the application of the optimal control theory suggests that more effort should be devoted to condom use as compared to educational campaigns. [ABSTRACT FROM AUTHOR]
- Published
- 2014
- Full Text
- View/download PDF
13. Modeling and Analysis of Epidemic Diffusion with Population Migration.
- Author
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Ming Liu and Yihong Xiao
- Subjects
- *
MATHEMATICAL models , *MATHEMATICAL analysis , *EPIDEMICS , *DISEASE susceptibility , *COMPUTER simulation , *EMIGRATION & immigration , *NUMERICAL analysis - Abstract
An improved Susceptible-Infected-Susceptible (SIS) epidemic diffusion model with population migration between two cities is modeled. Global stability conditions for both the disease-free equilibrium and the endemic equilibrium are analyzed and proved. The main contribution of this paper is reflected in epidemic modeling and analysis which considers unequal migration rates, and only susceptible individuals can migrate between the two cities. Numerical simulation shows when the epidemic diffusion system is stable, number of infected individuals in one city can reach zero, while the number of infected individuals in the other city is still positive. On the other hand, decreasing population migration in only one city seems not as effective as improving the recovery rate for controlling the epidemic diffusion. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
14. A Mutual-Evaluation Genetic Algorithm for Numerical and Routing Optimization.
- Author
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Chih-Hao Lin and Jiun-De He
- Subjects
- *
GENETIC algorithms , *NUMERICAL analysis , *ROUTING (Computer network management) , *MATHEMATICAL models , *MATHEMATICAL optimization , *CHROMOSOME banding , *BIOLOGICAL fitness - Abstract
Many real-world problems can be formulated as numerical optimization with certain objective functions. However, these objective functions often contain numerous local optima, which could trap an algorithm from moving toward the desired global solution. To improve the search efficiency of traditional genetic algorithms, this paper presents a mutual-evaluation genetic algorithm (MEGA). A novel mutual-evaluation approach is employed so that the merit of selected genes in a chromosome can be determined by comparing the fitness changes before and after interchanging with those in the mating chromosome. According to the determined genome merit, a therapy crossover can generate effective schemata to explore the solution space efficiently. The computational experiments for twelve numerical problems show that the MEGA can find near optimal solutions in all test benchmarks and achieve solutions with higher accuracy than those obtained by eight existing algorithms. This study also uses the MEGA to find optimal flow-allocation strategies for multipath-routing problems. Experiments on quality-of-service routing scenarios show that the MEGA can deal with these constrained routing problems effectively and efficiently. Therefore, the MEGA not only can reduce the effort of function analysis but also can deal with a wide spectrum of real-world problems. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
15. Analysis of the Mathematical Model for the Spread of Pine Wilt Disease.
- Author
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Xiangyun Shi and Guohua Song
- Subjects
- *
MATHEMATICAL models , *CONIFER wilt , *MATHEMATICAL symmetry , *EQUILIBRIUM , *DYNAMICAL systems , *NUMERICAL analysis , *COMPUTER simulation - Abstract
This paper formulates and analyzes a pine wilt disease model. Mathematical analyses of the model with regard to invariance of nonnegativity, boundedness of the solutions, existence of nonnegative equilibria, permanence, and global stability are presented. It is proved that the global dynamics are determined by the basic reproduction number Ro and the other value Rc which is larger than Ro. If Ro and Rc are both less than one, the disease-free equilibrium is asymptotically stable and the pine wilt disease always dies out. If one is between the two values, though the pine wilt disease could occur, the outbreak will stop. If the basic reproduction number is greater than one, a unique endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists at the endemic equilibrium state if it initially exists. Numerical simulations are carried out to illustrate the theoretical results, and some disease control measures are especially presented by these theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
16. A New Fractional Order Hold and Its Capability in Frequency Response and Zero Placement.
- Author
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Hashemzadeh, Farzad, Pish-Robat, Amin Rezaei, and Jabehdar-Maralani, Parviz
- Subjects
- *
FRACTIONAL calculus , *FREQUENCY response , *SIMULATION methods & models , *STATISTICAL sampling , *MATHEMATICAL models , *NUMERICAL analysis - Abstract
This paper introduces a new holder with application on digital control systems. This holder is a combination of fractional order hold (FROH) and zero-order hold (ZOH) that has the capability of both holders and a frequency response better than both of ZOH and FROH. For the stability of zeros of the sampled system two theorems are stated and proved with the assumption that the sampling period is very small. Also simulation results are studied to show the effectiveness of the proposed holder and better performance results in comparison with ZOH and FROH. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
17. The Point of Coincidence and Common Fixed Point for Three Mappings in Cone Metric Spaces.
- Author
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Kumar, Anil, Rathee, Savita, and Kumar, Navin
- Subjects
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COINCIDENCE , *FIXED point theory , *MATHEMATICAL mappings , *METRIC spaces , *SET theory , *GENERALIZATION , *MATHEMATICAL models , *NUMERICAL analysis - Abstract
The aim of this paper is to present the point of coincidence and common fixed point for three mappings in cone metric spaces over normal cone which satisfy a different contractive condition. Our result generalizes the recent related results proved by Stojan Radenović (2009) and Rangamma and Prudhvi (2012). [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
18. Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses.
- Author
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Hai Zhang, Jinde Cao, and Wei Jiang
- Subjects
- *
LINEAR differential equations , *CONTROLLABILITY in systems engineering , *FRACTIONAL calculus , *MATHEMATICAL models , *NUMERICAL analysis - Abstract
This paper is concerned with the controllability of linear fractional differential systems with delay in state and impulses. The factors of such systems including fractional derivative, impulses, and delay are taken into account synchronously. The expression of state response for such systems is derived, and the sufficient and necessary conditions of controllability criteria are established. Both the proposed criteria and illustrative examples show that the controllability property of the linear systems is dependent neither on the order of fractional derivative, on delay nor on impulses. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
19. Common Fixed Point Theorems of New Contractive Conditions in Fuzzy Metric Spaces.
- Author
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Jiang Zhu, Yuan Wang, and Shin Min Kang
- Subjects
- *
FIXED point theory , *METRIC spaces , *FUZZY algorithms , *GENERALIZATION , *MATHEMATICAL models , *NUMERICAL analysis - Abstract
Some new limit contractive conditions in fuzzy metric spaces are introduced, by using property (E.A), some common fixed point theorems for four maps are proved in GV-fuzzy metric spaces. As an application of our results, some new contractive conditions are presented, and some common fixed point theorems are proved under these contractive conditions. The contractive conditions presented in this paper contain or generalize many contractive conditions that appeared in the literatures. Some examples are given to illustrate that our results are real generalizations for the results in the references and to show that our limit contractive conditions are important for the existence of fixed point. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
20. FFekete-Szegő Inequality for a Subclass of p-Valent Analytic Functions.
- Author
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Raza, Mohsan, Arif, Muhammad, and Darus, Maslina
- Subjects
- *
ANALYTIC functions , *MATHEMATICAL inequalities , *MATHEMATICAL functions , *MATHEMATICAL convolutions , *MATHEMATICAL models , *NUMERICAL analysis - Abstract
Themain object of this paper is to study Fekete-Szegő problem for the class of P-valent functions. Fekete-Szego inequality of several classes is obtained as special cases fromour results. Applications of the results are also obtained on the class defined by convolution. [ABSTRACT FROM AUTHOR]
- Published
- 2013
- Full Text
- View/download PDF
21. An Efficient Numerical Method for a Class of Nonlinear Volterra Integro-Differential Equations.
- Author
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Daliri Birjandi, M. H., Saberi-Nadjafi, J., and Ghorbani, A.
- Subjects
INTEGRO-differential equations ,NUMERICAL analysis ,STOCHASTIC convergence ,APPROXIMATION theory ,MATHEMATICAL models - Abstract
We investigate an efficient numerical method for solving a class of nonlinear Volterra integro-differential equations, which is a combination of the parametric iteration method and the spectral collocation method. The implementation of the modified method is demonstrated by solving several nonlinear Volterra integro-differential equations. The results reveal that the developed method is easy to implement and avoids the additional computational work. Furthermore, the method is a promising approximate tool to solve this class of nonlinear equations and provides us with a convenient way to control and modify the convergence rate of the solution. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
22. A Numerical Study on Flow around Nonuniform Porous Fences.
- Author
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Huang, Long-Ming, Chan, H. C., and Lee, Jung-Tai
- Subjects
NUMERICAL analysis ,MATHEMATICAL forms ,POROUS materials ,WIND tunnels ,MATHEMATICAL models ,POROSITY - Abstract
The effects of a porous fence with a nonuniform porosity on flow fields are investigated numerically. First, an experiment with a non-uniform porous fence located in a wind tunnel is performed to obtain a reference data set. Then, a numerical model that utilizes the finite volume scheme with a weakly compressible-flow method to solve the continuity and momentum equations is developed. The numerical simulation is compared to experimental measurements for validation purposes. As a result, the numerical predictions show good agreements with the experimental data. Finally, the numerical investigations of the flow fields around porous fences with various combinations of upper and lower fence porosity are also presented. When the upper porosity is greater than the lower porosity, the Protection Index PI0.1, PI0.3 and PI0.5, representing the adverse sheltering effect, decreases compared to that of the uniform porous fence. When the upper porosity is less than the lower porosity, the PI0.5 increases and the variations of the PI0.1 and PI0.3, depend on the upper porosity, compared to that of the uniform porous fence. The results show that the porous fence with the upper fence porosity eU = 0% and the lower fence porosity eL = 30% gives the best sheltering effect among the porous fences in this study. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
23. Modeling and Analysis of Material Flows in Re-Entrant Supply Chain Networks Using Modified Partial Differential Equations.
- Author
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Fenglan He, Ming Dong, and Xiaofeng Shao
- Subjects
MATHEMATICAL models ,SUPPLY chain management ,PARTIAL differential equations ,NUMERICAL analysis ,CONTINUUM mechanics ,MATHEMATICAL physics - Abstract
The basic partial differential equation (PDE) models for supply chain networks with re-entrant nodes and their macroscopic are proposed. However, through numerical examples, the basic continuum models do not perform well formultiple re-entrant systems. Then, a new state equation considering the re-entrant degree of the products is introduced to improve the effectiveness of the basic continuum models. The applicability of the modified continuum models for re-entrant supply chains is illustrated through numerical examples. Finally, based on themodified continuum model, numerical examples of different re-entrant degrees are given, meanwhile, the changes in theWIP and outflux are analyzed in details for multiple re-entrant supply chain systems. [ABSTRACT FROM AUTHOR]
- Published
- 2011
- Full Text
- View/download PDF
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