Search results for: stochastic delay differential equations
3756 Mathematical Modelling of Spatial Distribution of Covid-19 Outbreak Using Diffusion Equation
Authors: Kayode Oshinubi, Brice Kammegne, Jacques Demongeot
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The use of mathematical tools like Partial Differential Equations and Ordinary Differential Equations have become very important to predict the evolution of a viral disease in a population in order to take preventive and curative measures. In December 2019, a novel variety of Coronavirus (SARS-CoV-2) was identified in Wuhan, Hubei Province, China causing a severe and potentially fatal respiratory syndrome, i.e., COVID-19. Since then, it has become a pandemic declared by World Health Organization (WHO) on March 11, 2020 which has spread around the globe. A reaction-diffusion system is a mathematical model that describes the evolution of a phenomenon subjected to two processes: a reaction process in which different substances are transformed, and a diffusion process that causes a distribution in space. This article provides a mathematical study of the Susceptible, Exposed, Infected, Recovered, and Vaccinated population model of the COVID-19 pandemic by the bias of reaction-diffusion equations. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined using the Lyapunov function are considered and the endemic equilibrium point exists and is stable if it satisfies Routh–Hurwitz criteria. Also, adequate conditions for the existence and uniqueness of the solution of the model have been proved. We showed the spatial distribution of the model compartments when the basic reproduction rate $\mathcal{R}_0 < 1$ and $\mathcal{R}_0 > 1$ and sensitivity analysis is performed in order to determine the most sensitive parameters in the proposed model. We demonstrate the model's effectiveness by performing numerical simulations. We investigate the impact of vaccination and the significance of spatial distribution parameters in the spread of COVID-19. The findings indicate that reducing contact with an infected person and increasing the proportion of susceptible people who receive high-efficacy vaccination will lessen the burden of COVID-19 in the population. To the public health policymakers, we offered a better understanding of the COVID-19 management.Keywords: COVID-19, SEIRV epidemic model, reaction-diffusion equation, basic reproduction number, vaccination, spatial distribution
Procedia PDF Downloads 1223755 Stimulated Raman Scattering of Ultra Intense Hollow Gaussian Beam
Authors: Prerana Sharma
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Effect of relativistic nonlinearity on stimulated Raman scattering of the propagating laser beam carrying null intensity in center (hollow Gaussian beam) by excited plasma wave are studied in a collisionless plasma. The construction of the equations is done employing the fluid theory which is developed with partial differential equation and Maxwell’s equations. The analysis is done using eikonal method. The phenonmenon of Stimulated Raman scattering is shown along with the excitation of seed plasma wave. The power of plasma wave and back reflectivity is observed for higher order of hollow Gaussian beam. Back reflectivity is studied numerically for various orders of HGLB with different value of plasma density, laser power and beam radius. Numerical analysis shows that these parameters play vital role on reflectivity characteristics.Keywords: Hollow Gaussian beam, relativistic nonlinearity, plasma physics, Raman scattering
Procedia PDF Downloads 6383754 Dynamic Analysis of Composite Doubly Curved Panels with Variable Thickness
Authors: I. Algul, G. Akgun, H. Kurtaran
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Dynamic analysis of composite doubly curved panels with variable thickness subjected to different pulse types using Generalized Differential Quadrature method (GDQ) is presented in this study. Panels with variable thickness are used in the construction of aerospace and marine industry. Giving variable thickness to panels can allow the designer to get optimum structural efficiency. For this reason, estimating the response of variable thickness panels is very important to design more reliable structures under dynamic loads. Dynamic equations for composite panels with variable thickness are obtained using virtual work principle. Partial derivatives in the equation of motion are expressed with GDQ and Newmark average acceleration scheme is used for temporal discretization. Several examples are used to highlight the effectiveness of the proposed method. Results are compared with finite element method. Effects of taper ratios, boundary conditions and loading type on the response of composite panel are investigated.Keywords: differential quadrature method, doubly curved panels, laminated composite materials, small displacement
Procedia PDF Downloads 3603753 Measuring Delay Using Software Defined Networks: Limitations, Challenges, and Suggestions for Openflow
Authors: Ahmed Alutaibi, Ganti Sudhakar
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Providing better Quality-of-Service (QoS) to end users has been a challenging problem for researchers and service providers. Building applications relying on best effort network protocols hindered the adoption of guaranteed service parameters and, ultimately, Quality of Service. The introduction of Software Defined Networking (SDN) opened the door for a new paradigm shift towards a more controlled programmable configurable behavior. Openflow has been and still is the main implementation of the SDN vision. To facilitate better QoS for applications, the network must calculate and measure certain parameters. One of those parameters is the delay between the two ends of the connection. Using the power of SDN and the knowledge of application and network behavior, SDN networks can adjust to different conditions and specifications. In this paper, we use the capabilities of SDN to implement multiple algorithms to measure delay end-to-end not only inside the SDN network. The results of applying the algorithms on an emulated environment show that we can get measurements close to the emulated delay. The results also show that depending on the algorithm, load on the network and controller can differ. In addition, the transport layer handshake algorithm performs best among the tested algorithms. Out of the results and implementation, we show the limitations of Openflow and develop suggestions to solve them.Keywords: software defined networking, quality of service, delay measurement, openflow, mininet
Procedia PDF Downloads 1653752 Nonlinear Evolution on Graphs
Authors: Benniche Omar
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We are concerned with abstract fully nonlinear differential equations having the form y’(t)=Ay(t)+f(t,y(t)) where A is an m—dissipative operator (possibly multi—valued) defined on a subset D(A) of a Banach space X with values in X and f is a given function defined on I×X with values in X. We consider a graph K in I×X. We recall that K is said to be viable with respect to the above abstract differential equation if for each initial data in K there exists at least one trajectory starting from that initial data and remaining in K at least for a short time. The viability problem has been studied by many authors by using various techniques and frames. If K is closed, it is shown that a tangency condition, which is mainly linked to the dynamic, is crucial for viability. In the case when X is infinite dimensional, compactness and convexity assumptions are needed. In this paper, we are concerned with the notion of near viability for a given graph K with respect to y’(t)=Ay(t)+f(t,y(t)). Roughly speaking, the graph K is said to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)), if for each initial data in K there exists at least one trajectory remaining arbitrary close to K at least for short time. It is interesting to note that the near viability is equivalent to an appropriate tangency condition under mild assumptions on the dynamic. Adding natural convexity and compactness assumptions on the dynamic, we may recover the (exact) viability. Here we investigate near viability for a graph K in I×X with respect to y’(t)=Ay(t)+f(t,y(t)) where A and f are as above. We emphasis that the t—dependence on the perturbation f leads us to introduce a new tangency concept. In the base of a tangency conditions expressed in terms of that tangency concept, we formulate criteria for K to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)). As application, an abstract null—controllability theorem is given.Keywords: abstract differential equation, graph, tangency condition, viability
Procedia PDF Downloads 1443751 Weak Instability in Direct Integration Methods for Structural Dynamics
Authors: Shuenn-Yih Chang, Chiu-Li Huang
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Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.Keywords: dynamic analysis, high frequency, integration method, overshoot, weak instability
Procedia PDF Downloads 2233750 Building Information Modelling for Construction Delay Management
Authors: Essa Alenazi, Zulfikar Adamu
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The Kingdom of Saudi Arabia (KSA) is not an exception in relying on the growth of its construction industry to support rapid population growth. However, its need for infrastructure development is constrained by low productivity levels and cost overruns caused by factors such as delays to project completion. Delays in delivering a construction project are a global issue and while theories such as Optimism Bias have been used to explain such delays, in KSA, client-related causes of delays are also significant. The objective of this paper is to develop a framework-based approach to explore how the country’s construction industry can manage and reduce delays in construction projects through building information modelling (BIM) in order to mitigate the cost consequences of such delays. It comprehensively and systematically reviewed the global literature on the subject and identified gaps, critical delay factors and the specific benefits that BIM can deliver for the delay management. A case study comprising of nine hospital projects that have experienced delay and cost overruns was also carried out. Five critical delay factors related to the clients were identified as candidates that can be mitigated through BIM’s benefits. These factors are: Ineffective planning and scheduling of the project; changes during construction by the client; delay in progress payment; slowness in decision making by the client; and poor communication between clients and other stakeholders. In addition, data from the case study projects strongly suggest that optimism bias is present in many of the hospital projects. Further validation via key stakeholder interviews and documentations are planned.Keywords: building information modelling (BIM), clients perspective, delay management, optimism bias, public sector projects
Procedia PDF Downloads 3243749 An Indoor Positioning System in Wireless Sensor Networks with Measurement Delay
Authors: Pyung Soo Kim, Eung Hyuk Lee, Mun Suck Jang
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In the current paper, an indoor positioning system is proposed with consideration of measurement delay. Firstly, an estimation filter with a measurement delay is designed for the indoor positioning mechanism under a weighted least square criterion, which utilizes only finite measurements on the most recent window. The proposed estimation filtering based scheme gives the filtered estimates for position, velocity and acceleration of moving target in real-time, while removing undesired noisy effects and preserving desired moving positions. Secondly, the proposed scheme is shown to have good inherent properties such as unbiasedness, efficiency, time-invariance, deadbeat, and robustness due to the finite memory structure. Finally, computer simulations shows that the performance of the proposed estimation filtering based scheme can outperform to the existing infinite memory filtering based mechanism.Keywords: indoor positioning system, wireless sensor networks, measurement delay
Procedia PDF Downloads 4823748 Two-Phase Sampling for Estimating a Finite Population Total in Presence of Missing Values
Authors: Daniel Fundi Murithi
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Missing data is a real bane in many surveys. To overcome the problems caused by missing data, partial deletion, and single imputation methods, among others, have been proposed. However, problems such as discarding usable data and inaccuracy in reproducing known population parameters and standard errors are associated with them. For regression and stochastic imputation, it is assumed that there is a variable with complete cases to be used as a predictor in estimating missing values in the other variable, and the relationship between the two variables is linear, which might not be realistic in practice. In this project, we estimate population total in presence of missing values in two-phase sampling. Instead of regression or stochastic models, non-parametric model based regression model is used in imputing missing values. Empirical study showed that nonparametric model-based regression imputation is better in reproducing variance of population total estimate obtained when there were no missing values compared to mean, median, regression, and stochastic imputation methods. Although regression and stochastic imputation were better than nonparametric model-based imputation in reproducing population total estimates obtained when there were no missing values in one of the sample sizes considered, nonparametric model-based imputation may be used when the relationship between outcome and predictor variables is not linear.Keywords: finite population total, missing data, model-based imputation, two-phase sampling
Procedia PDF Downloads 1313747 Modeling of a Stewart Platform for Analyzing One Directional Dynamics for Spacecraft Docking Operations
Authors: Leonardo Herrera, Shield B. Lin, Stephen J. Montgomery-Smith, Ziraguen O. Williams
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A one-directional dynamic model of a Stewart Platform was developed to assist NASA in analyzing the dynamic response in spacecraft docking operations. A simplified mechanical drawing was created, capturing the physical structure's main features. A simplified schematic diagram was developed into a lumped mass model from the mechanical drawing. Three differential equations were derived according to the schematic diagram. A Simulink diagram was created using MATLAB to represent the three equations. System parameters, including spring constants and masses, are derived in detail from the physical system. The model can be used for further analysis via computer simulation in predicting dynamic response in its main docking direction, i.e., up-and-down motion.Keywords: stewart platform, docking operation, spacecraft, spring constant
Procedia PDF Downloads 1993746 Stochastic Repair and Replacement with a Single Repair Channel
Authors: Mohammed A. Hajeeh
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This paper examines the behavior of a system, which upon failure is either replaced with certain probability p or imperfectly repaired with probability q. The system is analyzed using Kolmogorov's forward equations method; the analytical expression for the steady state availability is derived as an indicator of the system’s performance. It is found that the analysis becomes more complex as the number of imperfect repairs increases. It is also observed that the availability increases as the number of states and replacement probability increases. Using such an approach in more complex configurations and in dynamic systems is cumbersome; therefore, it is advisable to resort to simulation or heuristics. In this paper, an example is provided for demonstration.Keywords: repairable models, imperfect, availability, exponential distribution
Procedia PDF Downloads 2873745 An Intercontinental Comparison of Delay Discounting for Real and Hypothetical Money and Cigarettes among Cigarette Smokers
Authors: Steven R. Lawyer, Tereza Prihodova, Katerina Prihodova
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Delay discounting (DD) is one of the most frequently used behavioral-economic measures of impulsive choice, but there are few cross-cultural comparisons of discounting, and to the best of our knowledge, none compare patterns of DD across different commodities or compare real and hypothetical rewards across cultures. The purpose of this study was to compare patterns of DD for both real and hypothetical money and cigarettes among participants in the USA and the Czech Republic. Adult smokers from the United States and the Czech Republic completed standard measures of DD for hypothetical and real money (~$10USD) and cigarettes (1 pack, or 20 cigarettes). Contrary to data from the USA sample, Czech Republic participants discounted the value of real money steeper than hypothetical money, though this could be related to the relatively poor fit of the hyperbolic decay function to DD for hypothetical money in the Czech sample. These findings suggest that there might be cultural differences in delay discounting that warrant further attention.Keywords: delay discounting, temporal discounting, cigarette smoking, real rewards, hypothetical rewards
Procedia PDF Downloads 1883744 C Vibration Analysis of a Beam on Elastic Foundation with Elastically Restrained Ends Using Spectral Element Method
Authors: Hamioud Saida, Khalfallah Salah
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In this study, a spectral element method is employed to predict the free vibration of a Euler-Bernoulli beam resting on a Winkler foundation with elastically restrained ends. The formulation of the dynamic stiffness matrix has been established by solving the differential equation of motion, which was transformed to frequency domain. Non-dimensional natural frequencies and shape modes are obtained by solving the partial differential equations, numerically. Numerical comparisons and examples are performed to show the effectiveness of the SEM and to investigate the effects of various parameters, such as the springs at the boundaries and the elastic foundation parameter on the vibration frequencies. The obtained results demonstrate that the present method can also be applied to solve the more general problem of the dynamic analysis of structures with higher order precision.Keywords: elastically supported Euler-Bernoulli beam, free-vibration, spectral element method, Winkler foundation
Procedia PDF Downloads 1323743 A Method to Identify the Critical Delay Factors for Building Maintenance Projects of Institutional Buildings: Case Study of Eastern India
Authors: Shankha Pratim Bhattacharya
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In general building repair and renovation projects are minor in nature. It requires less attention as the primary cost involvement is relatively small. Although the building repair and maintenance projects look simple, it involves much complexity during execution. Many of the present research indicate that few uncertain situations are usually linked with maintenance projects. Those may not be read properly in the planning stage of the projects, and finally, lead to time overrun. Building repair and maintenance become essential and periodical after commissioning of the building. In Institutional buildings, the regular maintenance projects also include addition –alteration, modification activities. Increase in the student admission, new departments, and sections, new laboratories and workshops, up gradation of existing laboratories are very common in the institutional buildings in the developing nations like India. The project becomes very critical because it undergoes space problem, architectural design issues, structural modification, etc. One of the prime factors in the institutional building maintenance and modification project is the time constraint. Mostly it required being executed a specific non-work time period. The present research considered only the institutional buildings of the Eastern part of India to analyse the repair and maintenance project delay. A general survey was conducted among the technical institutes to find the causes and corresponding nature of construction delay factors. Five technical institutes are considered in the present study with repair, renovation, modification and extension type of projects. Construction delay factors are categorically subdivided into four groups namely, material, manpower (works), Contract and Site. The survey data are collected for the nature of delay responsible for a specific project and the absolute amount of delay through proposed and actual duration of work. In the first stage of the paper, a relative importance index (RII) is proposed for the delay factors. The occurrence of the delay factors is also judged by its frequency-severity nature. Finally, the delay factors are then rated and linked with the type of work. In the second stage, a regression analysis is executed to establish an empirical relationship between the actual time of a project and the percentage of delay. It also indicates the impact of the factors for delay responsibility. Ultimately, the present paper makes an effort to identify the critical delay factors for the repair and renovation type project in the Eastern Indian Institutional building.Keywords: delay factor, institutional building, maintenance, relative importance index, regression analysis, repair
Procedia PDF Downloads 2503742 Delay in the Diagnosis of Tuberculosis and Initiation of TB Treatment in the Private and Public Health Sectors, Udaipur District, Rajasthan, India, Nov 2013
Authors: Yogita Tulsian, R. S. Gupta, K. F. Laserson
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Background: Delays in the diagnosis and treatment of TB facilitates disease transmission in the community, so we conducted a study to evaluate the burden of and risk factors for delay in TB diagnosis and initiation of TB treatment among patients in the private and public sectors in Udaipur district, Rajasthan, India. Methods: A retrospective cohort study was conducted among 100 new sputum-positive TB. Patients were interviewed in the intensive phase of treatment September 2013-November 2013 Long total diagnosis delay (TDD) was defined as a time interval between first symptom to confirmed diagnosis > 30 days. Long health treatment delay (HTD) was defined as a time interval between confirmed diagnosis to treatment initiation > 7 days. Results: We observed a median TDD of 55 days (range: 7-136 days) in the public sector and of 92 days (11-380 days) in the private sector. Long TDD in the private sector was significantly associated with middle-higher socio-economic status (Risk Ratio (RR): 2;95% CI: 1.3-3). The reasons reported from the private sector for long TDD were suspect TB patients not advised for sputum examination (RR: 42; 95% CI:2.6-660), practise of self-medication (RR: 17.4; 95% CI: 1.1-267), or lack of awareness (RR: 9.7;95% CI: 0.6-145). The median HTD in the public sector was 3 days (range: 0-14 days), and in the private sector, 2 days (range: 0-11 days) (non-significant difference). Conclusions: Long TDD in private sector may be improved through sputum referral for all suspect TB cases and better education to all regarding TB.Keywords: diagnosis delay, treatment delay, privatesector, public sector
Procedia PDF Downloads 4273741 Ground Motion Modelling in Bangladesh Using Stochastic Method
Authors: Mizan Ahmed, Srikanth Venkatesan
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Geological and tectonic framework indicates that Bangladesh is one of the most seismically active regions in the world. The Bengal Basin is at the junction of three major interacting plates: the Indian, Eurasian, and Burma Plates. Besides there are many active faults within the region, e.g. the large Dauki fault in the north. The country has experienced a number of destructive earthquakes due to the movement of these active faults. Current seismic provisions of Bangladesh are mostly based on earthquake data prior to the 1990. Given the record of earthquakes post 1990, there is a need to revisit the design provisions of the code. This paper compares the base shear demand of three major cities in Bangladesh: Dhaka (the capital city), Sylhet, and Chittagong for earthquake scenarios of magnitudes 7.0MW, 7.5MW, 8.0MW and 8.5MW using a stochastic model. In particular, the stochastic model allows the flexibility to input region specific parameters such as shear wave velocity profile (that were developed from Global Crustal Model CRUST2.0) and include the effects of attenuation as individual components. Effects of soil amplification were analysed using the Extended Component Attenuation Model (ECAM). Results show that the estimated base shear demand is higher in comparison with code provisions leading to the suggestion of additional seismic design consideration in the study regions.Keywords: attenuation, earthquake, ground motion, Stochastic, seismic hazard
Procedia PDF Downloads 2493740 The Finite Element Method for Nonlinear Fredholm Integral Equation of the Second Kind
Authors: Melusi Khumalo, Anastacia Dlamini
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In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method.Keywords: finite element method, Galerkin approach, Fredholm integral equations, nonlinear integral equations
Procedia PDF Downloads 3763739 Natural Frequency Analysis of Spinning Functionally Graded Cylindrical Shells Subjected to Thermal Loads
Authors: Esmaeil Bahmyari
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The natural frequency analysis of the functionally graded (FG) rotating cylindrical shells subjected to thermal loads is studied based on the three-dimensional elasticity theory. The temperature-dependent assumption of the material properties is graded in the thickness direction, which varies based on the simple power law distribution. The governing equations and the appropriate boundary conditions, which include the effects of initial thermal stresses, are derived employing Hamilton’s principle. The initial thermo-mechanical stresses are obtained by the thermo-elastic equilibrium equation’s solution. As an efficient and accurate numerical tool, the differential quadrature method (DQM) is adopted to solve the thermo-elastic equilibrium equations, free vibration equations and natural frequencies are obtained. The high accuracy of the method is demonstrated by comparison studies with those existing solutions in the literature. Ultimately, the parametric studies are performed to demonstrate the effects of boundary conditions, temperature rise, material graded index, the thickness-to-length and the aspect ratios for the rotating cylindrical shells on the natural frequency.Keywords: free vibration, DQM, elasticity theory, FG shell, rotating cylindrical shell
Procedia PDF Downloads 843738 Free Vibration of Axially Functionally Graded Simply Supported Beams Using Differential Transformation Method
Authors: A. Selmi
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Free vibration analysis of homogenous and axially functionally graded simply supported beams within the context of Euler-Bernoulli beam theory is presented in this paper. The material properties of the beams are assumed to obey the linear law distribution. The effective elastic modulus of the composite was predicted by using the rule of mixture. Here, the complexities which appear in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using a relatively new approach called the Differential Transformation Method. This technique is applied for solving differential equation of transverse vibration of axially functionally graded beams. Natural frequencies and corresponding normalized mode shapes are calculated for different Young’s modulus ratios. MATLAB code is designed to solve the transformed differential equation of the beam. Comparison of the present results with the exact solutions proves the effectiveness, the accuracy, the simplicity, and computational stability of the differential transformation method. The effect of the Young’s modulus ratio on the normalized natural frequencies and mode shapes is found to be very important.Keywords: differential transformation method, functionally graded material, mode shape, natural frequency
Procedia PDF Downloads 3093737 Numerical Solution of Integral Equations by Using Discrete GHM Multiwavelet
Authors: Archit Yajnik, Rustam Ali
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In this paper, numerical method based on discrete GHM multiwavelets is presented for solving the Fredholm integral equations of second kind. There is hardly any article available in the literature in which the integral equations are numerically solved using discrete GHM multiwavelet. A number of examples are demonstrated to justify the applicability of the method. In GHM multiwavelets, the values of scaling and wavelet functions are calculated only at t = 0, 0.5 and 1. The numerical solution obtained by the present approach is compared with the traditional Quadrature method. It is observed that the present approach is more accurate and computationally efficient as compared to quadrature method.Keywords: GHM multiwavelet, fredholm integral equations, quadrature method, function approximation
Procedia PDF Downloads 4623736 Disadvantaged Adolescents and Educational Delay in South Africa: Impacts of Personal, Family, and School Characteristics
Authors: Rocio Herrero Romero, Lucie Cluver, James Hall, Janina Steinert
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Educational delay and non-completion are major policy concerns in South Africa. However, little research has focused on predictors for educational delay amongst adolescents in disadvantaged areas. This study has two aims: first, to use data integration approaches to compare the educational delay of 599 adolescents aged 16 to 18 from disadvantaged communities to national and provincial representative estimates in South Africa. Second, the paper also explores predictors for educational delay by comparing adolescents out of school (n=64) and at least one year behind (n=380), with adolescents in the age-appropriate grade or higher (n=155). Multinomial logistic regression models using self-report and administrative data were applied to look for significant associations of risk and protective factors. Significant risk factors for being behind (rather than in age-appropriate grade) were: male gender, past grade repetition, rural location and larger school size. Risk factors for being out of school (rather than in the age-appropriate grade) were: past grade repetition, having experienced problems concentrating at school, household poverty, and food insecurity. Significant protective factors for being in the age-appropriate grade (rather than out of school) were: living with biological parents or grandparents and access to school counselling. Attending school in wealthier communities was a significant protective factor for being in the age-appropriate grade (rather than behind). Our results suggest that both personal and contextual factors –family and school- predicted educational delay. This study provides new evidence to the significant effects of personal, family, and school characteristics on the educational outcomes of adolescents from disadvantaged communities in South Africa. This is the first longitudinal and quantitative study to systematically investigate risk and protective factors for post-compulsory educational outcomes amongst South African adolescents living in disadvantaged communities.Keywords: disadvantaged communities, quantitative analysis, school delay, South Africa
Procedia PDF Downloads 3483735 Critical Buckling Load of Carbon Nanotube with Non-Local Timoshenko Beam Using the Differential Transform Method
Authors: Tayeb Bensattalah, Mohamed Zidour, Mohamed Ait Amar Meziane, Tahar Hassaine Daouadji, Abdelouahed Tounsi
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In this paper, the Differential Transform Method (DTM) is employed to predict and to analysis the non-local critical buckling loads of carbon nanotubes with various end conditions and the non-local Timoshenko beam described by single differential equation. The equation differential of buckling of the nanobeams is derived via a non-local theory and the solution for non-local critical buckling loads is finding by the DTM. The DTM is introduced briefly. It can easily be applied to linear or nonlinear problems and it reduces the size of computational work. Influence of boundary conditions, the chirality of carbon nanotube and aspect ratio on non-local critical buckling loads are studied and discussed. Effects of nonlocal parameter, ratios L/d, the chirality of single-walled carbon nanotube, as well as the boundary conditions on buckling of CNT are investigated.Keywords: boundary conditions, buckling, non-local, differential transform method
Procedia PDF Downloads 3013734 Sliding Velocity in Impact with Friction in Three-Dimensional Multibody Systems
Authors: Hesham A. Elkaranshawy, Amr Abdelrazek, Hosam Ezzat
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This paper analyzes a single point rough collision in three dimensional rigid-multibody systems. A set of nonlinear different equations describing the progress and outcome of the impact are obtained. Specifically in case of the tangential, referred to as sliding, component of impact velocity is of great importance. Numerical methods are used to solve this problem. In this work, all these possible sliding behaviors during impact are identified, conditions leading to each behavior are specified, and an appropriate numerical procedure is suggested. A case of a four-degrees-of-freedom spatial robot that collides with its environment is investigated. The phase portrait of the tangential velocity, which presents the flow trajectories for different initial conditions, is calculated. Using the coefficient of friction as a control parameter, few phase portraits are drawn, each for a specific value of this coefficient. In addition, the bifurcation associated with the variation of this coefficient will be investigated.Keywords: friction impact, three-dimensional rigid multibody systems, sliding velocity, nonlinear ordinary differential equations, phase portrait
Procedia PDF Downloads 3813733 Mathematical Modeling of Nonlinear Process of Assimilation
Authors: Temur Chilachava
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In work the new nonlinear mathematical model describing assimilation of the people (population) with some less widespread language by two states with two various widespread languages, taking into account demographic factor is offered. In model three subjects are considered: the population and government institutions with the widespread first language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the population and government institutions with the widespread second language, influencing by means of state and administrative resources on the third population with some less widespread language for the purpose of their assimilation; the third population (probably small state formation, an autonomy), exposed to bilateral assimilation from two rather powerful states. Earlier by us it was shown that in case of zero demographic factor of all three subjects, the population with less widespread language completely assimilates the states with two various widespread languages, and the result of assimilation (redistribution of the assimilated population) is connected with initial quantities, technological and economic capabilities of the assimilating states. In considered model taking into account demographic factor natural decrease in the population of the assimilating states and a natural increase of the population which has undergone bilateral assimilation is supposed. At some ratios between coefficients of natural change of the population of the assimilating states, and also assimilation coefficients, for nonlinear system of three differential equations are received the two first integral. Cases of two powerful states assimilating the population of small state formation (autonomy), with different number of the population, both with identical and with various economic and technological capabilities are considered. It is shown that in the first case the problem is actually reduced to nonlinear system of two differential equations describing the classical model "predator - the victim", thus, naturally a role of the victim plays the population which has undergone assimilation, and a predator role the population of one of the assimilating states. The population of the second assimilating state in the first case changes in proportion (the coefficient of proportionality is equal to the relation of the population of assimilators in an initial time point) to the population of the first assimilator. In the second case the problem is actually reduced to nonlinear system of two differential equations describing type model "a predator – the victim", with the closed integrated curves on the phase plane. In both cases there is no full assimilation of the population to less widespread language. Intervals of change of number of the population of all three objects of model are found. The considered mathematical models which in some approach can model real situations, with the real assimilating countries and the state formations (an autonomy or formation with the unrecognized status), undergone to bilateral assimilation, show that for them the only possibility to avoid from assimilation is the natural demographic increase in population and hope for natural decrease in the population of the assimilating states.Keywords: nonlinear mathematical model, bilateral assimilation, demographic factor, first integrals, result of assimilation, intervals of change of number of the population
Procedia PDF Downloads 4703732 Parameter Identification Analysis in the Design of Rock Fill Dams
Authors: G. Shahzadi, A. Soulaimani
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This research work aims to identify the physical parameters of the constitutive soil model in the design of a rockfill dam by inverse analysis. The best parameters of the constitutive soil model, are those that minimize the objective function, defined as the difference between the measured and numerical results. The Finite Element code (Plaxis) has been utilized for numerical simulation. Polynomial and neural network-based response surfaces have been generated to analyze the relationship between soil parameters and displacements. The performance of surrogate models has been analyzed and compared by evaluating the root mean square error. A comparative study has been done based on objective functions and optimization techniques. Objective functions are categorized by considering measured data with and without uncertainty in instruments, defined by the least square method, which estimates the norm between the predicted displacements and the measured values. Hydro Quebec provided data sets for the measured values of the Romaine-2 dam. Stochastic optimization, an approach that can overcome local minima, and solve non-convex and non-differentiable problems with ease, is used to obtain an optimum value. Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE) are compared for the minimization problem, although all these techniques take time to converge to an optimum value; however, PSO provided the better convergence and best soil parameters. Overall, parameter identification analysis could be effectively used for the rockfill dam application and has the potential to become a valuable tool for geotechnical engineers for assessing dam performance and dam safety.Keywords: Rockfill dam, parameter identification, stochastic analysis, regression, PLAXIS
Procedia PDF Downloads 1463731 Numerical Solution of Porous Media Equation Using Jacobi Operational Matrix
Authors: Shubham Jaiswal
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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method
Procedia PDF Downloads 4393730 Modelling of Polymeric Fluid Flows between Two Coaxial Cylinders Taking into Account the Heat Dissipation
Authors: Alexander Blokhin, Ekaterina Kruglova, Boris Semisalov
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Mathematical model based on the mesoscopic theory of polymer dynamics is developed for numerical simulation of the flows of polymeric liquid between two coaxial cylinders. This model is a system of nonlinear partial differential equations written in the cylindrical coordinate system and coupled with the heat conduction equation including a specific dissipation term. The stationary flows similar to classical Poiseuille ones are considered, and the resolving equations for the velocity of flow and for the temperature are obtained. For solving them, a fast pseudospectral method is designed based on Chebyshev approximations, that enables one to simulate the flows through the channels with extremely small relative values of the radius of inner cylinder. The numerical analysis of the dependance of flow on this radius and on the values of dissipation constant is done.Keywords: dynamics of polymeric liquid, heat dissipation, singularly perturbed problem, pseudospectral method, Chebyshev polynomials, stabilization technique
Procedia PDF Downloads 2903729 Method of Parameter Calibration for Error Term in Stochastic User Equilibrium Traffic Assignment Model
Authors: Xiang Zhang, David Rey, S. Travis Waller
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Stochastic User Equilibrium (SUE) model is a widely used traffic assignment model in transportation planning, which is regarded more advanced than Deterministic User Equilibrium (DUE) model. However, a problem exists that the performance of the SUE model depends on its error term parameter. The objective of this paper is to propose a systematic method of determining the appropriate error term parameter value for the SUE model. First, the significance of the parameter is explored through a numerical example. Second, the parameter calibration method is developed based on the Logit-based route choice model. The calibration process is realized through multiple nonlinear regression, using sequential quadratic programming combined with least square method. Finally, case analysis is conducted to demonstrate the application of the calibration process and validate the better performance of the SUE model calibrated by the proposed method compared to the SUE models under other parameter values and the DUE model.Keywords: parameter calibration, sequential quadratic programming, stochastic user equilibrium, traffic assignment, transportation planning
Procedia PDF Downloads 2993728 A Mathematical Analysis of a Model in Capillary Formation: The Roles of Endothelial, Pericyte and Macrophages in the Initiation of Angiogenesis
Authors: Serdal Pamuk, Irem Cay
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Our model is based on the theory of reinforced random walks coupled with Michealis-Menten mechanisms which view endothelial cell receptors as the catalysts for transforming both tumor and macrophage derived tumor angiogenesis factor (TAF) into proteolytic enzyme which in turn degrade the basal lamina. The model consists of two main parts. First part has seven differential equations (DE’s) in one space dimension over the capillary, whereas the second part has the same number of DE’s in two space dimensions in the extra cellular matrix (ECM). We connect these two parts via some boundary conditions to move the cells into the ECM in order to initiate capillary formation. But, when does this movement begin? To address this question we estimate the thresholds that activate the transport equations in the capillary. We do this by using steady-state analysis of TAF equation under some assumptions. Once these equations are activated endothelial, pericyte and macrophage cells begin to move into the ECM for the initiation of angiogenesis. We do believe that our results play an important role for the mechanisms of cell migration which are crucial for tumor angiogenesis. Furthermore, we estimate the long time tendency of these three cells, and find that they tend to the transition probability functions as time evolves. We provide our numerical solutions which are in good agreement with our theoretical results.Keywords: angiogenesis, capillary formation, mathematical analysis, steady-state, transition probability function
Procedia PDF Downloads 1563727 Damage Localization of Deterministic-Stochastic Systems
Authors: Yen-Po Wang, Ming-Chih Huang, Ming-Lian Chang
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A scheme integrated with deterministic–stochastic subspace system identification and the method of damage localization vector is proposed in this study for damage detection of structures based on seismic response data. A series of shaking table tests using a five-storey steel frame has been conducted in National Center for Research on Earthquake Engineering (NCREE), Taiwan. Damage condition is simulated by reducing the cross-sectional area of some of the columns at the bottom. Both single and combinations of multiple damage conditions at various locations have been considered. In the system identification analysis, either full or partial observation conditions have been taken into account. It has been shown that the damaged stories can be identified from global responses of the structure to earthquakes if sufficiently observed. In addition to detecting damage(s) with respect to the intact structure, identification of new or extended damages of the as-damaged (ill-conditioned) counterpart has also been studied. The proposed scheme proves to be effective.Keywords: damage locating vectors, deterministic-stochastic subspace system, shaking table tests, system identification
Procedia PDF Downloads 327