Search results for: mathematical programming method

Authors: Jutharat Sunprasert, Ekapong Hirunsirisawat, Narongrit Waraporn, Somporn Peansukmanee

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Metal Ship and Robotic Car is one of the hands-on activities in the course, the Fundamental of Engineering that can be divided into three parts. The first part, the metal ships, was made by using engineering drawings, physics and mathematics knowledge. The second part is where the students learned how to construct a robotic car and control it using computer programming. In the last part, the students had to combine the workings of these two objects in the final testing. This aim of study was to investigate the effectiveness of hands-on activity by integrating Science, Technology, Engineering and Mathematics (STEM) concepts to develop scientific and engineering skills. The results showed that the majority of students felt this hands-on activity lead to an increased confidence level in the integration of STEM. Moreover, 48% of all students engaged well with the STEM concepts. Students could obtain the knowledge of STEM through hands-on activities with the topics science and mathematics, engineering drawing, engineering workshop and computer programming; most students agree and strongly agree with this learning process. This indicated that the hands-on activity: “Metal Ship and Robotic Car” is a useful tool to integrate each aspect of STEM. Furthermore, hands-on activities positively influence a student’s interest which leads to increased learning achievement and also in developing scientific and engineering skills.

Keywords: hands-on activity, STEM education, computer programming, metal work

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Authors: Saleem Z. Ramadan

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The material selection problem is concerned with the determination of the right material for a certain product to optimize certain performance indices in that product such as mass, energy density, and power-to-weight ratio. This paper is concerned about optimizing the selection of the manufacturing process along with the material used in the product under performance indices and availability constraints. In this paper, the material selection problem is formulated using binary programming and solved by genetic algorithm. The objective function of the model is to minimize the total manufacturing cost under performance indices and material and manufacturing process availability constraints.

Keywords: optimization, material selection, process selection, genetic algorithm

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Authors: B. Marasović, S. Pivac, S. V. Vukasović

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Constructing a portfolio of investments is one of the most significant financial decisions facing individuals and institutions. In accordance with the modern portfolio theory maximization of return at minimal risk should be the investment goal of any successful investor. In addition, the costs incurred when setting up a new portfolio or rebalancing an existing portfolio must be included in any realistic analysis. In this paper rebalancing an investment portfolio in the presence of transaction costs on the Croatian capital market is analyzed. The model applied in the paper is an extension of the standard portfolio mean-variance optimization model in which transaction costs are incurred to rebalance an investment portfolio. This model allows different costs for different securities, and different costs for buying and selling. In order to find efficient portfolio, using this model, first, the solution of quadratic programming problem of similar size to the Markowitz model, and then the solution of a linear programming problem have to be found. Furthermore, in the paper the impact of transaction costs on the efficient frontier is investigated. Moreover, it is shown that global minimum variance portfolio on the efficient frontier always has the same level of the risk regardless of the amount of transaction costs. Although efficient frontier position depends of both transaction costs amount and initial portfolio it can be concluded that extreme right portfolio on the efficient frontier always contains only one stock with the highest expected return and the highest risk.

Keywords: Croatian capital market, Markowitz model, fractional quadratic programming, portfolio optimization, transaction costs

Procedia PDF Downloads 358

Authors: Tahir Nawaz Cheema, Dumitru Baleanu, Ali Raza

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In this research work, we design intelligent computing through Bayesian Regularization artificial neural networks (BRANNs) introduced to solve the mathematical modeling of infectious diseases (Covid-19). The dynamical transmission is due to the interaction of people and its mathematical representation based on the system's nonlinear differential equations. The generation of the dataset of the Covid-19 model is exploited by the power of the explicit Runge Kutta method for different countries of the world like India, Pakistan, Italy, and many more. The generated dataset is approximately used for training, testing, and validation processes for every frequent update in Bayesian Regularization backpropagation for numerical behavior of the dynamics of the Covid-19 model. The performance and effectiveness of designed methodology BRANNs are checked through mean squared error, error histograms, numerical solutions, absolute error, and regression analysis.

Keywords: mathematical models, beysian regularization, bayesian-regularization backpropagation networks, regression analysis, numerical computing

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Authors: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: Minnie Y. Teng, Kathy Xie, Jarus Tal

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Rationale: The traditional approach to community programs for children with mental and/or developmental challenges often involves segregation from typically-developing peers. However, studies show that inclusive education improves children’s quality of life, self-concept, and long term health outcomes. Investigating factors that influence inclusion can thus have important implications in the design and facilitation of community programs such that all children - across a spectrum of needs and abilities - may benefit. Objectives: This study explores barriers and facilitators to inclusive community programming for children aged 0 to 12 with developmental/mental challenges. Methods: Using a participatory-action research methodology, semi-structured focus groups and interviews will be used to explore perspectives of sighted students, instructors, and staff. Data will be transcribed and coded thematically. Practice Implications or Results: By having a deeper understanding of the barriers and facilitators to inclusive programming in the community, researchers can work with the broader community to facilitate inclusion in children’s community programs. Conclusions: Expanding inclusive practices may improve the health and wellbeing of the pediatric populations with disabilities, which consistently reports lower levels of participation. These findings may help to identify gaps in existing practices and ways to approach them.

Keywords: aquatic programs, children, disabilities, inclusion, community programs

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Authors: Yenny Paola Morales Cortés, Fabián Rico Rodríguez, Juan Carlos Serrato Bermúdez, Carlos Arturo Martínez Riascos

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Numerous benefits of galactooligosaccharides (GOS) as prebiotics have motivated the study of enzymatic processes for their production. These processes have special complexities due to several factors that make difficult high productivity, such as enzyme type, reaction medium pH, substrate concentrations and presence of inhibitors, among others. In the present work the production of galactooligosaccharides (with different degrees of polymerization: two, three and four) from lactose was studied. The study considers the formulation of a mathematical model that predicts the production of GOS from lactose using the enzyme β-galactosidase. The effect of pH in the reaction was studied. For that, phosphate buffer was used and with this was evaluated three pH values (6.0.6.5 and 7.0). Thus it was observed that at pH 6.0 the enzymatic activity insignificant. On the other hand, at pH 7.0 the enzymatic activity was approximately 27 times greater than at 6.5. The last result differs from previously reported results. Therefore, pH 7.0 was chosen as working pH. Additionally, the enzyme concentration was analyzed, which allowed observing that the effect of the concentration depends on the pH and the concentration was set for the following studies in 0.272 mM. Afterwards, experiments were performed varying the lactose concentration to evaluate its effects on the process and to generate the data for the adjustment of the mathematical model parameters. The mathematical model considers the reactions of lactose hydrolysis and transgalactosylation for the production of disaccharides and trisaccharides, with their inverse reactions. The production of tetrasaccharides was negligible and, because of that, it was not included in the model. The reaction was monitored by HPLC and for the quantitative analysis of the experimental data the Matlab programming language was used, including solvers for differential equations systems integration (ode15s) and nonlinear problems optimization (fminunc). The results confirm that the transgalactosylation and hydrolysis reactions are reversible, additionally inhibition by glucose and galactose is observed on the production of GOS. In relation to the production process of galactooligosaccharides, the results show that it is necessary to have high initial concentrations of lactose considering that favors the transgalactosylation reaction, while low concentrations favor hydrolysis reactions.

Keywords: β-galactosidase, galactooligosaccharides, inhibition, lactose, Matlab, modeling

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Authors: Oscar Vega Camacho, Andrea Vargas, Ellery Ariza

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This paper presents the application of finite dynamic programming, specifically the "Markov Chain" model, as part of the decision making process of a company in the cosmetics sector located in the vicinity of Bogota DC. The objective of this process was to decide whether the company should completely reconstruct its waste water treatment plant or instead optimize the plant through the addition of equipment. The goal of both of these options was to make the required improvements in order to comply with parameters established by national legislation regarding the treatment of waste before it is released into the environment. This technique will allow the company to select the best option and implement a solution for the processing of waste to minimize environmental damage and the acquisition and implementation costs.

Keywords: decision making, markov chain, optimization, waste water

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Authors: Majid Khalili, Hamed Tayebi

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This paper considers a stochastic flexible job-shop scheduling (SFJSS) problem in the presence of production disruptions, and reactive scheduling is implemented in order to find the optimal solution under uncertainty. In this problem, there are two main disruptions including machine failure which influences operation time, and modification or cancellation of the order delivery date during production. In order to decrease the negative effects of these difficulties, two derived strategies from reactive scheduling are used; the first one is relevant to being able to allocate multiple machine to each job, and the other one is related to being able to select the best alternative process from other job while some disruptions would be created in the processes of a job. For this purpose, a Mixed Integer Linear Programming model is proposed.

Keywords: flexible job-shop scheduling, reactive scheduling, stochastic environment, mixed integer linear programming

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Authors: Melike Sultan Karasu Asnaz, Ayse Ozdogan Dolcek

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Crop drying, which aims to reduce the moisture content to a certain level, is a method used to extend the shelf life and prevent it from spoiling. One of the oldest food preservation techniques is open sunor shade drying. Even though this technique is the most affordable of all drying methods, there are some drawbacks such as contamination by insects, environmental pollution, windborne dust, and direct expose to weather conditions such as wind, rain, hail. However, solar dryers that provide a hygienic and controllable environment to preserve food and extend its shelf life have been developed and used to dry agricultural products. Thus, foods can be dried quickly without being affected by weather variables, and quality products can be obtained. This research is mainly devoted to investigating the modelling of drying kinetics of cantaloupe in a forced convection solar dryer. Mathematical models for the drying process should be defined to simulate the drying behavior of the foodstuff, which will greatly contribute to the development of solar dryer designs. Thus, drying experiments were conducted and replicated five times, and various data such as temperature, relative humidity, solar irradiation, drying air speed, and weight were instantly monitored and recorded. Moisture content of sliced and pretreated cantaloupe were converted into moisture ratio and then fitted against drying time for constructing drying curves. Then, 10 quasi-theoretical and empirical drying models were applied to find the best drying curve equation according to the Levenberg-Marquardt nonlinear optimization method. The best fitted mathematical drying model was selected according to the highest coefficient of determination (R²), and the mean square of the deviations (χ^²) and root mean square error (RMSE) criterial. The best fitted model was utilized to simulate a thin layer solar drying of cantaloupe, and the simulation results were compared with the experimental data for validation purposes.

Keywords: solar dryer, mathematical modelling, drying kinetics, cantaloupe drying

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Authors: Laurent Thiry, Michel Hassenforder

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This paper presents a general approach to implement efficient queries’ interpreters in a functional programming language. Indeed, most of the standard tools actually available use an imperative and/or object-oriented language for the implementation (e.g. Java for Jena-Fuseki) but other paradigms are possible with, maybe, better performances. To proceed, the paper first explains how to model data structures and queries in a functional point of view. Then, it proposes a general methodology to get performances (i.e. number of computation steps to answer a query) then it explains how to integrate some optimization techniques (short-cut fusion and, more important, data transformations). It then compares the functional server proposed to a standard tool (Fuseki) demonstrating that the first one can be twice to ten times faster to answer queries.

Keywords: data transformation, functional programming, information server, optimization

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Authors: Pirom Thangchitpianpol, Suttipong Jumroonrut

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This research investigates the distribution of food demand for animal food and the optimum amount of that food production at minimum cost. The data consist of customer purchase orders for the food of laying hens, price of food for laying hens, cost per unit for the food inventory, cost related to food of laying hens in which the food is out of stock, such as fine, overtime, urgent purchase for material. They were collected from January, 1990 to December, 2013 from a factory in Nakhonratchasima province. The collected data are analyzed in order to explore the distribution of the monthly food demand for the laying hens and to see the rate of inventory per unit. The results are used in a stochastic linear programming model for aggregate planning in which the optimum production or minimum cost could be obtained. Programming algorithms in MATLAB and tools in Linprog software are used to get the solution. The distribution of the food demand for laying hens and the random numbers are used in the model. The study shows that the distribution of monthly food demand for laying has a normal distribution, the monthly average amount (unit: 30 kg) of production from January to December. The minimum total cost average for 12 months is Baht 62,329,181.77. Therefore, the production planning can reduce the cost by 14.64% from real cost.

Keywords: animal food, stochastic linear programming, aggregate planning, production planning, demand uncertainty

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Authors: N. V. Kuznetsov, O. A. Kuznetsova, G. A. Leonov, M. V. Yuldashev, R. V. Yuldashev

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Nonlinear analysis of the phase locked loop (PLL)-based circuits is a challenging task. Thus, the simulation is widely used for their study. In this work, we consider a mathematical model of the optical Costas loop and demonstrate the limitations of simulation approach related to the existence of so-called hidden oscillations in the phase space of the model.

Keywords: optical Costas loop, mathematical model, simulation, hidden oscillation

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Authors: Zhenqiu Liu

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Visualizing the heterogeneity within cell-populations for single-cell RNA-seq data is crucial for studying the functional diversity of a cell. However, because of the high level of noises, outlier, and dropouts, it is very challenging to measure the cell-to-cell similarity (distance), visualize and cluster the data in a low-dimension. Minimum volume embedding (MVE) projects the data into a lower-dimensional space and is a promising tool for data visualization. However, it is computationally inefficient to solve a semi-definite programming (SDP) when the sample size is large. Therefore, it is not applicable to single-cell RNA-seq data with thousands of samples. In this paper, we develop an efficient algorithm with an accelerated proximal gradient method and visualize the single-cell RNA-seq data efficiently. We demonstrate that the proposed approach separates known subpopulations more accurately in single-cell data sets than other existing dimension reduction methods.

Keywords: single-cell RNA-seq, minimum volume embedding, visualization, accelerated proximal gradient method

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.

Keywords: Adomian’s decomposition method, magneto-thermoelasticity, finite conductivity, iteration method, thermal load

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Authors: Raziyeh Shamsi

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In this paper, we present a multiple objective linear programming (MOLP) problem in full fuzzy case and find Data Envelopment Analysis(DEA) targets. In the presented model, we are seeking the least inputs and the most outputs in the production possibility set (PPS) with the variable return to scale (VRS) assumption, so that the efficiency projection is obtained for all decision making units (DMUs). Then, we provide an algorithm for finding DEA targets interactively in the full fuzzy case, which solves the full fuzzy problem without defuzzification. Owing to the use of interactive methods, the targets obtained by our algorithm are more applicable, more realistic, and they are according to the wish of the decision maker. Finally, an application of the algorithm in 21 educational institutions is provided.

Keywords: DEA, MOLP, full fuzzy, target

Procedia PDF Downloads 282

Authors: Oscar Vega Camacho, Andrea Vargas Guevara, Ellery Rowina Ariza

Abstract:

This paper presents the application of finite dynamic programming, specifically the "Markov Chain" model, as part of the decision making process of a company in the cosmetics sector located in the vicinity of Bogota DC. The objective of this process was to decide whether the company should completely reconstruct its wastewater treatment plant or instead optimize the plant through the addition of equipment. The goal of both of these options was to make the required improvements in order to comply with parameters established by national legislation regarding the treatment of waste before it is released into the environment. This technique will allow the company to select the best option and implement a solution for the processing of waste to minimize environmental damage and the acquisition and implementation costs.

Keywords: decision making, Markov chain, optimization, wastewater

Procedia PDF Downloads 464

Authors: Tao Peng, Jing Zhao, Yanqing Xu, Jing Cai

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Due to missing/ambiguous boundaries between the prostate and neighboring structures, the presence of shadow artifacts, as well as the large variability in prostate shapes, ultrasound prostate segmentation is challenging. To handle these issues, this paper develops a hybrid method for ultrasound prostate segmentation by combining an optimized closed principal curve-based method and the evolutionary neural network; the former can fit curves with great curvature and generate a contour composed of line segments connected by sorted vertices, and the latter is used to express an appropriate map function (represented by parameters of evolutionary neural network) for generating the smooth prostate contour to match the ground truth contour. Both qualitative and quantitative experimental results showed that our proposed method obtains accurate and robust performances.

Keywords: ultrasound prostate segmentation, optimized closed polygonal segment method, evolutionary neural network, smooth mathematical model, principal curve

Procedia PDF Downloads 171

Authors: Gilbert Makanda, Roelf Sypkens

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A mathematical model for knowledge acquisition in teaching and learning is proposed. In this study we adopt the mathematical model that is normally used for disease modelling into teaching and learning. We derive mathematical conditions which facilitate knowledge acquisition. This study compares the effects of dropping out of the course at early stages with later stages of learning. The study also investigates effect of individual interaction and learning from other sources to facilitate learning. The study fits actual data to a general mathematical model using Matlab ODE45 and lsqnonlin to obtain a unique mathematical model that can be used to predict knowledge acquisition. The data used in this study was obtained from the tutorial test results for mathematics 2 students from the Central University of Technology, Free State, South Africa in the department of Mathematical and Physical Sciences. The study confirms already known results that increasing dropout rates and forgetting taught concepts reduce the population of knowledgeable students. Increasing teaching contacts and access to other learning materials facilitate knowledge acquisition. The effect of increasing dropout rates is more enhanced in the later stages of learning than earlier stages. The study opens up a new direction in further investigations in teaching and learning using differential equations.

Keywords: differential equations, knowledge acquisition, least squares nonlinear, dynamical systems

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Authors: Shunichi Ohmori, Sirawadee Arunyanart, Kazuho Yoshimoto

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We consider a periodic review inventory control problem of minimizing production cost, inventory cost, and lost-sales under demand uncertainty, in which product demands are not specified exactly and it is only known to belong to a given uncertainty set, yet the constraints must hold for possible values of the data from the uncertainty set. We propose a robust optimization formulation for obtaining lowest cost possible and guaranteeing the feasibility with respect to range of order quantity and inventory level under demand uncertainty. Our formulation is based on the adaptive robust counterpart, which suppose order quantity is affine function of past demands. We derive certainty equivalent problem via second-order cone programming, which gives 'not too pessimistic' worst-case.

Keywords: robust optimization, inventory control, supply chain managment, second-order programming

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Authors: H. C. Nguyen

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This contribution considers seismic effects on the stability of slope and footing resting on a slope. The seismic force is simply treated as static inertial force through the values of acceleration factor. All domains are assumed to be plasticity deformations approximated using node-based smoothed finite element method (NS-FEM). The failure mechanism and safety factor were then explored using numerical procedure based on upper bound approach in which optimization problem was formed as second order cone programming (SOCP). The data obtained confirm that upper bound procedure using NS-FEM and SOCP can give stable and rapid convergence results of seismic stability factors.

Keywords: upper bound analysis, safety factor, slope stability, footing resting on slope

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Authors: Ayse Ozturk

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The study extends the prior research on modeling competencies by positioning students’ cognitive and language resources as the fundamentals for pursuing their own inquiry and expression lines through mathematical modeling. This strategy aims to answer the question that guides this study, “How do students’ group approaches to modeling tasks affect their modeling competencies over a unit of instruction?” Six bilingual tenth-grade students worked on open-ended modeling problems along with the content focused on quantities over six weeks. Each group was found to have a unique cognitive approach for solving these problems. Three different problem-solving strategies affected how the groups’ modeling competencies changed. The results provide evidence that the discussion around groups’ solutions, coupled with their reflections, advances group interpreting and validating competencies in the mathematical modeling process

Keywords: cognition, collective learning, mathematical modeling competencies, problem-solving

Procedia PDF Downloads 134

Authors: Sophie Sakka, Rénald Gaboriau

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This paper describes a preliminary work aimed at setting a therapeutic support for autistic teenagers using three humanoid robots NAO shared by ASD (Autism Spectrum Disorder) subjects. The studied population had attended successfully a first year program, and were observed with a second year program using the robots. This paper focuses on the content and the effects of the second year program. The approach is based on a master puppet concept: the subjects program the robots, and use them as an extension for communication. Twenty sessions were organized, alternating ten preparatory sessions and ten robotics programming sessions. During the preparatory sessions, the subjects write a story to be played by the robots. During the robot programming sessions, the subjects program the motions to be realized to make the robot tell the story. The program was concluded by a public performance. The experiment involves five ASD teenagers aged 12-15, who had all attended the first year robotics training. As a result, a progress in voluntary and organized communication skills of the five subjects was observed, leading to improvements in social organization, focus, voluntary communication, programming, reading and writing abilities. The changes observed in the subjects general behavior took place in a short time, and could be observed from one robotics session to the next one. The approach allowed the subjects to draw the limits of their body with respect to the environment, and therefore helped them confronting the world with less anxiety.

Keywords: autism spectrum disorder, robot, therapeutic support, rob'autism

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Authors: Jong Woo Kim, Go Bong Choi, Sang Hwan Son, Dae Shik Kim, Jung Chul Suh, Jong Min Lee

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The Markov Decision Process (MDP) based methodology is implemented in order to establish the optimal schedule which minimizes the cost. Formulation of MDP problem is presented using the information about the current state of pipe, improvement cost, failure cost and pipe deterioration model. The objective function and detailed algorithm of dynamic programming (DP) are modified due to the difficulty of implementing the conventional DP approaches. The optimal schedule derived from suggested model is compared to several policies via Monte Carlo simulation. Validity of the solution and improvement in computational time are proved.

Keywords: Markov decision processes, dynamic programming, Monte Carlo simulation, periodic replacement, Weibull distribution

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Authors: S. Shahzadi, J. Rizk

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This paper describes the pulse width modulated control of a three phase, 4 polar DC brushless motor. To implement this practically the Atmel’s AVR ATmega 328 microcontroller embedded on an Arduino Eleven board is utilized. The microcontroller programming is done in an open source Arduino IDE development environment. The programming logic effectively manipulated a six MOSFET bridge which was used to energize the stator windings as per control requirements. The results obtained showed accurate, precise and efficient pulse width modulated operation. Another advantage offered by this pulse width modulated control was the efficient speed control of the motor. By varying the time intervals between successive commutations, faster energizing of the stator windings was possible thereby leading to quicker rotor alignment with these energized phases and faster revolutions.

Keywords: brushless DC motors, commutation, MOSFET, PWM

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Authors: Mostafa Sefidgar, Sohrab Zendehboudi, Hossein Bazmara, Madjid Soltani

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Based on findings from clinical applications, most drug treatments fail to eliminate malignant tumors completely even though drug delivery through systemic administration may inhibit their growth. Therefore, better understanding of tumor formation is crucial in developing more effective therapeutics. For this purpose, nowadays, solid tumor modeling and simulation results are used to predict how therapeutic drugs are transported to tumor cells by blood flow through capillaries and tissues. A solid tumor is investigated as a porous media for fluid flow simulation. Most of the studies use Darcy model for porous media. In Darcy model, the fluid friction is neglected and a few simplified assumptions are implemented. In this study, the effect of these assumptions is studied by considering Brinkman model. A multi scale mathematical method which calculates fluid flow to a solid tumor is used in this study to investigate how neglecting fluid friction affects the solid tumor simulation. In this work, the mathematical model in our previous studies is developed by considering two model of momentum equation for porous media: Darcy and Brinkman. The mathematical method involves processes such as fluid flow through solid tumor as porous media, extravasation of blood flow from vessels, blood flow through vessels and solute diffusion, convective transport in extracellular matrix. The sprouting angiogenesis model is used for generating capillary network and then fluid flow governing equations are implemented to calculate blood flow through the tumor-induced capillary network. Finally, the two models of porous media are used for modeling fluid flow in normal and tumor tissues in three different shapes of tumors. Simulations of interstitial fluid transport in a solid tumor demonstrate that the simplifications used in Darcy model affect the interstitial velocity and Brinkman model predicts a lower value for interstitial velocity than the values that Darcy model does.

Keywords: solid tumor, porous media, Darcy model, Brinkman model, drug delivery

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Authors: Badr Alkahtani

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In this poster, numerical solutions of two-dimensional and three-dimensional lid driven cavity are presented by solving the steady Navier-Stokes equations at high Reynolds numbers where it becomes difficult. Lid driven cavity is where the a fluid contained in a cube and the upper wall is moving. In two dimensions, we use the streamfunction-vorticity formulation to solve the problem in a square domain. A numerical method is employed to discretize the problem in the x and y directions with a spectral collocation method. The problem is coded in the MATLAB programming environment. Solutions at high Reynolds numbers are obtained up to Re=20000 on a fine grid of 131 * 131. Also in this presentation, the numerical solutions for the three-dimensional lid-driven cavity problem are obtained by solving the velocity-vorticity formulation of the Navier-Stokes equations (which is the first time that this has been simulated with special boundary conditions) for various Reynolds numbers. A spectral collocation method is employed to discretize the y and z directions and a finite difference method is used to discretize the x direction. Numerical solutions are obtained for Reynolds number up to 200. , The work prepared here is to show the efficiency of methods used to simulate the physical problem where accurate simulations of lid driven cavity are obtained at high Reynolds number as mentioned above. The result for the two dimensional problem is far from the previous researcher result.

Keywords: lid driven cavity, navier-stokes, simulation, Reynolds number

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Authors: Mohammad Sabbagh

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Anyone who reads the Torah or the Quran learns that GOD created everything that is around us, seen and unseen, in six days. Within HIS plan of creation, HE placed for us a key proof of HIS existence which is essentially computers and the ability to program them. Digital computer programming began with binary instructions, which eventually evolved to what is known as high-level programming languages. Any programmer in our modern time can attest that you are essentially giving the computer commands by words and when the program is compiled, whatever is processed as output is limited to what the computer was given as an ability and furthermore as an instruction. So one can deduce that GOD created everything around us with HIS words, programming everything around in six days, just like how we can program a virtual world on the computer. GOD did mention in the Quran that one day where GOD’s throne is, is 1000 years of what we count; therefore, one might understand that GOD spoke non-stop for 6000 years of what we count, and gave everything it’s the function, attributes, class, methods and interactions. Similar to what we do in object-oriented programming. Of course, GOD has the higher example, and what HE created is much more than OOP. So when GOD said that everything is already predetermined, it is because any input, whether physical, spiritual or by thought, is outputted by any of HIS creatures, the answer has already been programmed. Any path, any thought, any idea has already been laid out with a reaction to any decision an inputter makes. Exalted is GOD!. GOD refers to HIMSELF as The Fastest Accountant in The Quran; the Arabic word that was used is close to processor or calculator. If you create a 3D simulation of a supernova explosion to understand how GOD produces certain elements and fuses protons together to spread more of HIS blessings around HIS skies; in 2022 you are going to require one of the strongest, fastest, most capable supercomputers of the world that has a theoretical speed of 50 petaFLOPS to accomplish that. In other words, the ability to perform one quadrillion (1015) floating-point operations per second. A number a human cannot even fathom. To put in more of a perspective, GOD is calculating when the computer is going through those 50 petaFLOPS calculations per second and HE is also calculating all the physics of every atom and what is smaller than that in all the actual explosion, and it’s all in truth. When GOD said HE created the world in truth, one of the meanings a person can understand is that when certain things occur around you, whether how a car crashes or how a tree grows; there is a science and a way to understand it, and whatever programming or science you deduce from whatever event you observed, it can relate to other similar events. That is why GOD might have said in The Quran that it is the people of knowledge, scholars, or scientist that fears GOD the most! One thing that is essential for us to keep up with what the computer is doing and for us to track our progress along with any errors is we incorporate logging mechanisms and backups. GOD in The Quran said that ‘WE used to copy what you used to do’. Essentially as the world is running, think of it as an interactive movie that is being played out in front of you, in a full-immersive non-virtual reality setting. GOD is recording it, from every angle to every thought, to every action. This brings the idea of how scary the Day of Judgment will be when one might realize that it’s going to be a fully immersive video when we would be getting and reading our book.

Keywords: programming, the Quran, object orientation, computers and humans, GOD

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Authors: Peña A. Roland R., Lozano P. Jean P.

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The waterflooding process is an enhanced oil recovery (EOR) method that appears tremendously successful. This paper shows the importance of the role of the numerical modelling of waterflooding and how to provide a better description of the fluid flow during this process. The mathematical model is based on the mass conservation equations for the oil and water phases. Rock compressibility and capillary pressure equations are coupled to the mathematical model. For discretizing and linearizing the partial differential equations, we used the Finite Volume technique and the Newton-Raphson method, respectively. The results of three scenarios for waterflooding in porous media are shown. The first scenario was estimating the water saturation in the media without rock compressibility and without capillary pressure. The second scenario was estimating the front of the water considering the rock compressibility and capillary pressure. The third case is to compare different fronts of water saturation for three fluids viscosity ratios without and with rock compressibility and without and with capillary pressure. Results of the simulation indicate that the rock compressibility and the capillary pressure produce changes in the pressure profile and saturation profile during the displacement of the oil for the water.

Keywords: capillary pressure, numerical simulation, rock compressibility, two-phase flow

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Authors: Geetika Barman, B. S. Daya Sagar

Abstract:

In this article, we proposed a pixel-wise classification of hyperspectral images using a mathematical morphology operator-based distance metric called “dilation distance” and “erosion distance”. This method involves measuring the spatial distance between the spectral features of a hyperspectral image across the bands. The key concept of the proposed approach is that the “dilation distance” is the maximum distance a pixel can be moved without changing its classification, whereas the “erosion distance” is the maximum distance that a pixel can be moved before changing its classification. The spectral signature of the hyperspectral image carries unique class information and shape for each class. This article demonstrates how easily the dilation and erosion distance can measure spatial distance compared to other approaches. This property is used to calculate the spatial distance between hyperspectral image feature vectors across the bands. The dissimilarity matrix is then constructed using both measures extracted from the feature spaces. The measured distance metric is used to distinguish between the spectral features of various classes and precisely distinguish between each class. This is illustrated using both toy data and real datasets. Furthermore, we investigated the role of flat vs. non-flat structuring elements in capturing the spatial features of each class in the hyperspectral image. In order to validate, we compared the proposed approach to other existing methods and demonstrated empirically that mathematical operator-based distance metric classification provided competitive results and outperformed some of them.

Keywords: dilation distance, erosion distance, hyperspectral image classification, mathematical morphology

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