Search results for: mathematical%20concepts

Authors: Vildan Kistik, Tuncay Can

Abstract:

From a business perspective, cost and profit are two key factors for businesses. The intent of most businesses is to minimize the cost to maximize or equalize the profit, so as to provide the greatest benefit to itself. However, the physical system is very complicated because of technological constructions, rapid increase of competitive environments and similar factors. In such a system it is not easy to maximize profits or to minimize costs. Businesses must decide on the competence and competence of the personnel to be recruited, taking into consideration many criteria in selecting personnel. There are many criteria to determine the competence and competence of a staff member. Factors such as the level of education, experience, psychological and sociological position, and human relationships that exist in the field are just some of the important factors in selecting a staff for a firm. Personnel selection is a very important and costly process in terms of businesses in today's competitive market. Although there are many mathematical methods developed for the selection of personnel, unfortunately the use of these mathematical methods is rarely encountered in real life. In this study, unlike other methods, an exponential programming model was established based on the possibilities of failing in case the selected personnel was started to work. With the necessary transformations, the problem has been transformed into unconstrained Geometrical Programming problem and personnel selection problem is approached with geometric programming technique. Personnel selection scenarios for a classroom were established with the help of normal distribution and optimum solutions were obtained. In the most appropriate solutions, the personnel selection process for the classroom has been achieved with minimum cost.

Keywords: geometric programming, personnel selection, non-linear programming, operations research

Procedia PDF Downloads 251

Authors: Meitham Amereh, Mohsen Akbari, Ben Nadler

Abstract:

Cancer has been recognized as one of the most challenging problems in biology and medicine. Aggressive tumors are a lethal type of cancers characterized by high genomic instability, rapid progression, invasiveness, and therapeutic resistance. Their behavior involves complicated molecular biology and consequential dynamics. Although tremendous effort has been devoted to developing therapeutic approaches, there is still a huge need for new insights into the dark aspects of tumors. As one of the key requirements in better understanding the complex behavior of tumors, mathematical modeling and continuum physics, in particular, play a pivotal role. Mathematical modeling can provide a quantitative prediction on biological processes and help interpret complicated physiological interactions in tumors microenvironment. The pathophysiology of aggressive tumors is strongly affected by the extracellular cues such as stresses produced by mechanical forces between the tumor and the host tissue. During the tumor progression, the growing mass displaces the surrounding extracellular matrix (ECM), and due to the level of tissue stiffness, stress accumulates inside the tumor. The produced stress can influence the tumor by breaking adherent junctions. During this process, the tumor stops the rapid proliferation and begins to remodel its shape to preserve the homeostatic equilibrium state. To reach this, the tumor, in turn, upregulates epithelial to mesenchymal transit-inducing transcription factors (EMT-TFs). These EMT-TFs are involved in various signaling cascades, which are often associated with tumor invasiveness and malignancy. In this work, we modeled the tumor as a growing hyperplastic mass and investigated the effects of mechanical stress from surrounding ECM on tumor invasion. The invasion is modeled as volume-preserving inelastic evolution. In this framework, principal balance laws are considered for tumor mass, linear momentum, and diffusion of nutrients. Also, mechanical interactions between the tumor and ECM is modeled using Ciarlet constitutive strain energy function, and dissipation inequality is utilized to model the volumetric growth rate. System parameters, such as rate of nutrient uptake and cell proliferation, are obtained experimentally. To validate the model, human Glioblastoma multiforme (hGBM) tumor spheroids were incorporated inside Matrigel/Alginate composite hydrogel and was injected into a microfluidic chip to mimic the tumor’s natural microenvironment. The invasion structure was analyzed by imaging the spheroid over time. Also, the expression of transcriptional factors involved in invasion was measured by immune-staining the tumor. The volumetric growth, stress distribution, and inelastic evolution of tumors were predicted by the model. Results showed that the level of invasion is in direct correlation with the level of predicted stress within the tumor. Moreover, the invasion length measured by fluorescent imaging was shown to be related to the inelastic evolution of tumors obtained by the model.

Keywords: cancer, invasion, mathematical modeling, microfluidic chip, tumor spheroids

Procedia PDF Downloads 91

Authors: J. Thiele

Abstract:

Teachers working at vocational Colleges are often confronted with the problem, that many students graduated from different schools and therefore each had a different education. Especially in mathematics many students lack fundamentals or had different priorities at their previous schools. Furthermore, these vocational Colleges have to provide Graduations for many different working-fields, with different core themes. The Colleges are interested in measuring the different Education levels of their students and providing assistance for those who need to catch up. The Project mathe-meistern was initiated to remedy this problem at vocational Colleges. For this purpose, online-tests were developed. The aim of these tests is to evaluate basic mathematical abilities of the students. The tests are online Multiple-Choice-Tests with a total of 65 Items. They are accessed online with a unique Transaction-Number (TAN) for each participant. The content is divided in several Categories (Arithmetic, Algebra, Fractions, Geometry, etc.). After each test, the student gets a personalized summary depicting their strengths and weaknesses in mathematical Basics. Teachers can visit a special website to examine the results of their classes or single students. In total 5830 students did participate so far. For standardization and optimization purposes the tests are being evaluated, using the classic and probabilistic Test-Theory regarding Objectivity, Reliability and Validity, annually since 2015. This Paper is about the Optimization process considering the Rasch-scaling and Standardization of the tests. Additionally, current results using standardized tests will be discussed. To achieve this Competence levels and Types of errors of students attending vocational Colleges in Nordrheinwestfalen, Germany, were determined, using descriptive Data and Distractorevaluations.

Keywords: diagnostical tests in mathematics, distractor devaluation, test-optimization, test-theory

Procedia PDF Downloads 104

Authors: Gabriel Malgaresi, Sara Borazjani, Hadi Madani, Pavel Bedrikovetsky

Abstract:

Suspension-Colloidal flow in porous media occurs in numerous engineering fields, such as industrial water treatment, the disposal of industrial wastes into aquifers with the propagation of contaminants and low salinity water injection into petroleum reservoirs. The main effects are particle mobilization and captured by the porous rock, which can cause pore plugging and permeability reduction which is known as formation damage. Various factors such as fluid salinity, pH, temperature, and rock properties affect particle detachment. Formation damage is unfavorable specifically near injection and production wells. One way to control formation damage is pre-treatment of the rock with nanoparticles. Adsorption of nanoparticles on fines and rock surfaces alters zeta-potential of the surfaces and enhances the attachment force between the rock and fine particles. The main objective of this study is to develop a two-stage mathematical model for (1) flow and adsorption of nanoparticles on the rock in the pre-treatment stage and (2) fines migration and permeability reduction during the water production after the pre-treatment. The model accounts for adsorption and desorption of nanoparticles, fines migration, and kinetics of particle capture. The system of equations allows for the exact solution. The non-self-similar wave-interaction problem was solved by the Method of Characteristics. The analytical model is new in two ways: First, it accounts for the specific boundary and initial condition describing the injection of nanoparticle and production from the pre-treated porous media; second, it contains the effect of nanoparticle sorption hysteresis. The derived analytical model contains explicit formulae for the concentration fronts along with pressure drop. The solution is used to determine the optimal injection concentration of nanoparticle to avoid formation damage. The mathematical model was validated via an innovative laboratory program. The laboratory study includes two sets of core-flood experiments: (1) production of water without nanoparticle pre-treatment; (2) pre-treatment of a similar core with nanoparticles followed by water production. Positively-charged Alumina nanoparticles with the average particle size of 100 nm were used for the rock pre-treatment. The core was saturated with the nanoparticles and then flushed with low salinity water; pressure drop across the core and the outlet fine concentration was monitored and used for model validation. The results of the analytical modeling showed a significant reduction in the fine outlet concentration and formation damage. This observation was in great agreement with the results of core-flood data. The exact solution accurately describes fines particle breakthroughs and evaluates the positive effect of nanoparticles in formation damage. We show that the adsorbed concentration of nanoparticle highly affects the permeability of the porous media. For the laboratory case presented, the reduction of permeability after 1 PVI production in the pre-treated scenario is 50% lower than the reference case. The main outcome of this study is to provide a validated mathematical model to evaluate the effect of nanoparticles on formation damage.

Keywords: nano-particles, formation damage, permeability, fines migration

Procedia PDF Downloads 592

Authors: José María Agugusto-landa, Inmaculada García-Martínez, Lara Checa Domene, Óscar Gavín Chocano

Abstract:

Self-concept is the perception that a person has of himself, of his abilities, skills, traits, and values. Self-concept is composed of different dimensions, such as academic self-concept, physical self-concept, social self-concept, emotional self-concept, and family self-concept. The relationship between the dimensions of self-concept and mental health and academic performance among future teachers is a topic of interest for educational psychology. Some studies have found that: (i) There is a positive relationship between general self-concept, academic self-concept and academic performance, that is, students who have a more positive image of themselves tend to get better grades and be more motivated to learn. (ii) There is a positive relationship between emotional intelligence, physical self-concept and healthy habits, that is, students who regulate and understand their emotions better have a higher satisfaction with their physical appearance and follow a more balanced diet and a higher physical activity. As for gender differences in the dimensions of self-concept among future teachers, some studies have found that: (i) Girls tend to have a higher self-concept in the social, family and verbal dimensions, that is, they perceive themselves as more capable of relating to others, communicating effectively and receiving support from their family. (ii) Boys tend to have a higher self-concept in the physical, emotional and mathematical dimensions, that is, they perceive themselves as more capable of performing physical activities, controlling their emotions and solving mathematical problems. (iii) There are no significant differences between general self-concept and academic self-concept according to gender, that is, both girls and boys have a similar perception of their global worth and academic competence.

Keywords: preservice teachers, self-concept, academic performance, mental wellbeing

Procedia PDF Downloads 59

Authors: Wilma Coetzee

Abstract:

Statistics lecturers experience that many students who are taking a service course in statistics do not like statistics. Students in these courses tend to struggle and do not perform well. This research takes a look at the student’s perspective, with the aim to determine how to change the teaching of statistics so that students will enjoy it more and perform better. Questionnaires were used to determine the perspectives of first year service statistics students at a South African university. Factors addressed included motivation to study, attitude toward statistics, statistical anxiety, mathematical abilities and tendency to procrastinate. Logistic regression was used to determine what contributes to students performing badly in statistics. The results show that the factors that contribute the most to students performing badly are: statistical anxiety, not being motivated and having had mathematical literacy instead of mathematics in secondary school. Two open ended questions were included in the questionnaire: 'I will enjoy statistics more if…' and 'I will perform better in statistics if…'. The answers to these questions were analyzed using qualitative methods. Frequent themes were identified for each of the questions. A simulation study incorporating bootstrapping was done to determine the saturation of the themes. The majority of the students indicated that they would perform better in statistics if they studied more, managed their time better, had a flare for mathematics and if the lecturer was able to explain difficult concepts better. They also want more active learning. To ensure that students enjoy statistics more, they want an active learning experience. They want fun activities, more interaction with the lecturer and with one another, more computer based problems, and more challenges. They want a better understanding of the subject, want to understand the relevance of statistics to their future career and want excellent lecturers. These findings can be used to direct the improvement of the tuition of statistics.

Keywords: active learning, performance in statistics, statistical anxiety, statistics education

Procedia PDF Downloads 131

Authors: Yulii D. Shikhmurzaev

Abstract:

The modelling of the non-isothermal free-surface flows coupled with the solidification process has become the topic of intensive research with the advent of additive manufacturing, where complex 3-dimensional structures are produced by successive deposition and solidification of microscopic droplets of different materials. The issue is that both the spreading of liquids over solids and the propagation of the solidification front into the fluid and along the solid substrate pose fundamental difficulties for their mathematical modelling. The first of these processes, known as ‘dynamic wetting’, leads to the well-known ‘moving contact-line problem’ where, as shown recently both experimentally and theoretically, the contact angle formed by the free surfac with the solid substrate is not a function of the contact-line speed but is rather a functional of the flow field. The modelling of the propagating solidification front requires generalization of the classical Stefan problem, which would be able to describe the onset of the process and the non-equilibrium regime of solidification. Furthermore, given that both dynamic wetting and solification occur concurrently and interactively, they should be described within the same conceptual framework. The present work addresses this formidable problem and presents a mathematical model capable of describing the key element of additive manufacturing in a self-consistent and singularity-free way. The model is illustrated simple examples highlighting its main features. The main idea of the work is that both dynamic wetting and solidification, as well as some other fluid flows, are particular cases in a general class of flows where interfaces form and/or disappear. This conceptual framework allows one to derive a mathematical model from first principles using the methods of irreversible thermodynamics. Crucially, the interfaces are not considered as zero-mass entities introduced using Gibbsian ‘dividing surface’ but the 2-dimensional surface phases produced by the continuum limit in which the thickness of what physically is an interfacial layer vanishes, and its properties are characterized by ‘surface’ parameters (surface tension, surface density, etc). This approach allows for the mass exchange between the surface and bulk phases, which is the essence of the interface formation. As shown numerically, the onset of solidification is preceded by the pure interface formation stage, whilst the Stefan regime is the final stage where the temperature at the solidification front asymptotically approaches the solidification temperature. The developed model can also be applied to the flow with the substrate melting as well as a complex flow where both types of phase transition take place.

Keywords: dynamic wetting, interface formation, phase transition, solidification

Procedia PDF Downloads 44

Authors: Amin Moradi, Maryam Moeini

Abstract:

It is a widely held view that Ghiyath al-Din Jamshid-e-Kashani, also known as al-Kashi (1380-1429 CE), was the first who played a significant role in the interaction between mathematicians and architects by introducing theoretical knowledge in Islamic architecture. In academic discourses, geometric rules extracted from his splendid volume titled as Key of Arithmetic has uncritically believed by historians of architecture to contemplate the whole process of arch design all throughout the Islamic buildings. His theories tried to solve the fundamental problem of structural design and to understand what makes an Islamic structure safe or unsafe. As a result, al-Kashi arrived at the conclusion that a safe state of equilibrium is achieved through a specific geometry as a rule. This paper reassesses the stability of al-Kashi's systematized principal forms to evaluate the logic of his hypothesis with a special focus on large spans. Besides the empirical experiences of the author in masonry constructions, the finite element approach was proposed considering the current standards in order to get a better understanding of the validity of geometric rules proposed by al-Kashi for the equilibrium conditions of Islamic masonry arches and vaults. The state of damage of his reference arches under loading condition confirms beyond any doubt that his conclusion of the geometrical configuration measured through his treaties present some serious operational limits and do not go further than some individualized mathematical hypothesis. Therefore, the nature of his mathematical studies regarding Islamic arches is in complete contradiction with the practical knowledge of construction methodology.

Keywords: Jamshid al-Kashani, Islamic architecture, Islamic geometry, construction equilibrium, collapse mechanism

Procedia PDF Downloads 103

Authors: Ana Gabriela Diaz, Luis Fermín Córdova, Jr., Roberto Lamazares

Abstract:

The island of Cuba, the largest of the Greater Antilles, is located in the tropical North Atlantic. It is annually affected by numerous weather events, which have caused severe damage to our coastal areas. In the same way that many other coastlines around the world, the beautiful beaches of the Hicacos Peninsula also suffer from erosion. This leads to a structural regression of the coastline. If measures are not taken, the hotels will be exposed to the advance of the sea, and it will be a serious problem for the economy. With the aim of studying the intensity of this type of activity, specialists of group of coastal and marine engineering from CIH, in the framework of the research conducted within the project MEGACOSTAS 2, provide their research to simulate extreme events and assess their impact in coastal areas, mainly regarding the definition of flood volumes and morphodynamic changes in sandy beaches. The main objective of this work is the evaluation of the process of Varadero beach erosion (the coastal sector has an important impact in the country's economy) on the Hicacos Peninsula for different paths of hurricanes. The mathematical model XBeach, which was integrated into the Coastal engineering system introduced by the project of MEGACOSTA 2 to determine the area and the more critical profiles for the path of hurricanes under study, was applied. The results of this project have shown that Center area is the greatest dynamic area in the simulation of the three paths of hurricanes under study, showing high erosion volumes and the greatest average length of regression of the coastline, from 15- 22 m.

Keywords: beach, erosion, mathematical model, coastal areas

Procedia PDF Downloads 204

Authors: Richard L. Summers

Abstract:

The advanced computational analysis of biological systems is becoming increasingly dependent upon an understanding of the information-theoretic structure of the materials, energy and interactive processes that comprise those systems. The stability and survival of these living systems are fundamentally contingent upon their ability to acquire and process the meaning of information concerning the physical state of its biological continuum (biocontinuum). The drive for adaptive system reconciliation of a divergence from steady-state within this biocontinuum can be described by an information metric-based formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of Kullback-Leibler information minimization driven by survival replicator dynamics. If the mathematical expression of this process is the Lagrangian integrand for any change within the biocontinuum then it can also be considered as an action functional for the living system. In the direct method of Lyapunov, such a summarizing mathematical formulation of global system behavior based on the driving forces of energy currents and constraints within the system can serve as a platform for the analysis of stability. As the system evolves in time in response to biocontinuum perturbations, the summarizing function then conveys information about its overall stability. This stability information portends survival and therefore has absolute existential meaning for the living system. The first derivative of the Lyapunov energy information function will have a negative trajectory toward a system's steady state if the driving force is dissipating. By contrast, system instability leading to system dissolution will have a positive trajectory. The direction and magnitude of the vector for the trajectory then serves as a quantifiable signature of the meaning associated with the living system’s stability information, homeostasis and survival potential.

Keywords: meaning, information, Lyapunov, living systems

Procedia PDF Downloads 114

Authors: Belgherbi Aicha, Hadjidj Ismahen, Bessaid Abdelhafid

Abstract:

The interpretation of medical images benefits from anatomical and physiological priors to optimize computer- aided diagnosis applications. Segmentation of liver and liver lesion is regarded as a major primary step in computer aided diagnosis of liver diseases. Precise liver segmentation in abdominal CT images is one of the most important steps for the computer-aided diagnosis of liver pathology. In this papers, a semi- automated method for medical image data is presented for the liver and liver lesion segmentation data using mathematical morphology. Our algorithm is currency in two parts. In the first, we seek to determine the region of interest by applying the morphological filters to extract the liver. The second step consists to detect the liver lesion. In this task; we proposed a new method developed for the semi-automatic segmentation of the liver and hepatic lesions. Our proposed method is based on the anatomical information and mathematical morphology tools used in the image processing field. At first, we try to improve the quality of the original image and image gradient by applying the spatial filter followed by the morphological filters. The second step consists to calculate the internal and external markers of the liver and hepatic lesions. Thereafter we proceed to the liver and hepatic lesions segmentation by the watershed transform controlled by markers. The validation of the developed algorithm is done using several images. Obtained results show the good performances of our proposed algorithm

Keywords: anisotropic diffusion filter, CT images, hepatic lesion segmentation, Liver segmentation, morphological filter, the watershed algorithm

Procedia PDF Downloads 426

Authors: Farhad Salek, Shahaboddin Resalati

Abstract:

The production of electric vehicles (EVs) featuring lithium-ion battery technology has substantially escalated over the past decade, demonstrating a steady and persistent upward trajectory. The imminent retirement of electric vehicle (EV) batteries after approximately eight years underscores the critical need for their redirection towards recycling, a task complicated by the current inadequacy of recycling infrastructures globally. A potential solution for such concerns involves extending the operational lifespan of electric vehicle (EV) batteries through their utilization in stationary energy storage systems during secondary applications. Such adoptions, however, require addressing the safety concerns associated with batteries’ knee points and thermal runaways. This paper develops an accurate mathematical model representative of the second-life battery packs from a cell-to-pack scale using an equivalent circuit model (ECM) methodology. Neural network algorithms are employed to forecast the degradation parameters based on the EV batteries' aging history to develop a degradation model. The degradation model is integrated with the ECM to reflect the impacts of the cycle aging mechanism on battery parameters during operation. The developed model is tested under real-life load profiles to evaluate the life span of the batteries in various operating conditions. The methodology and the algorithms introduced in this paper can be considered the basis for Battery Management System (BMS) design and techno-economic analysis of such technologies.

Keywords: second life battery, electric vehicles, degradation, neural network

Procedia PDF Downloads 31

Authors: Justin Fu, Thomas Mazzuchi, Shahram Sarkani

Abstract:

A key factor in technological immaturity in defense weapons acquisition is lack of understanding critical integrations at the subsystem and component level. To address this shortfall, recent research in integration readiness level (IRL) combines with technology readiness level (TRL) to form a system readiness level (SRL). SRL can be enriched with more robust quantitative methods to provide the program manager a useful tool prior to committing to major weapons acquisition programs. This research harnesses previous mathematical models based on graph theory, Petri nets, and tropical algebra and proposes a modification of the desirable SRL mathematical properties such that a tightly integrated (multitude of interfaces) subsystem can display a lower SRL than an inherently less coupled subsystem. The synthesis of these methods informs an improved decision tool for the program manager to commit to expensive technology development. This research ties the separately developed manufacturing readiness level (MRL) into the network representation of the system and addresses shortfalls in previous frameworks, including the lack of integration weighting and the over-importance of a single extremely immature component. Tropical algebra (based on the minimum of a set of TRLs or IRLs) allows one low IRL or TRL value to diminish the SRL of the entire system, which may not be reflective of actuality if that component is not critical or tightly coupled. Integration connections can be weighted according to importance and readiness levels are modified to be a cardinal scale (based on an analytic hierarchy process). Integration arcs’ importance are dependent on the connected nodes and the additional integrations arcs connected to those nodes. Lack of integration is not represented by zero, but by a perfect integration maturity value. Naturally, the importance (or weight) of such an arc would be zero. To further explore the impact of grouping subsystems, a multi-objective genetic algorithm is then used to find various clusters or communities that can be optimized for the most representative subsystem SRL. This novel calculation is then benchmarked through simulation and using past defense acquisition program data, focusing on the newly introduced Middle Tier of Acquisition (rapidly field prototypes). The model remains a relatively simple, accessible tool, but at higher fidelity and validated with past data for the program manager to decide major defense acquisition program milestones.

Keywords: readiness, maturity, system, integration

Procedia PDF Downloads 62

Authors: A. O. Glazkov, A. S. Krylova, G. G. Nadareishvili, A. S. Terenchenko, S. I. Yudin

Abstract:

The topic of the presented materials concerns the design of the exhaust system for a certain internal combustion engine. The exhaust system can be divided into two parts. The first is the engine exhaust manifold, turbocharger, and catalytic converters, which are called “hot part.” The second part is the gas exhaust system, which contains elements exclusively for reducing exhaust noise (mufflers, resonators), the accepted designation of which is the "cold part." The design of the exhaust system from the point of view of acoustics, that is, reducing the exhaust noise to a predetermined level, consists of working on the second part. Modern computer technology and software make it possible to design "cold part" with high accuracy in a given frequency range but with the condition of accurately specifying the input parameters, namely, the amplitude spectrum of the input noise and the acoustic impedance of the noise source in the form of an engine with a "hot part". Getting this data is a difficult problem: high temperatures, high exhaust gas velocities (turbulent flows), and high sound pressure levels (non-linearity mode) do not allow the calculated results to be applied with sufficient accuracy. The aim of this work is to obtain the most reliable acoustic output parameters of an engine with a "hot part" based on a complex of computational and experimental studies. The presented methodology includes several parts. The first part is a finite element simulation of the "cold part" of the exhaust system (taking into account the acoustic impedance of radiation of outlet pipe into open space) with the result in the form of the input impedance of "cold part". The second part is a finite element simulation of the "hot part" of the exhaust system (taking into account acoustic characteristics of catalytic units and geometry of turbocharger) with the result in the form of the input impedance of the "hot part". The next third part of the technique consists of the mathematical processing of the results according to the proposed formula for the convergence of the mathematical series of summation of multiple reflections of the acoustic signal "cold part" - "hot part". This is followed by conducting a set of tests on an engine stand with two high-temperature pressure sensors measuring pulsations in the nozzle between "hot part" and "cold part" of the exhaust system and subsequent processing of test results according to a well-known technique in order to separate the "incident" and "reflected" waves. The final stage consists of the mathematical processing of all calculated and experimental data to obtain a result in the form of a spectrum of the amplitude of the engine noise and its acoustic impedance.

Keywords: acoustic impedance, engine exhaust system, FEM model, test stand

Procedia PDF Downloads 29

Authors: Oibar Martinez, Clara Oliver, Jose Miguel Miranda

Abstract:

The study of dispersion phenomena in electromagnetic waves reflected by conductors at infrared and lower frequencies is a topic which finds a number of applications. We aim to explain in this work what are the most relevant ones and how this phenomenon is modeled from both optics and electromagnetics points of view. We also explain here how the amplitude of an electromagnetic wave reflected by a lossy conductor could depend on both the frequency of the incident wave, as well as on the electrical properties of the conductor, and we illustrate this phenomenon with a practical example. The mathematical analysis made by a specialist in electromagnetics or a microwave engineer is apparently very different from the one made by a specialist in optics. We show here how both approaches lead to the same physical result and what are the key concepts which enable one to understand that despite the differences in the equations the solution to the problem happens to be the same. Our study starts with an analysis made by using the complex refractive index and the reflectance parameter. We show how this reflectance has a dependence with the square root of the frequency when the reflecting material is a good conductor, and the frequency of the wave is low enough. Then we analyze the same problem with a less known approach, which is based on the reflection coefficient of the electric field, a parameter that is most commonly used in electromagnetics and microwave engineering. In summary, this paper presents a mathematical study illustrated with a worked example which unifies the modeling of dispersion effects made by specialists in optics and the one made by specialists in electromagnetics. The main finding of this work is that it is possible to reproduce the dependence of the Fresnel reflectance with frequency from the intrinsic impedance of the reflecting media.

Keywords: dispersion, electromagnetic waves, microwaves, optics

Procedia PDF Downloads 103

Authors: Gintarė Sauliutė, Gintaras Svecevičius

Abstract:

Landfill leachates contain a number of persistent pollutants, including heavy metals. They have the ability to spread in ecosystems and accumulate in fish which most of them are classified as top-consumers of trophic chains. Fish are freely swimming organisms; but perhaps, due to their species-specific ecological and behavioral properties, they often prefer the most suitable biotopes and therefore, did not avoid harmful substances or environments. That is why it is necessary to evaluate the persistent pollutant dispersion in hydroecosystem using fish tissue metal concentration. In hydroecosystems of hybrid type (e.g. river-pond-river) the distance from the pollution source could be a perfect indicator of such a kind of metal distribution. The studies were carried out in the Kairiai landfill neighboring hybrid-type ecosystem which is located 5 km east of the Šiauliai City. Fish tissue (gills, liver, and muscle) metal concentration measurements were performed on two types of ecologically-different fishes according to their feeding characteristics: benthophagous (Gibel carp, roach) and predatory (Northern pike, perch). A number of mathematical models (linear, non-linear, using log and other transformations) have been applied in order to identify the most satisfactorily description of the interdependence between fish tissue metal concentration and the distance from the pollution source. However, the only one log-multiple regression model revealed the pattern that the distance from the pollution source is closely and positively correlated with metal concentration in all predatory fish tissues studied (gills, liver, and muscle).

Keywords: bioaccumulation in fish, heavy metals, hydroecosystem, landfill leachate, mathematical model

Procedia PDF Downloads 265

Authors: Charlene N. T. Mfangnia, Henri Tonnang, Berge Tsanou, Jeremy Herren

Abstract:

The Microsporidia MB found in the populations of anopheles is a recently discovered symbiont responsible for the Plasmodium transmission blocking. From early studies, it was established that the symbiont can be transmitted vertically and horizontally. The present study uses compartmental mathematical modelling approach to investigate the dynamics of Microsporidia transmission in the mosquito population with the mindset of establishing a mechanism for use to control malaria. Data and information obtained from laboratory experiments are used to estimate the model parameters with and without temperature dependency of mosquito traits. We carry out the mathematical analysis focusing on the equilibria states and their stability for the autonomous model. Through the modelling experiments, we are able to assess and confirm the contribution of vertical and horizontal transmission in the proliferation of Microsporidia MB in the mosquito population. In addition, the basic and target reproductions are computed, and some long-term behaviours of the model, such as the local (and global) stability of equilibrium points, are rigorously analysed and illustrated numerically. We establish the conditions responsible for the low prevalence of the symbiont-infected mosquitoes observed in nature. Moreover, we identify the male death rate, the mating rate and the attractiveness of MB-positive mosquitoes as mosquito traits that significantly influence the spread of Microsporidia MB. Furthermore, we highlight the influence of temperature in the establishment and persistence of MB-infected mosquitoes in a given area.

Keywords: microsporidia MB, vertical transmission, horizontal transmission, compartmental modelling approach, temperature-dependent mosquito traits, malaria, plasmodium-transmission blocking

Procedia PDF Downloads 107

Authors: Ella Tyuryumina, Alexey Neznanov

Abstract:

This study is an attempt to obtain reliable data on the natural history of breast cancer growth. We analyze the opportunities for using classical mathematical models (exponential and logistic tumor growth models, Gompertz and von Bertalanffy tumor growth models) to try to describe growth of the primary tumor and the secondary distant metastases of human breast cancer. The research aim is to improve predicting accuracy of breast cancer progression using an original mathematical model referred to CoMPaS and corresponding software. We are interested in: 1) modelling the whole natural history of the primary tumor and the secondary distant metastases; 2) developing adequate and precise CoMPaS which reflects relations between the primary tumor and the secondary distant metastases; 3) analyzing the CoMPaS scope of application; 4) implementing the model as a software tool. The foundation of the CoMPaS is the exponential tumor growth model, which is described by determinate nonlinear and linear equations. The CoMPaS corresponds to TNM classification. It allows to calculate different growth periods of the primary tumor and the secondary distant metastases: 1) ‘non-visible period’ for the primary tumor; 2) ‘non-visible period’ for the secondary distant metastases; 3) ‘visible period’ for the secondary distant metastases. The CoMPaS is validated on clinical data of 10-years and 15-years survival depending on the tumor stage and diameter of the primary tumor. The new predictive tool: 1) is a solid foundation to develop future studies of breast cancer growth models; 2) does not require any expensive diagnostic tests; 3) is the first predictor which makes forecast using only current patient data, the others are based on the additional statistical data. The CoMPaS model and predictive software: a) fit to clinical trials data; b) detect different growth periods of the primary tumor and the secondary distant metastases; c) make forecast of the period of the secondary distant metastases appearance; d) have higher average prediction accuracy than the other tools; e) can improve forecasts on survival of breast cancer and facilitate optimization of diagnostic tests. The following are calculated by CoMPaS: the number of doublings for ‘non-visible’ and ‘visible’ growth period of the secondary distant metastases; tumor volume doubling time (days) for ‘non-visible’ and ‘visible’ growth period of the secondary distant metastases. The CoMPaS enables, for the first time, to predict ‘whole natural history’ of the primary tumor and the secondary distant metastases growth on each stage (pT1, pT2, pT3, pT4) relying only on the primary tumor sizes. Summarizing: a) CoMPaS describes correctly the primary tumor growth of IA, IIA, IIB, IIIB (T1-4N0M0) stages without metastases in lymph nodes (N0); b) facilitates the understanding of the appearance period and inception of the secondary distant metastases.

Keywords: breast cancer, exponential growth model, mathematical model, metastases in lymph nodes, primary tumor, survival

Procedia PDF Downloads 324

Authors: Jun-Ki Choi

Abstract:

The usage of valuable resources and the potential for waste generation at the end of the life cycle of photovoltaic (PV) technologies necessitate a proactive planning for a PV recycling infrastructure. To ensure the sustainability of PV in large scales of deployment, it is vital to develop and institute low-cost recycling technologies and infrastructure for the emerging PV industry in parallel with the rapid commercialization of these new technologies. There are various issues involved in the economics of PV recycling and this research examine those at macro and micro levels, developing a holistic interpretation of the economic viability of the PV recycling systems. This study developed mathematical models to analyze the profitability of recycling technologies and to guide tactical decisions for allocating optimal location of PV take-back centers (PVTBC), necessary for the collection of end of life products. The economic decision is usually based on the level of the marginal capital cost of each PVTBC, cost of reverse logistics, distance traveled, and the amount of PV waste collected from various locations. Results illustrated that the reverse logistics costs comprise a major portion of the cost of PVTBC; PV recycling centers can be constructed in the optimally selected locations to minimize the total reverse logistics cost for transporting the PV wastes from various collection facilities to the recycling center. In the micro- process level, automated recycling processes should be developed to handle the large amount of growing PV wastes economically. The market price of the reclaimed materials are important factors for deciding the profitability of the recycling process and this illustrates the importance of the recovering the glass and expensive metals from PV modules.

Keywords: photovoltaic, recycling, mathematical models, sustainability

Procedia PDF Downloads 227

Authors: Eunice Christabel Chukwu

Abstract:

Introduction: Diabetes is a chronic medical condition which is characterized by high levels of glucose in the blood and urine; it is usually diagnosed by means of a glucose tolerance test (GTT). Diabetes can cause a range of health problems if left unmanaged, as it can lead to serious complications. It is essential to manage the condition effectively, particularly in the workplace where the impact on work productivity can be significant. This paper discusses the modelling of optimal control of diabetes in the workplace using a control theory approach. Background: Diabetes mellitus is a condition caused by too much glucose in the blood. Insulin, a hormone produced by the pancreas, controls the blood sugar level by regulating the production and storage of glucose. In diabetes, there may be a decrease in the body’s ability to respond to insulin or a decrease in insulin produced by the pancreas which will lead to abnormalities in the metabolism of carbohydrates, proteins, and fats. In addition to the health implications, the condition can also have a significant impact on work productivity, as employees with uncontrolled diabetes are at risk of absenteeism, reduced performance, and increased healthcare costs. While several interventions are available to manage diabetes, the most effective approach is to control blood glucose levels through a combination of lifestyle modifications and medication. Methodology: The control theory approach involves modelling the dynamics of the system and designing a controller that can regulate the system to achieve optimal performance. In the case of diabetes, the system dynamics can be modelled using a mathematical model that describes the relationship between insulin, glucose, and other variables. The controller can then be designed to regulate the glucose levels to maintain them within a healthy range. Results: The modelling of optimal control of diabetes in the workplace using a control theory approach has shown promising results. The model has been able to predict the optimal dose of insulin required to maintain glucose levels within a healthy range, taking into account the individual’s lifestyle, medication regimen, and other relevant factors. The approach has also been used to design interventions that can improve diabetes management in the workplace, such as regular glucose monitoring and education programs. Conclusion: The modelling of optimal control of diabetes in the workplace using a control theory approach has significant potential to improve diabetes management and work productivity. By using a mathematical model and a controller to regulate glucose levels, the approach can help individuals with diabetes to achieve optimal health outcomes while minimizing the impact of the condition on their work performance. Further research is needed to validate the model and develop interventions that can be implemented in the workplace.

Keywords: mathematical model, blood, insulin, pancreas, model, glucose

Procedia PDF Downloads 44

Authors: B. El Fadil, R. Najar

Abstract:

STEM education is promoted by many scholars and curricula around the world, but it is not yet well established in the province of Quebec in Canada. In addition, effective instructional STEM activities and design methods are required to ensure that students and teachers' needs are being met. One potential method is the Engineering Design Process (EDP), a methodology that emphasizes the importance of creativity and collaboration in problem-solving strategies. This article reports on a case study that focused on using the EDP to develop instructional materials by means of making a technological artifact to teach mathematical variables and functions at the secondary level. The five iterative stages of the EDP (design, make, test, infer, and iterate) were integrated into the development of the course materials. Data was collected from different sources: pre- and post-questionnaires, as well as a working document dealing with pupils' understanding based on designing, making, testing, and simulating. Twenty-four grade seven (13 years old) students in Northern Quebec participated in the study. The findings of this study indicate that STEM activities have a positive impact not only on students' engagement in classroom activities but also on learning new mathematical concepts. Furthermore, STEM-focused activities have a significant effect on problem-solving skills development in an interdisciplinary approach. Based on the study's results, we can conclude, inter alia, that teachers should integrate STEM activities into their teaching practices to increase learning outcomes and attach more importance to STEM-focused activities to develop students' reflective thinking and hands-on skills.

Keywords: engineering design process, motivation, stem, integration, variables, functions

Procedia PDF Downloads 68

Authors: Sanaz Ahmadzadeh Siyahrood, Arghavan Ebrahimi, Mohammadjavad Mahdavinejad

Abstract:

Islamic culture was accountable for a plethora of development in astronomy and science in the medieval term, and in geometry likewise. Geometric patterns are reputable in a considerable number of cultures, but in the Islamic culture the patterns have specific features that connect the Islamic faith to mathematics. In Islamic art, three fundamental shapes are generated from the circle shape: triangle, square and hexagon. Originating from their quiddity, each of these geometric shapes has its own specific structure. Even though the geometric patterns were generated from such simple forms as the circle and the square, they can be combined, duplicated, interlaced, and arranged in intricate combinations. So in order to explain geometrical interaction principles between square and equal triangle, in the first definition step, all types of their linear forces individually and in the second step, between them, would be illustrated. In this analysis, some angles will be created from intersection of their directions. All angles are categorized to some groups and the mathematical expressions among them are analyzed. Since the most geometric patterns in Islamic art and architecture are based on the repetition of a single motif, the evaluation results which are obtained from a small portion, is attributable to a large-scale domain while the development of infinitely repeating patterns can represent the unchanging laws. Geometric ornamentation in Islamic art offers the possibility of infinite growth and can accommodate the incorporation of other types of architectural layout as well, so the logic and mathematical relationships which have been obtained from this analysis are applicable in designing some architecture layers and developing the plan design.

Keywords: angle, equal triangle, square, structural hierarchy

Procedia PDF Downloads 170

Authors: Akaki Qatamidze

Abstract:

Implementation of the project will be a step forward in terms of reliability in Georgia and the improvement of the construction and the development of construction. Completion of the project is expected to result in a complete knowledge, which is expressed in concrete and stone structures of assessing the technical condition of the processing. This method is based on a detailed examination of the structure, in order to establish the injuries and the elimination of the possibility of changing the structural scheme of the new requirements and architectural preservationists. Reinforced concrete and stone structures research project carried out in a systematic analysis of the important approach is to optimize the process of research and development of new knowledge in the neighboring areas. In addition, the problem of physical and mathematical models of rational consent, the main pillar of the physical (in-situ) data and mathematical calculation models and physical experiments are used only for the calculation model specification and verification. Reinforced concrete and stone construction defects and failures the causes of the proposed research to enhance the effectiveness of their maximum automation capabilities and expenditure of resources to reduce the recommended system analysis of the methodological concept-based approach, as modern science and technology major particularity of one, it will allow all family structures to be identified for the same work stages and procedures, which makes it possible to exclude subjectivity and addresses the problem of the optimal direction. It discussed the methodology of the project and to establish a major step forward in the construction trades and practical assistance to engineers, supervisors, and technical experts in the construction of the settlement of the problem.

Keywords: building, reinforced concrete, expertise, stone structures

Procedia PDF Downloads 314

Authors: Pamela R. Jackson, Andrea Hawkins-Daarud, Cassandra R. Rickertsen, Kamala Clark-Swanson, Scott A. Whitmire, Kristin R. Swanson

Abstract:

Glioblastoma Multiforme (GBM), the most common primary brain tumor, often presents with hyperintensity on T2-weighted or T2-weighted fluid attenuated inversion recovery (T2/FLAIR) magnetic resonance imaging (MRI). This hyperintensity corresponds with vasogenic edema, however there are likely many infiltrating tumor cells within the hyperintensity as well. While MRIs do not directly indicate tumor cells, MRIs do reflect the microenvironmental water abnormalities caused by the presence of tumor cells and edema. The inherent heterogeneity and resulting MRI features of GBMs complicate assessing disease response. To understand how hyperintensity on T2/FLAIR MRI may correlate with edema in the extracellular space (ECS), a multi-compartmental MRI signal equation which takes into account tissue compartments and their associated volumes with input coming from a mathematical model of glioma growth that incorporates edema formation was explored. The reasonableness of two possible extracellular space schema was evaluated by varying the T2 of the edema compartment and calculating the possible resulting T2s in tumor and peripheral edema. In the mathematical model, gliomas were comprised of vasculature and three tumor cellular phenotypes: normoxic, hypoxic, and necrotic. Edema was characterized as fluid leaking from abnormal tumor vessels. Spatial maps of tumor cell density and edema for virtual tumors were simulated with different rates of proliferation and invasion and various ECS expansion schemes. These spatial maps were then passed into a multi-compartmental MRI signal model for generating simulated T2/FLAIR MR images. Individual compartments’ T2 values in the signal equation were either from literature or estimated and the T2 for edema specifically was varied over a wide range (200 ms – 9200 ms). T2 maps were calculated from simulated images. T2 values based on simulated images were evaluated for regions of interest (ROIs) in normal appearing white matter, tumor, and peripheral edema. The ROI T2 values were compared to T2 values reported in literature. The expanding scheme of extracellular space is had T2 values similar to the literature calculated values. The static scheme of extracellular space had a much lower T2 values and no matter what T2 was associated with edema, the intensities did not come close to literature values. Expanding the extracellular space is necessary to achieve simulated edema intensities commiserate with acquired MRIs.

Keywords: extracellular space, glioblastoma multiforme, magnetic resonance imaging, mathematical modeling

Procedia PDF Downloads 212

Authors: Gary Miller, Andriy Didenko, David Allison

Abstract:

The boundary of a region in the plane shrinks according to its curvature. A simple algorithm based upon this motion by curvature performed by a spreadsheet simulates the evaporation/dissipation behavior of oil spill boundaries.

Keywords: mathematical modeling, oil, evaporation, dissipation, boundary

Procedia PDF Downloads 488

Authors: Krishna Chandra Paudel

Abstract:

This paper explores the association between the perceived classroom environment and mathematics learning and test anxiety among secondary level students in Nepal. Categorizing the students in three dominant variables- gender, ethnicity and previous schooling, and selecting sample students with respect to higher mathematics anxiety from five heterogeneous classes, the research explores disparities in student's mathematics cognition and reveals nexus between classroom environment and mathematics learning and test anxiety. This research incorporates social learning theory and social development theory as interpretive tool for analyzing themes through qualitative data. Focussing on the interviews with highly mathematics learning anxious students, the study sheds light on how mathematics anxiety among the targeted students is interlinked with multiple factors. The research basically exposes the students’ lack of mathematical passion, their association with other students and participation in classroom learning, asymmetrical content and their lack of preparedness for the tests as caustic factors behind such anxieties. The study further reveals that students’ lack of foundational knowledge and complexity of mathematical content have jointly contributed to mathematics anxiety. Admitting learning as a reciprocal experience, the study points out that the students’ gender, ethnicity and disparities in previous schooling in the context of Nepal has very insignificant impact on students’ mathematics anxiety. It finally recommends that the students who get trapped into the vicious cycle of mathematics anxiety require positive and supportive classroom environment along with inspiring comments/compliments and symmetrical course contents.

Keywords: anxiety, asymmetry, cognition, habitus, pedagogy, preparedness

Procedia PDF Downloads 109

Authors: Javier Navarro Garcia, Narciso Vazquez Carretero

Abstract:

Eurocode 1, part 1-4, wind actions, includes in its article 1.5 the possibility of using numerical calculation methods to obtain information on the loads acting on a building. On the other hand, the analysis using computational fluids dynamics (CFD) in aerospace, aeronautical, and industrial applications is already in widespread use. The application of techniques based on CFD analysis on the building to study its aerodynamic behavior now opens a whole alternative field of possibilities for civil engineering and architecture; optimization of the results with respect to those obtained by applying the regulations, the possibility of obtaining information on pressures, speeds at any point of the model for each moment, the analysis of turbulence and the possibility of modeling any geometry or configuration. The present work compares the results obtained on a building, with respect to its aerodynamic behavior, from a mathematical model based on the analysis by CFD with the results obtained by applying Eurocode1, part1-4, wind actions. It is verified that the results obtained by CFD techniques suppose an optimization of the wind action that acts on the building with respect to the wind action obtained by applying the Eurocode1, part 1-4, wind actions. In order to carry out this verification, a 45m high square base truncated pyramid building has been taken. The mathematical model on CFD, based on finite volumes, has been calculated using the FLUENT commercial computer application using a scale-resolving simulation (SRS) type large eddy simulation (LES) turbulence model for an atmospheric boundary layer wind with turbulent component in the direction of the flow.

Keywords: aerodynamic, CFD, computacional fluids dynamics, computational mechanics

Procedia PDF Downloads 120

Authors: G. Martino, F. Silva, E. Marchal

Abstract:

The control over delivered iron ore blend characteristics is one of the most important aspects of the mining business. The iron ore price is a function of its composition, which is the outcome of the beneficiation process. So, end-to-end integrated planning of mine operations can reduce risks of penalties on the iron ore price. In a standard iron mining company, the production chain is composed of mining, ore beneficiation, and client supply. When mine planning and client supply decisions are made uncoordinated, the beneficiation plant struggles to deliver the best blend possible. Technological improvements in several fields allowed bridging the gap between departments and boosting integrated decision-making processes. Clusterization and classification algorithms over historical production data generate reasonable previsions for quality and volume of iron ore produced for each pile of run-of-mine (ROM) processed. Mathematical modeling can use those deterministic relations to propose iron ore blends that better-fit specifications within a delivery schedule. Additionally, a model capable of representing the whole production chain can clearly compare the overall impact of different decisions in the process. This study shows how flexibilization combined with a planning optimization model between the mine and the ore beneficiation processes can reduce risks of out of specification deliveries. The model capabilities are illustrated on a hypothetical iron ore mine with magnetic separation process. Finally, this study shows ways of cost reduction or profit increase by optimizing process indicators across the production chain and integrating the different plannings with the sales decisions.

Keywords: clusterization and classification algorithms, integrated planning, mathematical modeling, optimization, penalty minimization

Procedia PDF Downloads 102

Authors: Pooria Norouzi, Nicholas Tsang, Adam van der Goes, Joseph Yu, Douglas Zheng, Sirine Maleej

Abstract:

In this study, virtual meters will be designed and used for energy balance measurements of an air handling unit (AHU). The method aims to replace traditional physical sensors in heating, ventilation, and air conditioning (HVAC) systems with simulated virtual meters. Due to the inability to manage and monitor these systems, many HVAC systems have a high level of inefficiency and energy wastage. Virtual meters are implemented and applied in an actual HVAC system, and the result confirms the practicality of mathematical sensors for alternative energy measurement. While most residential buildings and offices are commonly not equipped with advanced sensors, adding, exploiting, and monitoring sensors and measurement devices in the existing systems can cost thousands of dollars. The first purpose of this study is to provide an energy consumption rate based on available sensors and without any physical energy meters. It proves the performance of virtual meters in HVAC systems as reliable measurement devices. To demonstrate this concept, mathematical models are created for AHU-07, located in building NE01 of the British Columbia Institute of Technology (BCIT) Burnaby campus. The models will be created and integrated with the system’s historical data and physical spot measurements. The actual measurements will be investigated to prove the models' accuracy. Based on preliminary analysis, the resulting mathematical models are successful in plotting energy consumption patterns, and it is concluded confidently that the results of the virtual meter will be close to the results that physical meters could achieve. In the second part of this study, the use of virtual meters is further assisted by artificial intelligence (AI) in the HVAC systems of building to improve energy management and efficiency. By the data mining approach, virtual meters’ data is recorded as historical data, and HVAC system energy consumption prediction is also implemented in order to harness great energy savings and manage the demand and supply chain effectively. Energy prediction can lead to energy-saving strategies and considerations that can open a window in predictive control in order to reach lower energy consumption. To solve these challenges, the energy prediction could optimize the HVAC system and automates energy consumption to capture savings. This study also investigates AI solutions possibility for autonomous HVAC efficiency that will allow quick and efficient response to energy consumption and cost spikes in the energy market.

Keywords: virtual meters, HVAC, artificial intelligence, energy consumption prediction

Procedia PDF Downloads 78

Authors: Yasin Tadayonrad

Abstract:

Most of the supply chain networks have many nodes starting from the suppliers’ side up to the customers’ side that each node sends/receives the raw materials/products from/to the other nodes. One of the major concerns in this kind of supply chain network is finding the best schedule for loading /unloading the shipments through the whole network by which all the constraints in the source and destination nodes are met and all the shipments are delivered on time. One of the main constraints in this problem is loading/unloading capacity in each source/ destination node at each time slot (e.g., per week/day/hour). Because of the different characteristics of different products/groups of products, the capacity of each node might differ based on each group of products. In most supply chain networks (especially in the Fast-moving consumer goods industry), there are different planners/planning teams working separately in different nodes to determine the loading/unloading timeslots in source/destination nodes to send/receive the shipments. In this paper, a mathematical problem has been proposed to find the best timeslots for loading/unloading the shipments minimizing the overall delays subject to respecting the capacity of loading/unloading of each node, the required delivery date of each shipment (considering the lead-times), and working-days of each node. This model was implemented on python and solved using Python-MIP on a sample data set. Finally, the idea of a heuristic algorithm has been proposed as a way of improving the solution method that helps to implement the model on larger data sets in real business cases, including more nodes and shipments.

Keywords: supply chain management, transportation, multiple-multiple network, timeslots management, mathematical modeling, mixed integer programming

Procedia PDF Downloads 65