Search results for: mathematical sciences

Authors: B. S.Akhmetov, S. T. Akhmetova, D. N. Nadeyev, V. Yu. Yegorov, V. V. Smogoonov

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Estimated probabilities of errors of the first and second kind for nonideal biometrics-neural transducers 256 outputs, the construction of nomograms based error probability of 'own' and 'alien' from the mathematical expectation and standard deviation of the normalized measures Hamming.

Keywords: modeling, errors, probability, biometrics, neural network, authentication

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Authors: A. Elragig, S. Townley, H. Dreiwi

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In this paper we introduce a bacteria-leukocyte model with bacteria chemotaxsis. We assume that bacteria develop a tactic defense mechanism as a response to Leukocyte phagocytosis. We explore the effect of this tactic motion on Turing space in two parameter spaces. A fine tuning of bacterial chemotaxis shows a significant effect on developing a non-uniform steady state.

Keywords: chemotaxis-diffusion driven instability, bacterial chemotaxis, mathematical biology, ecology

Procedia PDF Downloads 344

Authors: Ming Liu, Zhihui Sun, Xiaoning Zhang

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This paper studies a deterministic container transportation problem, jointly optimizing the berth allocation, quay crane assignment and yard storage allocation at container ports. The problem is formulated as an integer program to coordinate the decisions. Because of the large scale, it is then transformed into a set partitioning formulation, and a framework of branchand- price algorithm is provided to solve it.

Keywords: branch-and-price, container terminal, joint scheduling, maritime logistics

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Authors: Abderrahim Elmoataz

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More and more contemporary applications involve data in the form of functions defined on irregular and topologically complicated domains (images, meshs, points clouds, networks, etc). Such data are not organized as familiar digital signals and images sampled on regular lattices. However, they can be conveniently represented as graphs where each vertex represents measured data and each edge represents a relationship (connectivity or certain affinities or interaction) between two vertices. Processing and analyzing these types of data is a major challenge for both image and machine learning communities. Hence, it is very important to transfer to graphs and networks many of the mathematical tools which were initially developed on usual Euclidean spaces and proven to be efficient for many inverse problems and applications dealing with usual image and signal domains. Historically, the main tools for the study of graphs or networks come from combinatorial and graph theory. In recent years there has been an increasing interest in the investigation of one of the major mathematical tools for signal and image analysis, which are Partial Differential Equations (PDEs) variational methods on graphs. The normalized p-laplacian operator has been recently introduced to model a stochastic game called tug-of-war-game with noise. Part interest of this class of operators arises from the fact that it includes, as particular case, the infinity Laplacian, the mean curvature operator and the traditionnal Laplacian operators which was extensiveley used to models and to solve problems in image processing. The purpose of this paper is to introduce and to study a new class of normalized p-Laplacian on graphs. The introduction is based on the extension of p-harmonious function introduced in as discrete approximation for both infinity Laplacian and p-Laplacian equations. Finally, we propose to use these operators as a framework for solving many inverse problems in image processing.

Keywords: normalized p-laplacian, image processing, stochastic game, inverse problems

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Authors: Pawan Kumar Gupta, Sumana Ghosh

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Parkinson's Disease (PD) is a long-term neurodegenerative movement disorder of the central nervous system with vast symptoms related to the motor system. The common symptoms of PD are tremor, rigidity, bradykinesia/akinesia, and postural instability, but the clinical symptom includes other motor and non‐motor issues. The motor symptoms of the disease are consequence of death of the neurons in a region of the midbrain known as substantia nigra pars compacta, leading to decreased level of a neurotransmitter known as dopamine. The cause of this neuron death is not clearly known but involves formation of Lewy bodies, an abnormal aggregation or clumping of the protein alpha-synuclein in the neurons. Unfortunately, there is no cure for PD, and the management of this disease is challenging. Therefore, it is critical for a patient to be diagnosed at early stages. A limited choice of drugs is available to improve the symptoms, but those become less and less effective over time. Apart from that, with rapid growth in the field of science and technology, other methods such as multi-area brain stimulation are used to treat patients. In order to develop advanced techniques and to support drug development for treating PD patients, an accurate mathematical model is needed to explain the underlying relationship of dopamine secretion in the brain with the hand tremors. There has been a lot of effort in the past few decades on modeling PD tremors and treatment effects from a computational point of view. These models can effectively save time as well as the cost of drug development for the pharmaceutical industry and be helpful for selecting appropriate treatment mechanisms among all possible options. In this review paper, an effort is made to investigate studies on PD modeling and analysis and to highlight some of the key advances in the field over the past centuries with discussion on the current challenges.

Keywords: Parkinson's disease, deep brain stimulation, tremor, modeling

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Authors: Rashid S. Mohammad, Shicheng Zhang, Xinzhe Zhao

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In tight oil reservoirs, wettability alteration has generally been considered as an effective way to remove fracturing fluid retention on the surface of the fracture and consequently improved oil production. However, there is a lack of a reliable productivity prediction model to show the relationship between the wettability and oil production in tight oil well. In this paper, a new oil productivity prediction model of immiscible oil-water flow and miscible CO₂-oil flow accounting for wettability is developed. This mathematical model is established by considering two different length scales: nonporous network and propped fractures. CO₂ flow diffuses in the nonporous network and high velocity non-Darcy flow in propped fractures are considered by taking into account the effect of wettability alteration on capillary pressure and relative permeability. A laboratory experiment is also conducted here to validate this model. Laboratory experiments have been designed to compare the water saturation profiles for different contact angle, revealing the fluid retention in rock pores that affects capillary force and relative permeability. Four kinds of brines with different concentrations are selected here to create different contact angles. In water-wet porous media, as the system becomes more oil-wet, water saturation decreases. As a result, oil relative permeability increases. On the other hand, capillary pressure which is the resistance for the oil flow increases as well. The oil production change due to wettability alteration is the result of the comprehensive changes of oil relative permeability and capillary pressure. The results indicate that wettability is a key factor for fracturing fluid retention removal and oil enhancement in tight reservoirs. By incorporating laboratory test into a mathematical model, this work shows the relationship between wettability and oil production is not a simple linear pattern but a parabolic one. Additionally, it can be used for a better understanding of optimization design of fracturing fluids.

Keywords: wettability, relative permeability, fluid retention, oil production, unconventional and tight reservoirs

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Authors: N. Gharbi

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Constraint Satisfaction problems are mathematical problems that are often used to model many real-world problems for which we look if there exists a solution satisfying all its constraints. Table constraints are important for modeling parts of many problems since they list all combinations of allowed or forbidden values. However, they admit practical limitations because they are sometimes too large to be represented in a direct way. In this paper, we present a survey of the different categories of the proposed approaches to compress table constraints in order to reduce both space and time complexities.

Keywords: constraint programming, compression, data mining, table constraints

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Authors: Benjamin Castillo, Luis Pastenes, Fernando Cordova

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The pathogen growth in animal source foods is a common problem in the food industry, causing monetary losses due to the spoiling of products or food intoxication outbreaks in the community. In this sense, the quality of the product is reflected by the population of deteriorating agents present in it, which are mainly bacteria. The factors which are likely associated with freshness in animal source foods are temperature and processing, storage, and transport times. However, the level of deterioration of products depends, in turn, on the characteristics of the bacterial population, causing the decomposition or spoiling, such as pH level and toxins. Knowing the growth dynamics of the agents that are involved in product contamination allows the monitoring for more efficient processing. This means better quality and reasonable costs, along with a better estimation of necessary time and temperature intervals for transport and storage in order to preserve product quality. The objective of this project is to design a secondary model that allows measuring the impact on temperature bacterial growth and the competition for pH adequacy and release of bacteriocins in order to describe such phenomenon and, thus, estimate food product half-life with the least possible risk of deterioration or spoiling. In order to achieve this objective, the authors propose an analysis of a three-dimensional ordinary differential which includes; logistic bacterial growth extended by the inhibitory action of bacteriocins including the effect of the medium pH; change in the medium pH levels through an adaptation of the Luedeking-Piret kinetic model; Bacteriocin concentration modeled similarly to pH levels. These three dimensions are being influenced by the temperature at all times. Then, this differential system is expanded, taking into consideration the variable temperature and the concentration of pulsed bacteriocins, which represent characteristics inherent of the modeling, such as transport and storage, as well as the incorporation of substances that inhibit bacterial growth. The main results lead to the fact that temperature changes in an early stage of transport increased the bacterial population significantly more than if it had increased during the final stage. On the other hand, the incorporation of bacteriocins, as in other investigations, proved to be efficient in the short and medium-term since, although the population of bacteria decreased, once the bacteriocins were depleted or degraded over time, the bacteria eventually returned to their regular growth rate. The efficacy of the bacteriocins at low temperatures decreased slightly, which equates with the fact that their natural degradation rate also decreased. In summary, the implementation of the mathematical model allowed the simulation of a set of possible bacteria present in animal based products, along with their properties, in various transport and storage situations, which led us to state that for inhibiting bacterial growth, the optimum is complementary low constant temperatures and the initial use of bacteriocins.

Keywords: bacterial growth, bacteriocins, mathematical modelling, temperature

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Authors: H. Ghodbane, A. A. Taleb, O. Kraa

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This paper presents geometric design of induction heating system. The objective of this design is to improve the temperature distribution in the load. The study of such a device requires the use of models or modeling representation, physical, mathematical, and numerical. This modeling is the basis of the understanding, the design, and optimization of these systems. The optimization technique is to find values of variables that maximize or minimize the objective function.

Keywords: optimization, modeling, geometric design system, temperature increase

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Authors: Renata Masarova, Bohuslava Juhasova, Martin Juhas, Zuzana Sutova

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In dynamic system theory a mathematical model is often used to describe their properties. In order to find a transfer matrix of a dynamic system we need to calculate an inverse matrix. The paper contains the fusion of the classical theory and the procedures used in the theory of automated control for calculating the inverse matrix. The final part of the paper models the given problem by the Matlab.

Keywords: dynamic system, transfer matrix, inverse matrix, modeling

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Authors: Bayan Bevrani, Robert L. Burdett, Prasad K. D. V. Yarlagadda

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This article focuses upon multi-modal transportation systems (MMTS) and the issues surrounding the determination of system capacity. For that purpose a multi-objective framework is advocated that integrates all the different modes and many different competing capacity objectives. This framework is analytical in nature and facilitates a variety of capacity querying and capacity expansion planning.

Keywords: analytical model, capacity analysis, capacity query, multi-modal transportation system (MMTS)

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Authors: Merouane Salhi, Mohamed Roudane, Abdelkader Kirad

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In this work, we present a new form of characteristics method, which is a technique for solving partial differential equations. Typically, it applies to first-order equations; the aim of this method is to reduce a partial differential equation to a family of ordinary differential equations along which the solution can be integrated from some initial data. This latter developed under the real gas theory, because when the thermal and the caloric imperfections of a gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with the gas parameters. The gas doesn’t stay perfect. Its state equation change and it becomes for a real gas. The presented equations of the characteristics remain valid whatever area or field of study. Here we need have inserted the developed Prandtl Meyer function in the mathematical system to find a new model when the effect of stagnation pressure is taken into account. In this case, the effects of molecular size and intermolecular attraction forces intervene to correct the state equation, the thermodynamic parameters and the value of Prandtl Meyer function. However, with the assumptions that Berthelot’s state equation accounts for molecular size and intermolecular force effects, expressions are developed for analyzing the supersonic flow for thermally and calorically imperfect gas. The supersonic parameters depend directly on the stagnation parameters of the combustion chamber. The resolution has been made by the finite differences method using the corrector predictor algorithm. As results, the developed mathematical model used to design 2D minimum length nozzles under effect of the stagnation parameters of fluid flow. A comparison for air with the perfect gas PG and high temperature models on the one hand and our results by the real gas theory on the other of nozzles shapes and characteristics are made.

Keywords: numerical methods, nozzles design, real gas, stagnation parameters, supersonic expansion, the characteristics method

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Authors: Thomas Wetere

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Background: The coronavirus disease 2019 (COVID-19) pandemic (COVID-19) virus infection is a severe infectious disease with the highly transmissible variant, which become the global public health treat now. It has taken the life of more than 4 million people so far. What makes the disease the worst of all is no specific effective treatment available, its dynamics is not much researched and understood. Methodology: To end the global COVID-19 pandemic, implementation of multiple population-wide strategies, including vaccination, environmental factors, Government action, testing, and contact tracing, is required. In this article, a new mathematical model incorporating both temperature and government action to study the dynamics of the COVID-19 pandemic has been developed and comprehensively analysed. The model considers eight stages of infection: susceptible (S), infected Asymptomatic and Undetected(IAU ), infected Asymptomatic and detected(IAD), infected symptomatic and Undetected(ISU ), infected Symptomatic and detected(ISD), Hospitalized or threatened(H), Recovered(R) and Died(D). Results: The existence as well as non-negativity of the solution to the model is also verified, and the basic reproduction number is calculated. Besides, stability conditions are also checked, and finally, simulation results are compared with real data. The results demonstrates that effective government action will need to be combined with vaccination to end the ongoing COVID-19 pandemic. Conclusion: Vaccination and Government action are highly the crucial measures to control the COVID-19 pandemic. Besides, as the cost of vaccination might be high, we recommend an optimal control to reduce the cost and number of infected individuals. Moreover, in order to prevent COVID-19 pandemic, through the analysis of the model, the government must strictly manage the policy on COVID-19 and carry it out. This, in turn, helps for health campaigning and raising health literacy which plays a role to control the quick spread of the disease. We finally strongly believe that our study will play its own role in the current effort of controlling the pandemic.

Keywords: modeling, COVID-19, MCMC, stability

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Authors: Juliana Chiarini Balbino Fernandes

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This article aims to investigate the Spanish didactic book, entitled ‘El Calculo y La Medida en El Primer Grado de La Escuela Decroly’, written by Dr. O. Decroly and A. Hamaide, published in Madrid, in the year 1934. In addition to analyzing how mathematical knowledge is present in the proposed Centers of Interest. The textbooks, in addition to pedagogical tools, reflect a certain moment in society and allow the analysis of the theoretical-methodological proposal that can be implemented by the teacher. The study proposed here will be carried out by the lens of Cultural History, supported by Roger Chartier (1991) and by the concepts on textbooks, based on Alain Choppin (2004). The textbook selected for this study exposes a program of ideas associated with the method of Centers of Interest and arithmetic is linked to these interests. In the first courses (six to eight years), most centers can be considered to correspond to occasional calls, as they take advantage of events that arise spontaneously to work with observation, measurement, association and expression exercises. The program of ideas associated with Centers of Interest addresses the biological and social aspects of children, as long as they can express their needs for activities and games, satisfying the natural curiosity. Still, the program of associated ideas offers occasions for problems whose data are taken in observation exercises and concrete expressions (manuals, drawings). In the method applied at the school of L'Ermitage, school created by Decroly in Belgium in 1907, observation, is the basis of each center of interest. It offers the chance to compare and measure. To observe is more than to perceive; it is also to establish relations between the graded aspects of the same object, to seek relations between different intensities; is to verify successions, special and temporary relationships; is to make comparisons, to notice differences and similarities in block or datable (analysis), is to establish a bridge between the world and the thought. To make the observation more precise, it is important to compare, measure, and resort to considered objects as natural units of measure. Measurement and calculation are, therefore, quite naturally subject to observation. Thus, it is possible to make the child enter into the interest in the calculation, linking it to the observation. It was observed that the Centers of Interest, according to Decroly, should respond to the concerns and attend to the motivations of the students and the teaching of arithmetical must obey a logical seriation, considering the interest and the experience of the children. The teaching of arithmetical should not be limited to the schedule, it should cover every quantitative aspect that arises in the other disciplines. The feeling of unity is established in observation, association and expression, which coordinate a whole program of cultural activities, concentrating it around a central idea.

Keywords: didactic book, centers of interest, mathematical knowledge, primary education

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Authors: Bipin Popat Sonawane

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After 1988 Electron muon Collaboration (EMC) announcement of measurement of spin dependent structure function, it has been found that it has become a need to understand spin structure of a hadron. In the study of three-dimensional spin structure of a proton, we need to understand the foundation of quantum field theory in terms of electro-weak and strong theories using rigorous mathematical theories and models. In the process of understanding the inner dynamical stricture of proton we need understand the mathematical formalism in perturbative quantum chromodynamics (pQCD). In QCD processes like proton-proton collision at high energy we calculate cross section using conventional collinear factorization schemes. In this calculations, parton distribution functions (PDFs) and fragmentation function are used which provide the information about probability density of finding quarks and gluons ( partons) inside the proton and probability density of finding final hadronic state from initial partons. In transverse momentum dependent (TMD) PDFs and FFs, collectively called as TMDs, take an account for intrinsic transverse motion of partons. The TMD factorization in the calculation of cross sections provide a scheme of hadronic and partonic states in the given QCD process. In this study we review Transverse Momentum Dependent (TMD) factorization scheme using Collins-Soper-Sterman (CSS) Formalism. CSS formalism considers the transverse momentum dependence of the partons, in this formalism the cross section is written as a Fourier transform over a transverse position variable which has physical interpretation as impact parameter. Along with this we compare this formalism with improved CSS formalism. In this work we study the TMD evolution schemes and their comparison with other schemes. This would provide description in the process of measurement of transverse single spin asymmetry (TSSA) in hadro-production and electro-production of J/psi meson at RHIC, LHC, ILC energy scales. This would surely help us to understand J/psi production mechanism which is an appropriate test of QCD.

Keywords: QCD, PDF, TMD, CSS

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Authors: Mohd Sabri Minhat, Nurul Adilla Mohd Subha

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The 1MWth PUSPATI TRIGA Reactor (RTP) in Malaysia Nuclear Agency has been operating more than 35 years. The existing core power control is using conventional controller known as Feedback Control Algorithm (FCA). It is technically challenging to keep the core power output always stable and operating within acceptable error bands for the safety demand of the RTP. Currently, the system could be considered unsatisfactory with power tracking performance, yet there is still significant room for improvement. Hence, a new design core power control is very important to improve the current performance in tracking and regulating reactor power by controlling the movement of control rods that suit the demand of highly sensitive of nuclear reactor power control. In this paper, the proposed Model Predictive Control (MPC) law was applied to control the core power. The model for core power control was based on mathematical models of the reactor core, MPC, and control rods selection algorithm. The mathematical models of the reactor core were based on point kinetics model, thermal hydraulic models, and reactivity models. The proposed MPC was presented in a transfer function model of the reactor core according to perturbations theory. The transfer function model-based predictive control (TFMPC) was developed to design the core power control with predictions based on a T-filter towards the real-time implementation of MPC on hardware. This paper introduces the sensitivity functions for TFMPC feedback loop to reduce the impact on the input actuation signal and demonstrates the behaviour of TFMPC in term of disturbance and noise rejections. The comparisons of both tracking and regulating performance between the conventional controller and TFMPC were made using MATLAB and analysed. In conclusion, the proposed TFMPC has satisfactory performance in tracking and regulating core power for controlling nuclear reactor with high reliability and safety.

Keywords: core power control, model predictive control, PUSPATI TRIGA reactor, TFMPC

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Authors: Piyush Sharma, Laltu Chandra, P. S. Ghoshdastidar, Rajiv Shekhar

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Metals processing operations such as melting and heat treatment of metals are energy-intensive, requiring temperatures greater than 500oC. The desired temperature in these industrial furnaces is attained by circulating electrically-heated air. In most of these furnaces, electricity produced from captive coal-based thermal power plants is used. Solar thermal energy could be a viable heat source in these furnaces. A retrofitted solar convective furnace (SCF) concept, which uses solar thermal generated hot air, has been proposed. Critical to the success of a SCF is the design of an open volumetric air receiver (OVAR), which can heat air in excess of 800oC. The OVAR is placed on top of a tower and receives concentrated solar radiation from a heliostat field. Absorbers, mixer assembly, and the return air flow chamber (RAFC) are the major components of an OVAR. The absorber is a porous structure that transfers heat from concentrated solar radiation to ambient air, referred to as primary air. The mixer ensures uniform air temperature at the receiver exit. Flow of the relatively cooler return air in the RAFC ensures that the absorbers do not fail by overheating. In an earlier publication, the detailed design basis, fabrication, and characterization of a 2 kWth open volumetric air receiver (OVAR) based laboratory solar air tower simulator was presented. Development of an experimentally-validated, CFD based mathematical model which can ultimately be used for the design and scale-up of an OVAR has been the major objective of this investigation. In contrast to the published literature, where flow and heat transfer have been modeled primarily in a single absorber module, the present study has modeled the entire receiver assembly, including the RAFC. Flow and heat transfer calculations have been carried out in ANSYS using the LTNE model. The complex return air flow pattern in the RAFC requires complicated meshes and is computational and time intensive. Hence a simple, realistic 1-D mathematical model, which circumvents the need for carrying out detailed flow and heat transfer calculations, has also been proposed. Several important results have emerged from this investigation. Circumferential electrical heating of absorbers can mimic frontal heating by concentrated solar radiation reasonably well in testing and characterizing the performance of an OVAR. Circumferential heating, therefore, obviates the need for expensive high solar concentration simulators. Predictions suggest that the ratio of power on aperture (POA) and mass flow rate of air (MFR) is a normalizing parameter for characterizing the thermal performance of an OVAR. Increasing POA/MFR increases the maximum temperature of air, but decreases the thermal efficiency of an OVAR. Predictions of the 1-D mathematical are within 5% of ANSYS predictions and computation time is reduced from ~ 5 hours to a few seconds.

Keywords: absorbers, mixer assembly, open volumetric air receiver, return air flow chamber, solar thermal energy

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Authors: Jaemyoung Lee

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We propose a stable laser scanning leveler transmitter scheme. In the proposed scheme, the transmitter has a right angled mirror which can eliminates the mechanical up and down vibration from scanning the mirror of the transmitter. In this paper, the mathematical proof for the proposed scheme which is not disturbed by the swivel movement of the right angled mirror is derived.

Keywords: leveler, right angled mirror, sweeping, laser

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Authors: Titus G. Kassem, Izang A. Nyam

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A mathematical model is constructed to study the effect of predation on two competing species in which one of the competing species is a prey to the predator whilst the other species are not under predation. Conditions for the existence and stability of equilibrium solutions were determined. Numerical simulation results indicate the possibility of a stable coexistence of the three interacting species in form of stable oscillations under certain parameter values. We also noticed that under some certain parameter values, species under predation go into extinction.

Keywords: competition, predator-prey, species, ecology

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Authors: M. J. Park, S. H. Lee, C. H. Lee, O. M. Kwon

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This paper investigates stability problem for linear systems of neutral type with time-varying delay. By constructing various Lyapunov-Krasovskii functional, and utilizing some mathematical techniques, the sufficient stability conditions for the systems are established in terms of linear matrix inequalities (LMIs), which can be easily solved by various effective optimization algorithms. Finally, some illustrative examples are given to show the effectiveness of the proposed criterion.

Keywords: neutral systems, time-delay, stability, Lyapnov method, LMI

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Authors: Gurcharan Singh Buttar

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It has been discovered that although these two areas, statistics, and information theory, are independent in their nature, they can be combined to create applications in multidisciplinary mathematics. This is due to the fact that where in the field of statistics, statistical parameters (measures) play an essential role in reference to the population (distribution) under investigation. Information measure is crucial in the study of ambiguity, assortment, and unpredictability present in an array of phenomena. The following communication is a link between the two, and it has been demonstrated that the well-known conventional statistical measures can be used as a measure of information.

Keywords: probability distribution, entropy, concavity, symmetry, variance, central tendency

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Authors: Thomas Weber, Nina Strobel, Thomas Kohne, Eberhard Abele

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In context of the energy transition in Germany, the importance of so-called virtual power plants in the energy supply continues to increase. The progressive dismantling of the large power plants and the ongoing construction of many new decentralized plants result in great potential for optimization through synergies between the individual plants. These potentials can be exploited by mathematical optimization algorithms to calculate the optimal application planning of decentralized power and heat generators and storage systems. This also includes linear or linear mixed integer optimization. In this paper, procedures for reducing the number of decision variables to be calculated are explained and validated. On the one hand, this includes combining n similar installation types into one aggregated unit. This aggregated unit is described by the same constraints and target function terms as a single plant. This reduces the number of decision variables per time step and the complexity of the problem to be solved by a factor of n. The exact operating mode of the individual plants can then be calculated in a second optimization in such a way that the output of the individual plants corresponds to the calculated output of the aggregated unit. Another way to reduce the number of decision variables in an optimization problem is to reduce the number of time steps to be calculated. This is useful if a high temporal resolution is not necessary for all time steps. For example, the volatility or the forecast quality of environmental parameters may justify a high or low temporal resolution of the optimization. Both approaches are examined for the resulting calculation time as well as for optimality. Several optimization models for virtual power plants (combined heat and power plants, heat storage, power storage, gas turbine) with different numbers of plants are used as a reference for the investigation of both processes with regard to calculation duration and optimality.

Keywords: CHP, Energy 4.0, energy storage, MILP, optimization, virtual power plant

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Authors: Wang Shuai, Su Rong, K. J.Tseng, V. Viswanathan, S. Ramakrishna

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The More-Electric-Aircraft concept in aircraft industry levies an increasing demand on the embedded starter/generators (ESG). The high-speed and high-temperature environment within an engine poses great challenges to the operation of such machines. In view of such challenges, squirrel cage induction machines (SCIM) have shown advantages due to its simple rotor structure, absence of temperature-sensitive components as well as low torque ripples etc. The tight operation constraints arising from typical ESG applications together with the detailed operation principles of SCIMs have been exploited to derive the mathematical interpretation of the ESG-SCIM design process. The resultant non-linear mathematical treatment yielded unique solution to the SCIM design problem for each configuration of pole pair number p, slots/pole/phase q and conductors/slot zq, easily implemented via loop patterns. It was also found that not all configurations led to feasible solutions and corresponding observations have been elaborated. The developed mathematical procedures also proved an effective framework for optimization among electromagnetic, thermal and mechanical aspects by allocating corresponding degree-of-freedom variables. Detailed 3D FEM analysis has been conducted to validate the resultant machine performance against design specifications. To obtain higher power ratings, electrical machines often have to increase the slot areas for accommodating more windings. Since the available space for embedding such machines inside an engine is usually short in length, axial air gap arrangement appears more appealing compared to its radial gap counterpart. The aforementioned approach has been adopted in case studies of designing series of AFIMs and RFIMs respectively with increasing power ratings. Following observations have been obtained. Under the strict rotor diameter limitation AFIM extended axially for the increased slot areas while RFIM expanded radially with the same axial length. Beyond certain power ratings AFIM led to long cylinder geometry while RFIM topology resulted in the desired short disk shape. Besides the different dimension growth patterns, AFIMs and RFIMs also exhibited dissimilar performance degradations regarding power factor, torque ripples as well as rated slip along with increased power ratings. Parametric response curves were plotted to better illustrate the above influences from increased power ratings. The case studies may provide a basic guideline that could assist potential users in making decisions between AFIM and RFIM for relevant applications.

Keywords: axial flux induction machine, electrical starter/generator, finite element analysis, squirrel cage induction machine

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Authors: S. Jayasinghe, R. B. N. Dissanayake

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Optimization modelling together with the Network models and Linear Programming techniques is a powerful tool in problem solving and decision making in real world applications. This study developed a mathematical model to optimize the net profit by minimizing the transportation cost. This model focuses the transportation among decentralized production plants to a centralized distribution centre and then the distribution among island wide agencies considering the customer satisfaction as a requirement. This company produces basically 9 types of food items with 82 different varieties and 4 types of non-food items with 34 different varieties. Among 6 production plants, 4 were located near the city of Mawanella and the other 2 were located in Galewala and Anuradhapura cities which are 80 km and 150 km away from Mawanella respectively. The warehouse located in the Mawanella was the main production plant and also the only distribution plant. This plant distributes manufactured products to 39 agencies island-wide. The average values and average amount of the goods for 6 consecutive months from May 2013 to October 2013 were collected and then average demand values were calculated. The following constraints are used as the necessary requirement to satisfy the optimum condition of the model; there was one source, 39 destinations and supply and demand for all the agencies are equal. Using transport cost for a kilometer, total transport cost was calculated. Then the model was formulated using distance and flow of the distribution. Network optimization and linear programming techniques were used to originate the model while excel solver is used in solving. Results showed that company requires total transport cost of Rs. 146, 943, 034.50 to fulfil the customers’ requirement for a month. This is very much less when compared with data without using the model. Model also proved that company can reduce their transportation cost by 6% when distributing to island-wide customers. Company generally satisfies their customers’ requirements by 85%. This satisfaction can be increased up to 97% by using this model. Therefore this model can be used by other similar companies in order to reduce the transportation cost.

Keywords: mathematical model, network optimization, linear programming

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Authors: Ainas Belkacem, Fourar Ali

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The present study focuses on the mathematical modeling and calculation of physical parameters of water pollution by oil and sand in regime fully dispersed in water. In this study, the sand particles and oil are suspended in the case of fully developed turbulence. The study consists to understand, model and predict the viscosity, the structure and dynamics of these types of mixtures. The work carried out is Numerical and validated by experience.

Keywords: multi phase flow, pollution, suspensions, turbulence

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Authors: Matar Celine, Gaucel Sebastien, Gontard Nathalie, Guilbert Stephane, Guillard Valerie

Abstract:

To increase the very short shelf life of fresh fruits and vegetable, Modified Atmosphere Packaging (MAP) allows an optimal atmosphere composition to be maintained around the product and thus prevent its decay. This technology relies on the modification of internal packaging atmosphere due to equilibrium between production/consumption of gases by the respiring product and gas permeation through the packaging material. While, to the best of our knowledge, benefit of MAP for fresh fruits and vegetable has been widely demonstrated in the literature, its effect on shelf life increase has never been quantified and formalized in a clear and simple manner leading difficult to anticipate its economic and environmental benefit, notably through the decrease of food losses. Mathematical modelling of mass transfers in the food/packaging system is the basis for a better design and dimensioning of the food packaging system. But up to now, existing models did not permit to estimate food quality nor shelf life gain reached by using MAP. However, shelf life prediction is an indispensable prerequisite for quantifying the effect of MAP on food losses reduction. The objective of this work is to propose an innovative approach to predict shelf life of MAP food product and then to link it to a reduction of food losses and wastes. In this purpose, a ‘Virtual MAP modeling tool’ was developed by coupling a new predictive deterioration model (based on visual surface prediction of deterioration encompassing colour, texture and spoilage development) with models of the literature for respiration and permeation. A major input of this modelling tool is the maximal percentage of deterioration (MAD) which was assessed from dedicated consumers’ studies. Strawberries of the variety Charlotte were selected as the model food for its high perishability, high respiration rate; 50-100 ml CO₂/h/kg produced at 20°C, allowing it to be a good representative of challenging post-harvest storage. A value of 13% was determined as a limit of acceptability for the consumers, permitting to define products’ shelf life. The ‘Virtual MAP modeling tool’ was validated in isothermal conditions (5, 10 and 20°C) and in dynamic temperature conditions mimicking commercial post-harvest storage of strawberries. RMSE values were systematically lower than 3% for respectively, O₂, CO₂ and deterioration profiles as a function of time confirming the goodness of model fitting. For the investigated temperature profile, a shelf life gain of 0.33 days was obtained in MAP compared to the conventional storage situation (no MAP condition). Shelf life gain of more than 1 day could be obtained for optimized post-harvest conditions as numerically investigated. Such shelf life gain permitted to anticipate a significant reduction of food losses at the distribution and consumer steps. This food losses' reduction as a function of shelf life gain has been quantified using a dedicated mathematical equation that has been developed for this purpose.

Keywords: food losses and wastes, modified atmosphere packaging, mathematical modeling, shelf life prediction

Procedia PDF Downloads 165

Authors: Karen Koellner, Nanette Seago, Jennifer Jacobs, Helen Garnier

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Although studies of teacher professional development (PD) are prevalent, surprisingly most have only produced incremental shifts in teachers’ learning and their impact on students. There is a critical need to understand what teachers take up and use in their classroom practice after attending PD and why we often do not see greater changes in learning and practice. This paper is based on a mixed methods efficacy study of the Learning and Teaching Geometry (LTG) video-based mathematics professional development materials. The extent to which the materials produce a beneficial impact on teachers’ mathematics knowledge, classroom practices, and their students’ knowledge in the domain of geometry through a group-randomized experimental design are considered. In this study, we examine a small group of teachers to better understand their interpretations of the workshops and their classroom uptake. The participants included 103 secondary mathematics teachers serving grades 6-12 from two states in different regions. Randomization was conducted at the school level, with 23 schools and 49 teachers assigned to the treatment group and 18 schools and 54 teachers assigned to the comparison group. The case study examination included twelve treatment teachers. PD workshops for treatment teachers began in Summer 2016. Nine full days of professional development were offered to teachers, beginning with the one-week institute (Summer 2016) and four days of PD throughout the academic year. The same facilitator-led all of the workshops, after completing a facilitator preparation process that included a multi-faceted assessment of fidelity. The overall impact of the LTG PD program was assessed from multiple sources: two teacher content assessments, two PD embedded assessments, pre-post-post videotaped classroom observations, and student assessments. Additional data was collected from the case study teachers including additional videotaped classroom observations and interviews. Repeated measures ANOVA analyses were used to detect patterns of change in the treatment teachers’ content knowledge before and after completion of the LTG PD, relative to the comparison group. No significant effects were found across the two groups of teachers on the two teacher content assessments. Teachers were rated on the quality of their mathematics instruction captured in videotaped classroom observations using the Math in Common Observation Protocol. On average, teachers who attended the LTG PD intervention improved their ability to engage students in mathematical reasoning and to provide accurate, coherent, and well-justified mathematical content. In addition, the LTG PD intervention and instruction that engaged students in mathematical practices both positively and significantly predicted greater student knowledge gains. Teacher knowledge was not a significant predictor. Twelve treatment teachers were self-selected to serve as case study teachers to provide additional videotapes in which they felt they were using something from the PD they learned and experienced. Project staff analyzed the videos, compared them to previous videos and interviewed the teachers regarding their uptake of the PD related to content knowledge, pedagogical knowledge and resources used.

Keywords: teacher learning, professional development, pedagogical content knowledge, geometry

Procedia PDF Downloads 153

Authors: Mihir Halder

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The main aim and objective of the eighteen-month long Diploma in Primary Education (DPED) teacher education training course for in-service primary teachers in Bangladesh is to acquire professional knowledge as well as make them proficient in professional practice. The training, therefore, introduces a variety of theoretical and practical approaches as well as some professional development activities—lesson study being one of them. But, in the field of mathematics teaching, even after implementing the lesson study method, the desired practical teaching skills of the teachers have not been developed. In addition, elementary students also remain quite raw in mathematics. Although there have been various studies to solve the problem, the need for the teachers' views on mathematical ideas has not been taken into consideration. The researcher conducted the research to find out the cause of the discussed problem. In this case, two teams of nine DPED trainee teachers and two instructors conducted two lesson studies in two schools located in the city and town of Khulna Province, Bangladesh. The researcher observed group lesson planning by trainee teachers, followed by a trainee teacher teaching the planned lesson plan to an actual mathematics classroom, and finally, post-teaching reflective discussion in each lesson study. Two DPED instructors acted as mentors in the lesson study. DPED trainee teachers and instructors were asked about mathematical concepts and classroom practices through questionnaires as well as videotaped mathematics classroom teaching. For this study, the DPED mathematics course, curriculum, and assessment activities were analyzed. In addition, the mathematics lesson plans prepared by the trainee teachers for the lesson study and their pre-teaching and post-teaching reflective discussions were analyzed by some analysis categories and rubrics. As a result, it was found that the trainee teachers' views of mathematics are not mature, and therefore, their mathematics teaching practice is not appropriate. Therefore, in order to improve teachers' mathematics teaching, the researcher recommended including some action-oriented aspects in each phase of mathematics lesson study in DPED—for example, emphasizing mathematics concepts of the trainee teachers, preparing appropriate teaching materials, presenting lessons using the problem-solving method, using revised rubrics for assessing mathematics lesson study, etc.

Keywords: mathematics lesson study, knowledge of mathematics, knowledge of teaching mathematics, teachers' views

Procedia PDF Downloads 49

Authors: Priyanka Ghosh, Priti Kumar Roy

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Every year a considerable number of people die due to methyl alcohol poisoning, in which most of them die even before proper treatment. This work gives a simple and cheap first aid to those affected individuals by the administration of activated charcoal. In this article, we emphasise on the adsorption capability of activated charcoal for the treatment of poisoning and use an impulsive differential equation to study the effect of activated charcoal during adsorption. We also investigate the effects of various parameters on the adsorption which are incorporated in the model system.

Keywords: activated charcoal, adsorption, impulsive differential equation, methanol poisoning

Procedia PDF Downloads 286

Authors: Khalil H. Al-Bayati, G. Nasma, Hussein Ban H. Adel

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The purpose of the present work is to calculate the expectation value of potential energy for different spin states (ααα ≡ βββ, αβα ≡ βαβ) and compare it with spin states (αββ, ααβ ) for lithium excited state (1s2s3s) and Li-like ions (Be+, B+2) using Hartree-Fock wave function by partitioning technique. The result of inter particle expectation value shows linear behaviour with atomic number and for each atom and ion the shows the trend ααα < ααβ < αββ < αβα.

Keywords: lithium excited state, potential energy, 1s2s3s, mathematical physics

Procedia PDF Downloads 465