Abstract: The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.
Abstract: Digital Terrain Model (DTM) is a digital numerical representation of the Earth's surface. DTMs have been applied to a diverse field of tasks, such as urban planning, military, glacier mapping, disaster management. In the expression of the Earth' surface as a mathematical model, an infinite number of point measurements are needed. Because of the impossibility of this case, the points at regular intervals are measured to characterize the Earth's surface and DTM of the Earth is generated. Hitherto, the classical measurement techniques and photogrammetry method have widespread use in the construction of DTM. At present, RADAR, LiDAR, and stereo satellite images are also used for the construction of DTM. In recent years, especially because of its superiorities, Airborne Light Detection and Ranging (LiDAR) has an increased use in DTM applications. A 3D point cloud is created with LiDAR technology by obtaining numerous point data. However recently, by the development in image mapping methods, the use of unmanned aerial vehicles (UAV) for photogrammetric data acquisition has increased DTM generation from image-based point cloud. The accuracy of the DTM depends on various factors such as data collection method, the distribution of elevation points, the point density, properties of the surface and interpolation methods. In this study, the random data reduction method is compared for DTMs generated from image based point cloud data. The original image based point cloud data set (100%) is reduced to a series of subsets by using random algorithm, representing the 75, 50, 25 and 5% of the original image based point cloud data set. Over the ANS campus of Afyon Kocatepe University as the test area, DTM constructed from the original image based point cloud data set is compared with DTMs interpolated from reduced data sets by Kriging interpolation method. The results show that the random data reduction method can be used to reduce the image based point cloud datasets to 50% density level while still maintaining the quality of DTM.
Abstract: The incubation period is defined as the time from infection with a microorganism to development of symptoms. In this research, two disease models: one with incubation period and another without incubation period were studied. The study involves the use of a mathematical model with a single incubation period. The test for the existence and stability of the disease free and the endemic equilibrium states for both models were carried out. The fourth order Runge-Kutta method was used to solve both models numerically. Finally, a computer program in MATLAB was developed to run the numerical experiments. From the results, we are able to show that the endemic equilibrium state of the model with incubation period is locally asymptotically stable whereas the endemic equilibrium state of the model without incubation period is unstable under certain conditions on the given model parameters. It was also established that the disease free equilibrium states of the model with and without incubation period are locally asymptotically stable. Furthermore, results from numerical experiments using empirical data obtained from Nigeria Centre for Disease Control (NCDC) showed that the overall population of the infected people for the model with incubation period is higher than that without incubation period. We also established from the results obtained that as the transmission rate from susceptible to infected population increases, the peak values of the infected population for the model with incubation period decrease and are always less than those for the model without incubation period.
Abstract: Solid oxide electrolysis cells have an immense potential in converting CO2 and H2O into syngas during co-electrolysis operation. The produced syngas can be further converted into hydrocarbons. This kind of technology is called power-to-gas or power-to-liquid. To produce hydrocarbons via this route, durability of the cells is still a challenge, which needs to be further investigated in order to improve the cells. In this work, various nickel-yttria stabilized zirconia (Ni-YSZ) fuel electrode supported or YSZ electrolyte supported cells, cerium gadolinium oxide (CGO) barrier layer, and an oxygen electrode are investigated for durability under co-electrolysis conditions in both galvanostatic and potentiostatic conditions. While changing the gas on the oxygen electrode, keeping the fuel electrode gas composition constant, a change in the gas concentration arc was observed by impedance spectroscopy. Measurements of open circuit potential revealed the presence of leaks in the setup. It is speculated that the change in concentration impedance may be related to the leaks. Furthermore, the cells were also tested under pressurized conditions to find an inter-play between the leak rate and the pressure. A mathematical modeling together with electrochemical and microscopy analysis is presented.
Abstract: The biochemical technology has been developing extremely fast since the middle of the last century. The main reason for such development represents a requirement for large production of high-quality biologically manufactured products such as pharmaceuticals, foods, and beverages. The impact of the biochemical industry on the world economy is enormous. The great importance of this industry also results in intensive development in scientific disciplines relevant to the development of biochemical technology. In addition to developments in the fields of biology and chemistry, which enable to understand complex biochemical processes, development in the field of control theory and applications is also very important. In the paper, the control for the biochemical reactor for the milk fermentation was studied. During the fermentation process, the biophysical quantities must be precisely controlled to obtain the high-quality product. To control these quantities, the bioreactor’s stirring drive and/or heating system can be used. Available commercial biochemical reactors are equipped with open loop or conventional linear closed loop control system. Due to the outstanding parameters variations and the partial nonlinearity of the biochemical process, the results obtained with these control systems are not satisfactory. To improve the fermentation process, the self-tuning adaptive control system was proposed. The use of the self-tuning adaptive control is suggested because the parameters’ variations of the studied biochemical process are very slow in most cases. To determine the linearized mathematical model of the fermentation process, the recursive least square identification method was used. Based on the obtained mathematical model the linear quadratic regulator was tuned. The parameters’ identification and the controller’s synthesis are executed on-line and adapt the controller’s parameters to the fermentation process’ dynamics during the operation. The use of the proposed combination represents the original solution for the control of the milk fermentation process. The purpose of the paper is to contribute to the progress of the control systems for the biochemical reactors. The proposed adaptive control system was tested thoroughly. From the obtained results it is obvious that the proposed adaptive control system assures much better following of the reference signal as a conventional linear control system with fixed control parameters.
Abstract: Diagnosis and deciding about diseases in medical fields is facing innate uncertainty which can affect the whole process of treatment. This decision is made based on expert knowledge and the way in which an expert interprets the patient's condition, and the interpretation of the various experts from the patient's condition may be different. Fuzzy logic can provide mathematical modeling for many concepts, variables, and systems that are unclear and ambiguous and also it can provide a framework for reasoning, inference, control, and decision making in conditions of uncertainty. In systems with high uncertainty and high complexity, fuzzy logic is a suitable method for modeling. In this paper, we use type-2 fuzzy logic for uncertainty modeling that is in diagnosis of leukemia. The proposed system uses an indirect-direct approach and consists of two stages: In the first stage, the inference of blood test state is determined. In this step, we use an indirect approach where the rules are extracted automatically by implementing a clustering approach. In the second stage, signs of leukemia, duration of disease until its progress and the output of the first stage are combined and the final diagnosis of the system is obtained. In this stage, the system uses a direct approach and final diagnosis is determined by the expert. The obtained results show that the type-2 fuzzy expert system can diagnose leukemia with the average accuracy about 97%.
Abstract: The operating principle of magnetically controlled microelectromechanical system (MEMS) switches is based on controlling the beam movement under the influence of a magnetic field. Currently, there is a MEMS switch design with a flexible ferromagnetic electrode in the form of a fixed-terminal beam, with an electrode fastened on a straight or cranked anchor. The basic performance characteristics of magnetically controlled MEMS switches (service life, sensitivity, contact resistance, fast response) are largely determined by the flexible electrode design. To ensure the stable and controlled motion of the flexible electrode, it is necessary to provide the optimal design of a flexible electrode.
Abstract: Today, the treatment of cancer, in a relatively short
period, with minimum adverse effects is a great concern for
oncologists. In this paper, based on a recently used mathematical
model for cancer, a guideline has been proposed for the amount
and duration of drug doses for cancer treatment by immunotherapy.
Dynamically speaking, the mathematical ordinary differential
equation (ODE) model of cancer has different equilibrium points;
one of them is unstable, which is called the no tumor equilibrium
point. In this paper, based on the number of tumor cells an
intelligent soft computing controller (a combination of fuzzy logic
controller and genetic algorithm), decides regarding the amount
and duration of drug doses, to eliminate the tumor cells and
stabilize the unstable point in a relatively short time. Two different
immunotherapy approaches; active and adoptive, have been studied
and presented. It is shown that the rate of decay of tumor cells is
faster and the doses of drug are lower in comparison with the result
of some other literatures. It is also shown that the period of
treatment and the doses of drug in adoptive immunotherapy are
significantly less than the active method. A recommendation to
oncologists has also been presented.
Abstract: Fuel Metering Unit (FMU) in fuel system of an aeroengine sometimes has direct influence on the engine performance, which is neglected for the sake of easy access to mathematical model of the engine in most cases. In order to verify the influence of FMU on an engine model, this paper presents a co-simulation of a stepping motor driven FMU (digital FMU) in a turboshaft aeroengine, using AMESim and MATLAB to obtain the steady and dynamic characteristics of the FMU. For this method, mechanical and hydraulic section of the unit is modeled through AMESim, while the stepping motor is mathematically modeled through MATLAB/Simulink. Combining these two sub-models yields an AMESim/MATLAB co-model of the FMU. A simplified component level model for the turboshaft engine is established and connected with the FMU model. Simulation results on the full model show that the engine model considering FMU characteristics describes the engine more precisely especially in its transition state. An FMU dynamics will cut down the rotation speed of the high pressure shaft and the inlet pressure of the combustor during the step response. The work in this paper reveals the impact of FMU on engine operation characteristics and provides a reference to an engine model for ground tests.
Abstract: Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.
Abstract: The development of Global Navigation Satellite System (GNSS) technology has led to increasingly widely and successful applications of GNSS surveys for monitoring crustal movements. Instead of the multi-period GNSS solutions, this study utilizes GNSS time series that are required to more precisely determine the vertical deformations in the study area. In recent years, the surface deformations that are parallel and semi-parallel to Bolvadin fault have occurred in Western Anatolia. These surface deformations have continued to occur in Bolvadin settlement area that is located mostly on alluvium ground. Due to these surface deformations, a number of cracks in the buildings located in the residential areas and breaks in underground water and sewage systems have been observed. In order to determine the amount of vertical surface deformations, two continuous GNSS stations have been established in the region. The stations have been operating since 2015 and 2017, respectively. In this study, GNSS observations from the mentioned two GNSS stations were processed with GAMIT/GLOBK (GNSS Analysis Massachusetts Institute of Technology/GLOBal Kalman) program package to create coordinate time series. With the time series analyses, the GNSS stations’ behaviour models (linear, periodical, etc.), the causes of these behaviours, and mathematical models were determined. The study results from the time series analysis of these two 2 GNSS stations show approximately 50-90 mm/yr vertical movement.
Abstract: The use of renewable energies is growing significantly worldwide. Faced with the increasing demand for electrical energy, mainly for the needs of remote, deserted and mountainous regions, numerous applications use photovoltaic energy. In this sense, the proposed study concerns a mathematical modeling and an experimental validation for the recovery of essential oil by a steam distillation system using photovoltaic energy. In this paper, we proceed to a modeling of the solar system that includes a photovoltaic (PV) generator with an electronic power converter allowing a continuation of the optimum operating point. The results obtained are promising and are validated practically.
Abstract: This paper presents the two loop proportional integral (PI) controller for speed control of permanent magnet DC motor (PMDC) motor drive with H-bridge DC chopper. PMDC motors are widely used in many applications because of having a good performance and it is easy to apply the speed control. The speed can be adjusted by using armature voltage control as it had only the armature circuit. H-bridge DC chopper circuit is used to obtain the desired speed in any direction. In this system, the two loop PI controller is designed by using pole-zero cancellation method. The speed and current controller gains are considered depending on the sampling frequency of the microcontroller. An Arduino IO package is used to implement the control algorithm. Both simulation and experimental results are presented to prove the correctness of the mathematical model.
Abstract: In this paper, the DC-link voltage control of DC-DC boost converter–inverter system is proposed. The mathematical model is developed from four different sub-circuits that depended on the switch positions. The developed differential equations are combined to develop the dynamic model. Transfer function is generated from the switched function model. Fluctuation of DC-link voltage causes connected loads malfunction. For this problem, a kind of traditional controller, the PI controller is applied to achieve constant DC-link voltage. The PI controller gains are obtained based on transfer function step response. The simulation work has been studied by using MATLAB/Simulink software and hardware prototype is implemented with a low-cost microcontroller Arduino Nano. Experimental results are collected by using ArduinoIO library package. Closed-loop DC-link voltage control system is tested with various line and load disturbances. It is found that the experimental results give equal responses with the simulation results.
Abstract: The current study investigated the effect of catalyst ratio and methanol to oil ratio on biodiesel production by using central composite design. Biodiesel was produced by transesterification using sodium hydroxide as a homogeneous catalyst, a laboratory scale reactor consisting of flat bottom flask mounts with a reflux condenser, and a heating plate was used to produce biodiesel. Key parameters, including time, temperature, and mixing rate was kept constant at 60 minutes, 60 oC and 600 RPM, respectively. From the results obtained, it was observed that the biodiesel yield depends on catalyst ratio and methanol to oil ratio. The highest yield of 50.65% was obtained at catalyst ratio of 0.5 wt.% and methanol to oil mole ratio 10.5. The analysis of variances of biodiesel yield showed the R Squared value of 0.8387. A quadratic mathematical model was developed to predict the biodiesel yield in the specified parameters ranges.
Abstract: In electrical discharge machining (EDM), a complete and clear theory has not yet been established. The developed theory (physical models) yields results far from reality due to the complexity of the physics. It is difficult to select proper parameter settings in order to achieve better EDM performance. However, modelling can solve this critical problem concerning the parameter settings. Therefore, the purpose of the present work is to develop mathematical model to predict performance characteristics of EDM on Ti-5Al-2.5Sn titanium alloy. Response surface method (RSM) and artificial neural network (ANN) are employed to develop the mathematical models. The developed models are verified through analysis of variance (ANOVA). The ANN models are trained, tested, and validated utilizing a set of data. It is found that the developed ANN and mathematical model can predict performance of EDM effectively. Thus, the model has found a precise tool that turns EDM process cost-effective and more efficient.
Abstract: This paper investigated the simulation of two-phase interleaved boost converter (IBC) with free and open-source software Scilab/Xcos. By using interleaved method, it can reduce current stress on components, components size, input current ripple and output voltage ripple. The required mathematical model is obtained from the equivalent circuit of its different four modes of operation for simulation. The equivalent circuits are considered in continuous conduction mode (CCM). The average values of the system variables are derived from the state-space equation to find the equilibrium point. Scilab is now becoming more and more popular among students, engineers and scientists because it is open-source software and free of charge. It gives a great convenience because it has powerful computation and simulation function. The waveforms of output voltage, input current and inductors current are obtained by using Scilab/Xcos.
Abstract: In this paper, the average input current mode control is proposed for two-phase interleaved boost converter with two separate input inductors operating in continuous conduction mode (CCM). The required mathematical model is obtained from the equivalent circuits of its different four modes of operation. The small ripple approximation is derived to find the transfer functions from dynamic model using switching function. In average input current mode control, the inner current loop and outer voltage loop are designed with PI controller using bode analysis. Anti-windup structure is applied for PI controllers in control system. Moreover, the simulation work is carried out by MATLAB/Simulink. And, the hardware prototype is implemented by using low-cost microcontroller Arduino Nano. Finally, the laboratory prototype, available from the local market, is constructed to validate the mathematical model. The results show that the output voltage response is the faster rise time and settling time with acceptable overshoot.
Abstract: Nowadays, there is an increasing attention to the resources scarcity issues. Because of failure in present patterns in the field of the allocation of exhaustible resources between generations and the challenges related to economic justice supply, it is supposed, to present a pattern from the Islamic perspective in this essay. By using content analysis of religious texts, we conclude that governments should remove the gap which is exists between the per capita income of the poor and their minimum consumption (necessary consumption). In order to preserve the exhaustible resources for poor people) not for all), between all generations, government should invest exhaustible resources on endless resources according to Hartwick’s criteria and should spend these benefits for poor people. But, if benefits did not cover the gap between minimum consumption and per capita income of poor levels in one generation, in this case, the government is responsible for covering this gap through the direct consumption of exhaustible resources. For an exact answer to this question, ‘how much of exhaustible resources should expense to maintain justice between generations?’ The theoretical and mathematical modeling has been used and proper function has been provided. The consumption pattern is presented for economic policy makers in Muslim countries, and non-Muslim even, it can be useful.
Abstract: This paper deals with measuring and modelling of the quality of the machined surface of the metal machining process. The average surface roughness (Ra) which represents the quality of the machined part was measured during the dry turning of the AISI 4140 steel. A large number of factors with the unknown relations among them influences this parameter, and that is why mathematical modelling is extremely complicated. Different values of cutting speed, feed rate, depth of cut (cutting regime) and workpiece hardness causes different surface roughness values. Modelling with soft computing techniques may be very useful in such cases. This paper presents the usage of the fuzzy logic-based system for determining metal machining process parameter in order to find the proper values of cutting regimes.