Search results for: timing equation

Authors: Julia B. Kischkat, Charlie D. Waters

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This research aims to understand the factors that may affect the survival and productivity of Pacific salmonids through two components. The first component is lab-based and aims to improve high-performance liquid chromatography to better quantify vitamin deficiencies such as thiamine. The lab work is conducted at the National Oceanic and Atmospheric Administration (NOAA) Ted Stevens Marine Research Institute in Juneau, Alaska. Deficiencies in thiamine have been shown to reduce the survival of salmonids at early life stages. The second component involves the analysis of a 22-year data set of migration timing of juvenile Coho Salmon, Dolly Varden, Steelhead, and returning adult Steelhead at Little Port Walter, Alaska. The statistical analysis quantifies their migration fluctuations and whether they correlate to various environmental conditions such as temperature, salinity, and precipitation.

Keywords: climate change, smolt timing, phenology, migration timing, salmon, time series analysis, ecology, chemistry, fisheries science

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Authors: Ognjen Vukovic

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Chern-Simons equation represents the cornerstone of quantum physics. The question that is often asked is if the aforementioned equation can be successfully applied to the interaction in international financial markets. By analysing the time series in financial theory, it is proved that Chern-Simons equation can be successfully applied to financial time-series. The aforementioned statement is based on one important premise and that is that the financial time series follow the fractional Brownian motion. All variants of Chern-Simons equation and theory are applied and analysed. Financial theory time series movement is, firstly, topologically analysed. The main idea is that exchange rate represents two-dimensional projections of three-dimensional Brownian motion movement. Main principles of knot theory and topology are applied to financial time series and setting is created so the Chern-Simons equation can be applied. As Chern-Simons equation is based on small particles, it is multiplied by the magnifying factor to mimic the real world movement. Afterwards, the following equation is optimised using Solver. The equation is applied to n financial time series in order to see if it can capture the interaction between financial time series and consequently explain it. The aforementioned equation represents a novel approach to financial time series analysis and hopefully it will direct further research.

Keywords: Brownian motion, Chern-Simons theory, financial time series, econophysics

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Authors: Paschal A. Ochang, Emmanuel C. Oji

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The Duffing’s Equation is a second order system that is very important because they are fundamental to the behaviour of higher order systems and they have applications in almost all fields of science and engineering. In the biological area, it is useful in plant stem dependence and natural frequency and model of the Brain Crash Analysis (BCA). In Engineering, it is useful in the study of Damping indoor construction and Traffic lights and to the meteorologist it is used in the prediction of weather conditions. However, most Problems in real life that occur are non-linear in nature and may not have analytical solutions except approximations or simulations, so trying to find an exact explicit solution may in general be complicated and sometimes impossible. Therefore we aim to find out if it is possible to obtain one analytical fixed point to the non-linear ordinary equation using fixed point analytical method. We started by exposing the scope of the Duffing’s equation and other related works on it. With a major focus on the fixed point and fixed point iterative scheme, we tried different iterative schemes on the Duffing’s Equation. We were able to identify that one can only see the fixed points to a Damped Duffing’s Equation and not to the Undamped Duffing’s Equation. This is because the cubic nonlinearity term is the determining factor to the Duffing’s Equation. We finally came to the results where we identified the stability of an equation that is damped, forced and second order in nature. Generally, in this research, we approximate the solution of Duffing’s Equation by converting it to a system of First and Second Order Ordinary Differential Equation and using Fixed Point Iterative approach. This approach shows that for different versions of Duffing’s Equations (damped), we find fixed points, therefore the order of computations and running time of applied software in all fields using the Duffing’s equation will be reduced.

Keywords: damping, Duffing's equation, fixed point analysis, second order differential, stability analysis

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Levicatus Mugenyi, Joaniter Nankabirwa, Emmanuel Arinaitwe, John Rek, Niel Hens, Moses Kamya, Grant Dorsey

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Background: Indoor residual spraying (IRS) reduces vector densities and malaria transmission, however, the most effective spraying intervals for IRS have not been well established. We aim to estimate the optimal timing interval for IRS using a modeling approach. Methods: We use a generalized additive model to estimate the optimal timing interval for IRS using the predicted malaria incidence. The model is applied to post IRS cohort clinical data from children aged 0.5–10 years in selected households in Tororo, historically a high malaria transmission setting in Uganda. Six rounds of IRS were implemented in Tororo during the study period (3 rounds with bendiocarb: December 2014 to December 2015, and 3 rounds with actellic: June 2016 to July 2018). Results: Monthly incidence of malaria from October 2014 to February 2019 decreased from 3.25 to 0.0 per person-years in the children under 5 years, and 1.57 to 0.0 for 5-10 year-olds. The optimal time interval for IRS differed between bendiocarb and actellic and by IRS round. It was estimated to be 17 and 40 weeks after the first round of bendiocarb and actellic, respectively. After the third round of actellic, 36 weeks was estimated to be optimal. However, we could not estimate from the data the optimal time after the second and third rounds of bendiocarb and after the second round of actellic. Conclusion: We conclude that to sustain the effect of IRS in a high-medium transmission setting, the second rounds of bendiocarb need to be applied roughly 17 weeks and actellic 40 weeks after the first round, and the timing differs for subsequent rounds. The amount of rainfall did not influence the trend in malaria incidence after IRS, as well as the IRS timing intervals. Our results suggest that shorter intervals for the IRS application can be more effective compared to the current practice, which is about 24 weeks for bendiocarb and 48 weeks for actellic. However, when considering our findings, one should account for the cost and drug resistance associated with IRS. We also recommend that the timing and incidence should be monitored in the future to improve these estimates.

Keywords: incidence, indoor residual spraying, generalized additive model, malaria

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Authors: Sachin Kumar

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

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

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Authors: Chor Nejmeddine, Ines Ben Omrane, Mohamed Abdelwahed

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In this paper, we present a posteriori analysis of the discretization of the heat equation by spectral element method. We apply Euler's implicit scheme in time and spectral method in space. We propose two families of error indicators, both of which are built from the residual of the equation and we prove that they satisfy some optimal estimates. We present some numerical results which are coherent with the theoretical ones.

Keywords: heat equation, spectral elements discretization, error indicators, Euler

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

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Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two-dimensional Schrodinger equation

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Authors: A. Suparmi, C. Cari, M. Yunianto, B. N. Pratiwi

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D-dimensional Dirac equations of q-deformed shape invariant potentials were solved using supersymmetric quantum mechanics (SUSY QM) in the case of exact spin symmetry. The D dimensional radial Dirac equation for shape invariant potential reduces to one-dimensional Schrodinger type equation by an appropriate variable and parameter change. The relativistic energy spectra were analyzed by using SUSY QM and shape invariant properties from radial D dimensional Dirac equation that have reduced to one dimensional Schrodinger type equation. The SUSY operator was used to generate the D dimensional relativistic radial wave functions, the relativistic energy equation reduced to the non-relativistic energy in the non-relativistic limit.

Keywords: D-dimensional dirac equation, non-central potential, SUSY QM, radial wave function

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Authors: Weiping Liu

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This paper presents an equation to calculate stock prices of different growth model. This equation is mathematically derived by using discounted cash flow method. It has the advantages of being very easy to use and very accurate. It can still be used even when the first stage is lengthy. This equation is more generalized because it can be used for all the three popular stock price models. It can be programmed into financial calculator or electronic spreadsheets. In addition, it can be extended to a multistage model. It is more versatile and efficient than the traditional methods.

Keywords: stock price, multistage model, different growth model, discounted cash flow method

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Authors: Eugene Benilov, Mikhail Benilov

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The Enskog-Vlasov (EV) equation is a widely used semi-phenomenological model of gas/liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an H-theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications.

Keywords: Enskog collision integral, hard spheres, kinetic equation, phase transition

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Authors: Abdulrahman Abdulrahman

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When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.

Keywords: channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow

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Authors: A. Zerarka, W. Djoudi

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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.

Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation

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Authors: Hebert Montegranario, Mauricio Londoño

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Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.

Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion

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Authors: Chun Pao Kuo, Chi Tong Lin

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The study explored atomization characteristics of tire pyrolysis fuel and its impacts on using three types of fuel: diesel oil mixed with 10% of tire pyrolysis fuel (called T10), diesel oil mixed with 20% tire pyrolysis (called T20), and consumer-grade diesel oil (D100). The investigators used the fuel for simulation and tests at various fuel injection timing, engine speed, and fuel injection speed to inspect impacts from fuel type on oil droplet atomization speed and output power. Actual vehicle tests were conducted using a 5-ton sedan (Hino) with 3660 cc displacement and a front-end inline four-cylinder diesel engine, and this type of vehicle is easily available from the market. A dynamometer was used to set up three engine speeds for the dynamometer testing at different injection timing and pressure. Next, an exhaust analyzer was used to measure exhaust pollution at different conditions to explore the effect of fuel types and injection speeds on output power in order to establish the best operation conditions for tire pyrolysis fuel.

Keywords: diesel engine, exhaust pollution, fuel injection timing, tire pyrolysis oil

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Authors: Imen Ben Abda

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Languages have been classified into different rhythm classes. 'Stress-timed' languages are exemplified by English, 'syllable-timed' languages by French and 'mora-timed' languages by Japanese. However, to our best knowledge, acoustic studies have not been unanimous in strictly establishing which rhythm category a given language belongs to and failed to show empirical evidence for isochrony. Perception seems to be a good approach to categorize languages into different rhythm classes. This study, within the scope of experimental phonetics, includes an account of different perceptual experiments using cues from natural and inverted speech, as well as pitch extracted from speech data. It is an attempt to categorize speech rhythm over a large set of Arabic (Tunisian, Algerian, Lebanese and Moroccan) and English dialects (Welsh, Irish, Scottish and Texan) as well as other languages such as Chinese, Japanese, French, and German. Listeners managed to classify the different languages and dialects into different rhythm classes using suprasegmental cues mainly rhythm and pitch (F0). They also perceived rhythmic differences even among languages and dialects belonging to the same rhythm class. This may show that there are different subclasses within very broad rhythmic typologies.

Keywords: F0, inverted speech, mora-timing, rhythm variation, stress-timing, syllable-timing

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Authors: Yani Shi, Jiaqi Yan

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A new product is important for companies to extend consumers and manifest competitiveness. New product often involves new features that consumers might not be familiar with while it may also have a competitive advantage to attract consumers compared to established products. However, although most online retailers employ recommendation agents (RA) to influence consumers’ product choice decision, recommended new products are not accepted and chosen as expected. We argue that it might also be caused by providing a new product recommendation in the wrong way at the wrong time. This study seeks to discuss how new product evaluations sourced from third parties could be employed in RAs as evidence of the superiority for the new product and how the new product recommendation could be provided to a consumer at the right time so that it can be accepted and finally chosen during the consumer’s decision-making process. A 2*2 controlled laboratory experiment was conducted to understand the selection of new product recommendation sources and recommendation timing. Human subjects were randomly assigned to one of the four treatments to minimize the effects of individual differences on the results. Participants were told to make purchase choices from our product categories. We find that a new product recommended right after a similar existing product and with the source of the expert review will be more likely to be accepted. Based on this study, both theoretical and practical contributions are provided regarding new product recommendation.

Keywords: new product recommendation, recommendation timing, recommendation source, recommendation agents

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Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha

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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.

Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law

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Authors: Fadi Awawdeh, O. Alsayyed, S. Al-Shará

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Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.

Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media

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Authors: Seyed Sadegh Naseralavi

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This paper presents a Kernel parallelization equation for damage identification in structures under unknown periodic excitations. Herein, the dynamic differential equation of the motion of structure is viewed as a mapping from displacements to external forces. Utilizing this viewpoint, a new method for damage detection in structures under periodic loads is presented. The developed method requires only two periods of load. The method detects the damages without finding the input loads. The method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering the concept, kernel parallelization equation (KPE) is derived for damage detection under unknown periodic loads. The method is verified for a case study under periodic loads.

Keywords: Kernel, unknown periodic load, damage detection, Kernel parallelization equation

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Authors: Johnson Oladele Fatokun, I. P. Akpan

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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

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Authors: T. Kizza, M. Muyinda

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Irrigation schedules are normally given in terms of frequency (irrigation days). Specific timings within a given day are not usually included. This study examined the effect of irrigation timing for a two-day irrigation schedule of a surface drip-irrigated tomato field on yield. It was carried out for three dry seasons; July-Sept 2016, Jan-April 2017 and Jan-March 2018, at MuZARDI research station. Four irrigation treatments; T1 morning (8.00hrs), T2 noon (12:00hrs), T3 evening (17:00hr) and T4, a combination of morning and evening, were evaluated. The irrigation duration was one hour for T1-T3 and split into 30 minutes for T4. First season results indicated noon watering as having the best yield over other treatments at 51.59t/ha followed closely by morning watering at 50.6t/ha. Plants watered at noon had the highest number of fruits at 19/plant with an average weight of 94g/fruit. Plants watered in the morning had fruits with the highest average weight at 111.2g/fruit but they were the lowest number at 16 fruits/plant. The three-season data indicated the highest yield at 45.9t/ha for morning watering, followed by noon watering at 44.3t/ha and the least yield was for evening watering at 40.9t/ha. Watering tomatoes in the morning will give optimum yields for a two-day irrigation schedule.

Keywords: drip irrigation, irrigation schedule, irrigation timing, tomato yield

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Authors: Boguslaw Schreyer

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In some types of wheeled robots it is important to secure starting acceleration and deceleration maxima while at the same time maintaining transversal stability. In this paper torque distribution between the front and rear wheels as well as the timing of torque application have been calculated. Both secure an optimum traction coefficient. This paper also identifies required input signals to a control unit, which controls the torque values and timing. Using a three dimensional, two mass model of a robot developed by the author a computer simulation was performed confirming the calculations presented in this paper. These calculations were also implemented and confirmed during military robot testing.

Keywords: robot dynamics, torque distribution, traction coefficient, wheeled robots

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Authors: Takashi Shimizu, Tomoaki Hashimoto

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Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: observer systems, unscented Kalman filter, nonlinear systems, Burgers' equation

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Authors: Narumol Chintaganun

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In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy.

Keywords: central differencing scheme, STG, advection equation, burgers equation

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Authors: Chung To Kong, Siu Ming Yiu

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Rubik's cube was invented in 1974. Since then, speedcubers all over the world try their best to break the world record again and again. The newest record is 3.47 seconds. There are many factors that affect the timing, including turns per second (tps), algorithm, finger trick, hardware of the cube. In this paper, the lower bound of the cube solving time will be discussed using convex optimization. Extended analysis of the world records will be used to understand how to improve the timing. With the understanding of each part of the solving step, the paper suggests a list of speed improvement techniques. Based on the analysis of the world record, there is a high possibility that the 3 seconds mark will be broken soon.

Keywords: Rubik's Cube, speed, finger trick, optimization

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Authors: H. Ozbasaran

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IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.

Keywords: cantilever, IPN, IPE, lateral torsional buckling

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Authors: Alirıza Kaleli, M. Akif Ceviz, Erdoğan Güner, Köksal Erentürk

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The cyclic variations in spark ignition engines occurring especially under specific engine operating conditions make the maximum pressure variable for successive in-cylinder pressure cycles. Minimization of cyclic variations has a great importance in effectively operating near to lean limit, or at low speed and load. The cyclic variations may reduce the power output of the engine, lead to operational instabilities, and result in undesirable engine vibrations and noise. In this study, spark timing is controlled in order to reduce the cyclic variations in spark ignition engines. Firstly, an ARMAX model has developed between spark timing and maximum pressure using system identification techniques. By using this model, the maximum pressure of the next cycle has been predicted. Then, self-tuning minimum variance controller has been designed to change the spark timing for consecutive cycles of the first cylinder of test engine to regulate the in-cylinder maximum pressure. The performance of the proposed controller is illustrated in real time and experimental results show that the controller has a reliable effect on cycle to cycle variations of maximum cylinder pressure when the engine works under low speed conditions.

Keywords: cyclic variations, cylinder pressure, SI engines, self tuning controller

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Authors: H. Triki, Y. Hamaizi, A. El-Akrmi

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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.

Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution

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Authors: Khatija Bahdur, Duane Dell’Oca

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There is limited information on how altitude impacts performance in a team sport. Most altitude research in football has been conducted at high elevation ( > 2500m), resulting in a chasm of understanding whether low to moderate altitude affects performance. The South African Premier Soccer League (PSL) fixtures entail matches played at altitudes from sea level to 1700m above mean sea level. Despite coaches highlighting the effect of altitude on performance outcomes in matches, further research is needed to establish whether altitude does impact match results. Greater insight into if and how altitude impacts performance in the PSL will assist coaches in deciding if and how to incorporate altitude in their planning. The purpose of this study is to fill in this gap through the use of a retrospective analysis of PSL matches. This quantitative study is based on a descriptive analysis of 181 PSL matches involving one team based at sea-level, taking place over a period of thirteen seasons. The following data were obtained: altitude at which the match was played, match result, the timing of goals, and timing of substitutions. The altitude was classified in 2 ways: inland ( > 500m) and coastal ( < 500m) and also further subdivided into narrower categories ( < 500m, 500-1000m, 1000-1300m; 1300-1500m, > 1500m). The analysis included a 2-sample t-test to determine differences in total goals scored and timing of goals for inland and coastal matches and the chi-square test to identify the significance of altitude on match results. The level of significance was set at the alpha level of 0.05. Match results are significantly affected by the altitude and level of altitude within inland teams most likely to win when playing at inland venues (p=0.000). The proportion of draws was slightly higher at the coast. At altitudes between 500-1000m, 1300-1500m, and 1500-1700m, a greater percentage of matches were won by coastal teams as opposed to draws. The timing of goals varied based on the team’s base altitude and the match elevation. The most significant differences were between 36-40 minutes (p=0.023), 41-45 minutes (p=0.000) and 50-65 minutes (p=0.000). When breaking down inland team’s matches to different altitude categories, greater differences were highlighted. Inland teams scored more goals per minute between 10-20 minute (p=0.009), 41-45 minutes (p=0.003) and 50-65 minutes (p=0.015). The total number of goals scored per match at different altitudes by a) inland teams (p=0.000), b) coastal teams (p=0.006). Coastal teams made significantly more substitutions when playing at altitude (p=0.034), although there were no significant differences when comparing the different altitude categories. The timing of all three changes, however, did vary significantly at the different altitudes. There were no significant differences in timing or number of substitutions for inland teams. Match results and timing of goals are influenced by altitude, with differences between the level of altitude also playing a role. The trends indicate that inland teams win more matches when playing at altitude against coastal teams, and they score more goals just prior to half-time and in the first quarter of the second half.

Keywords: coastal teams, inland teams, timing of goals, results, substitutions

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