Search results for: hypotenuse leg difference method

Authors: P. K. Rahul Krishna, S. Sandeep Kumar, Jayanthi Sunder Raj

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The article explores one of the important relations between numbers-the Pythagorean triples (triplets) which finds its application in distance measurement, construction of roads, towers, buildings and wherever Pythagoras theorem finds its application. The Pythagorean triples are numbers, that satisfy the condition “In a given set of three natural numbers, the sum of squares of two natural numbers is equal to the square of the other natural number”. There are numerous methods and equations to obtain the triplets, which have their own merits and demerits. Here, quadratic approach for generating triples uses the hypotenuse leg difference method. The advantage is that variables are few and finally only three independent variables are present.

Keywords: arithmetic progression, hypotenuse leg difference method, natural numbers, Pythagorean triplets, quadratic equation

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Authors: Nesrine T. Lamie

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Four, accurate, precise, and sensitive spectrophotometric methods are developed for the simultaneous determination of a binary mixture containing amlodipine besylate (AM) and atenolol (AT) where AM is determined at its λmax 360 nm (0D), while atenolol can be determined by different methods. Method (A) is absorpotion factor (AFM). Method (B) is the new Ratio Difference method(RD) which measures the difference in amplitudes between 210 and 226 nm of ratio spectrum., Method (C) is novel constant center spectrophotometric method (CC) Method (D) is mean centering of the ratio spectra (MCR) at 284 nm. The calibration curve is linear over the concentration range of 10–80 and 4–40 μg/ml for AM and AT, respectively. These methods are tested by analyzing synthetic mixtures of the cited drugs and they are applied to their commercial pharmaceutical preparation. The validity of results was assessed by applying standard addition technique. The results obtained were found to agree statistically with those obtained by a reported method, showing no significant difference with respect to accuracy and precision.

Keywords: amlodipine, atenolol, absorption factor, constant center, mean centering, ratio difference

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Authors: Reza Mollapourasl, Majid Haghi

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In this study, we develop local meshfree methods known as radial basis function-generated finite difference (RBF-FD) method and Hermite finite difference (RBF-HFD) method to design stencil weights and spatial discretization for Helmholtz equation. The convergence and stability of schemes are investigated numerically in three dimensions with irregular shaped domain. These localized meshless methods incorporate the advantages of the RBF method, finite difference and Hermite finite difference methods to handle the ill-conditioning issue that often destroys the convergence rate of global RBF methods. Moreover, numerical illustrations show that the proposed localized RBF type methods are efficient and applicable for problems with complex geometries. The convergence and accuracy of both schemes are compared by solving a test problem.

Keywords: radial basis functions, Hermite finite difference, Helmholtz equation, stability

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Authors: Ramzi B. Albadarneh

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In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

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Authors: Zainab Almukhtar, Adel Merabet

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In this paper, a method for maximum power point tracking of a photovoltaic energy conversion system is presented. This method is based on using the difference between the power from the solar panel and an estimated power value to control the DC-DC converter of the photovoltaic system. The difference is continuously compared with a preset error permitted value. If the power difference is more than the error, the estimated power is multiplied by a factor and the operation is repeated until the difference is less or equal to the threshold error. The difference in power will be used to trigger a DC-DC boost converter in order to raise the voltage to where the maximum power point is achieved. The proposed method was experimentally verified through a PV energy conversion system driven by the OPAL-RT real time controller. The method was tested on varying radiation conditions and load requirements, and the Photovoltaic Panel was operated at its maximum power in different conditions of irradiation.

Keywords: control system, error, solar panel, MPPT tracking

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Authors: Nguyen Van Loi, Le Thanh Son, Tran Trung Kien

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The paper deals with the problem of the formation of range profiles (RPs) for an X-band coastal surveillance radar. Two popular methods, the difference operator method, and the window-based method, are reviewed and analyzed via two tests with different datasets. The test results show that although the original window-based method achieves a better performance than the difference operator method, it has three main drawbacks that are the use of 3 or 4 peaks of an RP for creating the windows, the extension of the window size using the power sum of three adjacent cells in the left and the right sides of the windows and the same threshold applied for all types of vessels to finish the formation process of RPs. These drawbacks lead to inaccurate RPs due to the low signal-to-clutter ratio. Therefore, some suggestions are proposed to improve the original window-based method.

Keywords: range profile, difference operator method, window-based method, automatic target recognition

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Authors: Khairil I. Othman, Mahfuzah Mahayaddin, Zarina Bibi Ibrahim

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We develop and demonstrate a computationally efficient numerical technique to solve first order stiff differential equations. This technique is based on block method whereby three approximate points are calculated. The Cholistani of varied step sizes are presented in divided difference form. Stability regions of the formulae are briefly discussed in this paper. Numerical results show that this block method perform very well compared to existing methods.

Keywords: block method, divided difference, stiff, computational

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Authors: Toshanlal Meenpal, Ankita Meenpal

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A very important technique in reversible data hiding field is Difference expansion. Secret message as well as the cover image may be completely recovered without any distortion after data extraction process due to reversibility feature. In general, in any difference expansion scheme embedding is performed by integer transform in the difference image acquired by grouping two neighboring pixel values. This paper proposes an improved reversible difference expansion embedding scheme. We mainly consider edge direction for embedding by modifying the difference of two neighboring pixels values. In general, the larger difference tends to bring a degraded stego image quality than the smaller difference. Image quality in the range of 0.5 to 3.7 dB in average is achieved by the proposed scheme, which is shown through the experimental results. However payload wise it achieves almost similar capacity in comparisons with previous method.

Keywords: information hiding, wedge direction, difference expansion, integer transform

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Authors: N. R. Mohamad, H. Ono, H. Haroon, A. Salleh, N. M. Z. Hashim

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In this research, we have studied and analyzed the modulation of light and liquid crystal in HPDLCs using Finite Domain Time Difference (FDTD) method. HPDLCs are modeled as a mixture of polymer and liquid crystals (LCs) that categorized as an anisotropic medium. FDTD method is directly solves Maxwell’s equation with less approximation, so this method can analyze more flexible and general approach for the arbitrary anisotropic media. As the results from FDTD simulation, the highest diffraction efficiency occurred at ±19 degrees (Bragg angle) using p polarization incident beam to Bragg grating, Q > 10 when the pitch is 1µm. Therefore, the liquid crystal is assumed to be aligned parallel to the grating constant vector during these parameters.

Keywords: birefringence, diffraction efficiency, finite domain time difference, nematic liquid crystals

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: Nguyen Huy Hoang, Do Thanh Quan, Tran Vu Kien

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The use of the active radar to measure the coordinates of ultra-light drones is frequently difficult due to long-distance, absolutely small radar cross-section (RCS) and obstacles. Since ultra-light drones are usually controlled by the Time Difference of Arrival (RF), the paper proposed a method to measure the coordinates of ultra-light drones in the space based on the arrival time of the signal at receiving antennas and the time difference of arrival (TDOA). The experimental results demonstrate that the proposed method is really potential and highly accurate.

Keywords: ultra-light drone, TDOA, radar cross-section (RCS), RF

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Authors: Romella C. Lina, Matthew Daniel V. Leysa, Zarah D. F. Libozada, Maria Francesca I. Lirio, Angelo A. Liwag, Gabriel D. Ramos, Margaret M. Natividad

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This study aimed to determine the effectiveness of Buteyko Method in asthma control and quality of life of school-age children wherein a pretest-posttest design was utilized to measure the changes after the administration of Buteyko Method. Fourteen (14) subjects with bronchial asthma, aged 7-11 participated in the study. They were equally divided into two groups: the control group received no intervention while the experimental group was asked to attend sessions of Buteyko Method lecture and demonstration. The experimental group was visited for three (3) consecutive weeks to monitor their progress and compliance. Both groups were asked to answer ACQ pre- and post-intervention and PAQLQ before the start of the intervention phase and every week during the follow-up visits. In comparing the asthma control pre-test and post-test mean scores of the control group, no significant difference was noted (p=0.177) while the experimental group showed a significant difference after the administration of Buteyko Method (p=0.002). Moreover, the quality of life pre-test and post-test mean scores of the control group showed no significant difference in any week within one month of follow-up (p=0.736, 0.604, 0.689) while the experimental group showed a significant difference on the third week (p = 0.035) and fourth week (p=0.002) but no significant difference on the second week (p=0.111). Therefore, the use of Buteyko Method within 3-4 weeks as an adjunct to conventional management of asthma helps in improving asthma control and quality of life of school-age children.

Keywords: Buteyko Method, asthma, school-age children, asthma control, quality of life

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Abdel-Maksoud Abdel-Kader Soliman

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The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

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Authors: Chao-Qing Dai

Abstract:

In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: N. Fusun Oyman Serteller

Abstract:

In this paper, the techniques to solve time dependent electromagnetic wave propagation equations based on the Finite Difference Method (FDM) are proposed by comparing the results with Finite Element Method (FEM) in 2D while discussing some special simulation examples.  Here, 2D dynamical wave equations for lossy media, even with a constant source, are discussed for establishing symbolic manipulation of wave propagation problems. The main objective of this contribution is to introduce a comparative study of two suitable numerical methods and to show that both methods can be applied effectively and efficiently to all types of wave propagation problems, both linear and nonlinear cases, by using symbolic computation. However, the results show that the FDM is more appropriate for solving the nonlinear cases in the symbolic solution. Furthermore, some specific complex domain examples of the comparison of electromagnetic waves equations are considered. Calculations are performed through Mathematica software by making some useful contribution to the programme and leveraging symbolic evaluations of FEM and FDM.

Keywords: finite difference method, finite element method, linear-nonlinear PDEs, symbolic computation, wave propagation equations

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Authors: Alexander P. Smirnov, Sergey A. Matveev, Dmitry A. Zheltkov, Eugene E. Tyrtyshnikov

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We propose a new computational technique for multidimensional (multicomponent) Smoluchowski coagulation equation. Using low-rank approximations in Tensor Train format of both the solution and the coagulation kernel, we accelerate the classical finite-difference Runge-Kutta scheme keeping its level of accuracy. The complexity of the taken finite-difference scheme is reduced from O(N^2d) to O(d^2 N log N ), where N is the number of grid nodes and d is a dimensionality of the problem. The efficiency and the accuracy of the new method are demonstrated on concrete problem with known analytical solution.

Keywords: tensor train decomposition, multicomponent Smoluchowski equation, runge-kutta scheme, convolution

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Authors: Akhilesh Kumar, Sathyanarayan G., Nirmala S.

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An unusual approach is developed to determine the orbit of satellites/space objects. The determination of orbits is considered a boundary value problem and has been solved using the finite difference method (FDM). Only positions of the satellites/space objects are known at two end times taken as boundary conditions. The technique of finite difference has been used to calculate the orbit between end times. In this approach, the governing equation is defined as the satellite's equation of motion with a perturbed acceleration. Using the finite difference method, the governing equations and boundary conditions are discretized. The resulting system of algebraic equations is solved using Tri Diagonal Matrix Algorithm (TDMA) until convergence is achieved. This methodology test and evaluation has been done using all GPS satellite orbits from National Geospatial-Intelligence Agency (NGA) precise product for Doy 125, 2023. Towards this, two hours of twelve sets have been taken into consideration. Only positions at the end times of each twelve sets are considered boundary conditions. This algorithm is applied to all GPS satellites. Results achieved using FDM compared with the results of NGA precise orbits. The maximum RSS error for the position is 0.48 [m] and the velocity is 0.43 [mm/sec]. Also, the present algorithm is applied on the IRNSS satellites for Doy 220, 2023. The maximum RSS error for the position is 0.49 [m], and for velocity is 0.28 [mm/sec]. Next, a simulation has been done for a Highly Elliptical orbit for DOY 63, 2023, for the duration of 6 hours. The RSS of difference in position is 0.92 [m] and velocity is 1.58 [mm/sec] for the orbital speed of more than 5km/sec. Whereas the RSS of difference in position is 0.13 [m] and velocity is 0.12 [mm/sec] for the orbital speed less than 5km/sec. Results show that the newly created method is reliable and accurate. Further applications of the developed methodology include missile and spacecraft targeting, orbit design (mission planning), space rendezvous and interception, space debris correlation, and navigation solutions.

Keywords: finite difference method, grid generation, NavIC system, orbit perturbation

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Authors: Pouya Molana, Zeinab Alimohammadi

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Determining wind wave characteristics is essential for implementing projects related to Coastal and Marine engineering such as designing coastal and marine structures, estimating sediment transport rates and coastal erosion rates in order to predict significant wave height (H_s), this study applies the third generation spectral wave model, Mike 21 SW, along with CEM model. For SW model calibration and verification, two data sets of meteorology and wave spectroscopy are used. The model was exposed to time-varying wind power and the results showed that difference ratio mean, standard deviation of difference ratio and correlation coefficient in SW model for H_s parameter are 1.102, 0.279 and 0.983, respectively. Whereas, the difference ratio mean, standard deviation and correlation coefficient in The Choice Experiment Method (CEM) for the same parameter are 0.869, 1.317 and 0.8359, respectively. Comparing these expected results it is revealed that the Choice Experiment Method CEM has more errors in comparison to MIKE 21 SW third generation spectral wave model and higher correlation coefficient does not necessarily mean higher accuracy.

Keywords: MIKE 21 SW, CEM method, significant wave height, difference ratio

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Authors: Pranvera Shehaj

Abstract:

Unlike any prior analysis on the withholding tax rates negotiated in tax treaties, this study looks at the treaty heterogeneity content, by investigating the impact of the residence country’s double tax relief method and of tax-sparing agreements, on the difference between developing countries’ domestic withholding taxes on dividends on one side, and treaty negotiated withholding taxes at source on portfolio dividends on the other side. Using a dyadic panel dataset of asymmetric double tax treaties between 2005 and 2019, this study suggests first that the difference between domestic and negotiated WHTs on portfolio dividends is higher when the OECD member uses the credit method, as compared to when it uses the exemption method. Second, results suggest that the inclusion of tax-sparing provisions vanishes the positive effect of the credit method at home on the difference between domestic and negotiated WHTs on portfolio dividends, incentivizing developing countries to negotiate higher withholding taxes.

Keywords: double tax treaties, asymmetric investments, withholding tax, dividends, double tax relief method, tax sparing

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Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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Authors: Norhashidah Hj. Mohd Ali, Teng Wai Ping

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In this paper, we present a high order group explicit method in solving the two dimensional Helmholtz equation. The presented method is derived from a nine-point fourth order finite difference approximation formula obtained from a 45-degree rotation of the standard grid which makes it possible for the construction of iterative procedure with reduced complexity. The developed method will be compared with the existing group iterative schemes available in literature in terms of computational time, iteration counts, and computational complexity. The comparative performances of the methods will be discussed and reported.

Keywords: explicit group method, finite difference, helmholtz equation, rotated grid, standard grid

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Authors: Kelemewerk Destalem, Joongjae Cho, Jaeseong Lee, Ju H. Park, Joonhyuk Yoo

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Background subtraction and temporal difference are often used for moving object detection in video. Both approaches are computationally simple and easy to be deployed in real-time image processing. However, while the background subtraction is highly sensitive to dynamic background and illumination changes, the temporal difference approach is poor at extracting relevant pixels of the moving object and at detecting the stopped or slowly moving objects in the scene. In this paper, we propose a moving object detection scheme based on adaptive background subtraction and temporal difference exploiting dynamic background updates. The proposed technique consists of a histogram equalization, a linear combination of background and temporal difference, followed by the novel frame-based and pixel-based background updating techniques. Finally, morphological operations are applied to the output images. Experimental results show that the proposed algorithm can solve the drawbacks of both background subtraction and temporal difference methods and can provide better performance than that of each method.

Keywords: background subtraction, background updating, real time, light weight algorithm, temporal difference

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Authors: H. Samadiyeh, R. Khajavi

Abstract:

A new FD-based procedure, modal finite difference method (MFDM), is proposed for seismic wave propagation modeling, in which simulation is dealt with in the modal space. The method employs eigenvalues of a characteristic matrix formed by appropriate time-space FD stencils. Since MFD runs for different modes are totally independent of each other, MFDM can easily be parallelized while considerable simplicity in parallel-algorithm is also achieved. There is no requirement to any domain-decomposition procedure and inter-core data exchange. More important is the possibility to skip processing of less-significant modes, which enables one to adjust the procedure up to the level of accuracy needed. Thus, in addition to considerable ease of parallel programming, computation and storage costs are significantly reduced. The method is qualified for its efficiency by some numerical examples.

Keywords: Finite Difference Method, Graphics Processing Unit (GPU), Message Passing Interface (MPI), Modal, Wave propagation

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Authors: Kimi Ueda, Kosuke Sugita, Soma Kawamoto, Hiroshi Shimoda, Hirotake Ishii, Fumiaki Obayashi, Kazuhiro Taniguchi, Ayaka Suzuki

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The authors have focused on the thermal difference between office rooms and break rooms, and proposed an integrated thermal control method to improve workers’ intellectual concentration. First, a trial experiment was conducted to verify the effect of temperature difference on workers’ intellectual concentration with using two experimental rooms; a thermally neutral break room and a cooler office room. As the result of the experiment, it was found that the thermal difference had a significant effect on improving their intellectual concentration. Workers, however, often take a short break at their desks without moving to a break room, so that the thermal difference cannot be given to them. So utilization of airflow was proposed as an integrated thermal control method instead of the temperature difference to realize the similar effect. Concretely, they are exposed to airflow when working in order to reduce their effective temperature while it is weakened when taking a break. Another experiment was conducted to confirm the effect of the airflow control on their intellectual concentration. As the result of concentration index and questionnaire survey, their intellectual concentration was significantly improved in the integrated thermal controlled environment. It was also found that most of them felt more comfortable and had higher motivation and higher degree of concentration in the environment.

Keywords: airflow, evaluation experiment, intellectual concentration, thermal difference

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Authors: L. Srikanth, D. Neelima Satyam

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The transmission line towers are one of the important life line structures in the distribution of power from the source to the various places for several purposes. The predominant external loads which act on these towers are wind and earthquake loads. In this present study tower is analyzed using Indian Standards IS: 875:1987 (Wind Load), IS: 802:1995 (Structural Steel), IS:1893:2002 (Earthquake) and dynamic analysis of tower has been performed considering ground motion of 2001 Bhuj Earthquake (India). The dynamic analysis was performed considering a tower system consisting two towers spaced 800m apart and 35m height each. This analysis has been performed using numerical time stepping finite difference method which is central difference method were employed by a developed MATLAB program to get the normalized ground motion parameters includes acceleration, frequency, velocity which are important in designing the tower. The tower is analyzed using response spectrum analysis.

Keywords: response spectra, dynamic analysis, central difference method, transmission tower

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Authors: Vijay Kumar Kukreja, Ravneet Kaur

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In this paper, one dimensional advection diffusion model is analyzed using finite difference method based on Crank-Nicolson scheme. A practical problem of filter cake washing of chemical engineering is analyzed. The model is converted into dimensionless form. For the grid Ω × ω = [0, 1] × [0, T], the Crank-Nicolson spatial derivative scheme is used in space domain and forward difference scheme is used in time domain. The scheme is found to be unconditionally convergent, stable, first order accurate in time and second order accurate in space domain. For a test problem, numerical results are compared with the analytical ones for different values of parameter.

Keywords: Crank-Nicolson scheme, Lax-Richtmyer theorem, stability, consistency, Peclet number, Greschgorin circle

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Authors: Y. N. Reddy

Abstract:

The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

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Authors: Sandeep Santosh, O. P. Sahu

Abstract:

We simulate an efficient multiple wideband and nonstationary source localization algorithm by exploiting both the non-stationarity of the signals and the array geometric information.This algorithm is based on joint diagonalization structure (JDS) of a set of short time power spectrum matrices at different time instants of each frequency bin. JDS can be used for quick and accurate multiple non-stationary source localization. The JDS algorithm is a one stage process i.e it directly searches the Direction of arrivals (DOAs) over the continuous location parameter space. The JDS method requires that the number of sensors is not less than the number of sources. By observing the simulation results, one can conclude that the JDS method can localize two sources when their difference is not less than 7 degree but the Wideband MUSIC is able to localize two sources for difference of 18 degree.

Keywords: joint diagonalization structure (JDS), wideband direction of arrival (DOA), wideband MUSIC

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