Search results for: Ricatti equation mapping approach

Authors: Ch. Surawut, D. Sukawat

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In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.

Keywords: dynamic equation, downscaling, inverse distance, weight interpolation

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Authors: Jawad Zakir, Syed Irtiza Ali Shah, Rana Shaharyar, Sidra Mahmood

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Y-force equation comprises aerodynamic forces, drag and side force with side slip angle β and weight component along with the coupled roll (φ) and pitch angles (θ). This research deals with the linearization of Y-force equation using Small Disturbance theory assuming equilibrium flight conditions for different state variables of aircraft. By using assumptions of Small Disturbance theory in non-linear Y-force equation, finally reached at linearized lateral rigid body equation of motion; which says that in linearized Y-force equation, the lateral acceleration is dependent on the other different aerodynamic and propulsive forces like vertical tail, change in roll rate (Δp) from equilibrium, change in yaw rate (Δr) from equilibrium, change in lateral velocity due to side force, drag and side force components due to side slip, and the lateral equation from coupled rotating frame to decoupled rotating frame. This paper describes implementation of this lateral linearized equation for aircraft control systems. Another significant parameter considered on which y-force equation depends is ‘c’ which shows that any change bought in the weight of aircrafts wing will cause Δφ and cause lateral force i.e. Y_c. This simplification also leads to lateral static and dynamic stability. The linearization of equations is required because much of mathematics control system design for aircraft is based on linear equations. This technique is simple and eases the linearization of the rigid body equations of motion without using any high-speed computers.

Keywords: Y-force linearization, small disturbance theory, side slip, aerodynamic force drag, lateral rigid body equation of motion

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Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma

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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.

Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental

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Authors: Adriano Valdes-Gomez, Francisco Javier Sevilla

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We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature.

Keywords: diffusion on the sphere, Fokker-Planck equation on the sphere, non equilibrium processes on the sphere, numerical methods for diffusion on the sphere

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Authors: S. O. Oyamakin, A. U. Chukwu

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Richard's growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richard's growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richard's growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richard's nonlinear growth models better than the classical Richard's growth model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, Richard's, stochastic

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Authors: Ilija Plecas, Dalibor Arbutina

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The leaching rate of 60Co from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source, an equation for diffusion coupled to a first order equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.

Keywords: cement, concrete, immobilization, leaching, permeability, radioactivity, waste

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Authors: Nasim Babazadeh

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Growing demand for a quieter dwelling environment has turned the attention of construction companies to reducing the propagated noise of their project. In inner-city constructions, close distance between the construction site and surrounding buildings lessens the efficiency of passive noise control methods. Dwellers of the nearby areas may file complaints and lawsuits against the construction companies due to the emitted construction noise, thereby leading to the interruption of processes, compensation costs, or even suspension of the project. Therefore, construction noise should be predicted along with the project schedule. The advantage of managing the noise in the pre-construction phase is two-fold. Firstly, changes in the time plan and construction methods can be applied more flexibly. Thus, the costs related to rescheduling can be avoided. Secondly, noise-related legal problems are expected to be reduced. To implement noise mapping methods for the mentioned prediction, the required detailed information (such as the location of the noisy process, duration of the noisy work) can be exported from the 4D BIM model. The results obtained from the noise maps would be used to help the planners to define different work scenarios. The proposed approach has been applied for the foundation and earthwork of a site located in a residential area, and the obtained results are discussed.

Keywords: building information modeling, construction noise management, noise mapping, 4D BIM

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In the paper, our purpose is to enhance the ability to solve a nonlinear differential equation which is about the motion of an incompressible fluid flow going down of an inclined plane without thermal effect with a simple and innovative approach which we have named it new method. Comparisons are made amongst the Numerical, new method, and HPM methods, and the results reveal that this method is very effective and simple and can be applied to other nonlinear problems. It is noteworthy that there are some valuable advantages in this way of solving differential equations, and also most of the sets of differential equations can be answered in this manner which in the other methods they do not have acceptable solutions up to now. A summary of the excellence of this method in comparison to the other manners is as follows: 1) Differential equations are directly solvable by this method. 2) Without any dimensionless procedure, we can solve equation(s). 3) It is not necessary to convert variables into new ones. According to the afore-mentioned assertions which will be proved in this case study, the process of solving nonlinear equation(s) will be very easy and convenient in comparison to the other methods.

Keywords: viscos fluid, incompressible fluid flow, inclined plane, nonlinear phenomena

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Authors: Souici Abdelaziz, Tehami Mohamed, Rahal Nacer, Said Mohamed Bekkouche, Berthet Jean-Fabien

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In this paper, the influence of the concrete slab creep on the initial deformability of a bent composite beam is modelled. This deformability depends on the rate of creep. This means the rise in value of the longitudinal strain ε c(x,t), the displacement D eflec(x,t) and the strain energy E(t). The variation of these three parameters can easily affect negatively the good appearance and the serviceability of the structure. Therefore, an analytical approach is designed to control the status of the deformability of the beam at the instant t. This approach is based on the Boltzmann’s superposition principle and very particularly on the irreversible law of deformation. For this, two conditions of compatibility and two other static equilibrium equations are adopted. The two first conditions are set according to the rheological equation of Dischinger. After having done a mathematical arrangement, we have reached a system of two differential equations whose integration allows to find the mathematical expression of each generalized internal force in terms of the ability of the concrete slab to creep.

Keywords: composite section, concrete, creep, deformation, differential equation, time

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Authors: Aziz Sezgin

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We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.

Keywords: backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems

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Authors: Sumit Kumar Vishwakarma

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The aim of the paper is to investigate the influence of inhomogeneity associated with the elastic constants and density of the orthotropic medium. The inhomogeneity is considered as exponential function of depth. The impact of gravity had been discussed. Using the concept of separation of variables, the system of a partial differential equation (equation of motion) has been converted into ordinary differential equation, which is coupled in nature. It further reduces to a biquadratic equation whose roots were found by using MATLAB. A suitable boundary condition is employed to derive the dispersion equation in a closed-form. Numerical simulations had been performed to show the influence of the inhomogeneity parameter. It was observed that as the numerical values of increases, the phase velocity of Rayleigh waves decreases at a particular wavenumber. Graphical illustrations were drawn to visualize the effect of the increasing and decreasing values of the inhomogeneity parameter. It can be concluded that it has a remarkable bearing on the phase velocity as well as damping velocity.

Keywords: Rayleigh waves, orthotropic medium, gravity field, inhomogeneity

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Authors: Medjadj Tarek, Ghribi Hayet

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This study aims to develop a flood sensitivity assessment tool using machine learning (ML) techniques and geographic information system (GIS). The importance of this study is integrating the geographic information systems (GIS) and machine learning (ML) techniques for mapping flood risks, which help decision-makers to identify the most vulnerable areas and take the necessary precautions to face this type of natural disaster. To reach this goal, we will study the case of the city of M'sila, which is among the areas most vulnerable to floods. This study drew a map of flood-prone areas based on the methodology where we have made a comparison between 3 machine learning algorithms: the xGboost model, the Random Forest algorithm and the K Nearest Neighbour algorithm. Each of them gave an accuracy respectively of 97.92 - 95 - 93.75. In the process of mapping flood-prone areas, the first model was relied upon, which gave the greatest accuracy (xGboost).

Keywords: Geographic information systems (GIS), machine learning (ML), emergency mapping, flood disaster management

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Authors: Wanhyun Cho, Seongchae Seo, Soonja Kang

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In this work, we propose a variational technique for image contrast enhancement which utilizes global and local information around each pixel. The energy functional is defined by a weighted linear combination of three terms which are called on a local, a global contrast term and dispersion term. The first one is a local contrast term that can lead to improve the contrast of an input image by increasing the grey-level differences between each pixel and its neighboring to utilize contextual information around each pixel. The second one is global contrast term, which can lead to enhance a contrast of image by minimizing the difference between its empirical distribution function and a cumulative distribution function to make the probability distribution of pixel values becoming a symmetric distribution about median. The third one is a dispersion term that controls the departure between new pixel value and pixel value of original image while preserving original image characteristics as well as possible. Second, we derive the Euler-Lagrange equation for true image that can achieve the minimum of a proposed functional by using the fundamental lemma for the calculus of variations. And, we considered the procedure that this equation can be solved by using a gradient decent method, which is one of the dynamic approximation techniques. Finally, by conducting various experiments, we can demonstrate that the proposed method can enhance the contrast of colour images better than existing techniques.

Keywords: color image, contrast enhancement technique, variational approach, Euler-Lagrang equation, dynamic approximation method, EME measure

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Authors: Fahrudin Nugroho, Halim Hamadi, Yusril Yusuf, Pekik Nurwantoro, Ari Setiawan, Yoshiki Hidaka

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We investigate the Nikolaevskiy equation numerically using exponential time differencing method and pseudo-spectral method. This equation develops a long-wavelength modulation that behaves as a Nambu–Goldstone mode, and short-wavelength instability and exhibit turbulence. Using the autocorrelation analysis, the statistical properties of the turbulence governed by the equation are investigated. The autocorrelation then has been fitted with The Kohlrausch– Williams–Watts (KWW) expression. By varying the control parameter, we show a transition from compressed to stretched exponential for the auto-correlation function of Nikolaevskiy turbulence. The compressed exponential is an indicator of the existence of dynamical heterogeneity while the stretched indicates aging process. Thereby, we revealed the existence of dynamical heterogeneity and aging in the turbulence governed by Nikolaevskiy equation.

Keywords: compressed exponential, dynamical heterogeneity, Nikolaevskiy equation, stretched exponential, turbulence

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Authors: Mohammed Raza Mehdi, Kamran Ahmed

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Mega-city Karachi has numerous unplanned slum areas and squatter settlements with irregular growth of building structures. Due to weak development policy and lack of development control, such settlements are increasing at a rapid pace. Mapping such areas for planning and infrastructure development requires an integrated approach of socio-spatial and technological tools. Therefore in this study, an attempt is made to create GIS information layers on complex inbound built-up areas of slums at the coastal belt of Karachi by using a stereo pair of satellite images. The outcome expected is technological application to aid planning institutions for crisis management and infrastructure development in irregularly developed slum areas of Karachi, Pakistan.

Keywords: slum, satellite imageries, GIS, Karachi, Pakistan

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Authors: Rakesh Kumar Meena, Tanushree Chatterjee

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Okra (Abelmoschus esculentas L. Moench) or lady’s finger is an important vegetable crop belonging to the Malvaceae family. Unfortunately, production and productivity of Okra are majorly affected by Yellow Vein mosaic virus (YVMV). The AO: 189 (resistant parent) X AO: 191(susceptible parent) used for the development of mapping population. The mapping population has 143 individuals (F₂:F₃). Population was characterized by physiological and pathological observations. Screening of 360 DNA markers was performed to survey for parental polymorphism between the contrasting parents’, i.e., AO: 189 and AO: 191. Out of 360; 84 polymorphic markers were used for genotyping of the mapping population. Total markers were distributed into four linkage groups (LG1, LG2, LG3, and LG4). LG3 covered the longest span (106.8cM) with maximum number of markers (27) while LG1 represented the smallest linkage group in terms of length (71.2cM). QTL identification using the composite interval mapping approach detected two prominent QTLs, QTL1 and QTL2 for resistance against YVMV disease. These QTLs were placed between the marker intervals of NBS-LRR72-Path02 and NBS-LRR06- NBS-LRR65 on linkage group 02 and linkage group 04 respectively. The LOD values of QTL1 and QTL2 were 5.7 and 6.8 which accounted for 19% and 27% of the total phenotypic variation, respectively. The findings of this study provide two linked markers which can be used as efficient diagnostic tools to distinguish between YVMV resistant and susceptible Okra cultivars/genotypes. Lines identified as highly resistant against YVMV infection can be used as donor lines for this trait. This will be instrumental in accelerating the trait improvement program in Okra and will substantially reduce the yield losses due to this viral disease.

Keywords: Okra, yellow vein mosaic virus, resistant, linkage map, QTLs

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Authors: Hongbo Zhang, Xinlu Tang, Jiangwei Li, Chi Yan

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Home zone parking pilot (HPP) is a fast-growing segment in low-speed autonomous driving applications. It requires the car automatically cruise around a parking lot and park itself in a range of up to 100 meters inside a recurrent home/office parking lot, which requires precise parking lot mapping and localization solution. Although Lidar is ideal for SLAM, the car OEMs favor a low-cost fish-eye camera based visual SLAM approach. Recent approaches have employed segmentation models to extract semantic features and improve mapping accuracy, but these AI models are memory unfriendly and computationally expensive, making deploying on embedded ADAS systems difficult. To address this issue, we proposed a new method that utilizes object detection models to extract robust and accurate parking lot features. The proposed method could reduce computational costs while maintaining high accuracy. Once combined with vehicles’ wheel-pulse information, the system could construct maps and locate the vehicle in real-time. This article will discuss in detail (1) the fish-eye based Around View Monitoring (AVM) with transparent chassis images as the inputs, (2) an Object Detection (OD) based feature point extraction algorithm to generate point cloud, (3) a low computational parking lot mapping algorithm and (4) the real-time localization algorithm. At last, we will demonstrate the experiment results with an embedded ADAS system installed on a real car in the underground parking lot.

Keywords: ADAS, home zone parking pilot, object detection, visual SLAM

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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: Aria Ratmandanu

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Boson stars can be viewed as zero temperature ground state, Bose-Einstein condensates, characterized by enormous occupation numbers. Time-dependent spherically symmetric spacetime can be a model of Boson Star. We use (3+1) split of Einstein equation (ADM formulation of general relativity) to solve Einstein field equation coupled to a complex scalar field (Einstein-Klein-Gordon Equation) on time-dependent spherically symmetric spacetime, We get the result that Boson stars are pulsating stars with the frequency of oscillation equal to its density. We search for interior solution of Boson stars and get the T.O.V. (Tollman-Oppenheimer-Volkoff) equation for Boson stars. Using T.O.V. equation, we get the equation of state and the relation between pressure and density, its total mass and along with its gravitational Mass. We found that the hypothetical particle Axion could form a Boson star with the size of a milky way galaxy and make it a candidate for a dark galaxy, (a galaxy that consists almost entirely of dark matter).

Keywords: axion, boson star, dark galaxy, time-dependent spherically symmetric spacetime

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Authors: Kitjapat Phuvoravan, Phattaraphong Ponsorn

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In the design of Castellated beams (CB), the web post buckling acted by horizontal shear force is one of the important failure modes that have to be considered. It is also a dominant governing mode when design following the AISC 31 design guideline which is just published. However, the equation of the web post buckling given by the guideline is still questionable for most of the engineers. So the purpose of this paper is to study and provide a proposed equation for design the web post buckling with more simplified and convenient to use. The study is also including the improper of the safety factor given by the guideline. The proposed design equation is acquired by regression method based on the results of finite element analysis. An amount of Cellular beam simulated to study is modelled by using shell element, analysis with both geometric and material nonlinearity. The results of the study show that the use of the proposed equation to design the web post buckling in Castellated beams is more simple and precise for computation than the equations provided from the guideline.

Keywords: castellated beam, web opening, web post buckling, design equation

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Authors: Maryam Mosleh, Mahmood Otadi

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

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Authors: Esraa Alhadad

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Recently, there has been considerable debate surrounding the definition, conservation, and management of heritage. Over the past few years, there has been a growing call for the inclusion of local communities in heritage management. However, the perspectives on involvement, especially concerning key stakeholders like community members, often diverge significantly. While the theoretical foundation for community involvement is reasonably established, the application of this approach in heritage management has been sluggish. Achieving a balance to fulfill the diverse goals of stakeholders in any involvement project proves challenging in practice. Consequently, there is a dearth of empirical studies exploring the practical implications of effective tools in heritage management, and limited indication exists to persuade current authorities, such as governmental organizations, to share their influence with local community members. This research project delves into community involvement within heritage management as a potent means of constructing a robust management framework. Its objective is to assess both the extent and caliber of involvement within the management of heritage sites overall, utilizing a cultural mapping-centered methodology. The findings of this study underscore the significance of engaging the local community in both heritage management and planning endeavors. Ultimately, this investigation furnishes crucial empirical evidence and extrapolates valuable theoretical and practical insights that advance understanding of cultural mapping in pivotal areas, including the catalysts for involvement and collaborative decision-making processes.

Keywords: community involvement, heritage management, cultural mapping, stakeholder mangement

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Authors: Orhan Akınoğlu, Arif Çömek, Ersin Elmacı, Tuğba Gündoğdu

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The concept map is known to be a powerful tool to organize the ideas and concepts of an individuals’ mind. This tool is a kind of visual map that illustrates the relationships between the concepts of a certain subject. The effect of concept mapping on cognitive and affective qualities is one of the research topics among educational researchers for last decades. We educators want to utilize it both as an instructional tool or an assessment tool in classes. For that reason, this study aimed to determine the effect of concept mapping as a learning strategy in science classes on students’ academic achievement and attitude. The research employed a randomized pre-test post-test control group design. Data collected from 60 sixth grade students participated in the study from a randomly selected primary school in Turkey. Sixth-grade classes of the school were analyzed according to students’ academic achievement, science attitude, gender, mathematics, science courses grades, and their GPAs before the implementation. Two of the classes found to be equivalent (t=0,983, p>0,05) and one of them was defined as experimental and the other one control group randomly. During a 5-weeks period, the experimental group students (N=30) used the paper-based concept mapping method while the control group students (N=30) were taught with the traditional approach according to the science and technology education curriculum for light and sound subject. Both groups were taught by the same teacher who is experienced using concept mapping in science classes. Before the implementation, the teacher explained the theory of the concept maps and showed how to create paper-based concept mapping individually to the experimental group students for two hours. Then for two following hours she asked them to create some concept maps related to their former science subjects and gave them feedback by reviewing their concept maps to be sure that they can create during the implementation. The data were collected by science achievement test, science attitude scale and personal information form. Science achievement test and science attitude scale were implemented as pre-test and post-test while personal information form was implemented just as once. The reliability coefficient of the achievement test was KR20=0,76 and Cronbach’s Alpha of the attitude scale was 0,89. SPSS statistical software was used to analyze the data. According to the results, there was a statistically significant difference between the experimental and control group for academic achievement but not for attitude. The experimental group had significantly greater gains from academic achievement test than the control group (t=0,02, p<0,05). The findings showed that the paper-and-pencil concept mapping can be used as an effective method for students’ academic achievement in science classes. The results have implications for further researches.

Keywords: concept mapping, science education, constructivism, academic achievement, science attitude

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Authors: Olayiwola Moruf Oyedunsi

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This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: Arash Jafari, Mehdi Taghaddosi, Azin Parvin

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In this study, a vibrational differential equation governing on swinging single-degree-of-freedom pendulum in a viscous fluid has been investigated. The damping process is characterized according to two different regimes: at first, damping in stationary viscous fluid, in the second, damping in flowing viscous fluid with constant velocity. Our purpose is to enhance the ability of solving the mentioned nonlinear differential equation with a simple and innovative approach. Comparisons are made between new method and Numerical Method (rkf45). The results show that this method is very effective and simple and can be applied for other nonlinear problems.

Keywords: oscillating systems, angular frequency and damping ratio, pendulum at fluid, locus of maximum

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Authors: Michael Mickson

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The recent development of unmanned aerial vehicles (UAVs) has been increasing the number of technical solutions that can be used to identify, map, and manage the effects of geohazards. UAVs are generally cheaper and more versatile than traditional remote-sensing techniques, and they can be therefore considered as a good alternative for the acquisition of imagery and other remote sensing data before, during and after a natural hazard event. This study aims to use UAV for investigating areas susceptible to high mobility flows such as debris flow in Dominica, especially after the 2017 Hurricane Maria. The use of UAVs in identifying, mapping and managing of natural hazards helps to mitigate the negative effects of natural hazards on livelihood, properties and the built environment.

Keywords: unmanned aerial vehicle (UAV), geohazards, remote sensing, mapping, Dominica

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Authors: Tyler T. Procko, Steve Collins

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New features in .NET (6 and above) permit streamlined access to information residing in JSON-capable relational databases, such as SQL Server (2016 and above). Traditional methods of data access now comparatively involve unnecessary steps which compromise system performance. This work posits that the established ORM (Object Relational Mapping) based methods of data access in applications and APIs result in common issues, e.g., object-relational impedance mismatch. Recent developments in C# and .NET Core combined with a framework of modern SQL Server coding conventions have allowed better technical solutions to the problem. As an amelioration, this work details the language features and coding conventions which enable this streamlined approach, resulting in an open-source .NET library implementation called Codeless Data Access (CODA). Canonical approaches rely on ad-hoc mapping code to perform type conversions between the client and back-end database; with CODA, no mapping code is needed, as JSON is freely mapped to SQL and vice versa. CODA streamlines API data access by improving on three aspects of immediate concern to web developers, database engineers and cybersecurity professionals: Simplicity, Speed and Security. Simplicity is engendered by cutting out the “middleman” steps, effectively making API data access a whitebox, whereas traditional methods are blackbox. Speed is improved because of the fewer translational steps taken, and security is improved as attack surfaces are minimized. An empirical evaluation of the speed of the CODA approach in comparison to ORM approaches ] is provided and demonstrates that the CODA approach is significantly faster. CODA presents substantial benefits for API developer workflows by simplifying data access, resulting in better speed and security and allowing developers to focus on productive development rather than being mired in data access code. Future considerations include a generalization of the CODA method and extension outside of the .NET ecosystem to other programming languages.

Keywords: API data access, database, JSON, .NET core, SQL server

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Authors: M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation

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Authors: Shubham Jaiswal

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During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: space fractional order linear/nonlinear reaction-advection diffusion equation, shifted Jacobi polynomials, operational matrix, collocation method, Caputo derivative

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