Search results for: shallow water equations

Authors: Prasanna Kumar Khaund, Sukanya Talukdar

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A concrete gravity dam is a major hydraulic structure and it is very essential to consider the earthquake forces, to get a proper design base width, so that the entire weight of the dam resists the overturning moment due to earthquake and other forces. The main objective of this study is to obtain the design base width of a dam for different seismic conditions by varying the earthquake coefficients in both vertical and horizontal directions. This shall be done by equating the factor of safety against overturning, factor of safety against sliding and factor of safety against shear friction factor for a dam with their limiting values, under both tail water and no tail water condition. The shape of the Mettur dam in India is considered for the study. The study has been done taking a constant head of water at the reservoir, which is the maximum reservoir water level and a constant height of tail water. Using linear approximation method of Newton Raphson, the obtained equations against different factors of safety under different earthquake conditions are solved using a programme in C++ to get different values of base width of dam for varying earthquake conditions.

Keywords: design base width, horizontal earthquake coefficient, tail water, vertical earthquake coefficient

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Apoorva Vinod, Archana Mathur, Snehanshu Saha

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Though there exists a plethora of Activation Functions (AFs) used in single and multiple hidden layer Neural Networks (NN), their behavior always raised curiosity, whether used in combination or singly. The popular AFs –Sigmoid, ReLU, and Tanh–have performed prominently well for shallow and deep architectures. Most of the time, AFs are used singly in multi-layered NN, and, to the best of our knowledge, their performance is never studied and analyzed deeply when used in combination. In this manuscript, we experiment with multi-layered NN architecture (both on shallow and deep architectures; Convolutional NN and VGG16) and investigate how well the network responds to using two different AFs (Sigmoid-Tanh, Tanh-ReLU, ReLU-Sigmoid) used alternately against a traditional, single (Sigmoid-Sigmoid, Tanh-Tanh, ReLUReLU) combination. Our results show that using two different AFs, the network achieves better accuracy, substantially lower loss, and faster convergence on 4 computer vision (CV) and 15 Non-CV (NCV) datasets. When using different AFs, not only was the accuracy greater by 6-7%, but we also accomplished convergence twice as fast. We present a case study to investigate the probability of networks suffering vanishing and exploding gradients when using two different AFs. Additionally, we theoretically showed that a composition of two or more AFs satisfies Universal Approximation Theorem (UAT).

Keywords: activation function, universal approximation function, neural networks, convergence

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Authors: T. Bouchabchoub, A. Bendahmane, A. Haouriqui, N. Attou

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This paper presents simulation results of Forex predicting model equations in order to give approximately a prevision of interest rates. First, Hall-Taylor (HT) equations have been used with Taylor rule (TR) to adapt them to European and American Forex Markets. Indeed, initial Taylor Rule equation is conceived for all Forex transactions in every States: It includes only one equation and six parameters. Here, the model has been used with Hall-Taylor equations, initially including twelve equations which have been reduced to only three equations. Analysis has been developed on the following base macroeconomic variables: Real change rate, investment wages, anticipated inflation, realized inflation, real production, interest rates, gap production and potential production. This model has been used to specifically study the impact of an inflation shock on macroeconomic director interest rates.

Keywords: interest rate, Forex, Taylor rule, production, European Central Bank (ECB), Federal Reserve System (FED).

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Authors: Adetunji A. Adeyanju., Mathew O. Omeike, Johnson O. Adeniran, Biodun S. Badmus

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In this paper, we discuss certain conditions for uniform asymptotic stability and uniform ultimate boundedness of solutions to some systems of Aizermann-type of differential equations by means of second method of Lyapunov. In achieving our goal, some Lyapunov functions are constructed to serve as basic tools. The stability results in this paper, extend some stability results for some Aizermann-type of differential equations found in literature. Also, we prove some results on uniform boundedness and uniform ultimate boundedness of solutions of systems of equations study.

Keywords: Aizermann, boundedness, first order, Lyapunov function, stability

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Authors: Zuhier Altawallbeh

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This paper investigates the approximate analytical solutions of general form of Volterra integro-differential equations system by using the residual power series method (for short RPSM). The proposed method produces the solutions in terms of convergent series requires no linearization or small perturbation and reproduces the exact solution when the solution is polynomial. Some examples are given to demonstrate the simplicity and efficiency of the proposed method. Comparisons with the Laplace decomposition algorithm verify that the new method is very effective and convenient for solving system of pantograph equations.

Keywords: integro-differential equation, pantograph equations, system of initial value problems, residual power series method

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Authors: Xinhai Li, Huidong Tian, Yumin Guo

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Bird migration is fantastic natural phenomenon. In recent years, the use of GPS transmitters has generated a vast amount of data, and the Movebank platform has made these data publicly accessible. For researchers, what they need are data analysis tools. Although there are approximately 90 R packages dedicated to animal movement analysis, the capacity for comprehensive processing of bird migration data remains limited. Hence, we introduce a novel package called migrationR. This package enables the calculation of movement speed, direction, changes in direction, flight duration, daily and annual movement distances. Furthermore, it can pinpoint the starting and ending dates of migration, estimate nest site locations and stopovers, and visualize movement trajectories at various time scales. migrationR distinguishes individuals through NMDS (non-metric multidimensional scaling) coordinates based on movement variables such as speed, flight duration, path tortuosity, and migration timing. A distinctive aspect of the package is the development of a hetero-occurrences species distribution model that takes into account the daily rhythm of individual birds across different landcover types. Habitat use for foraging and roosting differs significantly for many waterbirds. For example, White-naped Cranes at Poyang Lake in China typically forage in croplands and roost in shallow water areas. Both of these occurrence types are of equal importance. Optimal habitats consist of a combination of crop lands and shallow waters, whereas suboptimal habitats lack both, which necessitates birds to fly extensively. With migrationR, we conduct species distribution modeling for foraging and roosting separately and utilize the moving distance between crop lands and shallow water areas as an index of overall habitat suitability. This approach offers a more nuanced understanding of the habitat requirements for migratory birds and enhances our ability to analyze and interpret their movement patterns effectively. The functions of migrationR are demonstrated using our own tracking data of 78 White-naped Crane individuals from 2014 to 2023, comprising over one million valid locations in total. migrationR can be installed from a GitHub repository by executing the following command: remotes::install_github("Xinhai-Li/migrationR").

Keywords: bird migration, hetero-occurrences species distribution model, migrationR, R package, satellite telemetry

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Authors: Anthony Credoz, Nathalie Nief, Remy Hedacq, Salvador Jordana, Laurent Cazes

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Groundwater monitoring is classically performed in a network of piezometers in industrial sites. Groundwater flow parameters, such as direction, sense and velocity, are deduced from indirect measurements between two or more piezometers. Groundwater sampling is generally done on the whole column of water inside each borehole to provide concentration values for each piezometer location. These flow and concentration values give a global ‘static’ image of potential plume of contaminants evolution in the shallow aquifer with huge uncertainties in time and space scales and mass discharge dynamic. TOTAL R&D Subsurface Environmental team is challenging this classical approach with an innovative dynamic way of characterization of shallow aquifer groundwater. The current study aims at optimizing the tools and methodologies for (i) a direct and multilevel measurement of groundwater velocities in each piezometer and, (ii) a calculation of potential flux of dissolved contaminant in the shallow aquifer. Lab-scale experiments have been designed to test commercial and R&D tools in a controlled sandbox. Multiphysics modeling were performed and took into account Darcy equation in porous media and Navier-Stockes equation in the borehole. The first step of the current study focused on groundwater flow at porous media/piezometer interface. Huge uncertainties from direct flow rate measurements in the borehole versus Darcy flow rate in the porous media were characterized during experiments and modeling. The structure and location of the tools in the borehole also impacted the results and uncertainties of velocity measurement. In parallel, direct-push tool was tested and presented more accurate results. The second step of the study focused on mass flux of dissolved contaminant in groundwater. Several active and passive commercial and R&D tools have been tested in sandbox and reactive transport modeling has been performed to validate the experiments at the lab-scale. Some tools will be selected and deployed in field assays to better assess the mass discharge of dissolved contaminants in an industrial site. The long-term subsurface environmental strategy is targeting an in-situ, real-time, remote and cost-effective monitoring of groundwater.

Keywords: dynamic characterization, groundwater flow, lab-scale, mass flux

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Authors: Mustafa Ekici

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Natural convection is a basic process which is important in a wide variety of practical applications. In essence, a heated fluid expands and rises from buoyancy due to decreased density. Numerous papers have been written on natural or mixed convection in vertical ducts heated on the side. These equations have been proved to be valuable tools for the modelling of many phenomena such as fluid dynamics. Finding solutions to such equations or system of equations are in general not an easy task. We propose a method, which is called differential transform method, of solving a non-linear equations and compare the results with some of the other techniques. Illustrative examples shows that the results are in good agreement.

Keywords: differential transform method, momentum, energy equation, boundry value problem

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Authors: D. Alromi, A. Alansari, S. Alghamdi, E. Jambi

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As the need for water is increasing globally, and the available water resources are barely meeting the current quality of life and economy. Air conditioning (AC) condensate water could be explored as an alternative water source, which could be considered within the global calculations of the water supply. The objective of this study is to better understand the potential for recovery of condensate water from air conditioning systems. The results generated so far showed that the AC produces a high quantity of water, and data analysis revealed that the amount of water is positively and significantly correlated with the humidity (P <= 0.05). In the meantime, the amount of heavy metals has been measuring using ICP-OES. The results, in terms of quantity, clearly show that the AC can be used as an alternative source of water, especially in the regions characterized by high humidity. The results also showed that the amount of produced water depends on the type of AC.

Keywords: air conditioning systems, water quantity, water resources, wastewater

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Authors: Aziza Barrek, Mohamed Haythem Msaddek, Ismail Chenini

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Excessive groundwater pumping due to the increasing water demand, especially in the agricultural sector, causes groundwater scarcity. Groundwater recharge is the most important process that contributes to the water's durability. This paper is based on the Analytic Hierarchy Process multicriteria analysis to establish a groundwater recharge susceptibility map. To delineate aquifer suitability for groundwater recharge, eight parameters were used: soil type, land cover, drainage density, lithology, NDVI, slope, transmissivity, and rainfall. The impact of each factor was weighted. This method was applied to the El Fahs plain shallow aquifer. Results suggest that 37% of the aquifer area has very good and good recharge suitability. The results have been validated by the Receiver Operating Characteristics curve. The accuracy of the prediction obtained was 89.3%.

Keywords: AHP, El Fahs aquifer, empirical formula, groundwater recharge zone, remote sensing, semi-arid region

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Authors: Imessaoudene Y., Mouhouche B., Sengouga A., Kadir M.

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The objective of this work is to determine the virtual water of main crops grown in the province of Djelfa and water use efficiency (W.U.E.), Which is essential to approach the application and better integration with the offer in the region. In the case of agricultural production, virtual water is the volume of water evapo-transpired by crops. It depends on particular on the expertise of its producers and its global production area, warm and dry climates induce higher consumption. At the scale of the province, the determination of the quantities of virtual water is done by calculating the unit water requirements related to water irrigated hectare and total rainfall over the crop using the Cropwat 8.0 F.A.O. software. Quantifying the volume of agricultural virtual water of crops practiced in the study area demonstrates the quantitative importance of these volumes of water in terms of available water resources in the province, so the advantages which can be the concept of virtual water as an analysis tool and decision support for the management and distribution of water in scarcity situation.

Keywords: virtual water, water use efficiency, water requirements, Djelfa

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Authors: Meziane Belkacem

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We aim at converting the original 3D Lorenz-Haken equations, which describe laser dynamics –in terms of self-pulsing and chaos- into 2-second-order differential equations, out of which we extract the so far missing mathematics and corroborations with respect to nonlinear interactions. Leaning on basic trigonometry, we pull out important outcomes; a fundamental result attributes chaos to forbidden periodic solutions inside some precisely delimited region of the control parameter space that governs the bewildering dynamics.

Keywords: Physics, optics, nonlinear dynamics, chaos

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Mohamed Elkashouty, Mohamed Elkammar, Mohamed Gomma, Menal Elminiami

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Lake Bardawil is considered as one of the major morphological features of northern Sinai. It represents the largest fish production lake for export in Egypt. Nineteen and thirty one samples were collected from lake water during winter and summer (2005). TDS, cations, anions, Cd, Cu, Fe, Mn, Zn, Ni, Co and Pb concentrations were measured within winter and summer seasons. During summer, in the eastern sector of the lake, TDS concentration is decreased due northeastern part (38000 ppm), it is attributed to dilution from seawater through Boughaz II. The TDS concentration increased generally in the central and southern parts of the lake (44000 and 42000 ppm, respectively). It is caused by they are far from dilution from seawater, disconnected water body, shallow depth (mean 2 m), and high evaporation rate. In the western sector, the TDS content ranged from low (38000 ppm) in the northeastern part to high (50000 ppm) in the western part. Generally, the TDS concentration in the western sector is higher than those in the eastern. It is attributed to low volume of water body for the former, high evaporation rate, and therefore increase in TDS content in the lake water.During winter season, in the eastern sector, the wind velocity is high which enhance the water current to inflow into the lake through Boughaz I and II. The resultant water lake is diluted by seawater and rainfall in the winter season. The TDS concentration increased due southern part of the lake (42000 ppm) and declined in the northern part (36000 ppm). The concentration of Co, Ni, Pb, Fe, Cd, Zn, Cu, Mn and Pb within winter and summery seasons, in lake water are low, which considered as background concentrations with respect to seawater. Therefore, there are no industrial, agricultural and sanitary wastewaters dump into the lake. This confirms the statement that has been written at the entrance of Lake Bardawil at El-Telool area "Lake Bardawil, one of the purest lakes in the world". It indicate that the Lake Bardawil is excellent area for fish production for export (current state) and is the second main fish source in Egypt after the Mediterranean Sea after the illness of Lake Manzala.

Keywords: lake Bardawil, water quality, major ions, toxic metals

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Authors: Gaspar J. Machado, Stéphane Clain, Raphael Loubère

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The goal of the present work is to numerically study steady-state nonlinear hyperbolic equations in the context of the finite volume framework. We will consider the unidimensional Burgers' equation as the reference case for the scalar situation and the unidimensional Euler equations for the vectorial situation. We consider two approaches to solve the nonlinear equations: a time marching algorithm and a direct steady-state approach. We first develop the necessary and sufficient conditions to obtain the existence and unicity of the solution. We treat regular examples and solutions with a steady shock and to provide very-high-order finite volume approximations we implement a method based on the MOOD technology (Multi-dimensional Optimal Order Detection). The main ingredient consists in using an 'a posteriori' limiting strategy to eliminate non physical oscillations deriving from the Gibbs phenomenon while keeping a high accuracy for the smooth part.

Keywords: Euler equations, finite volume, MOOD, steady-state

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Aishath Shakeela

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At a global level, water stewardship, water stress and water security are crucial factors in tourism planning and development considerations. Challenges associated with water is of particular concern to the Maldives as there is limited availability of freshwater, high dependency on desalinated water, and high unit cost associated with desalinating water. While the Maldives is promoted as an example of sustainable tourism, a key sustainability challenge facing tourism dependent communities is the efficient use and management of available water resources. A water crisis event in the capital island of Maldives highlighted how precarious water related issues are in this tourism dependent destination. Applying netnography, the focus of this working paper is to present community perceptions of how government policies addressed Malé Water and Sewerage Company (MWSC) water crisis event.

Keywords: crisis management, government policies, Maldives, tourism, water

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Authors: Zahid Ullah, Atlas Khan

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This research endeavors to explore the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. These equations hold significance in understanding complex physical systems like porous media flow, with applications spanning various branches of mathematics. The focus is on unraveling and analyzing regularity results to gain insights into the smoothness of solutions for these highly degenerate equations. Elliptic equations, fundamental in expressing and understanding diverse physical phenomena through partial differential equations (PDEs), are particularly adept at modeling steady-state and equilibrium behaviors. However, within the realm of elliptic equations, the subset of extremely degenerate cases presents a level of complexity that challenges traditional analytical methods, necessitating a deeper exploration of mathematical theory. While elliptic equations are celebrated for their versatility in capturing smooth and continuous behaviors across different disciplines, the introduction of degeneracy adds a layer of intricacy. Extremely degenerate elliptic equations are characterized by coefficients approaching singular behavior, posing non-trivial challenges in establishing classical solutions. Still, the exploration of extremely degenerate cases remains uncharted territory, requiring a profound understanding of mathematical structures and their implications. The motivation behind this research lies in addressing gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations. The study of extreme degeneracy is prompted by its prevalence in real-world applications, where physical phenomena often exhibit characteristics defying conventional mathematical modeling. Whether examining porous media flow or highly anisotropic materials, comprehending the regularity of solutions becomes crucial. Through this research, the aim is to contribute not only to the theoretical foundations of mathematics but also to the practical applicability of mathematical models in diverse scientific fields.

Keywords: elliptic equations, extremely degenerate, regularity results, partial differential equations, mathematical modeling, porous media flow

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Authors: Numair A. Siddiqui, Usman Muhammad, Manoj J. Mathew, Ramkumar M., Benjamin Sautter, Muhammad A. K. El-Ghali, David Menier, Shiqi Zhang

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The sedimentological parameterization of shallow-marine siliciclastic reservoirs in terms of reservoir quality and heterogeneity from outcrop study can help improve the subsurface reservoir prediction. An architectural analysis has documented variations in sandstone geometry and rock properties within shallow-marine sandstone exposed in the Miocene Sandakan Formation of Sabah, Borneo. This study demonstrates reservoir sandstone quality assessment for subsurface rock evaluation, from well-exposed successions of the Sandakan Formation, Borneo, with which applicable analogues can be identified. The analyses were based on traditional conventional field investigation of outcrops, grain-size and petrographic studies of hand specimens of different sandstone facies and gamma-ray and permeability measurements. On the bases of these evaluations, the studied sandstone was grouped into three qualitative reservoir rock classes; high (Ø=18.10 – 43.60%; k=1265.20 – 5986.25 mD), moderate (Ø=17.60 – 37%; k=21.36 – 568 mD) and low quality (Ø=3.4 – 15.7%; k=3.21 – 201.30 mD) for visualization and prediction of subsurface reservoir quality. These results provided analogy for shallow marine sandstone reservoir complexity that can be utilized in the evaluation of reservoir quality of regional and subsurface analogues.

Keywords: architecture and sedimentology, subsurface rock evaluation, reservoir quality, borneo

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Authors: A. Bayle, F. Plouraboué

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Water Distribution Network (WDN) still suffers from a lack of knowledge about fast pressure transient events prediction, although the latter may considerably impact their durability. Accidental or planned operating activities indeed give rise to complex pressure interactions and may drastically modified the local pressure value generating leaks and, in rare cases, pipe’s break. In this context, a numerical predictive analysis is conducted to prevent such event and optimize network management. A couple of Python/FORTRAN 90, home-made software, has been developed using Method Of Characteristic (MOC) solving for water-hammer equations. The solver is validated by direct comparison with theoretical and experimental measurement in simple configurations whilst afterward extended to network analysis. The algorithm's most costly steps are designed for parallel computation. A various set of boundary conditions and energetic losses models are considered for the network simulations. The results are analyzed in both real and frequencies domain and provide crucial information on the pressure distribution behavior within the network.

Keywords: energetic losses models, method of characteristic, numerical predictive analysis, water distribution network, water hammer

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Authors: Miraz Hafiz Rossy

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As part of planning to address shortfalls in fresh water supply for the world, Sea water can be a huge source of fresh water. But Desalinating sea water to get fresh water could require a lots of fossil fuels. To save the fossil fuel in terms of save the green world but meet the up growing need for fresh water, a very useful but energy efficient method needs to be introduced. Vacuum desalination of sea water using only the Renewable energy can be an effective solution to this issue. Taking advantage of sensitivity of water's boiling point to air pressure a vacuum desalination water treatment plant can be designed which would only use sea water as feed water and solar energy as fuel to produce fresh drinking water. The study indicates that reducing the air pressure to a certain value water can be boiled at very low temperature. Using solar energy to provide the condensation and the vacuum creation would be very useful and efficient. Compared to existing resources, desalination is considered to be expensive, but using only renewable energy the cost can be reduced significantly. Despite its very few drawbacks, it can be considered a possible solution to the world's fresh water shortages.

Keywords: desalination, scarcity of fresh water, water purification, water treatment

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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In this paper, a convenient analytical solution for a system of coupled differential equations, derived from thermo-hydro-mechanical analysis of three-phase porous media such as unsaturated soils is developed. This kind of analysis can be used in various fields such as geothermal energy systems and seepage of leachate from buried municipal and domestic waste in geomaterials. Initially, a system of coupled differential equations, including energy, mass, and momentum conservation equations is considered, and an analytical method called AGM is employed to solve the problem. The method is straightforward and comprehensible and can be used to solve various nonlinear partial differential equations (PDEs). Results indicate the accuracy of the applied method for solving nonlinear partial differential equations.

Keywords: AGM, analytical solution, porous media, thermo-hydro-mechanical, unsaturated soils

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Authors: Nivine Abbas, Sergio Lagomarsino, Serena Cattari

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The resistance domain of a generally loaded rigid shallow foundation is normally represented as an interaction diagram limited by a failure surface in the three dimensional (3D) load space (N, V, M), where N is the vertical centric load component, V is the horizontal load component and M is the bending moment component. Usually, this resistance domain is constructed neglecting the foundation sliding mechanism that take place at the level of soil-foundation interface once the applied horizontal load exceeds the interface frictional resistance of the foundation. This issue is translated in the literature by the fact that the failure limit in the (2D) load space (N, V) is constructed as a parabola having an initial slope, at the center of the coordinate system, that depends, in some works, only of the soil friction angle, and in other works, has an empirical value. However, considering a given geometry of the foundation lying on a given soil type, the initial slope of the failure limit must change, for instance, when varying the roughness of the foundation surface at its interface with the soil. The present study discusses the effect of the soil-foundation interface condition on the construction of the resistance domain, and proposes a correction to be applied to the failure limit in order to overcome this effect.

Keywords: soil-foundation interface, sliding mechanism, soil shearing, resistance domain, rigid shallow foundation

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Authors: Jessada Tariboon

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In this article, using distribution kernel, we study the nonlinear equations with n-dimensional telegraph operator iterated k-times.

Keywords: telegraph operator, elementary solution, distribution kernel, nonlinear equations

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Authors: Trilok Mathur, Shivi Agarwal

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This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods.

Keywords: Caputo-type fuzzy fractional derivative, Fractional Riccati differential equations, Laplace-Adomian-Pade method, Mittag Leffler function

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Authors: Y. N. Reddy

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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: Alireza Abbasi Moshaii, Shaghayegh Nasiri, Mehdi Tale Masouleh

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The main purpose of this study is static analysis of two three-degree of freedom parallel mechanisms: 3-RCC and 3-RRS. Geometry of these mechanisms is expressed and static equilibrium equations are derived for the whole chains. For these mechanisms due to the equal number of equations and unknowns, the solution is as same as 3-RCC mechanism. Mathematical software is used to solve the equations. In order to prove the results obtained from solving the equations of mechanisms, their CAD model has been simulated and their static is analysed in ADAMS software. Due to symmetrical geometry of the mechanisms, the force and external torque acting on the end-effecter have been considered asymmetric to prove the generality of the solution method. Finally, the results of both softwares, for both mechanisms are extracted and compared as graphs. The good achieved comparison between the results indicates the accuracy of the analysis.

Keywords: robotic, static analysis, 3-RCC, 3-RRS

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Authors: Pius Babuna, Xiaohua Yang, Roberto Xavier Supe Tulcan, Bian Dehui, Mohammed Takase, Bismarck Yelfogle Guba, Chuanliang Han, Doris Abra Awudi, Meishui Lia

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Water inequality, water security, and water governance are fundamental parameters that affect the sustainable use of water resources. Through policy formulation and decision-making, water governance determines both water security and water inequality. Largely, where water inequality exists, water security is undermined through unsustainable water use practices that lead to pollution of water resources, conflicts, hoarding of water, and poor sanitation. Incidentally, the interconnectedness of water governance, water inequality, and water security has not been investigated previously. This study modified the Gini coefficient and used a Logistics Growth of Water Resources (LGWR) Model to access water inequality and water security mathematically, and discussed the connected role of water governance. We tested the validity of both models by calculating the actual water inequality and water security of Ghana. We also discussed the implications of water inequality on water security and the overarching role of water governance. The results show that regional water inequality is widespread in some parts. The Volta region showed the highest water inequality (Gini index of 0.58), while the central region showed the lowest (Gini index of 0.15). Water security is moderately sustainable. The use of water resources is currently stress-free. It was estimated to maintain such status until 2132 ± 18, when Ghana will consume half of the current total water resources of 53.2 billion cubic meters. Effectively, water inequality is a threat to water security, results in poverty, under-development heightens tensions in water use, and causes instability. With proper water governance, water inequality can be eliminated through formulating and implementing approaches that engender equal allocation and sustainable use of water resources.

Keywords: water inequality, water security, water governance, Gini coefficient, moran index, water resources management

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Authors: Jemai Rabeb, Benhmidene Ali, Hidouri Khaoula, Chaouachi Bechir

Abstract:

The diffusion-absorption refrigeration cycle consists of a generator bubble pump, an absorber, an evaporator and a condenser, and usually operates with ammonia/water/ hydrogen or helium as the working fluid. The aim of this paper is to study the stability problem a bubble pump. In fact instability can caused a reduction of bubble pump efficiency. To achieve this goal, we have simulated the behaviour of two-phase flow in a bubble pump by using a drift flow model. Equations of a drift flow model are formulated in the transitional regime, non-adiabatic condition and thermodynamic equilibrium between the liquid and vapour phases. Equations resolution allowed to define void fraction, and liquid and vapour velocities, as well as pressure and mixing enthalpy. Ammonia-water mixing is used as working fluid, where ammonia mass fraction in the inlet is 0.6. Present simulation is conducted out for a heating flux of 2 kW/m² to 5 kW/m² and bubble pump tube length of 1 m and 2.5 mm of inner diameter. Simulation results reveal oscillations of vapour and liquid velocities along time. Oscillations decrease with time and with heat flux. For sufficient time the steady state is established, it is characterised by constant liquid velocity and void fraction values. However, vapour velocity does not have the same behaviour, it increases for steady state too. On the other hand, pressure drop oscillations are studied.

Keywords: bubble pump, drift flow model, instability, simulation

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