Search results for: fractional evolution equations

Authors: Alaa Sheta

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Economic Load Dispatch (ELD) is one of the vital optimization problems in power system planning. Solving the ELD problems mean finding the best mixture of power unit outputs of all members of the power system network such that the total fuel cost is minimized while sustaining operation requirements limits satisfied across the entire dispatch phases. Many optimization techniques were proposed to solve this problem. A famous one is the Quadratic Programming (QP). QP is a very simple and fast method but it still suffer many problem as gradient methods that might trapped at local minimum solutions and cannot handle complex nonlinear functions. Numbers of metaheuristic algorithms were used to solve this problem such as Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO). In this paper, another meta-heuristic search algorithm named Differential Evolution (DE) is used to solve the ELD problem in power systems planning. The practicality of the proposed DE based algorithm is verified for three and six power generator system test cases. The gained results are compared to existing results based on QP, GAs and PSO. The developed results show that differential evolution is superior in obtaining a combination of power loads that fulfill the problem constraints and minimize the total fuel cost. DE found to be fast in converging to the optimal power generation loads and capable of handling the non-linearity of ELD problem. The proposed DE solution is able to minimize the cost of generated power, minimize the total power loss in the transmission and maximize the reliability of the power provided to the customers.

Keywords: economic load dispatch, power systems, optimization, differential evolution

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Authors: T. Zitoun, M. Bouhadef

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When a partially or completely immersed solid moves in a liquid such as water, it undergoes a force called hydrodynamic drag. Reducing this force has always been the objective of hydrodynamic engineers to make water slide better on submerged bodies. This paper deals with the examination of the different terms composing the analytical solution of the flow over an obstacle embedded at the bottom of a hydraulic channel. We have chosen to use a linear method to study a two-dimensional flow over an obstacle, in order to understand the evolution of the drag. We set the following assumptions: incompressible inviscid fluid, irrotational flow, low obstacle height compared to the water height. Those assumptions allow overcoming the difficulties associated with modelling these waves. We will mathematically formulate the equations that allow the determination of the stream function, and then the free surface equation. A similar method is used to determine the exact analytical solution for an obstacle in the shape of a sinusoidal arch.

Keywords: analytical solution, free-surface wave, hydraulic channel, inviscid fluid

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Authors: Ilya A. Snegirev

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The article focuses on the comparative study of Russian military poetry of the 20th century. To make a complete description, the verse of different genres, mainly minor lyrical form, is taken. The study makes it possible to emphasize the idea that genre is not completely representative for a comprehensive research, as it is also necessary to dwell upon the strategies of war description in verse. Furthermore, the tendency of lyrical hero individualization is noted. This tendency can be traced throughout the whole second half of the 20th century – the poets of the Second World War – and further, to the whole post-war poetry. To characterize these changes, the texts by K.M. Simonov and A.A. Surkov are being analyzed as the examples of the qualitative transition to an individual hero.

Keywords: literature’s evolution, narrator, storytelling poetry, tradition

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Authors: Mohamed Rahal, Djaouida Guetta

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In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions. The convergence of the method is studied and the algorithm can be applied to systems of nonlinear equations. Finally, some numerical examples are presented and illustrate the efficiency of the present approach.

Keywords: global optimization, Hölder functions, sequential covering method, systems of nonlinear equations

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Authors: Luke Ukpebor, C. E. Abhulimen

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Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy.

Keywords: A-stable, exponentially fitted, four step, predator-corrector, second derivative, stiff initial value problems

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Authors: Yi Yu, Vu Xuan Nguyen, Gaoxi Xiao

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Opinion formation in complex social networks may exhibit complex system dynamics even when based on some simplest system evolution models. An interesting and important issue is the effects of the initial state on the final steady-state opinion distribution. By carrying out extensive simulations and providing necessary discussions, we show that, while different initial opinion distributions certainly make differences to opinion evolution in social systems without noises, in systems with noises, given enough time, different initial states basically do not contribute to making any significant differences in the final steady state. Instead, it is the basal distribution of the preferred opinions that contributes to deciding the final state of the systems. We briefly explain the reasons leading to the observed conclusions. Such an observation contradicts with a long-term belief on the roles of system initial state in opinion formation, demonstrating the dominating role that opinion mutation can play in opinion formation given enough time. The observation may help to better understand certain observations of opinion evolution dynamics in real-life social networks.

Keywords: opinion formation, Deffuant model, opinion mutation, consensus making

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Authors: Yu Zhang, Jie Wu, Li Dong

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Rural tourism is the service industry which regards the agricultural production, rural life, rural nature and cultural landscape as the tourist attraction. It aims to meet the needs of the city tourists such as country sightseeing, vacation, and leisure. According to the difference of the tourist resources, the rural settlements can be divided into different types: The type of tourism resources, scenic spot, and peri-urban. In the past ten years, the rural tourism has promoted the industrial transformation and economic growth in rural areas of China. And it is conducive to the coordinated development of urban and rural areas and has greatly improved the ecological environment and the standard of living for farmers in rural areas. At the same time, a large number of buildings and sites are built in the countryside in order to enhance the tourist attraction and the ability of tourist reception and also to increase the travel comfort and convenience, which has significant influence on the spatial evolution of the village settlement. This article takes the XiangYing Subdistrict, which is in JinPu District of Dalian in China as the exemplification and uses the technology of Remote Sensing (RS), Geographic Information System (GIS) and the technology of Landscape Spatial Analysis to study the influence of the rural tourism development in the rural settlement spaces in four steps. First, acquiring the remote sensing image data at different times of 8 administrative villages in the XiangYing Subdistrict, by using the remote sensing application EDRAS8.6; second, vectoring basic maps of XiangYing Subdistrict including its land-use map with the application of ArcGIS 9.3, associating with social and economic attribute data of rural settlements and analyzing on the rural evolution visually; third, quantifying the comparison of these patches in rural settlements by using the landscape spatial calculation application Fragstats 3.3 and analyzing on the evolution of the spatial structure of settlement in macro and medium scale; finally, summarizing the evolution characteristics and internal reasons of tourism-oriented rural settlements. The main findings of this article include: first of all, there is difference in the evolution of the spatial structure between the developing rural settlements and undeveloped rural settlements among the eight administrative villages; secondly, the villages relying on the surrounding tourist attractions, the villages developing agricultural ecological garden and the villages with natural or historical and cultural resources have different laws of development; then, the rural settlements whose tourism development in germination period, development period and mature period have different characteristics of spatial evolution; finally, the different evolution modes of the tourism-oriented rural settlement space have different influences on the protection and inheritance of the village scene. The development of tourism has a significant impact on the spatial evolution of rural settlement. The intensive use of rural land and natural resources is the fundamental principle to protect the rural cultural landscape and ecological environment as well as the critical way to improve the attraction of rural tourism and promote the sustainable development of countryside.

Keywords: landscape pattern, rural settlement, spatial evolution, tourism-oriented, Xiangying Subdistrict

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Authors: Subramanian Chidambaran

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Right from the Vedic period, we have instances of human heroes being deified and later even assimilated into other deities. Many scholars opine Indra to be one such Vedic deity who rose from a ‘human leader’ to the position of Devata. We also see the assimilation of the Vedic deity Rudra into Śiva in post-Vedic period. Thus the current deities and Gods we worship in the polytheistic Hindu system have been a result of many such deifications and assimilations. Hanumān is one such contemporary character in Indian culture that changed from a valiant hero of the Rāmāyaṇa to a prominent deity in present days. There are also many arguments on whether Hanumān was truly a monkey or a human as the term ‘vānara’ could be interpreted as ‘vā narah’ i.e. ‘or a human’. Despite the popularity of this deity, there is very little academic research done on the genesis and evolution of him. There are many questions that arise - Does Hanumān find any mention (in any form) in literature or archaeological evidence prior to Vālmῑki Rāmāyaṇa? What is the character of Hanumān in the Vālmῑki Rāmāyaṇa? How has this evolved in later Indian literature and where do we see the deification process beginning? What’s the character of Hanumān in literature beyond Indian shores such as Southeast Asian literature and how does it compare with those in Indian literature? This paper is an attempt to answer these questions and trace the evolution of the character Hanumān right from the Vālmῑki Rāmāyaṇa to other Indian literature as well as Southeast Asian literature.

Keywords: Hanumān, Indian, Rāmāyaṇa, Southeast Asia

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Authors: Hamdy Elgohary, Majid Assas

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Estimation of lateral displacement and interstory drifts represent a major step in multistory frames design. In the preliminary design stage, it is essential to perform a fast check for the expected values of lateral deformations. This step will help to ensure the compliance of the expected values with the design code requirements. Also, in some cases during or after the detailed design stage, it may be required to carry fast check of lateral deformations by design reviewer. In the present paper, a parametric study is carried out on the factors affecting in the lateral displacements of multistory frame buildings. Based on the results of the parametric study, simplified empirical equations are recommended for the direct determination of the lateral deflection of multistory frames. The results obtained using the recommended equations have been compared with the results obtained by finite element analysis. The comparison shows that the proposed equations lead to good approximation for the estimation of lateral deflection of multistory RC frame buildings.

Keywords: lateral deflection, interstory drift, approximate analysis, multistory frames

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Authors: Eugene Stepanov, Arkadi Ponossov

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Many mathematical models used in biological and other applications are ill-posed. The reason for that is the nature of differential equations, where the nonlinearities are assumed to be step functions, which is done to simplify the analysis. Prominent examples are switched systems arising from gene regulatory networks and neural field equations. This simplification leads, however, to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid feedback controls to regularize the problem. Roughly speaking, one attaches a finite state control (‘automaton’), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. This ‘hybridization’ is shown to regularize the original switched system and gives rise to efficient hybrid numerical schemes. Several examples are provided in the presentation, which supports the suggested analysis. The method can be of interest in other applied fields, where differential equations contain step-like nonlinearities.

Keywords: hybrid feedback control, ill-posed problems, singular perturbation analysis, step-like nonlinearities

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Authors: Iftekhar Hassan, Sayedil Morsalin, Easir A Khan

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Accidents involving fire occur frequently in recent times and their causes showing a great deal of variety which require intervention methods and risk assessment strategies are unique in each case. On September 4, 2020, a fire and explosion occurred in a confined space caused by a methane gas leak from an underground pipeline in Baitus Salat Jame mosque during Night (Esha) prayer in Narayanganj District, Bangladesh that killed 34 people. In this research, this incident is simulated using Fire Dynamics Simulator (FDS) software to analyze and understand the nature of the accident and associated consequences. FDS is an advanced computational fluid dynamics (CFD) system of fire-driven fluid flow which solves numerically a large eddy simulation form of the Navier–Stokes’s equations for simulation of the fire and smoke spread and prediction of thermal radiation, toxic substances concentrations and other relevant parameters of fire. This study focuses on understanding the nature of the fire and consequence evaluation due to thermal radiation caused by vapor cloud explosion. An evacuation modeling was constructed to visualize the effect of evacuation time and fractional effective dose (FED) for different types of agents. The results were presented by 3D animation, sliced pictures and graphical representation to understand fire hazards caused by thermal radiation or smoke due to vapor cloud explosion. This study will help to design and develop appropriate respond strategy for preventing similar accidents.

Keywords: consequence modeling, fire and explosion, fire dynamics simulation (FDS), thermal radiation

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Authors: Guoqin Ge, Minhui Huang, Yazhou Zhou

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The growth of the Chengdu-Chongqing urban agglomeration has been designated as a national strategy in China. Analyzing its spatial evolution characteristics is crucial for devising relevant development strategies. This paper enhances the gravitational model by using temporal distance as a factor. It applies this improved model to assess the economic interconnection and concentration level of each geographical unit within the Chengdu-Chongqing urban agglomeration between 2011 and 2019. On this basis, this paper examines the spatial correlation characteristics of economic agglomeration intensity and urban-rural development equalization by employing spatial autocorrelation analysis. The study findings indicate that the spatial integration in the Chengdu-Chongqing urban agglomeration is currently in the "point-axis" development stage. The spatial organization structure is becoming more flattened, and there is a stronger economic connection between the core of the urban agglomeration and the peripheral areas. The integration of the Chengdu-Chongqing urban agglomeration is currently hindered by conflicting interests and institutional heterogeneity between Chengdu and Chongqing. Additionally, the connections between the relatively secondary spatial units are largely loose and weak. The strength and scale of economic ties and the level of urban-rural equilibrium among spatial units within the Chengdu-Chongqing urban agglomeration have increased, but regional imbalances have continued to widen, and such positive and negative changes have been characterized by the spatial and temporal synergistic evolution of the "core-periphery". Ultimately, this paper presents planning ideas for the future integration development of the Chengdu-Chongqing urban agglomeration, drawing from the findings.

Keywords: integration, planning strategy, space organization, space evolution, urban agglomeration

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Authors: Shreeyam, Ranjan Kumar Sah, Shivangi

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Recognizing and solving handwritten mathematical expressions can be a challenging task, particularly when certain characters are segmented and classified. This project proposes a solution that uses Convolutional Neural Network (CNN) and image processing techniques to accurately solve various types of equations, including arithmetic, quadratic, and trigonometric equations, as well as logical operations like logical AND, OR, NOT, NAND, XOR, and NOR. The proposed solution also provides a graphical solution, allowing users to visualize equations and their solutions. In addition to equation solving, the platform, called CNNCalc, offers a comprehensive learning experience for students. It provides educational content, a quiz platform, and a coding platform for practicing programming skills in different languages like C, Python, and Java. This all-in-one solution makes the learning process engaging and enjoyable for students. The proposed methodology includes horizontal compact projection analysis and survey for segmentation and binarization, as well as connected component analysis and integrated connected component analysis for character classification. The compact projection algorithm compresses the horizontal projections to remove noise and obtain a clearer image, contributing to the accuracy of character segmentation. Experimental results demonstrate the effectiveness of the proposed solution in solving a wide range of mathematical equations. CNNCalc provides a powerful and user-friendly platform for solving equations, learning, and practicing programming skills. With its comprehensive features and accurate results, CNNCalc is poised to revolutionize the way students learn and solve mathematical equations. The platform utilizes a custom-designed Convolutional Neural Network (CNN) with image processing techniques to accurately recognize and classify symbols within handwritten equations. The compact projection algorithm effectively removes noise from horizontal projections, leading to clearer images and improved character segmentation. Experimental results demonstrate the accuracy and effectiveness of the proposed solution in solving a wide range of equations, including arithmetic, quadratic, trigonometric, and logical operations. CNNCalc features a user-friendly interface with a graphical representation of equations being solved, making it an interactive and engaging learning experience for users. The platform also includes tutorials, testing capabilities, and programming features in languages such as C, Python, and Java. Users can track their progress and work towards improving their skills. CNNCalc is poised to revolutionize the way students learn and solve mathematical equations with its comprehensive features and accurate results.

Keywords: AL, ML, hand written equation solver, maths, computer, CNNCalc, convolutional neural networks

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Authors: Rajendra Kumar Dubey

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Einstein’s field equations with variable cosmological term Λ are considered in the presence of viscous fluid for Bianchi type I space time. Exact solutions of Einstein’s field equations are obtained by assuming cosmological term Λ Proportional to (R is a scale factor and m is constant). We observed that the shear viscosity is found to be responsible for faster removal of initial anisotropy in the universe. The physical significance of the cosmological models has also been discussed.

Keywords: bianchi type, I cosmological model, viscous fluid, cosmological constant Λ

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Authors: Hussaini Doko Ibrahim, Hamilton Cyprian Chinwenyi, Henrietta Nkem Ude

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In this paper, efforts were made to examine and compare the algorithmic iterative solutions of the conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax=b, where A is a real n×n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3×3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi, and conjugate gradient methods), respectively. From the results obtained, we discovered that the conjugate gradient method converges faster to exact solutions in fewer iterative steps than the two other methods, which took many iterations, much time, and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, gauss-seidel, Jacobi, algorithm

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Authors: Malika Elkyal

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We consider an iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm does not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Accordingly, we note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, differential algebraic equations

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Authors: Deyu Zhou, Xiao Xue, Lizhen Cui

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With the increasing collaboration among various services and the growing complexity of user demands, there are more and more factors affecting the stable development of the cloud manufacturing service economic system (CMSE). This poses new challenges to the evolution analysis of the CMSE. Many researchers have modeled and analyzed the evolution process of CMSE from the perspectives of individual learning and internal factors influencing the system, but without considering other important characteristics of the system's individuals (such as heterogeneity, bounded rationality, etc.) and the impact of external environmental factors. Therefore, this paper proposes an integrated artificial social model for the cloud manufacturing service economic system, which considers both the characteristics of the system's individuals and the internal and external influencing factors of the system. The model consists of three parts: the Agent model, environment model, and rules model (Agent-Environment-Rules, AER): (1) the Agent model considers important features of the individuals, such as heterogeneity and bounded rationality, based on the adaptive behavior mechanisms of perception, action, and decision-making; (2) the environment model describes the activity space of the individuals (real or virtual environment); (3) the rules model, as the driving force of system evolution, describes the mechanism of the entire system's operation and evolution. Finally, this paper verifies the effectiveness of the AER model through computational and experimental results.

Keywords: cloud manufacturing service economic system (CMSE), AER model, artificial social modeling, integrated framework, computing experiment, agent-based modeling, social networks

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Authors: K. Digheche, K. Saadi, Z. Boumerzoug

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Welding is one of the most important technological processes used in many branches of industry such as industrial engineering, shipbuilding, pipeline fabrication among others. Generally, welding is the preferred joining method and most common steels are weldable. This investigation is a contribution to scientific work of welding of low carbon steel. This work presents the results of the isothermal heat treatment effect at 200, 400 and 600 °C on microstructural evolution in weld region of X70 pipeline steel. The welding process has been realized in three passes by industrial arc welding. We have found that the heat treatments cause grain growth reaction.

Keywords: heat treatments, low carbon steel, microstructures, welding

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Authors: Mohammad R. Kavian Nezhad, Carlos F. Lange, Brian A. Fleck

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This research presents the validation study of a computational fluid dynamics (CFD) model developed to simulate the scalar dispersion emitted from rooftop sources around the buildings at the University of Alberta North Campus. The ANSYS CFX code was used to perform the numerical simulation of the wind regime and pollutant dispersion by solving the 3D steady Reynolds-averaged Navier-Stokes (RANS) equations on a building-scale high-resolution grid. The validation study was performed in two steps. First, the CFD model performance in 24 cases (eight wind directions and three wind speeds) was evaluated by comparing the predicted flow fields with the available data from the previous measurement campaign designed at the North Campus, using the standard deviation method (SDM), while the estimated results of the numerical model showed maximum average percent errors of approximately 53% and 37% for wind incidents from the North and Northwest, respectively. Good agreement with the measurements was observed for the other six directions, with an average error of less than 30%. In the second step, the reliability of the implemented turbulence model, numerical algorithm, modeling techniques, and the grid generation scheme was further evaluated using the Mock Urban Setting Test (MUST) dispersion dataset. Different statistical measures, including the fractional bias (FB), the geometric mean bias (MG), and the normalized mean square error (NMSE), were used to assess the accuracy of the predicted dispersion field. Our CFD results are in very good agreement with the field measurements.

Keywords: CFD, plume dispersion, complex urban geometry, validation study, wind flow

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Authors: Mustafa Taskin, Ozgur Demir, M. Mert Serveren

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The precise study of the impact of underwater explosions on structures is of great importance in the design and engineering calculations of floating structures, especially those used for military purposes, as well as power generation facilities such as offshore platforms that can become a target in case of war. Considering that ship and submarine structures are mostly curved surfaces, it is extremely important and interesting to examine the destructive effects of underwater explosions on curvilinear surfaces. In this study, geometric nonlinear dynamic analysis of cylindrical composite sandwich shells subjected to instantaneous pressure load is performed. The instantaneous pressure load is defined as an underwater explosion and the effects of the liquid medium are taken into account. There are equations in the literature for pressure due to underwater explosions, but these equations have been obtained for flat plates. For this reason, the instantaneous pressure load equations are arranged to be suitable for curvilinear structures before proceeding with the analyses. Fluid-solid interaction is defined by using Taylor's Plate Theory. The lower and upper layers of the cylindrical composite sandwich shell are modeled as composite laminate and the middle layer consists of soft core. The geometric nonlinear dynamic equations of the shell are obtained by Hamilton's principle, taken into account the von Kàrmàn theory of large displacements. Then, time dependent geometric nonlinear equations of motion are solved with the help of generalized differential quadrature method (GDQM) and dynamic behavior of cylindrical composite sandwich shells exposed to underwater explosion is investigated. An algorithm that can work parametrically for the solution has been developed within the scope of the study.

Keywords: cylindrical composite sandwich shells, generalized differential quadrature method, geometric nonlinear dynamic analysis, underwater explosion

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Authors: Yu Zhang, Mingxue Lang, Li Dong

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The hundreds of years of slow succession of living environment in rural area is a crucial carrier of China’s long history of culture and national wisdom. In recent years, the space evolution of traditional rural settlements has been promoted by the intervention of tourism development, among which the public architecture and outdoor activity areas together served as the major places for villagers, and tourists’ social activities are an important characterization for settlement spatial evolution. Traditional public space upgrade and layout study of new public space can effectively promote the tourism industry development of traditional rural settlements. This article takes Qi County, one China Traditional Culture Village as the exemplification and uses the technology of Remote Sensing (RS), Geographic Information System (GIS) and Space Syntax, studies the evolution features of public space of tourism-oriented traditional rural settlements in four steps. First, acquire the 2003 and 2016 image data of Qi County, using the remote sensing application EDRAS8.6. Second, vectorize the basic maps of Qi County including its land use map with the application of ArcGIS 9.3 meanwhile, associating with architectural and site information concluded from field research. Third, analyze the accessibility and connectivity of the inner space of settlements using space syntax; run cross-correlation with the public space data of 2003 and 2016. Finally, summarize the evolution law of the public space of settlements; study the upgrade pattern of traditional public space and location plan for new public space. Major findings of this paper including: first, location layout of traditional public space has a larger association with the calculation results of space syntax and further confirmed the objective value of space syntax in expressing the space and social relations. Second, the intervention of tourism development generates remarkable impact on public space location of tradition rural settlements. Third, traditional public space produces the symbols of both strengthening and decline and forms a diversified upgrade pattern for the purpose of meeting the different tourism functional needs. Finally, space syntax provides an objective basis for location plan of new public space that meets the needs of tourism service. Tourism development has a significant impact on the evolution of public space of traditional rural settlements. Two types of public space, architecture, and site are both with changes seen from the perspective of quantity, location, dimension and function after the intervention of tourism development. Function upgrade of traditional public space and scientific layout of new public space are two important ways in achieving the goal of sustainable development of tourism-oriented traditional rural settlements.

Keywords: public space evolution, Qi county, space syntax, tourism oriented, traditional rural settlements

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Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

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Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.

Keywords: Adomian’s decomposition method, magneto-thermoelasticity, finite conductivity, iteration method, thermal load

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Authors: Pradeepa Teegala, Ramreddy Chetteti

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This work emphasizes the effects of heat generation/absorption and Joule heating on chemically reacting micropolar fluid flow over a truncated cone with convective boundary condition. For this complex fluid flow problem, the similarity solution does not exist and hence using non-similarity transformations, the governing fluid flow equations along with related boundary conditions are transformed into a set of non-dimensional partial differential equations. Several authors have applied the spectral quasi-linearization method to solve the ordinary differential equations, but here the resulting nonlinear partial differential equations are solved for non-similarity solution by using a recently developed method called the spectral quasi-linearization method (SQLM). Comparison with previously published work on special cases of the problem is performed and found to be in excellent agreement. The influence of pertinent parameters namely Biot number, Joule heating, heat generation/absorption, chemical reaction, micropolar and magnetic field on physical quantities of the flow are displayed through graphs and the salient features are explored in detail. Further, the results are analyzed by comparing with two special cases, namely, vertical plate and full cone wherever possible.

Keywords: chemical reaction, convective boundary condition, joule heating, micropolar fluid, spectral quasilinearization method

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Authors: Elmongi Elbellili, Ben Lauwens, Daan Huybrechs

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The increasing complexity of modern engineering systems presents a challenge to the digital simulation of these systems which usually can be represented by differential equations. The Linearly Implicit Quantized State System (LIQSS) offers an alternative approach to traditional numerical integration techniques for solving Ordinary Differential Equations (ODEs). This method proved effective for handling discontinuous and large stiff systems. However, the inherent discrete nature of LIQSS may introduce oscillations that result in unnecessary computational steps. The current oscillation detection mechanism relies on a condition that checks the significance of the derivatives, but it could be further improved. This paper describes a different cycle detection mechanism and presents the outcomes using LIQSS order one in simulating the Advection Diffusion problem. The efficiency of this new cycle detection mechanism is verified by comparing the performance of the current solver against the new version as well as a reference solution using a Runge-Kutta method of order14.

Keywords: numerical integration, quantized state systems, ordinary differential equations, stiffness, cycle detection, simulation

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Authors: Idowu Ibikunle Albert, Atilade Adesanya Oluwafemi, Okedeyi Abiodun Sikiru, Mustapha Rilwan Adewale

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These present-day all areas of transport have experienced large advances characterized by increases in the speeds and weight of vehicles. As a result, this paper considered the Transverse Vibration of an Elastic Beam Resting on a Variable Elastic Foundation Subjected to a moving Load. The beam is presumed to be uniformly distributed and has simple support at both ends. The moving distributed moving mass is assumed to move with constant velocity. The governing equations, which are fourth-order partial differential equations, were reduced to second-order partial differential equations using an analytical method in terms of series solution and solved by a numerical method using mathematical software (Maple). Results show that an increase in the values of beam parameters, moving Mass M, and k-stiffness K, significantly reduces the deflection profile of the vibrating beam. In the results, it was equally found that moving mass is greater than moving force.

Keywords: elastic beam, moving load, response of structure, variable elastic foundation

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Authors: Dixon, Lieh-Chi Su, Hsiao-Ling Yu, Ren-Yi Huang, Yung-Tan Lee

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The present paper analyzed the major, trace elements, rare earth elements of these Cenozoic basalts and combined with Sr-Nd isotopic compositions to discuss the petrogenesis of these basalts and the tectonic setting of the study area. Based on major, trace elements and fractional crystallization model we suggest that the basaltic magma has experienced olivine, clinopyroxene, and plagioclase fractionation during its evolution. Spidergrams and REE patterns reveal that Cenozoic basalts found in the Jiashan County, Anhui Province have geochemical characteristics similar to those of ocean island basalts(OIB) suggesting a derivation related to OIB-like mantle source. The slight positive Nb and Ti anomalies found in basaltic rocks of this study suggest the presence of Ti-bearing minerals in the mantle source and these Ti-bearing minerals had contributed to basaltic magma during partial melting, indicating a metasomatic event might have occurred before the partial melting. Based on 143Nd/144Nd vs. 87Sr/86Sr diagram we suggest that basalts of this study can be produced by MORB and EM-I components mixing and small degree of partial melting may be the major controlling factor during generation of basaltic magma. Some basaltic magma may be derived from partial melting of EM-Ⅰ heated by the upwelling asthenospheric mantle. The basalts fall within the WPB field in the discriminant plot of 2Nb-Zr/4-Y indicate that the volcanic activities in this region may be closely related to deep continental rifting process.

Keywords: geochemistry, cenozoic basalts, Anhui Province, Nushan Geopark, tectonic setting, fractionation

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Authors: Kushakov Kholmurodjon, Muhammadjonov Akbarshox

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This present paper is devoted to a system of second-order nonlinear differential equations with a special right-hand side, exactly, the linear part and a third-order polynomial of a special form. It is shown that for some relations between the parameters, there is a second-order curve in which trajectories leaving the points of this curve remain in the same place. Thus, the curve is invariant with respect to the given system. Moreover, this system is invariant under a non-degenerate linear transformation of variables. The form of this curve, depending on the relations between the parameters and the eigenvalues of the matrix, is proved. All solutions of this system of differential equations are shown analytically.

Keywords: dynamic system, ellipse, hyperbola, Hess system, polar coordinate system

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Authors: Muhammad Faraz, Talat Rafique, Jang Min Park

Abstract:

In this article, rotational flow above a permeable surface with a variable free stream angular velocity is considered. Main interest is to solve the associated heat/mass transport equations under different situations. Firstly, heat transport phenomena occurring in generalized vortex flow are analyzed under two altered heating processes, namely, the (i) prescribed surface temperature and (ii) prescribed heat flux. The vortex motion imposed at infinity is assumed to follow a power-law form 〖(r/r_0)〗^((2n-1)) where r denotes the radial coordinate, r_0 the disk radius, and n is a power-law parameter. Assuming a similar solution, the governing Navier-Stokes equations transform into a set of coupled ODEs which are treated numerically for the aforementioned thermal conditions. Secondly, mass transport phenomena accompanied by activation energy are incorporated into the generalized vortex flow situation. After finding self-similar equations, a numerical solution is furnished by using MATLAB's built-in function bvp4c.

Keywords: bödewadt flow, vortex flow, rotating flows, prescribed heat flux, permeable surface, activation energy

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Authors: Mauricio Cruz, Andrés Díaz García, Martha Isabel Gómez, Juan Carlos Serrato Bermúdez

Abstract:

The disadvantages of using natural substrates in SSF processes have been well recognized and mainly are associated to gradual decomposition of the substrate, formation of agglomerates and decrease of porosity bed generating limitations in the mass and heat transfer. Additionally, in several cases, materials with a high agricultural value such as sour milk, beets, rice, beans and corn have been used. Thus, the use of economic inert supports (natural or synthetic) in combination with a nutrient suspension for the production of biocontrol microorganisms is a good alternative in SSF processes, but requires further studies in the fields of modeling and optimization. Therefore, the aim of this work is to compare the performance of two inert supports, a synthetic (polyurethane foam) and a natural one (rice husk), identifying the factors that have the major effects on the productivity of T. asperellum Th204 and the maximum specific growth rate in a PROPHYTA L05® fixed bed bioreactor. For this, the six factors C:N ratio, temperature, inoculation rate, bed height, air moisture content and airflow were evaluated using a fractional design. The factors C:N and air flow were identified as significant on the productivity (expressed as conidia/dry substrate•h). The polyurethane foam showed higher maximum specific growth rate (0.1631 h-1) and productivities of 3.89 x107 conidia/dry substrate•h compared to rice husk (2.83x106) and natural substrate based on rice (8.87x106) used as control. Finally, a quadratic model was generated and validated, obtaining productivities higher than 3.0x107 conidia/dry substrate•h with air flow at 0.9 m3/h and C:N ratio at 18.1.

Keywords: bioprocess, scale up, fractional design, C:N ratio, air flow

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Authors: Vandana N. Purav

Abstract:

The Dynamical systems concept is a mathematical formalization for any fixed rule that describes the time dependence of a points position in its ambient space. e.g. pendulum of a clock, the number of fish each spring in a lake, the number of rabbits spring in an enclosure, etc. The Dynamical system theory used to describe the complex nature that is dynamical systems with differential equations called continuous dynamical system or dynamical system with difference equations called discrete dynamical system. The concept of dynamical system has its origin in Newtonian mechanics.

Keywords: dynamical systems, Fibonacci numbers, Newtonian mechanics, discrete dynamical system

Procedia PDF Downloads 468