Search results for: fundamental equation

Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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

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

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Authors: Clarinda Vitorino Nhangumbe, Fredericks Ebrahim, Betuel Canhanga

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The price of an option weather derivatives can be approximated as a solution of the two-dimensional convection-diffusion dominant partial differential equation derived from the Ornstein-Uhlenbeck process, where one variable represents the weather dynamics and the other variable represent the underlying weather index. With appropriate financial boundary conditions, the solution of the pricing equation is approximated using a nonstandard finite difference method. It is shown that the proposed numerical scheme preserves positivity as well as stability and consistency. In order to illustrate the accuracy of the method, the numerical results are compared with other methods. The model is tested for real weather data.

Keywords: nonstandard finite differences, Ornstein-Uhlenbeck process, partial differential equations approach, weather derivatives

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Authors: Punit Kumar, Niraj Kumar

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The influence of transverse surface roughness on EHL characteristics has been investigated numerically using an extensive set of full EHL line contact simulations for shear-thinning lubricants under pure sliding condition. The shear-thinning behavior of lubricant is modeled using Carreau viscosity equation along with Doolittle-Tait equation for lubricant compressibility. The surface roughness is assumed to be sinusoidal and it is present on the stationary surface. It is found that surface roughness causes sharp pressure peaks along with reduction in central and minimum film thickness. With increasing amplitude of surface roughness, the minimum film thickness decreases much more rapidly as compared to the central film thickness.

Keywords: EHL, Carreau, shear-thinning, surface roughness, amplitude, wavelength

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Authors: S. P. Raut, S. K. Soni, A. W. Kolhatkar

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Denim is widely used by every age of people all over the world. As the use of denim is increasing progressively, till now the handle properties of denim fabric not reported at significant level. In the present study, five commercial denim fabric samples were used. Denim samples, weighing from 8.5oz/sq yds to 14.5 oz/sq yds, were processed as per standard commercial procedure for denim finishing. These finished denim samples were tested on Kawabata Evaluation System(KES) for low stress mechanical properties. The results of KES values are used for calculation of Total Hand value(THV) using equation for summer suit. The obtained result for THV using equation for summer suit for denim samples is in the range from 1.62 to 3.30. These values of low stress mechanical properties values given by KES, can be used to engineer the denim fabric for bottom wear.

Keywords: denim, handle value, Kawabata evaluation system, objective evaluation

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Authors: Juan Ignacio Arango, Andres Diaz, Giacomo Barbieri

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In soilless culture, the definition of efficient fertigation strategies is fundamental for the growth of crops. Flexible test-benches able to independently manage groups of crops are key for investigating efficient fertigation practices through experimentation. These test-benches must be able to provide nutrient solution (NS) in a precise, uniform and repeatable way in order to effectively implement and compare different fertigation strategies. This article describes a distribution module for investigating fertigation practices able to control the fertigation dose and frequency. The proposed solution is characterized in terms of precision, uniformity and repeatability since these parameters are fundamental in the implementation of effective experiments for the investigation of fertigation practices. After a calibration process, the implemented system reaches a precision of 1mL, a uniformity of 98.5% at a total cost of 735USD.

Keywords: recision horticulture, test-bench, fertigation strategy, automation, flexibility

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Authors: Arunroong Wongkungwan

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This study aimed to investigate the influence of selected antecedents, which were tourists’ satisfaction towards attractions in Bangkok, perceived value of the attractions, feelings of engagement with the attractions, acquaintance with the attractions, push factors, pull factors and motivation to seek novelty, on foreign tourist’s loyalty towards tourist attractions in Bangkok. By using multi stage sampling technique, 400 international tourists were sampled. After that, Semi Structural Equation Model was utilized in the analysis stage by LISREL. The Semi Structural Equation Model of the selected antecedents of tourist’s loyalty attractions had a correlation with the empirical data through the following statistical descriptions: Chi- square = 3.43, df = 4, P- value = 0.48893; RMSEA = 0.000; CFI = 1.00; CN = 1539.75; RMR = 0.0022; GFI = 1.00 and AGFI = 0.98. The findings indicated that all antecedents were able together to predict the loyalty of the foreign tourists who visited Bangkok at 73 percent.

Keywords: antecedent, Bangkok, foreign tourists, loyalty, tourist attractions

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Authors: Stephen Kirkup

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This paper discusses the implementation of the boundary element method (BEM) on an Excel spreadsheet and how it can be used in teaching vector calculus and simulation. There are two separate spreadheets, within which Laplace equation is solved by the BEM in two dimensions (LIBEM2) and axisymmetric three dimensions (LBEMA). The main algorithms are implemented in the associated programming language within Excel, Visual Basic for Applications (VBA). The BEM only requires a boundary mesh and hence it is a relatively accessible method. The BEM in the open spreadsheet environment is demonstrated as being useful as an aid to teaching and learning. The application of the BEM implemented on a spreadsheet for educational purposes in introductory vector calculus and simulation is explored. The development of assignment work is discussed, and sample results from student work are given. The spreadsheets were found to be useful tools in developing the students’ understanding of vector calculus and in simulating heat conduction.

Keywords: boundary element method, Laplace’s equation, vector calculus, simulation, education

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Authors: L. A. Ostrovsky, Yu. A. Stepanyants

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Effect of Earth rotation on nonlinear waves is a practically important and theoretically challenging problem of fluid mechanics and geophysics. Whereas the large-scale, geostrophic processes such as Rossby waves are a classical object of oceanic and atmospheric physics, rotation effects on mesoscale waves are not well studied. In particular, the Coriolis force can radically modify the behavior of nonlinear internal gravity waves in the ocean having spatial scales of 1-10 kilometers and time durations of few hours. In the last decade, such a non-trivial behavior was observed more than once. Similar effects are possible for magnetic sound in the ionosphere. Here we outline the main physical peculiarities in the behavior of nonlinear internal waves due to the rotation effect and present some results of our recent studies. The consideration is based on the fourth-order equation derived by one of the authors as a rotation-modified Korteweg–de Vries (rKdV) equation which includes two types of dispersion: one is responsible for the finiteness of depth as in the classical KdV equation; another is due to the Coriolis effect. This equation is, in general, non-integrable; moreover, under the conditions typical of oceanic waves (positive dispersion parameter), it does not allow solitary solutions at all. In the opposite case (negative dispersion) which is possible for, e.g., magnetic sound, solitary solutions do exist and can form complex bound states (multisoliton). Another non-trivial properties of nonlinear internal waves with rotation include, to name a few, the ‘terminal’ damping of the initial KdV soliton disappearing in a finite time due to radiation losses caused by Earth’s rotation, and eventual transformation of a KdV soliton into a wave packet (an envelope soliton). The new results to be discussed refer to the interaction of a soliton with a long background wave. It is shown, in particular, that in this case internal solitons can exist since the radiation losses are compensated by energy pumping from the background wave. Finally, the relevant oceanic observations of rotation effect on internal waves are briefly described.

Keywords: Earth rotation, internal waves, nonlinear waves, solitons

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Authors: Dara Singh, Keikhosrow Firouzbakhsh, Mohammad Taghi Ahmadian

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In this paper, conventional laser Keratoplasty surgeries in the human eye are studied. For this purpose, a validated 3D finite volume model of the human eye is introduced. In this model the fluid flow has also been considered. The discretized domain of the human eye incorporates a bio-heat transfer equation coupled with a Boussinesq equation. Both continuous and pulsed lasers have been modeled and the results are compared. Moreover, two different conventional surgical positions that are upright and recumbent are compared for these laser therapies. The simulation results show that in these conventional surgeries, the temperature rises above the critical values at the laser insertion areas. However, due to the short duration and the localized nature, the potential damages are restricted to very small regions and can be ignored. The conclusion is that the present day lasers are acceptably safe to the human eye.

Keywords: eye, heat-transfer, keratoplasty laser, surgery

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis

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Authors: Mohd Khairezan Rahmat

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Since the impetus of becoming a develop country by the year 2020, the Malaysian government have been proactive in strengthening the integration of ICT into the national educational system. Teacher-education programs have the responsibility to prepare the nation future teachers by instilling in them the desire, confidence, and ability to fully utilized the potential of ICT into their instruction process. In an effort to fulfill this responsibility, teacher-education program are beginning to create alternatives means for preparing cutting-edge teachers. One of the alternatives is the student’s learning portal. In line with this mission, this study investigates the Faculty of Education, University Teknologi MARA (UiTM) pre-service teachers’ perception of usefulness, attitude, and ability toward the usage of the university learning portal, known as iLearn. The study also aimed to predict factors that might hinder the pre-service teachers’ decision to used iLearn as their platform in learning. The Structural Equation Modeling (SEM), was employed in analyzed the survey data. The suggested findings informed that pre-service teacher’s successful integration of the iLearn was highly influenced by their perception of usefulness of the system. The findings also suggested that the more familiar the pre-service teacher with the iLearn, the more possibility they will use the system. In light of similar study, the present findings hope to highlight the important to understand the user’s perception toward any proposed technology.

Keywords: e-learning, prediction factors, pre-service teacher, structural equation modeling (SEM)

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Authors: Neeraj Kumar, J. P. Narayan

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The effects of multiple Structure-Soil-Structure Interactions (SSSI) on the seismic wave-field is generally disregarded by earthquake engineers, particularly the surface waves which cause more damage to buildings. Closely built high rise buildings exchange substantial seismic energy with each other and act as a full-coupled dynamic system. In this paper, SSI effects on the building responses and the free field motion due to a small city consisting 25- homogenous buildings blocks of 10-storey are quantified. The rocking and translational behavior of building under Rayleigh wave loading is studied for different dimensions of the building. The obtained dynamic parameters of buildings revealed a reduction in building roof drift with an increase in number of buildings ahead of the considered building. The strain developed by vertical component of Rayleigh may cause tension in structural components of building. A matching of fundamental frequency of building for the horizontal component of Rayleigh wave with that for vertically incident SV-wave is obtained. Further, the fundamental frequency of building for the vertical vibration is approximately twice to that for horizontal vibration. The city insulation has caused a reduction of amplitude of Rayleigh wave up to 19.3% and 21.6% in the horizontal and vertical components, respectively just outside the city. Further, the insulating effect of city was very large at fundamental frequency of buildings for both the horizontal and vertical components. Therefore, it is recommended to consider the insulating effects of city falling in the path of Rayleigh wave propagation in seismic hazard assessment for an area.

Keywords: structure-soil-structure interactions, Rayleigh wave propagation, finite difference simulation, dynamic response of buildings

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Authors: Somnath Bhattacharyya

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The mobile adsorbed surface charge on hydrophobic surfaces can modify the velocity slip condition as well as create a Marangoni stress at the interface. The functionalized hydrophobic walls of micro/nanopores, e.g., graphene nanochannels, may possess physio-sorbed ions. The lateral mobility of the physisorbed absorbed ions creates a friction force as well as an electric force, leading to a modification in the velocity slip condition at the hydrophobic surface. In addition, the non-uniform distribution of these surface ions creates a surface tension gradient, leading to a Marangoni stress. The impact of the mobile surface charge on streaming potential and electrochemical energy conversion efficiency in a pressure-driven flow of ionized liquid through the nanopore is addressed. Also, enhanced electro-osmotic flow through the hydrophobic nanochannel is also analyzed. The mean-filed electrokinetic model is modified to take into account the short-range non-electrostatic steric interactions and the long-range Coulomb correlations. The steric interaction is modeled by considering the ions as charged hard spheres of finite radius suspended in the electrolyte medium. The electrochemical potential is modified by including the volume exclusion effect, which is modeled based on the BMCSL equation of state. The electrostatic correlation is accounted for in the ionic self-energy. The extremal of the self-energy leads to a fourth-order Poisson equation for the electric field. The ion transport is governed by the modified Nernst-Planck equation, which includes the ion steric interactions; born force arises due to the spatial variation of the dielectric permittivity and the dielectrophoretic force on the hydrated ions. This ion transport equation is coupled with the Navier-Stokes equation describing the flow of the ionized fluid and the 3fourth-order Poisson equation for the electric field. We numerically solve the coupled set of nonlinear governing equations along with the prescribed boundary conditions by adopting a control volume approach over a staggered grid arrangement. In the staggered grid arrangements, velocity components are stored on the midpoint of the cell faces to which they are normal, whereas the remaining scalar variables are stored at the center of each cell. The convection and electromigration terms are discretized at each interface of the control volumes using the total variation diminishing (TVD) approach to capture the strong convection resulting from the highly enhanced fluid flow due to the modified model. In order to link pressure to the continuity equation, we adopt a pressure correction-based iterative SIMPLE (Semi-Implicit Method for Pressure-Linked Equations) algorithm, in which the discretized continuity equation is converted to a Poisson equation involving pressure correction terms. Our results show that the physisorbed ions on a hydrophobic surface create an enhanced slip velocity when streaming potential, which enhances the convection current. However, the electroosmotic flow attenuates due to the mobile surface ions.

Keywords: microfluidics, electroosmosis, streaming potential, electrostatic correlation, finite sized ions

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Authors: L. M. Hayyan ul Haq, Lalu Sabardi

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This research is aimed at exploring an appropriate regulatory model in coherencing a diametrical interest between the state, Adat legal community, and private interests in utilising and optimizing land in Indonesia. This work is also highly relevant to coherencing the obligation of the state to respect, to fulfill and to protect the fundamental rights of people, especially to protect the communal or adat community rights to the land. In visualizing those ideas, this research will use the normative legal research to elaborate the normative problem in land use, as well as redesigning and creating an appropriate regulatory model in bridging and protecting all interest parties, especially, the state, Adat legal community, and private parties. In addition, it will also employ an empirical legal research for identifying some operational problems in protecting and optimising the land. In detail, this research will not only identify the problems at the normative level, such as conflicted norms, the absence of the norms, and the unclear norm in land law, but also the problems at operational level, such as institutional relationship in managing the land use. At the end, this work offers an appropriate regulatory model at the systems level, which covers value and norms in land use, as well as the appropriate mechanism in managing the utilization of the land for the state, Adat legal community, and private sector. By manifesting this objective, the government will not only fulfill its obligation to regulate the land for people and private, but also to protect the fundamental rights of people, as mandated by the Indonesian 1945 Constitution.

Keywords: adat community rights, fundamental rights, investment, land law, private sector

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Authors: S. F. Bayona, J. Nunez, D. Paez

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The diagnostic processes have been consolidated as fundamental tools in the adequate knowledge of organizations and their processes. The diagnosis is related to the interpretation of the data, findings and the relevant information, to determine problems, causes, or the simple state and behavior of a process, without including a solution to the problems detected. The objective of this work is to identify the necessary stages to diagnose the logistic processes in a metalworking company, from the literary revision of different disciplines. A total of 62 articles were chosen to identify, through bibliometric analysis, the most cited articles, as well as the most frequent authors and journals. The results allowed to identify the two fundamental stages in the diagnostic process: a primary phase (general) based on the logical subjectivity of the knowledge of the person who evaluates, and the secondary phase (specific), related to the interpretation of the results, findings or data. Also, two phases were identified, one related to the definition of the scope of the actions to be developed and the other, as an initial description of what was observed in the process.

Keywords: business, diagnostic, management, process

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Authors: O. G. Omogunloye, J. B. Olaleye, O. E. Abiodun, J. O. Odumosu, O. G. Ajayi

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The focus of the study is to proffer easy formulation and computation of least square observation equation’s design matrix by using an efficient book keeping strategy. Usually, for a large network of many triangles and stations, a rigorous task is involved in the computation and placement of the values of the differentials of each observation with respect to its station coordinates (latitude and longitude), in their respective rows and columns. The efficient book keeping strategy seeks to eliminate or reduce this rigorous task involved, especially in large network, by simple skillful arrangement and development of a short program written in the Matlab environment, the formulation and computation of least square observation equation’s design matrix can be easily achieved.

Keywords: design, differential, geodetic, matrix, network, station

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Authors: Charline David, Alexandre Blondin Massé, Arnaud Zinflou

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In 2016, Clements, Hurn, and Li proposed a multiple equation time series approach for the short-term load forecasting, reporting an average mean absolute percentage error (MAPE) of 1.36% on an 11-years dataset for the Queensland region in Australia. We present an adaptation of their model to the electrical power load consumption for the whole Quebec province in Canada. More precisely, we take into account two additional meteorological variables — cloudiness and wind speed — on top of temperature, as well as the use of multiple meteorological measurements taken at different locations on the territory. We also consider other minor improvements. Our final model shows an average MAPE score of 1:79% over an 8-years dataset.

Keywords: short-term load forecasting, special days, time series, multiple equations, parallelization, clustering

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Davood Domiri Danji

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In this conference, our aims are accuracy, capabilities and power at solving of the complicated non-linear partial differential. Our purpose is to enhance the ability to solve the mentioned nonlinear differential equations at basic science and engineering field and similar issues with a simple and innovative approach. As we know most of engineering system behavior in practical are nonlinear process (especially basic science and engineering field, etc.) and analytical solving (no numeric) these problems are difficult, complex, and sometimes impossible like (Fluids and Gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure an innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical method (Runge-Kutta 4th). Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear partial differential equations, with help of that there is no difficulty for solving all nonlinear differential equations. Advantages and ability of this method (AGM) as follow: (a) Non-linear Differential equations (ODE, PDE) are directly solvable by this method. (b) In this method (AGM), most of the time, without any dimensionless procedure, we can solve equation(s) by any boundary or initial condition number. (c) AGM method always is convergent in boundary or initial condition. (d) Parameters of exponential, Trigonometric and Logarithmic of the existent in the non-linear differential equation with AGM method no needs Taylor expand which are caused high solve precision. (e) AGM method is very flexible in the coding system, and can solve easily varieties of the non-linear differential equation at high acceptable accuracy. (f) One of the important advantages of this method is analytical solving with high accuracy such as partial differential equation in vibration in solids, waves in water and gas, with minimum initial and boundary condition capable to solve problem. (g) It is very important to present a general and simple approach for solving most problems of the differential equations with high non-linearity in engineering sciences especially at civil engineering, and compare output with numerical method (Runge-Kutta 4th) and Exact solutions.

Keywords: new approach, AGM, sets of coupled nonlinear differential equation, exact solutions, numerical

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Authors: Bavneet Kaur Sidhu, Manoj Tiwari

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Global Developmental Delay (GDD) is a common pediatric condition. Etiologies of GDD might, however, differ in developing countries. In the last decade, sporadic families are being reported in various countries. As to the author’s best knowledge, many risk factors and their correlation with the prevalence of GDD have been studied but its statistical correlation has not been done. Thus we propose the present study by targeting the risk factor, prevalence and their statistical correlation with GDD. FMR1 gene was studied to confirm the disease and its penetrance. A complete questionnaire-based performance was designed for the statistical studies having a personal, past and present medical history along with their socio-economic status as well. Methods: We distributed the children’s age in 4 different age groups having 5-year intervals and applied structural equation modeling (SEM) techniques, Spearman’s rank correlation coefficient, Karl Pearson correlation coefficient, and chi-square test.Result: A total of 1100 families were enrolled for this study; among them, 330 were clinically and biologically confirmed (radiological studies) for the disease, 204 were males (61.8%), 126 were females (38.18%). We found that 27.87% were genetic and 72.12 were sporadic, out of 72.12 %, 43.277% cases from urban and 56.72% from the rural locality, the mothers' literacy rate was 32.12% and working women numbers were 41.21%. Conclusions: There is a significant association between mothers' age and GDD prevalence, which is also followed by mothers' literacy rate and mothers' occupation, whereas there was no association between fathers' age and GDD.

Keywords: global developmental delay, FMR1 gene, spearman’ rank correlation coefficient, structural equation modeling

Procedia PDF Downloads 107

Authors: J. Marx, D. Smazna, R. Adelung, B. Fiedler

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Aerographite is a 3D interconnected carbon foam. Its tetrapodal morphology is based on the zinc oxide (ZnO) template structure, which is replicated in the chemical vapour deposition (CVD) into a hollow carbon structure. This replication process is analyzed in ex-situ studies via interrupted synthesis and the observation of the reaction progress by using scanning electron (SEM), transmission electron microscopy (TEM) and Raman spectroscopy techniques. Based on the epitaxial growth process, with a layer-by-layer growth behaviour of the wall thickness or number of layers and the catalytical graphitization of the deposited amorphous carbon into graphitic carbon by zinc, a growth model is created. The properties of aerographite, such as the electrical conductivity is dependent on the graphitization and number of layer (wall thickness). Wall thicknesses between 3 nm and 22 nm are achieved by a controlled stepwise reduction of the synthesis time on the basis of the developed growth model, and by a further thermal treatment at 1800 °C the graphitization of the presented carbon foam is modified. The variation of the wall thickness leads to an optimum defect density (ID/IG ratio) and the graphitization to an improvement in the electrical conductivity. Furthermore, a metallic conducting behaviour of untreated and 1800 °C treated aerographite can be observed. Due to these structural and defective modifications, a fundamental structural-property equation for the description of their influences on the electrical conductivity is developed.

Keywords: electrical conductivity, electron microscopy (SEM/TEM), graphitization, wall thickness

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Authors: Mary Chriselda A

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This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe.

Keywords: Chapman Kolmogorov forward differential equations, fourier transformation, hubble's parameter, ornstein-uhlenbeck process , stochastic differential equations

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Authors: K. Yathish, K. G. Binu, B. S. Shenoy, D. S. Rao, R. Pai

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Load carrying capacity of an oil lubricated two-axial groove journal bearing is simulated by taking into account the viscosity variations in lubricant due to the addition of TiO2 nanoparticles as lubricant additive. Shear viscosities of TiO2 nanoparticle dispersions in oil are measured for various nanoparticle additive concentrations. The viscosity model derived from the experimental viscosities is employed in a modified Reynolds equation to obtain the pressure profiles and load carrying capacity of two-axial groove journal bearing. Results reveal an increase in load carrying capacity of bearings operating on nanoparticle dispersions as compared to plain oil

Keywords: journal bearing, TiO2 nanoparticles, viscosity model, Reynold's equation, load carrying capacity

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Authors: Muath Awadalla, Maen Awadallah

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Banking sector covers different activities including lending money to customers. However, it is commonly known that customers pay money they have borrowed including an added amount called interest. Compound interest rate is an approach used in determining the interest to be paid. The instant compounded amount to be paid by a debtor is obtained through a differential equation whose main parameters are the rate and the time. The rate used by banks in a country is often defined by the government of the said country. In Switzerland, for instance, a negative rate was once applied. In this work, a new approach of modeling the compound interest is proposed using Hadamard fractional derivative. As a result, it appears that depending on the fraction value used in derivative the amount to be paid by a debtor might either be higher or lesser than the amount determined using the classical approach.

Keywords: compound interest, fractional differential equation, hadamard fractional derivative, optimization

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Authors: Muhammad Danish Khan, Imran Naeem, Mudassar Imran

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In this article, we study time-space Fractional Advection-Dispersion (FADE) equation and time-space Fractional Whitham-Broer-Kaup (FWBK) equation that have a significant role in hydrology. We introduce suitable transformations to convert fractional order derivatives to integer order derivatives and as a result these equations transform into Partial Differential Equations (PDEs). Then the Lie symmetries and corresponding optimal systems of the resulting PDEs are derived. The symmetry reductions and exact independent solutions based on optimal system are investigated which constitute the exact solutions of original fractional differential equations.

Keywords: modified Riemann-Liouville fractional derivative, lie-symmetries, optimal system, invariant solutions

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Authors: Kunwar Mrityunjai Sharma, Trilok Nath Singh

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The Navier-Stokes equation is used to study nonlinear fluid flow in rough 2D fractures. The major goal is to investigate the influence of inertial flow owing to fracture wall roughness on nonlinear flow behavior. Roughness profiles are developed using Barton's Joint Roughness Coefficient (JRC) and used as fracture walls to assess wall roughness. Four JRC profiles (5, 11, 15, and 19) are employed in the study, where a higher number indicates higher roughness. A parametric study has been performed using varying pressure gradients, and the corresponding Forchheimer number is calculated to observe the nonlinear behavior. The results indicate that the fracture roughness has a significant effect on the onset of nonlinearity. Additionally, the validity of the cubic law is evaluated and observed that it overestimates the flow in rough fractures and should be used with utmost care.

Keywords: fracture flow, nonlinear flow, cubic law, Navier-stokes equation

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Authors: Xie Kefeng, Zhang He

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For the stability and control demand of offshore small floating platform, a 2-HUS/U parallel mechanism was presented as offshore platform. Inverse kinematics was obtained by institutional constraint equation, and the dynamic model of offshore 2-HUS/U parallel platform was derived based on rigid body’s Lagrangian method. The equivalent moment of inertia, damping and driving force/torque variation of offshore 2-HUS/U parallel platform were analyzed. A numerical example shows that, for parallel platform of given motion, system’s equivalent inertia changes 1.25 times maximally. During the movement of platform, they change dramatically with the system configuration and have coupling characteristics. The maximum equivalent drive torque is 800 N. At the same time, the curve of platform’s driving force/torque is smooth and has good sine features. The control system needs to be adjusted according to kinetic equation during stability and control and it provides a basis for the optimization of control system.

Keywords: 2-HUS/U platform, dynamics, Lagrange, parallel platform

Procedia PDF Downloads 320

Authors: Wedad Albalawi

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The mathematical inequalities have been the core of mathematical study and used in almost all branches of mathematics as well in various areas of science and engineering. The inequalities by Hardy, Littlewood and Polya were the first significant composition of several science. This work presents fundamental ideas, results and techniques, and it has had much influence on research in various branches of analysis. Since 1934, various inequalities have been produced and studied in the literature. Furthermore, some inequalities have been formulated by some operators; in 1989, weighted Hardy inequalities have been obtained for integration operators. Then, they obtained weighted estimates for Steklov operators that were used in the solution of the Cauchy problem for the wave equation. They were improved upon in 2011 to include the boundedness of integral operators from the weighted Sobolev space to the weighted Lebesgue space. Some inequalities have been demonstrated and improved using the Hardy–Steklov operator. Recently, a lot of integral inequalities have been improved by differential operators. Hardy inequality has been one of the tools that is used to consider integrity solutions of differential equations. Then, dynamic inequalities of Hardy and Coposon have been extended and improved by various integral operators. These inequalities would be interesting to apply in different fields of mathematics (functional spaces, partial differential equations, mathematical modeling). Some inequalities have been appeared involving Copson and Hardy inequalities on time scales to obtain new special version of them. A time scale is an arbitrary nonempty closed subset of the real numbers. Then, the dynamic inequalities on time scales have received a lot of attention in the literature and has become a major field in pure and applied mathematics. There are many applications of dynamic equations on time scales to quantum mechanics, electrical engineering, neural networks, heat transfer, combinatorics, and population dynamics. This study focuses on Hardy and Coposon inequalities, using Steklov operator on time scale in double integrals to obtain special cases of time-scale inequalities of Hardy and Copson on high dimensions. The advantage of this study is that it uses the one-dimensional classical Hardy inequality to obtain higher dimensional on time scale versions that will be applied in the solution of the Cauchy problem for the wave equation. In addition, the obtained inequalities have various applications involving discontinuous domains such as bug populations, phytoremediation of metals, wound healing, maximization problems. The proof can be done by introducing restriction on the operator in several cases. The concepts in time scale version such as time scales calculus will be used that allows to unify and extend many problems from the theories of differential and of difference equations. In addition, using chain rule, and some properties of multiple integrals on time scales, some theorems of Fubini and the inequality of H¨older.

Keywords: time scales, inequality of hardy, inequality of coposon, steklov operator

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Authors: Denis Ushakov

Abstract:

Fast growing international migration as a factor of labor globalization now is one of the most important trends of world economy and determinant of social-political transformations. Study of fundamental economical reasons for international migration is relevant due to their prognostic, predictable and normative potential, which can be used in conditions of global economic non-stability. This paper analyzes role of natural-resources, financial and labor factors in economic growth of the modern states; studies relationships between stimulating role of natural resources, finance and labor with levels of modern countries’ economy development. Based on achieved results, findings about fundamental reasons of international migration; transformation of labor factor’s role in providing an economical progress of the states; efficiency of positive impact of manufacturing factors (domestic and attracted from international markets) were offered.

Keywords: international migration, migrant, labor productivity, economy efficiency of migration, migration policy

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Authors: Shyam Sunder Gupta

Abstract:

GOD is the infinite source of knowledge and from time to time, as per the need of mankind, keeps revealing a portion of HIS knowledge as” Words” through chosen messengers. In the course of time, ” Words” get converted into scripture. This process of conversion happens after a long gap of time and with the involvement of a large number of persons; and unintentionally scientific and other types of errors get into scriptures; otherwise scriptures are in reality, truly scientific. Description of Chronology of life in the womb (Fetal Development), Five types of rotations of celestial bodies, Speed of the Sun, Rotation of Universe, Multiple verses, Spherical shape of the earth, Measurement of time, Classification of species by nature of birth, Evolution process of non-living matter and living species, etc., most convincing prove that scriptures are truly scientific. In fact, there are many facts for which, till date, science has not found answers, but are available in scriptures; like source of Singularity from which the Big Bang took place and the Universe was created, the Infinite number of Universes, the most fundamental particle, Param-anu( God particle), fundamental of measurement of time and many more.

Keywords: Big Bang, God Particle, Scientific, Scriptures, Singularity, Universe

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Authors: Francys Souza, Alberto Ohashi, Dorival Leao

Abstract:

We present a general solution for finding the ε-optimal controls for non-Markovian stochastic systems as stochastic differential equations driven by Brownian motion, which is a problem recognized as a difficult solution. The contribution appears in the development of mathematical tools to deal with modeling and control of non-Markovian systems, whose applicability in different areas is well known. The methodology used consists to discretize the problem through a random discretization. In this way, we transform an infinite dimensional problem in a finite dimensional, thereafter we use measurable selection arguments, to find a control on an explicit form for the discretized problem. Then, we prove the control found for the discretized problem is a ε-optimal control for the original problem. Our theory provides a concrete description of a rather general class, among the principals, we can highlight financial problems such as portfolio control, hedging, super-hedging, pairs-trading and others. Therefore, our main contribution is the development of a tool to explicitly the ε-optimal control for non-Markovian stochastic systems. The pathwise analysis was made through a random discretization jointly with measurable selection arguments, has provided us with a structure to transform an infinite dimensional problem into a finite dimensional. The theory is applied to stochastic control problems based on path-dependent stochastic differential equations, where both drift and diffusion components are controlled. We are able to explicitly show optimal control with our method.

Keywords: dynamic programming equation, optimal control, stochastic control, stochastic differential equation

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