Search results for: stiff ordinary differential equation

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

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

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

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Authors: Abdulsamad Qadir Hussien

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The development of new technology in recent years has offered ordinary people various online digital platform tools and internet access to provide news stories, information, and subjects of public interest in the Kurdistan Region Government-Iraq (KRI). This shifting aspect has offered more chances for ordinary people to engage with other individuals on many issues in order to discuss and argue matters relating to their everyday lives. The key purpose of this research project will examine the role of citizen journalism in the increase of public awareness in the Kurdish community in the KRi; particularly, citizen journalism provides a new opportunity for ordinary people to raise their voices about problems and public matters in the KRI. The sample of this research project encompasses ordinary people who use social media platforms as sources of information and news concerning the KRI government policy. In the research project, the focus is on the ordinary people who are interacting with the blogs, posts, and footage that are produced by citizen journalism. The questionnaire was sent to more than 1,000 participants in the Kurdish community; this aspect produces statistically acceptable numbers to obtain a significant result for this research project. The sampling process is mainly based on the survey method in this study. The online questionnaire form includes many sections, which are divided into four key sections. The first section contains socio-demographic questions, including gender, age, and level of education. The research project applied the survey method in order to gather data and information surrounding the role of citizen journalism in increasing awareness of individuals in the Kurdish community. For this purpose, the researcher designed a questionnaire as the primary tool for the data collection process from ordinary people who use social media as a source of news and information. During the research project, online questionnaires were mailed in two ways – via Facebook and email – to participants in the Kurdish community, and this questionnaire looked for answers to questions from ordinary people, such as to what extent citizen journalism helps users to obtain information and news about public affairs and government policy. The research project found that citizen journalism has an essential role in increasing awareness of the Kurdish community, especially mainstream journalism has helped ordinary people to raise their voices in the KRI. Furthermore, citizen journalism carries more advantages as digital sources of news, footage, and information related to public affairs. This study provides useful tools to fore the news stories that are unreachable to professional journalists in the KRI.

Keywords: citizen journalism, public awareness, demonstration and democracy, social media news

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Authors: Jatindra Lahkar

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The effect of chemical reaction on laminar mixed convection flow and heat and mass transfer along a vertical unsteady stretching sheet is investigated, in the presence of heat generation/absorption with variable viscosity and viscous dissipation. The governing non-linear partial differential equations are reduced to ordinary differential equations using similarity transformation and solved numerically using the fourth order Runge-Kutta method along with shooting technique. The effects of various flow parameters on the velocity, temperature and concentration distributions are analyzed and presented graphically. Skin-friction coefficient, Nusselt number and Sherwood number are derived at the sheet. It is observed that the influence of chemical reaction, the fluid flow along the sheet accelerate with the increase of chemical reaction parameter, on the other hand, temperature of the fluid increases with increase of chemical reaction parameter but concentration of the fluid reduces with it. The boundary layer decreases on the surface of the sheet for all values of unsteadiness parameter, increasing values of the chemical reaction parameter. The increases in the values of Sc cause the species concentration and its boundary layer thickness to decrease resulting in less induced flow and higher fluid temperatures. This is depicted in the decreases in the velocity and species concentration and increases in the fluid temperature as Sc increases.

Keywords: chemical reaction, heat generation/absorption, magnetic number, unsteadiness, variable viscosity

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Authors: Dorit Lemberger

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Wittgenstein directly used the term "metaphor" only infrequently and with reservations, but his writings include a number of metaphors that have become imprinted in the philosophical memory of Western thought. For example, the ladder in his book Tractatus, or in Philosophical investigations - the ancient city, the beetle in a box, the fly in the fly-bottle, and the duck-rabbit. In light of Wittgenstein's stressing, throughout his investigations, that the only language that exists is ordinary language, and that there is no "second-order" language, the question should be asked: How do these metaphors function, specifically, and in general, how are we to relate to language use that exceeds the normal? Wittgenstein did not disregard such phenomena, but he proposed viewing them in a different way, that would enable understanding them as uses in ordinary language, without necessarily exceeding such language. Two important terms that he coined in this context are "secondary sense" and "experience of meaning". Each denotes language use as reflective of a subjective element characteristic of the speaker, such as intent, experience, or emphasis of a certain aspect. More recent Wittgenstein scholars added the term "quasi-metaphor", that refers to his discussion of the possibility of aesthetic judgment. This paper will examine how, according to Wittgenstein, these terms function without exceeding ordinary language, and will illustrate how they can be applied, in an analysis of the poem "Butterfly" by Nelly Sachs.

Keywords: metaphor, quasi-metaphor, secondary sense, experience of meaning

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Authors: Yanpei Zhen

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The nonlinear Schrödinger (NLS) equation models wave dynamics in many physical problems related to fluids, plasmas, and optics. The standing periodic waves are known to be modulationally unstable, and rogue waves (localized perturbations in space and time) have been observed on their backgrounds in numerical experiments. The exact solutions for rogue waves arising on the periodic standing waves have been obtained analytically. It is natural to ask if the rogue waves persist on the standing periodic waves in the integrable discretizations of the integrable NLS equation. We study the standing periodic waves in the semidiscrete integrable system modeled by the high-order Ablowitz-Ladik (AL) equation. The standing periodic wave of the high-order AL equation is expressed by the Jacobi cnoidal elliptic function. The exact solutions are obtained by using the separation of variables and one-fold Darboux transformation. Since the cnoidal wave is modulationally unstable, the rogue waves are generated on the periodic background.

Keywords: Darboux transformation, periodic wave, Rogue wave, separating the variables

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Authors: Abdullah M. Almeshal, Mohammad R. Alenezi, Muhammad Moaz

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In this paper, we discuss the performance of applying hybrid spiral dynamic bacterial chemotaxis (HSDBC) optimisation algorithm on an intelligent controller for a differential drive robot. A unicycle class of differential drive robot is utilised to serve as a basis application to evaluate the performance of the HSDBC algorithm. A hybrid fuzzy logic controller is developed and implemented for the unicycle robot to follow a predefined trajectory. Trajectories of various frictional profiles and levels were simulated to evaluate the performance of the robot at different operating conditions. Controller gains and scaling factors were optimised using HSDBC and the performance is evaluated in comparison to previously adopted optimisation algorithms. The HSDBC has proven its feasibility in achieving a faster convergence toward the optimal gains and resulted in a superior performance.

Keywords: differential drive robot, hybrid fuzzy controller, optimization, path tracking, unicycle robot

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

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Authors: Dede Basturk, Metin Kaya, Halil Taskin, Nurtekin Erkmen

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In total, 29 students studying in Selçuk University Physical Training and Sports School who are recreationally active participated voluntarilyin this study which was carried out in order to examine effects of Vertimax trainings on agility, quickness and acceleration. 3 groups took their parts in this study as Vertimax training group (N=10), Ordinary training group (N=10) and Control group (N=9). Measurements were carried out in performance laboratory of Selçuk University Physical Training and Sports School. A training program for quickness and agility was followed up for subjects 3 days a week (Monday, Wednesday, Friday) for 8 weeks. Subjects taking their parts in vertimax training group and ordinary training group participated in the training program for quickness and agility. Measurements were applied as pre-test and post-test. Subjects of vertimax training group followed the training program with vertimax device and subjects of ordinary training group followed the training program without vertimax device. As to control group who are recreationally active, they did not participate in any program. 4 gate photocells were used for measuring and measurement of distances was carried out in m. Furthermore, single gate photocell and honi were used for agility test. Measurements started with 15 minutes of warm-up. Acceleration, quickness and agility tests were applied on subjects. 3 measurements were made for each subject at 3 minutes resting intervals. The best rating of three measurements was recorded. 5 m quickness pre-test value of vertimax training groups has been determined as 1,11±0,06 s and post-test value has been determined as 1,06 ± 0,08 s (P<0,05). 5 m quickness pre-test value of ordinary training group has been determined as 1,11±0,06 s and post-test value has been determined as 1,07±0,07 s (P<0,05).5 m quickness pre-test value of control group has been determined as 1,13±0,08 s and post-test value has been determined as 1,10 ± 0,07 s (P>0,05). Upon examination of 10 m acceleration value before and after the training, 10 m acceleration pre-test value of vertimax training group has been determined as 1,82 ± 0,07 s and post-test value has been determined as 1,76±0,83 s (P>0,05). 10 m acceleration pre-test value of ordinary training group has been determined as 1,83±0,05 s and post-test value has been determined as 1,78 ± 0,08 s (P>0,05).10 m acceleration pre-test value of control group has been determined as 1,87±0,11 s and post-test value has been determined as 1,83 ± 0,09 s (P>0,05). Upon examination of 15 m acceleration value before and after the training, 15 m acceleration pre-test value of vertimax training group has been determined as 2,52±0,10 s and post-test value has been determined as 2,46 ± 0,11 s (P>0,05).15 m acceleration pre-test value of ordinary training group has been determined as 2,52±0,05 s and post-test value has been determined as 2,48 ± 0,06 s (P>0,05). 15 m acceleration pre-test value of control group has been determined as 2,55 ± 0,11 s and post-test value has been determined as 2,54 ± 0,08 s (P>0,05).Upon examination of agility performance before and after the training, agility pre-test value of vertimax training group has been determined as 9,50±0,47 s and post-test value has been determined as 9,66 ± 0,47 s (P>0,05). Agility pre-test value of ordinary training group has been determined as 9,99 ± 0,05 s and post-test value has been determined as 9,86 ± 0,40 s (P>0,05). Agility pre-test value of control group has been determined as 9,74 ± 0,45 s and post-test value has been determined as 9,92 ± 0,49 s (P>0,05). Consequently, it has been observed that quickness and acceleration features were developed significantly following 8 weeks of vertimax training program and agility features were not developed significantly. It is suggested that training practices used for the study may be used for situations which may require sudden moves and in order to attain the maximum speed in a short time. Nevertheless, it is also suggested that this training practice does not make contribution in development of moves which may require sudden direction changes. It is suggested that productiveness and innovation may come off in terms of training by using various practices of vertimax trainings.

Keywords: vertimax, training, quickness, agility, acceleration

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Authors: Sarun Phibanchon, Yuttakarn Rattanachai

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The quadratic-cubic nonlinear Schrodinger equation can be explained the weakly ion-acoustic waves in magnetized plasma with a slightly non-Maxwellian electron distribution by using the Madelung's fluid picture. However, the soliton solution to the quadratic-cubic nonlinear Schrodinger equation is determined by using the direct integration. By the characteristics of a soliton, the solution can be claimed that it's a soliton by considering its time evolution and their collisions between two solutions. These results are shown by applying the spectral method.

Keywords: soliton, ion-acoustic waves, plasma, spectral method

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Authors: Qinghua Zhang, Yanhe Zhu, Xiang Zhao, Yeqin Yang, Hongwei Jing, Guoan Zhang, Jie Zhao

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This paper presents a wearable reconfigurable supernumerary robotic limb with differential actuated joints, which is lightweight, compact and comfortable for the wearers. Compared to the existing supernumerary robotic limbs which mostly adopted series structure with large movement space but poor carrying capacity, a prototype with the series-parallel configuration to better adapt to different task requirements has been developed in this design. To achieve a compact structure, two kinds of cable-driven mechanical structures based on guide pulleys and differential actuated joints were designed. Moreover, two different tension devices were also designed to ensure the reliability and accuracy of the cable-driven transmission. The proposed device also employed self-designed bearings which greatly simplified the structure and reduced the cost.

Keywords: cable-driven, differential actuated joints, reconfigurable, supernumerary robotic limb

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Authors: Ih-Ching Hsu

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Inspired by the so called Jacobi Identity (x y) z + (y z) x + (z x) y = 0, the following class of functional equations EQ I: F [F (x, y), z] + F [F (y, z), x] + F [F (z, x), y] = 0 is proposed, researched and generalized. Research methodologies begin with classical methods for functional equations, then evolve into discovering of any implicit algebraic structures. One of this paper’s major findings is that EQ I, under two additional conditions F (x, x) = 0 and F (x, y) + F (y, x) = 0, proves to be a fundamental functional equation for Lie Algebras. Existence of non-trivial solutions for EQ I can be proven by defining F (p, q) = [p q] = pq –qp, where p and q are quaternions, and pq is the quaternion product of p and q. EQ I can be generalized to the following class of functional equations EQ II: F [G (x, y), z] + F [G (y, z), x] + F [G (z, x), y] = 0. Concluding Statement: With a major finding proven, and non-trivial solutions derived, this research paper illustrates and provides a new functional equation scheme for studies in two major areas: (1) What underlying algebraic structures can be defined and/or derived from EQ I or EQ II? (2) What conditions can be imposed so that conditional general solutions to EQ I and EQ II can be found, investigated and applied?

Keywords: fundamental functional equation, generalized functional equations, Lie algebras, quaternions

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Authors: Haniye Dehestani, Yadollah Ordokhani

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In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective.

Keywords: collocation method, fractional partial differential equations, legendre-laguerre functions, pseudo-operational matrix of integration

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Authors: Olukunle C. Olawole, Dilip Kumar De

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We have modified Richardson-Dushman equation considering thermal expansion of lattice and change of chemical potential with temperature in material. The corresponding modified Richardson-Dushman (MRDE) equation fits quite well the experimental data of thermoelectronic current density (J) vs T from carbon nanotubes. It provides a unique technique for accurate determination of W0 Fermi energy, EF0 at 0 K and linear thermal expansion coefficient of carbon nano-tube in good agreement with experiment. From the value of EF0 we obtain the charge carrier density in excellent agreement with experiment. We describe application of the equations for the evaluation of performance of concentrated solar thermionic energy converter (STEC) with emitter made of carbon nanotube for future applications.

Keywords: carbon nanotube, modified Richardson-Dushman equation, fermi energy at 0 K, charge carrier density

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Authors: Daniil Karzanov

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This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modeled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of stochastic differential equations to the pre-and after-report period using the Maximum Likelihood Estimation and Grid Search of parameters method. By examining the change in the model parameters after reports’ publication, the study reveals that the reports have enough evidence to be a structural breakpoint, meaning that all the forecast models exploited are not applicable for forecasting and should be refitted shortly.

Keywords: stock market, earnings reports, financial time series, structural breaks, stochastic differential equations

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Authors: Asabe Ahmad Tijani, Y. A. Yahaya

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The paper considers the derivation of implicit Adams-Moulton type method, with k=4 and 5. We adopted the method of interpolation and collocation of power series approximation to generate the continuous formula which was evaluated at off-grid and some grid points within the step length to generate the proposed block schemes, the schemes were investigated and found to be consistent and zero stable. Finally, the methods were tested with numerical experiments to ascertain their level of accuracy.

Keywords: Adam-Moulton Type (AMT), off-grid, block method, consistent and zero stable

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Authors: Mustapha Rilwan Adewale, Salau Ayobami Muhammed

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This study focuses on the heat transfer analysis of magneto-hydrodynamics (MHD) squeezing flow between parallel disks, considering a viscous incompressible fluid. The upper disk exhibits both upward and downward motion, while the lower disk remains stationary but permeable. By employing similarity transformations, a system of nonlinear ordinary differential equations is derived to describe the flow behavior. To solve this system, a numerical approach, namely the Chebyshev collocation method, is utilized. The study investigates the influence of flow parameters and compares the obtained results with existing literature. The significance of this research lies in understanding the heat transfer characteristics of MHD squeezing flow, which has practical implications in various engineering and industrial applications. By employing the similarity transformations, the complex governing equations are simplified into a system of nonlinear ordinary differential equations, facilitating the analysis of the flow behavior. To obtain numerical solutions for the system, the Chebyshev collocation method is implemented. This approach provides accurate approximations for the nonlinear equations, enabling efficient computations of the heat transfer properties. The obtained results are compared with existing literature, establishing the validity and consistency of the numerical approach. The study's major findings shed light on the influence of flow parameters on the heat transfer characteristics of the squeezing flow. The analysis reveals the impact of parameters such as magnetic field strength, disk motion amplitude, fluid viscosity on the heat transfer rate between the disks, the squeeze number(S), suction/injection parameter(A), Hartman number(M), Prandtl number(Pr), modified Eckert number(Ec), and the dimensionless length(δ). These findings contribute to a comprehensive understanding of the system's behavior and provide insights for optimizing heat transfer processes in similar configurations. In conclusion, this study presents a thorough heat transfer analysis of magneto-hydrodynamics squeezing flow between parallel disks. The numerical solutions obtained through the Chebyshev collocation method demonstrate the feasibility and accuracy of the approach. The investigation of flow parameters highlights their influence on heat transfer, contributing to the existing knowledge in this field. The agreement of the results with previous literature further strengthens the reliability of the findings. These outcomes have practical implications for engineering applications and pave the way for further research in related areas.

Keywords: squeezing flow, magneto-hydro-dynamics (MHD), chebyshev collocation method(CCA), parallel manifolds, finite difference method (FDM)

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Authors: Lukas Vierus, Thomas Schuster

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A general framework is examined for dynamic tensor field tomography within an inhomogeneous medium characterized by refraction and absorption, treated as an inverse source problem concerning the associated transport equation. Guided by Fermat’s principle, the Riemannian metric within the specified domain is determined by the medium's refractive index. While considerable literature exists on the inverse problem of reconstructing a tensor field from its longitudinal ray transform within a static Euclidean environment, limited inversion formulas and algorithms are available for general Riemannian metrics and time-varying tensor fields. It is established that tensor field tomography, akin to an inverse source problem for a transport equation, persists in dynamic scenarios. Framing dynamic tensor tomography as an inverse source problem embodies a comprehensive perspective within this domain. Ensuring well-defined forward mappings necessitates establishing existence and uniqueness for the underlying transport equations. However, the bilinear forms of the associated weak formulations fail to meet the coercivity condition. Consequently, recourse to viscosity solutions is taken, demonstrating their unique existence within suitable Sobolev spaces (in the static case) and Sobolev-Bochner spaces (in the dynamic case), under a specific assumption restricting variations in the refractive index. Notably, the adjoint problem can also be reformulated as a transport equation, with analogous results regarding uniqueness. Analytical solutions are expressed as integrals over geodesics, facilitating more efficient evaluation of forward and adjoint operators compared to solving partial differential equations. Certainly, here's the revised sentence in English: Numerical experiments are conducted using a Nesterov-accelerated Landweber method, encompassing various fields, absorption coefficients, and refractive indices, thereby illustrating the enhanced reconstruction achieved through this holistic modeling approach.

Keywords: attenuated refractive dynamic ray transform of tensor fields, geodesics, transport equation, viscosity solutions

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Authors: Sabrina Ladjama, Aicha Rizi, Azzedine Abbaci

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In this work, we use the crossover model to formulate a comprehensive fundamental equation of state for the thermodynamic properties for several n-alkanes in the critical region that extends to the classical region. This equation of state is constructed on the basis of comparison of selected measurements of pressure-density-temperature data, isochoric and isobaric heat capacity. The model can be applied in a wide range of temperatures and densities around the critical point for n-heptane. It is found that the developed model represents most of the reliable experimental data accurately.

Keywords: crossover model, critical region, fundamental equation, n-heptane

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Authors: Smriti Pahwa, Karishma Vats, Aditi Macwan, Jija Dutt, Sumukhi Vaid

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Age approporiate complementary feeding has been stressed upon for sound young child nutrition and appropriate growth. National Infant and Young Child Feeding guidelines, policies and programs indicate cognizance of the issue taken by the country’s government, policy makers and technical experts. However, it is important that ordinary people, the caregivers of young children too understand the importance of appropriate feeding. For this, an interface might be required where ordinary people could participate in assessing the gaps in IYCF as a first step to take subsequent action. In this context an attempt was made to extrapolate a citizen led learning level survey that has been involving around 25000 ordinary citizens to reach out to 600,000 children annually for over a decade in India. Based on this philosophy of involving ordinary people in simple assessments to produce understandable actionable evidence, a rapid diet assessment tool was developed and collected from caregivers of 90 < 3year children from two urban clusters in Ahmedabad and Baroda, Gujarat. Target sample for pilot was selected after cluster census. Around half the mothers reported that they had not yet introduced water or other fluids to their < 6 month babies. However, about a third were already feeding them food other than mother’s milk. Although complementary feeding was initiated in almost all (95%) children more than 6 months old, frequency was suboptimal in 60%; in 80% cases no measure was taken to either improve energy or nutrient density; only 33% were fed protective foods; Green Leafy Vegetables consumption was negligible (1.4%). Anganwadi food was not consumed. By engaging ordinary people to generate evidence and understand the gaps, such assessments have the potential to be used to generate useful evidence for action at scale as well as locally.

Keywords: citizen led, grass root engagement, IYCF (Infant and Young Child Feeding), rapid diet assessment, under nutrition

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Authors: Sam Teek Ling, Norhashidah Hj. Mohd. Ali

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We investigate the formulation and implementation of new explicit group iterative methods in solving the two-dimensional Poisson equation with Dirichlet boundary conditions. The methods are derived from a fourth order compact nine point finite difference discretization. The methods are compared with the existing second order standard five point formula to show the dramatic improvement in computed accuracy. Numerical experiments are presented to illustrate the effectiveness of the proposed methods.

Keywords: explicit group iterative method, finite difference, fourth order compact, Poisson equation

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

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

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

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Authors: Clarinda V. Nhangumbe, Ercília Sousa

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Weather Derivatives are financial instruments used to cover non-catastrophic weather events and can be expressed in the form of standard or plain vanilla products, structured or exotics products. The underlying asset, in this case, is the weather index, such as temperature, rainfall, humidity, wind, and snowfall. The complexity of the Weather Derivatives structure shows the weakness of the Black Scholes framework. Therefore, under the risk-neutral probability measure, the option price of a weather contract can be given as a unique solution of a two-dimensional partial differential equation (parabolic in one direction and hyperbolic in other directions), with an initial condition and subjected to adequate boundary conditions. To calculate the price of the option, one can use numerical methods such as the Monte Carlo simulations and implicit finite difference schemes conjugated with Semi-Lagrangian methods. This paper is proposed two explicit methods, namely, first-order upwind in the hyperbolic direction combined with Lax-Wendroff in the parabolic direction and first-order upwind in the hyperbolic direction combined with second-order upwind in the parabolic direction. One of the advantages of these methods is the fact that they take into consideration the boundary conditions obtained from the financial interpretation and deal efficiently with the different choices of the convection coefficients.

Keywords: incomplete markets, numerical methods, partial differential equations, stochastic process, weather derivatives

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Authors: Nordila Ahmad, Thamer Mohammad, Bruce W. Melville, Zuliziana Suif

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Current methods for predicting local scour at wide bridge piers, were developed on the basis of laboratory studies and very limited scour prediction were tested with field data. Laboratory wide pier scour equation from previous findings with field data were presented. A wide range of field data were used and it consists of both live-bed and clear-water scour. A method for assessing the quality of the data was developed and applied to the data set. Three other wide pier-scour equations from the literature were used to compare the performance of each predictive method. The best-performing scour equation were analyzed using statistical analysis. Comparisons of computed and observed scour depths indicate that the equation from the previous publication produced the smallest discrepancy ratio and RMSE value when compared with the large amount of laboratory and field data.

Keywords: field data, local scour, scour equation, wide piers

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Authors: Jurriaan Gillissen

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This work is concerned with stabilizing the numerical integration of the Navier-Stokes equation (NSE), backwards in time. Applications involve the detection of sources of, e.g., sound, heat, and pollutants. Stable reverse numerical integration of parabolic differential equations is also relevant for image de-blurring. While the literature addresses the reverse integration problem of the advection-diffusion equation, the problem of numerical reverse integration of the NSE has, to our knowledge, not yet been addressed. Owing to the presence of viscosity, the NSE is irreversible, i.e., when going backwards in time, the fluid behaves, as if it had a negative viscosity. As an effect, perturbations from the perfect solution, due to round off errors or discretization errors, grow exponentially in time, and reverse integration of the NSE is inherently unstable, regardless of using an implicit time integration scheme. Consequently, some sort of filtering is required, in order to achieve a stable, numerical, reversed integration. The challenge is to find a filter with a minimal adverse affect on the accuracy of the reversed integration. In the present work, we explore an adjoint gradient method (AGM) to achieve this goal, and we apply this technique to two-dimensional (2D), decaying turbulence. The AGM solves for the initial velocity field u0 at t = 0, that, when integrated forward in time, produces a final velocity field u1 at t = 1, that is as close as is feasibly possible to some specified target field v1. The initial field u0 defines a minimum of a cost-functional J, that measures the distance between u1 and v1. In the minimization procedure, the u0 is updated iteratively along the gradient of J w.r.t. u0, where the gradient is obtained by transporting J backwards in time from t = 1 to t = 0, using the adjoint NSE. The AGM thus effectively replaces the backward integration by multiple forward and backward adjoint integrations. Since the viscosity is negative in the adjoint NSE, each step of the AGM is numerically stable. Nevertheless, when applied to turbulence, the AGM develops instabilities, which limit the backward integration to small times. This is due to the exponential divergence of phase space trajectories in turbulent flow, which produces a multitude of local minima in J, when the integration time is large. As an effect, the AGM may select unphysical, noisy initial conditions. In order to improve this situation, we propose two remedies. First, we replace the integration by a sequence of smaller integrations, i.e., we divide the integration time into segments, where in each segment the target field v1 is taken as the initial field u0 from the previous segment. Second, we add an additional term (regularizer) to J, which is proportional to a high-order Laplacian of u0, and which dampens the gradients of u0. We show that suitable values for the segment size and for the regularizer, allow a stable reverse integration of 2D decaying turbulence, with accurate results for more then O(10) turbulent, integral time scales.

Keywords: time reversed integration, parabolic differential equations, adjoint gradient method, two dimensional turbulence

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Authors: Bing Chen, Xiang Ni, Eric Li

Abstract:

With the population ageing, the number of patients suffering from chronic diseases is increasing, among which stroke is a high incidence for the elderly. In addition, there is a gradual increase in the number of patients with orthopedic or neurological conditions such as spinal cord injuries, nerve injuries, and other knee injuries. These diseases are chronic, with high recurrence and complications, and normal walking is difficult for such patients. Nowadays, robotic knee exoskeletons have been developed for individuals with knee impairments. However, the currently available robotic knee exoskeletons are generally developed with heavyweight, which makes the patients uncomfortable to wear, prone to wearing fatigue, shortening the wearing time, and reducing the efficiency of exoskeletons. Some lightweight materials, such as carbon fiber and titanium alloy, have been used for the development of robotic knee exoskeletons. However, this increases the cost of the exoskeletons. This paper illustrates the design of a new ultra-light and ultra-stiff truss type of lattice structure. The lattice structures are arranged in a fan shape, which can fit well with circular arc surfaces such as circular holes, and it can be utilized in the design of rods, brackets, and other parts of a robotic knee exoskeleton to reduce the weight. The metamaterial is formed by continuous arrangement and combination of small truss structure unit cells, which changes the diameter of the pillar section, geometrical size, and relative density of each unit cell. It can be made quickly through additive manufacturing techniques such as metal 3D printing. The unit cell of the truss structure is small, and the machined parts of the robotic knee exoskeleton, such as connectors, rods, and bearing brackets, can be filled and replaced by gradient arrangement and non-uniform distribution. Under the condition of satisfying the mechanical properties of the robotic knee exoskeleton, the weight of the exoskeleton is reduced, and hence, the patient’s wearing fatigue is relaxed, and the wearing time of the exoskeleton is increased. Thus, the efficiency and wearing comfort, and safety of the exoskeleton can be improved. In this paper, a brief description of the hardware design of the prototype of the robotic knee exoskeleton is first presented. Next, the design of the ultra-light and ultra-stiff truss type of lattice structures is proposed, and the mechanical analysis of the single-cell unit is performed by establishing the theoretical model. Additionally, simulations are performed to evaluate the maximum stress-bearing capacity and compressive performance of the uniform arrangement and gradient arrangement of the cells. Finally, the static analysis is performed for the cell-filled rod and the unmodified rod, respectively, and the simulation results demonstrate the effectiveness and feasibility of the designed ultra-light and ultra-stiff truss type of lattice structures. In future studies, experiments will be conducted to further evaluate the performance of the designed lattice structures.

Keywords: additive manufacturing, lattice structures, metamaterial, robotic knee exoskeleton

Procedia PDF Downloads 107

Authors: Khaled Moaddy

Abstract:

In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: standard finite difference schemes, non-standard schemes, Laplace equation, Dirichlet boundary conditions

Procedia PDF Downloads 132

Authors: Karim Akkouche, Amine Nekmouche, Leyla Bouzid

Abstract:

This study focuses on the development of a multifunctional Expert System (ES) called post-seismic damage inspection tool (PSDIT), a powerful tool which allows the evaluation, the processing, and the archiving of the collected data stock after earthquakes. PSDIT can be operated by two user types; an ordinary user (ingineer, expert, or architect) for the damage visual inspection and an administrative user for updating the knowledge and / or for adding or removing the ordinary user. The knowledge acquisition is driven by a hierarchical knowledge model, the Information from investigation reports and those acquired through feedback from expert / engineer questionnaires are part.

Keywords: .disaster, damaged structures, damage assessment, expert system

Procedia PDF Downloads 82

Authors: Roman Kalvin, Anam Nadeem, Shahab Khushnood

Abstract:

Differential is an integral part of four wheeled vehicle, and its main function is to transmit power from drive shaft to wheels. Differential assembly allows both rear wheels to turn at different speed along curved paths. It consists of four gears which are assembled together namely pinion, ring, spider and bevel gears. This research focused on the spider gear and its static structural analysis using ANSYS. The main aim was to evaluate the distribution of stresses on the teeth of the spider gear. This study also analyzed total deformation that may occur during its working along with bevel gear that is meshed with spider gear. Structural steel was chosen for spider gear in this research. Modeling and assembling were done on SolidWorks for both spider and bevel gear. They were assembled exactly same as in a differential assembly. This assembly was then imported to ANSYS. After observing results that maximum amount of stress and deformation was produced in the spider gear, it was concluded that structural steel material for spider gear possesses greater amount of strength to bear maximum stress.

Keywords: ANSYS, differential, spider gear, structural steel

Procedia PDF Downloads 186

Authors: Fernando Maass, Pablo Martin, Jorge Olivares

Abstract:

Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

Procedia PDF Downloads 197

Authors: Kirill D. Kapustin, Mikhail B. Krasilnikov, Anatoly A. Kudryavtsev

Abstract:

Physical formation mechanisms of differential electron fluxes is high pressure positive column gas discharge are discussed. It is shown that the spatial differential fluxes of the electrons are directed both inward and outward depending on the energy relaxation law. In some cases the direction of energy differential flux at intermediate energies (5-10eV) in whole volume, except region near the wall, appeared to be down directed, so electron in this region dissipate more energy than gain from axial electric field. Paradoxical behaviour of electron flux in spatial-energy space is presented.

Keywords: plasma kinetics, electron distribution function, excitation and radiation rates, local and nonlocal EDF

Procedia PDF Downloads 400