Search results for: symmetric solutions.

Authors: Viera Zatkalíková, Lenka Markovičová, Aneta Tor-Swiatek

Abstract:

The effect of molybdate addition to chloride environment on resistance of AISI 316Ti stainless steel to pitting corrosion was studied. Potentiodynamic polarisation tests were performed in 1 M and 0.1 M chloride acidified solutions with various additions of sodium molybdate at room temperature. The presented results compare the effect of molybdate anions on quality of passive film (expressed by the pitting potential) in both chloride solutions. The pitting potential increases with the increase inhibitor concentration. The inhibitive effect of molybdate ions is stronger in chloride solution of lower aggressiveness (0.1M).

Keywords: AISI 316Ti steel, molybdate inhibitor, pitting corrosion, pitting potential, potentiodynamic polarization.

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Authors: Alireza Rezaei, Fatemeh Baharifard, Kourosh Parand

Abstract:

In this paper we improve the quasilinearization method by barycentric Lagrange interpolation because of its numerical stability and computation speed to achieve a stable semi analytical solution. Then we applied the improved method for solving the Fin problem which is a nonlinear equation that occurs in the heat transferring. In the quasilinearization approach the nonlinear differential equation is treated by approximating the nonlinear terms by a sequence of linear expressions. The modified QLM is iterative but not perturbative and gives stable semi analytical solutions to nonlinear problems without depending on the existence of a smallness parameter. Comparison with some numerical solutions shows that the present solution is applicable.

Keywords: Quasilinearization method, Barycentric lagrange interpolation, nonlinear ODE, fin problem, heat transfer.

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Authors: L. Mahdavian, M. Raouf

Abstract:

Three dimensional nanostructure materials have attracted the attention of many researches because the possibility to apply them for near future devices in sensors, catalysis and energy related. Tin dioxide is the most used material for gas sensing because its three-dimensional nanostructures and properties are related to the large surface exposed to gas adsorption. We propose the use of branch SnO2 nanowhiskers in interaction with ethanol. All Sn atoms are symmetric. The total energy, potential energy and Kinetic energy calculated for interaction between SnO2 and ethanol in different distances and temperatures. The calculations achieved by methods of Langevin Dynamic and Mont Carlo simulation. The total energy increased with addition ethanol molecules and temperature so interactions between them are endothermic.

Keywords: Tin dioxide, nanowhisker, Ethanol, Langevin Dynamic and Mont Carlo Simulation.

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Authors: Meng-Hui Chen, Chen-Yu Kao, Chia-Yu Hsu, Pei-Chann Chang

Abstract:

The main idea in this paper is using sequential pattern mining to find the information which is helpful for finding high performance solutions. By combining this information, it is defined as blocks. Using the blocks to generate artificial chromosomes (ACs) could improve the structure of solutions. Estimation of Distribution Algorithms (EDAs) is adapted to solve the combinatorial problems. Nevertheless many of these approaches are advantageous for this application, but only some of them are used to enhance the efficiency of application. Generating ACs uses patterns and EDAs could increase the diversity. According to the experimental result, the algorithm which we proposed has a better performance to solve the permutation flow-shop problems.

Keywords: Combinatorial problems, Sequential Pattern Mining, Estimation of Distribution Algorithms, Artificial Chromosomes.

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Authors: Jianqin Qu

Abstract:

This paper proposes a rigid point set matching algorithm in arbitrary dimensions based on the idea of symmetric covariant function. A group of functions of the points in the set are formulated using rigid invariants. Each of these functions computes a pair of correspondence from the given point set. Then the computed correspondences are used to recover the unknown rigid transform parameters. Each computed point can be geometrically interpreted as the weighted mean center of the point set. The algorithm is compact, fast, and dimension free without any optimization process. It either computes the desired transform for noiseless data in linear time, or fails quickly in exceptional cases. Experimental results for synthetic data and 2D/3D real data are provided, which demonstrate potential applications of the algorithm to a wide range of problems.

Keywords: Covariant point, point matching, dimension free, rigid registration.

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Authors: Bahi-Eddine Lahouel, Mohamed Guenfoud

Abstract:

In this study, a vibration analysis was carried out of symmetric angle-ply laminated composite plates with and without square hole when subjected to compressive loads, numerically. A buckling analysis is also performed to determine the buckling load of laminated plates. For each fibre orientation, the compression load is taken equal to 50% of the corresponding buckling load. In the analysis, finite element method (FEM) was applied to perform parametric studies, the effects of degree of orthotropy and stacking sequence upon the fundamental frequencies and buckling loads are discussed. The results show that the presence of a constant compressive load tends to reduce uniformly the natural frequencies for materials which have a low degree of orthotropy. However, this reduction becomes non-uniform for materials with a higher degree of orthotropy.

Keywords: Vibration, Buckling, Cutout, Laminated composite, FEM

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Authors: Hao Wu, Jonathan L. Shapiro

Abstract:

The Bayesian Optimization Algorithm (BOA) is an algorithm based on the estimation of distributions. It uses techniques from modeling data by Bayesian networks to estimating the joint distribution of promising solutions. To obtain the structure of Bayesian network, different search algorithms can be used. The key point that BOA addresses is whether the constructed Bayesian network could generate new and useful solutions (strings), which could lead the algorithm in the right direction to solve the problem. Undoubtedly, this ability is a crucial factor of the efficiency of BOA. Varied search algorithms can be used in BOA, but their performances are different. For choosing better ones, certain suitable method to present their ability difference is needed. In this paper, a greedy search algorithm and a stochastic search algorithm are used in BOA to solve certain optimization problem. A method using Kullback-Leibler (KL) Divergence to reflect their difference is described.

Keywords: Bayesian optimization algorithm, greedy search, KL divergence, stochastic search.

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Authors: Yongseok Kwon, Woowon Jeong, Eunjin Cho, Sangkug Chung, Kyehan Rhee

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Steady streaming flow fields induced by a 500 mm bubble oscillating at 12 kHz were measured using microscopic particle image velocimetry (PIV). The accuracy of velocity measurement using a micro PIV system was checked by comparing the measured velocity fields with the theoretical velocity profiles in fully developed laminar flow. The steady streaming flow velocities were measured in the sagittal plane of the bubble attached on the wall. Measured velocity fields showed upward jet flow with two symmetric counter-rotating vortices, and the maximum streaming velocity was about 12 mm/s, which was within the velocity ranges measured by other researchers. The measured streamlines were compared with the analytical solution, and they also showed a reasonable agreement.

Keywords: Oscillating bubble, Particle-Image-Velocimetry microstreaming.

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Authors: G. Revathi, P. Saikrishnan

Abstract:

In the present analysis an unsteady laminar forced convection water boundary layer flow is considered. The fluid properties such as viscosity and Prandtl number are taken as variables such that those are inversely proportional to temperature. By using quasi-linearization technique the nonlinear coupled partial differential equations are linearized and the numerical solutions are obtained by using implicit finite difference scheme with the appropriate selection of step sizes. Non-similar solutions have been obtained from the starting point of the stream-wise coordinate to the point where skin friction value vanishes. The effect non-uniform mass transfer along the surface of the cylinder through slot is studied on the skin friction and heat transfer coefficients.

Keywords: Boundary layer, heat transfer, non-similar solution, non-uniform mass, unsteady flow.

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Authors: Aqeel-ur-Rehman, Zubair A. Shaikh

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This paper is to present context-aware sensor grid framework for agriculture and its design challenges. Use of sensor networks in the domain of agriculture is not new. However, due to the unavailability of any common framework, solutions that are developed in this domain are location, environment and problem dependent. Keeping the need of common framework for agriculture, Context-Aware Sensor Grid Framework is proposed. It will be helpful in developing solutions for majority of the problems related to irrigation, pesticides spray, use of fertilizers, regular monitoring of plot and yield etc. due to the capability of adjusting according to location and environment. The proposed framework is composed of three layer architecture including context-aware application layer, grid middleware layer and sensor network layer.

Keywords: Agriculture, Context-Awareness, Grid Computing, and Sensor Grid.

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Authors: Dimitar Georgiev, Bogdan Bogdanov, Irena Markovska, Yancho Hristov, Dencho Stanev

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The present paper reports the removal of Cd(II) and Zn(II) ions using synthetic Zeolit NaA. The adsorption capacity of the sorbent (Zeolite NaA) strongly depends on simultaneous or not simultaneous (concurrent) presence of Cd(II) and Zn(II) in the sorbate. When Cd(II) and Zn(II) are present simultaneously (concurrently) in the sorbate, Zn(II) ions were sorbed at higher rate. Equilibrium data fitted Langmuir, Freundlich and Tempkin isotherms well. The applicability of the isotherm equation to describe the adsorption process was judged by the correlation coefficients R2. The Langmuir model yielded the best fit with R2 values equal to or higher than 0.970, as compared to the Freundlich and Tempkin models. The fact that 1/n values range from 0.322 to 0.755 indicates that the adsorption of Cd(II) and Zn(II) ions from aqueous solutions also favored by the Freundlich model.

Keywords: Adsorption, adsorption capacity, kinetic sorption, Zeolite NaA

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Authors: Fuziyah Ishak, Siti Norazura Ahmad

Abstract:

Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.

Keywords: Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.

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Authors: Salem Ali Jebreil

Abstract:

In this work, a polyaniline/Iron oxide (PANI/Fe2O3) composite was chemically prepared by oxidative polymerization of aniline in acid medium, in presence of ammonium persulphate as an oxidant and amount of Fe2O3. The composite was characterized by a scanning electron microscopy (SEM). The prepared composite has been used as adsorbent to remove Tartrazine dye form aqueous solutions. The effects of initial dye concentration and temperature on the adsorption capacity of PANI/Fe2O3 for Tartrazine dye have been studied in this paper. The Langmuir and Freundlich adsorption models have been used for the mathematical description of adsorption equilibrium data. The best fit is obtained using the Freundlich isotherm with an R2 value of 0.998. The change of Gibbs energy, enthalpy, and entropy of adsorption has been also evaluated for the adsorption of Tartrazine onto PANI/ Fe2O3. It has been proved according the results that the adsorption process is endothermic in nature.

Keywords: Adsorption, Composite, dye, Polyaniline, Tartrazine.

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Authors: Ahmed Chalak Shakir, GuXuemai, Jia Min

Abstract:

Recently, wireless sensor networks have been paid more interest, are widely used in a lot of commercial and military applications, and may be deployed in critical scenarios (e.g. when a malfunctioning network results in danger to human life or great financial loss). Such networks must be protected against human intrusion by using the secret keys to encrypt the exchange messages between communicating nodes. Both the symmetric and asymmetric methods have their own drawbacks for use in key management. Thus, we avoid the weakness of these two cryptosystems and make use of their advantages to establish a secure environment by developing the new method for encryption depending on the idea of code conversion. The code conversion-s equations are used as the key for designing the proposed system based on the basics of logic gate-s principals. Using our security architecture, we show how to reduce significant attacks on wireless sensor networks.

Keywords: logic gates, code conversions, Gray-code, and clustering.

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Authors: Sara Ramezanzadeh, Nashid Nabian

Abstract:

Historically, pandemics in different periods have caused compulsory changes in human life. In the case of COVID-19, according to the limitations and established care instructions, spatial alignment with the conditions is important. Following the outbreak of COVID-19, the question raised in this study is how to do spatial design in five scales, namely object, space, architecture, city, and infrastructure, in response to the consequences created in the realms under study. From the beginning of the pandemic until now, some changes in the spatial realm have been created spontaneously or by space users. These transformations have been mostly applied in modifiable parts such as furniture arrangement, especially in work-related spaces. To implement other comprehensive requirements, flexibility and adaptation of space design to the conditions resulting from the pandemics are needed during and after the outbreak. Studying the effects of pandemics from the past to the present, this research covers eight major realms, including three categories of ramifications, solutions, and paradigm shifts, and analytical conclusions about the solutions that have been created in response to them. Finally, by the consideration of epidemiology as a modern discipline influencing the design, spatial solutions in the five scales mentioned (in response to the effects of the eight realms for spatial adaptation in the face of pandemics and their following conditions) are presented as a series of guidelines. Due to the unpredictability of possible pandemics in the future, the possibility of changing and updating the provided guidelines is considered.

Keywords: Pandemics, COVID-19, spatial design, ramifications, paradigm shifts, guidelines.

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Authors: A. K. Al-Othman

Abstract:

This study presents a new approach based on Tanaka's fuzzy linear regression (FLP) algorithm to solve well-known power system economic load dispatch problem (ELD). Tanaka's fuzzy linear regression (FLP) formulation will be employed to compute the optimal solution of optimization problem after linearization. The unknowns are expressed as fuzzy numbers with a triangular membership function that has middle and spread value reflected on the unknowns. The proposed fuzzy model is formulated as a linear optimization problem, where the objective is to minimize the sum of the spread of the unknowns, subject to double inequality constraints. Linear programming technique is employed to obtain the middle and the symmetric spread for every unknown (power generation level). Simulation results of the proposed approach will be compared with those reported in literature.

Keywords: Economic Dispatch, Fuzzy Linear Regression (FLP)and Optimization.

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Authors: Petra Balla, Gabor Manhertz, Akos Antal

Abstract:

Nowadays spinal deformities are very frequent problems among teenagers. Scheuermann disease is a one dimensional deformity of the spine, but it has prevalence over 11% of the children. A traditional technology, the moiré method was used by us for screening and diagnosing this type of spinal deformity. A LabVIEW program has been developed to evaluate the moiré pictures of patients with Scheuermann disease. Two different solutions were tested in this computer program, the extreme and the inflexion point calculation methods. Effects using these methods were compared and according to the results both solutions seemed to be appropriate. Statistical results showed better efficiency in case of the extreme search method where the average difference was only 6,09⁰.

Keywords: Spinal deformity, picture evaluation, moiré method, Scheuermann disease, curve detection, moiré topography.

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Authors: Yongkun Li, Meng Hu

Abstract:

A stage-structured predator-prey system with two time delays is considered. By analyzing the corresponding characteristic equation, the local stability of a positive equilibrium is investigated and the existence of Hopf bifurcations is established. Formulae are derived to determine the direction of bifurcations and the stability of bifurcating periodic solutions by using the normal form theory and center manifold theorem. Numerical simulations are carried out to illustrate the theoretical results. Based on the global Hopf bifurcation theorem for general functional differential equations, the global existence of periodic solutions is established.

Keywords: Predator-prey system, stage structure, time delay, HOPF bifurcation, periodic solution, stability.

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Authors: Alan C. Lin, Dean K. Sheu

Abstract:

This paper aims to study the methodology of building the knowledge of planning adequate punches in order to complete the task of strip layout for shearing processes, using progressive dies. The proposed methodology uses die design rules and characteristics of different types of punches to classify them into five groups: prior use (the punches must be used first), posterior use (must be used last), compatible use (may be used together), sequential use (certain punches must precede some others) and simultaneous use (must be used together). With these five groups of punches, the searching space of feasible designs will be greatly reduced, and superimposition becomes a more effective method of punch layout. The superimposition scheme will generate many feasible solutions, an evaluation function based on number of stages, moment balancing and strip stability is developed for helping designers to find better solutions.

Keywords: Manufacturing systems, advances in metal forming, computer-aided design, progressive die.

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Authors: V.V. Lyahov, V.M. Neshchadim

Abstract:

The structural stability of the model of a nonelectroneutral current sheath is investigated. The stationary model of a current sheath represents the system of four connected nonlinear differential first-order equations and thus they should manifest structural instability property, i.e. sensitivity to the infinitesimal changes of parameters and starting conditions. Domains of existence of the solutions of current sheath type are found. Those solutions of the current sheath type are realized only in some regions of sevendimensional space of parameters of the problem. The phase volume of those regions is small in comparison with the whole phase volume of the definition range of those parameters. It is shown that the offered model of a nonelectroneutral current sheath is applicable for theoretical interpretation of the bifurcational current sheaths observed in the magnetosphere.

Keywords: Distribution function, electromagnetic field, magnetoactive plasma, nonelectroneutral current sheath, structural instability, bifurcational current sheath.

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Authors: Man Young Kim, Gyo Woo Lee

Abstract:

In this numerical study, we want to present the design of highly efficient extruded-type heat sink. The symmetrically arranged extruded-type heat sinks are used instead of a single extruded or swaged-type heat sink. In this parametric study, the maximum temperatures, the base temperatures between heaters, and the heat release rates were investigated with respect to the arrangements of heat sources, air flow rates, and amounts of heat input. Based on the results we believe that the use of both side of heat sink is to be much better for release the heat than the use of single side. Also from the results, it is believed that the symmetric arrangement of heat sources is recommended to achieve a higher heat transfer from the heat sink.

Keywords: Heat Sink, Forced Convection, Heat Transfer, Performance Evaluation, Symmetrically Arranged.

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Authors: Dylan M. Copeland

Abstract:

We present new finite element methods for Helmholtz and Maxwell equations on general three-dimensional polyhedral meshes, based on domain decomposition with boundary elements on the surfaces of the polyhedral volume elements. The methods use the lowest-order polynomial spaces and produce sparse, symmetric linear systems despite the use of boundary elements. Moreover, piecewise constant coefficients are admissible. The resulting approximation on the element surfaces can be extended throughout the domain via representation formulas. Numerical experiments confirm that the convergence behavior on tetrahedral meshes is comparable to that of standard finite element methods, and equally good performance is attained on more general meshes.

Keywords: Boundary elements, finite elements, Helmholtz equation, Maxwell equations.

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Authors: Nina Robson, Kenneth John Faller II, Vishalkumar Ahir, Arthur Ricardo Deps Miguel Ferreira, John Buchanan, Amarnath Banerjee

Abstract:

This paper describes the development of a virtual-reality system ARWED, which will be used in physical rehabilitation of patients with reduced upper extremity mobility to increase limb Active Range of Motion (AROM). The ARWED system performs a symmetric reflection and real-time mapping of the patient’s healthy limb on to their most affected limb, tapping into the mirror neuron system and facilitating the initial learning phase. Using the ARWED, future experiments will test the extension of the action-observation priming effect linked to the mirror-neuron system on healthy subjects and then stroke patients.

Keywords: Physical rehabilitation, mirror neuron, virtual reality, stroke therapy.

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Authors: Greg Turner, Bin Lu, Cheer-Sun Yang

Abstract:

As computing technology advances, smartphone applications can assist student learning in a pervasive way. For example, the idea of using mobile apps for the PA Common Trees, Pests, Pathogens, in the field as a reference tool allows middle school students to learn about trees and associated pests/pathogens without bringing a textbook. While working on the development of three heterogeneous mobile apps, we ran into numerous challenges. Both the traditional waterfall model and the more modern agile methodologies failed in practice. The waterfall model emphasizes the planning of the duration for each phase. When the duration of each phase is not consistent with the availability of developers, the waterfall model cannot be employed. When applying Agile Methodologies, we cannot maintain the high frequency of the iterative development review process, known as ‘sprints’. In this paper, we discuss the challenges and solutions. We propose a hybrid model known as the Relay Race Methodology to reflect the concept of racing and relaying during the process of software development in practice. Based on the development project, we observe that the modeling of the relay race transition between any two phases is manifested naturally. Thus, we claim that the RRM model can provide a de fecto rather than a de jure basis for the core concept in the software development model. In this paper, the background of the project is introduced first. Then, the challenges are pointed out followed by our solutions. Finally, the experiences learned and the future works are presented.

Keywords: Agile methods, mobile apps, software process model, waterfall model.

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Authors: Sayyed R Mousavi

Abstract:

The Far From Most Strings Problem (FFMSP) is to obtain a string which is far from as many as possible of a given set of strings. All the input and the output strings are of the same length, and two strings are said to be far if their hamming distance is greater than or equal to a given positive integer. FFMSP belongs to the class of sequences consensus problems which have applications in molecular biology. The problem is NP-hard; it does not admit a constant-ratio approximation either, unless P = NP. Therefore, in addition to exact and approximate algorithms, (meta)heuristic algorithms have been proposed for the problem in recent years. On the other hand, in the recent years, hybrid algorithms have been proposed and successfully used for many hard problems in a variety of domains. In this paper, a new metaheuristic algorithm, called Constructive Beam and Local Search (CBLS), is investigated for the problem, which is a hybridization of constructive beam search and local search algorithms. More specifically, the proposed algorithm consists of two phases, the first phase is to obtain several candidate solutions via the constructive beam search and the second phase is to apply local search to the candidate solutions obtained by the first phase. The best solution found is returned as the final solution to the problem. The proposed algorithm is also similar to memetic algorithms in the sense that both use local search to further improve individual solutions. The CBLS algorithm is compared with the most recent published algorithm for the problem, GRASP, with significantly positive results; the improvement is by order of magnitudes in most cases.

Keywords: Bioinformatics, Far From Most Strings Problem, Hybrid metaheuristics, Matheuristics, Sequences consensus problems.

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Authors: Nadaniela Egidi, Pierluigi Maponi

Abstract:

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 second kind. This integral equation provides a formulation for the direct scattering problem but has to be solved several times 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. To improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning and propose an algorithm to evaluate 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: Somayeh Tourani, Alireza Behvandi

Abstract:

The peng-Robinson (PR), a cubic equation of state (EoS), is extended to polymers by using a single set of energy (A1, A2, A3) and co-volume (b) parameters per polymer fitted to experimental volume data. Excellent results for the volumetric behavior of the 11 polymer up to 2000 bar pressure are obtained. The EoS is applied to the correlation and prediction of Henry constants in polymer solutions comprising three polymer and many nonpolar and polar solvents, including supercritical gases. The correlation achieved with two adjustable parameter is satisfactory compared with the experimental data. As a result, the present work provides a simple and useful model for the prediction of Henry's constant for polymer containing systems including those containing polar, nonpolar and supercritical fluids.

Keywords: Equation of state, Henry's constant, Peng-Robinson, polymer solution.

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Authors: E. Neamatollahi, M. Bannayan, A. Souhani Darban, A. Ghanbari

Abstract:

In production of medicinal plants, seed germination is very important problem. The treated seeds (control, hydro priming and ZnSO4) of Cumin (Cuminum cyminum L.) were evaluated at germination and seedling growth for tolerance to salt (NaCl and Na2SO4) conditions at the same water potentials of 0.0, -0.3, -0.6, - 0.9 and -1.2MPa. Electrical conductivity (EC) values of the NaCl solutions were 0.0, 6.5, 12.7, 18.4 and 23.5 dSm-1, respectively. The objective of the study was to determine factors responsible for germination and early seedling growth due to salt toxicity or osmotic effect and to optimize the best priming treatment for these stress conditions. Results revealed that germination delayed in both solutions, having variable germination with different priming treatments. Germination, shoot and weight, root and shoot length were higher but mean germination time and abnormal germination percentage were lower in NaCl than Na2SO4 at the same water potential. The root / shoot weight and R/S length increased with increase in osmotic potential in both NaCl and Na2SO4 solutions. NaCl had less inhibitor effect on seedling growth than the germination. It was concluded that inhibition of germination at the same water potential of NaCl and Na2SO4 resulted from salt toxicity rather than osmotic effect. Hydro priming increased germination and seedling growth under salt stress. This protocol has practical importance and could be recommended to farmers to achieve higher germination and uniform emergence under field conditions.

Keywords: Priming, Germination, Nacl, ZnSo4, Na2So4.

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Authors: R. Sabre

Abstract:

This work focuses on the symmetric alpha stable process with continuous time frequently used in modeling the signal with indefinitely growing variance, often observed with an unknown additive error. The objective of this paper is to estimate this error from discrete observations of the signal. For that, we propose a method based on the smoothing of the observations via Jackson polynomial kernel and taking into account the width of the interval where the spectral density is non-zero. This technique allows avoiding the “Aliasing phenomenon” encountered when the estimation is made from the discrete observations of a process with continuous time. We have studied the convergence rate of the estimator and have shown that the convergence rate improves in the case where the spectral density is zero at the origin. Thus, we set up an estimator of the additive error that can be subtracted for approaching the original signal without error.

Keywords: Spectral density, stable processes, aliasing, p-adic.

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Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat

Abstract:

The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge- Kutta solution using 38 time steps.

Keywords: Impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision.

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