Search results for: differential shrinkage

Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Black-Scholes partial differential equations, Ito process, option price valuation, partial differential equations

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Authors: Zhan Chen, Wenquan Bi, Xiaoyun Wang

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The Midori family of light weight block cipher is proposed in ASIACRYPT2015. It has attracted the attention of numerous cryptanalysts. There are two versions of Midori: Midori64 which takes a 64-bit block size and Midori128 the size of which is 128-bit. In this paper an improved 10-round impossible differential attack on Midori64 is proposed. Pre-whitening keys are considered in this attack. A better impossible differential path is used to reduce time complexity by decreasing the number of key bits guessed. A hash table is built in the pre-computation phase to reduce computational complexity. Partial abort technique is used in the key seiving phase. The attack requires 259 chosen plaintexts, 214.58 blocks of memory and 268.83 10-round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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Authors: Aeslina Binti Abdul Kadir, Ahmad Shayuti Bin Abdul Rahim

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Brick is one of the most common masonry units used as building material. Due to the demand, different types of waste have been investigated to be incorporated into the bricks. Many types of sludge have been incorporated in fired clay brick for example marble sludge, stone sludge, water sludge, sewage sludge, and ceramic sludge. The utilization of these waste materials in fired clay bricks usually has positive effects on the properties such as lightweight bricks with improved shrinkage, porosity, and strength. This paper reviews on utilization of different types of sludge wastes into fired clay bricks. Previous investigations have demonstrated positive effects on the physical and mechanical properties as well as less impact towards the environment. Thus, the utilizations of sludge waste could produce a good quality of brick and could be one of alternative disposal methods for the sludge wastes.

Keywords: fired clay brick, sludge waste, compressive strength, shrinkage, water absorption

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Authors: Mahmood Otadi, Maryam Mosleh

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The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: fuzzy number, fuzzy ODE, HAM, approximate method

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Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Sara Akbari

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In this study, we investigate building structures nonlinear behavior also solving analytic of nonlinear differential at vibrations. As we know most of engineering systems behavior in practical are non- linear process (especial at structural) and analytical solving (no numerical) these problems are complex, difficult and sometimes impossible (of course at form of analytical solving). In this symposium, we are going to exposure one method in engineering, that can solve sets of nonlinear differential equations with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical Method (Runge-Kutte 4th) and exact solutions. Finally, we can proof AGM method could be created huge evolution for researcher and student (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software, we can analytical solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations.

Keywords: new method AGM, vibrations, beam-column, angular frequency, energy dissipated, critical load

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Authors: A. M. Sagir

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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

Keywords: block method, first order ordinary differential equations, linear multistep, self-starting

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Authors: Palwinder Singh, Munish Sandhir, Tejinder Singh

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The ordinary differential equations (ODE) represent a natural framework for mathematical modeling of many real-life situations in the field of engineering, control systems, physics, chemistry and astronomy etc. Such type of differential equations can be solved by analytical methods or by numerical methods. If the solution is calculated using analytical methods, it is done through calculus theories, and thus requires a longer time to solve. In this paper, we compare the numerical accuracy of the solutions given by the three main types of one-step initial value solvers: Taylor’s Series Method, Euler’s Method and Runge-Kutta Fourth Order Method (RK4). The comparison of accuracy is obtained through comparing the solutions of ordinary differential equation given by these three methods. Furthermore, to verify the accuracy; we compare these numerical solutions with the exact solutions.

Keywords: Ordinary differential equations (ODE), Taylor’s Series Method, Euler’s Method, Runge-Kutta Fourth Order Method

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Authors: Weihua Ruan, Kuan-Chou Chen

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This paper is concerned with a system of Hamilton-Jacobi-Bellman equations coupled with an autonomous dynamical system. The mathematical system arises in the differential game formulation of political economy models as an infinite-horizon continuous-time differential game with discounted instantaneous payoff rates and continuously and discretely varying state variables. The existence of a weak solution of the PDE system is proven and a computational scheme of approximate solution is developed for a class of such systems. A model of democratization is mathematically analyzed as an illustration of application.

Keywords: Hamilton-Jacobi-Bellman equations, infinite-horizon differential games, continuous and discrete state variables, political-economy models

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Authors: Martin K. Steiger, Lukas Heisler, Hans-Georg Brachtendorf

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Deep neural networks and their variants form the backbone of many AI applications. Based on the so-called residual networks, a continuous formulation of such models as ordinary differential equations (ODEs) has proven advantageous since different techniques may be applied that significantly increase the learning speed and enable controlled trade-offs with the resulting error at the same time. For the evaluation of such models, high-performance numerical differential equation solvers are used, which also provide the gradients required for training. However, whether classical gradient-based methods are even applicable or which one yields the best results has not been discussed yet. This paper aims to redeem this situation by providing empirical results for different applications.

Keywords: deep neural networks, gradient-based learning, image processing, ordinary differential equation networks

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Authors: N. Bouhamou, F. Mostefa, A. Mebrouki, N. Belas

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Every year, millions of cube meters are dredged from dams and restraints as an entertaining and prevention procedure all over the world. These dredged sediments are considered as natural waste leading to an environmental, ecological and even an economical problem in their processing and deposing. Nevertheless, in the context of the sustainable development policy, a way of management is opened aiming to the valorization of sediments as a building material and particularly as a new binder that can be industrially exploited and that improve the physical, chemical and mechanical characteristics of the concrete. This study is a part of the research works realized in the civil engineering department at the university of Mostaganem (Algeria), on the impact of the dredged mud of Fergoug dam on the behaviour of self-consolidating concrete in fresh and hardened state, such as the mechanical performance of SCC and its impact on the differed deformations (shrinkage). The work aims to valorize this mud in SCC and to show eventual interactions between constituents. The results obtained presents a good perspectives in order to perform SCC based in calcined mud.

Keywords: sediment, calcination, reuse, self-consolidating concrete, fresh state, hard state, shrinkage

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Authors: Chao-Qing Dai

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In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

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Authors: Benmalek M. Larbi, R. Harbi, S. Boukor

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This paper reports an experimental work that aimed to investigate the effects of clay brick waste, as part of fine aggregate, on rendering mortar performance. The brick, in crushed form, was from a local brick manufacturer that was rejected due to being of-standard. It was used to replace 33.33 %, 50 %, 66.66 % and 100 % by weight of the quarry sand in mortar. Effects of the brick replacement on the mortar key properties intended for wall plastering were investigated; these are workability, compressive strength, flexural strength, linear shrinkage, water absorption by total immersion and by capillary suction. The results showed that as the brick replacement level increased, the mortar workability reduced. The linear shrinkage increases over time and decreases with the introduction of brick waste. The compressive and flexural strengths decrease with the increase of brick waste because of their great water absorption.

Keywords: clay brick waste, mortar, properties, quarry sand

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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: Malika Elkyal

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

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

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Authors: T. Vamsee Kiran, A. Gopi

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The undesired torque and flux ripple may occur in conventional direct torque control (DTC) induction motor drive. DTC can improve the system performance at low speeds by continuously tuning the regulator by adjusting the Kp, Ki values. In this differential evolution (DE) is proposed to adjust the parameters (Kp, Ki) of the speed controller in order to minimize torque ripple, flux ripple, and stator current distortion.The DE based PI controller has resulted is maintaining a constant speed of the motor irrespective of the load torque fluctuations.

Keywords: differential evolution, direct torque control, PI controller

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Authors: Taraneh Estedlal

Abstract:

The objective of this study was to review in-vivo and in-vitro studies to compare the effectiveness of bulk-fill and conventional resin composites with regard to marginal adaptation, polymerization shrinkage, and other mechanical properties.PubMed and Scopus databases was investigated for in-vitro studies and randomized clinical trials comparing incidence of fractures, color stability, marginal adaptation, pain and discomfort, recurrent caries, occlusion, pulpal reaction, and proper proximal contacts of restorations made with conventional and bulk resins. The failure rate of conventional and flowable bulk-fill resin composites was not significantly different to sculptable bulk-fill resin composites. The objective of this study was to review in-vivo and in-vitro studies to compare the effectiveness of bulk-fill and conventional resin composites with regard to marginal adaptation, polymerization shrinkage, and other mechanical properties. PubMed and Scopus databases was investigated for in-vitro studies and randomized clinical trials comparing one of the pearlier mentioned properties between bulk-fill and control composites. Despite differences in physical and in-vitro properties, failure rate of conventional and flowable bulk-fill resin composites was not significantly different to sculptable bulk-fill resin composites.

Keywords: polymerization shrinkage, color stability, marginal adaptation, recurrent caries, occlusion, pulpal reaction

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Authors: Nthabiseng Portia Mahumapelo, Andre van Niekerk, Ndabenhle Sosibo, Nirdesh Singh

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The foundry industry generates large quantities of solid waste in the form of waste foundry sand. The ever-increasing quantities of this type of industrial waste put pressure on land-filling space and its proper management has become a global concern. The South African foundry industry is not different when it comes to this solid waste generation. Utilizing the foundry waste sand in other applications has become an attractive avenue to deal with this waste stream. In the present paper, an evaluation was done on the suitability of foundry waste sand as an additive in clay masonry products. Purchased clay was added to the foundry waste sand sample in a 50/50 ratio. The mixture was named FC sample. The FC sample was mixed with water in a pan mixer until the mixture was consistent and suitable for extrusion. The FC sample was extruded and cut into briquettes. Water absorption, shrinkage and modulus of rupture tests were conducted on the resultant briquettes. Foundry waste sand and FC samples were respectively characterized mineralogically using X-Ray Diffraction, and the major and trace elements were determined using Inductively Coupled Plasma Optical Emission Spectroscopy. Adding purchased clay to the foundry waste sand positively influenced the workability of the test sample. Another positive characteristic was the low linear shrinkage, which indicated that products manufactured from the FC sample would not be susceptible to cracking. The water absorption values were acceptable and the unfired and fired strength values of the briquette’s samples were acceptable. In conclusion, tests showed that foundry waste sand can be used as an additive in masonry clay bricks, provided it is blended with good quality clay.

Keywords: foundry waste sand, masonry clay bricks, modulus of rupture, shrinkage

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Authors: Jiya Mohammed, Ibrahim Ismail Giwa

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Unsteady squeezing flow of a viscous fluid between parallel plates is considered. The two plates are considered to be approaching each other symmetrically, causing the squeezing flow. Two-dimensional rectangular Cartesian coordinate is considered. The Navier-Stokes equation was reduced using similarity transformation to a single fourth order non-linear ordinary differential equation. The energy equation was transformed to a second order coupled differential equation. We obtained solution to the resulting ordinary differential equations via Homotopy Perturbation Method (HPM). HPM deforms a differential problem into a set of problem that are easier to solve and it produces analytic approximate expression in the form of an infinite power series by using only sixth and fifth terms for the velocity and temperature respectively. The results reveal that the proposed method is very effective and simple. Comparisons among present and existing solutions were provided and it is shown that the proposed method is in good agreement with Variation of Parameter Method (VPM). The effects of appropriate dimensionless parameters on the velocity profiles and temperature field are demonstrated with the aid of comprehensive graphs and tables.

Keywords: coupled differential equation, Homotopy Perturbation Method, plates, squeezing flow

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Authors: Maryam Mosleh, Mahmood Otadi

Abstract:

The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

Procedia PDF Downloads 511

Authors: Mohamed Ahmed Kenawi Abdallah

Abstract:

Chemical composition, cooking loss, shrinkage value, texture coefficient indices, Feder value, microbial examination, and sensory evaluation were done in order to examine the effect of adding 15% germinated quinoa seeds flour as extender to chicken wings meat to produce low fat chicken burger, packaged in two different packing materials and stored frozen for nine months. The data indicated reduction in the moisture content, crude either extract, and increase in the ash content, pH value, and total acidity for the samples extended by quinoa flour compared with the control one. The data showed that the extended samples with quinoa flour had the lowest values of TBA, cooking loss, and shrinkage value compared with the control ones. The data also revealed that, the sample contained quinoa flour had total bacterial count and psychrophilic bacterial count lower than the control sample. In addition, it has higher evaluation values for overall acceptability than the control one.

Keywords: chicken wings, low fat chicken burger, quinoa flour, vacuum packaging.

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Authors: Luxi He, Tianfang Zhang, Zhengbin He, Songlin Yi

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Heat treatment has been widely recognized for its effectiveness in enhancing the physicochemical properties of wood, including hygroscopicity and dimensional stability. Nonetheless, the non-negligible volumetric shrinkage and loss of mechanical strength resulting from heat treatment may diminish the wood recovery and its product value. In this study, tung oil was used to alleviate heat-induced shrinkage and reduction in mechanical properties of wood during heat treatment. Tung oil was chosen as a modifier because it is a traditional Chinese plant oil that has been widely used for over a thousand years to protect wooden furniture and buildings due to its biodegradable and non-toxic properties. The effects of different heating media (air, tung oil) and their effective treatment parameters (temperature, duration) on the changes in the physical properties (morphological characteristics, pore structures, micromechanical properties), and chemical properties (chemical structures, chemical composition) of wood were investigated by using scanning electron microscopy, confocal laser scanning microscopy, atomic force microscopy, X-ray photoelectron spectroscopy, and dynamic vapor sorption. Meanwhile, the correlation between the mass changes and the color change, volumetric shrinkage, and hygroscopicity was also investigated. The results showed that the thermal degradation of wood cell wall components was the most important factor contributing to the changes in heat-induced shrinkage, color, and moisture adsorption of wood. In air-heat-treated wood samples, there was a significant correlation between mass change and heat-induced shrinkage, brightness, and moisture adsorption. However, the presence of impregnated tung oil in oil-heat-treated wood appears to disrupt these correlations among physical properties. The results of micromechanical properties demonstrated a significant decrease in elastic modulus following high-temperature heat treatment, which was mitigated by tung oil treatment. Chemical structure and compositional analyses indicated that the changes in chemical structure primarily stem from the degradation of hemicellulose and cellulose, and the presence of tung oil created an oxygen-insulating environment that slowed down this degradation process. Morphological observation results showed that tung oil permeated the wood structure and penetrated the cell walls through transportation channels, altering the micro-morphology of the cell wall surface, obstructing primary water passages (e.g., vessels and pits), and impeding the release of volatile degradation products as well as the infiltration and diffusion of water. In summary, tung oil treatment represents an environmentally friendly and efficient method for maximizing wood recovery and increasing product value. This approach holds significant potential for industrial applications in wood heat treatment.

Keywords: tung oil, heat treatment, physicochemical properties, wood cell walls

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Authors: Davood Yazdani Cherati, Hussein Hashemi Senejani

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

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

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Authors: W. Tahri, B. Samet, F. Pacheco-Torgal, J. L. Barroso de Aguiar, S. Baklouti

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Infrastructure rehabilitation represents a multitrillion dollar opportunity for the construction industry. Since the majority of the existent infrastructures are Portland cement concrete based this means that concrete infrastructure rehabilitation is a hot issue to be dealt with. Geopolymers are novel inorganic binders with high potential to replace Portland cement based ones. So far very few studies in the geopolymer field have addressed the rehabilitation of deteriorated concrete structures. This paper discloses results of an investigation concerning the development geopolymeric repair mortars. The mortars are based on Tunisian natural clay plus calcium hydroxide, sodium silicate and sodium hydroxide. Results show that the geopolymeric mortar has a high compressive strength and a lower unrestrained shrinkage performance as long as partial replacement by metakaolin is carried out. The results also show that Tunisian calcined clay based mortars have hydration products with typical geopolymeric phases.

Keywords: geopolymeric mortars, infrastructure repair, compressive strength, shrinkage

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Authors: Somveer Singh, Vineet Kumar Singh

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We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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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: Ramdas Sonawane, Mahaveer Gadiya

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The control problem associated with nuclear dynamics is represented by nonlinear integro-differential equation with additive controls. To control chain reaction, certain amount of neutrons is added into (or withdrawn out of) chamber as and when required. It is not realistic. So, we can think of controlling the reactor dynamics by bilinear control, which enters the system as coefficient of state. In this paper, we study the approximate and exact controllability of parabolic integro-differential equation controlled by bilinear control with non-homogeneous boundary conditions in bounded domain. We prove the existence of control and propose an explicit control strategy.

Keywords: approximate control, exact control, bilinear control, nuclear dynamics, integro-differential equations

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Authors: T. Manzur

Abstract:

Concrete is the predominant construction material in Bangladesh. In large projects, stringent quality control procedures are usually followed under the supervision of experienced engineers and skilled labors. However, in the case of small projects and particularly at distant locations from major cities, proper quality control is often an issue. It has been found from experience that such quality related issues mainly arise from inappropriate proportioning of concrete mixes and improper curing conditions. In most cases external curing method is followed which requires supply of adequate quantity of water along with proper protection against evaporation. Often these conditions are found missing in the general construction sites and eventually lead to production of weaker concrete both in terms of strength and durability. In this study, an attempt has been made to investigate the performance of general concreting works of the country when subjected to several adverse curing conditions that are quite common in various small to medium construction sites. A total of six different types of adverse curing conditions were simulated in the laboratory and samples were kept under those conditions for several days. A set of samples was also submerged in normal curing condition having proper supply of curing water. Performance of concrete was evaluated in terms of compressive strength, tensile strength, chloride permeability and drying shrinkage. About 37% and 25% reduction in 28-day compressive and tensile strength were observed respectively, for samples subjected to most adverse curing condition as compared to the samples under normal curing conditions. Normal curing concrete exhibited moderate permeability (close to low permeability) whereas concrete under adverse curing conditions showed very high permeability values. Similar results were also obtained for shrinkage tests. This study, thus, will assist concerned engineers and supervisors to understand the importance of quality assurance during the curing period of concrete.

Keywords: adverse, concrete, curing, compressive strength, drying shrinkage, permeability, tensile strength

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Authors: Hassan Manouzi, Taous-Meriem Laleg-Kirati

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In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated.

Keywords: eigenvalue problem, Wick product, SPDEs, finite element, Wiener-Ito chaos expansion

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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: 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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