Search results for: associated linear equations ALEs

Authors: Soltani Amir, Wang Xuan

Abstract:

The advantage of using non-linear passive damping system in vibration control of two adjacent structures is investigated under their base excitation. The base excitation is El Centro earthquake record acceleration. The damping system is considered as an optimum and effective non-linear viscous damper that is connected between two adjacent structures. A Matlab program is developed to produce the stiffness and damping matrices and to determine a time history analysis of the dynamic motion of the system. One structure is assumed to be flexible while the other has a rule as laterally supporting structure with rigid frames. The response of the structure has been calculated and the non-linear damping coefficient is determined using optimum LQR algorithm in an optimum vibration control system. The non-linear parameter of damping system is estimated and it has shown a significant advantage of application of this system device for vibration control of two adjacent tall building.

Keywords: active control, passive control, viscous dampers, structural control, vibration control, tall building

Procedia PDF Downloads 515

Authors: S. Obregon-Cano, R. Moreno-Rojas, E. Cartea-Gonzalez, A. De Haro-Bailon

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The potential of near-infrared spectroscopy (NIRS) for screening the total glucosinolate (t-GSL) content, and also, the aliphatic glucosinolates gluconapin (GNA), progoitrin (PRO) and glucobrassicanapin (GBN) in turnip greens and turnip tops was assessed. This crop is grown for edible leaves and stems for human consumption. The reference values for glucosinolates, as they were obtained by high performance liquid chromatography on the vegetable samples, were regressed against different spectral transformations by modified partial least-squares (MPLS) regression (calibration set of samples n= 350). The resulting models were satisfactory, with calibration coefficient values from 0.72 (GBN) to 0.98 (tGSL). The predictive ability of the equations obtained was tested using a set of samples (n=70) independent of the calibration set. The determination coefficients and prediction errors (SEP) obtained in the external validation were: GNA=0.94 (SEP=3.49); PRO=0.41 (SEP=1.08); GBN=0.55 (SEP=0.60); tGSL=0.96 (SEP=3.28). These results show that the equations developed for total glucosinolates, as well as for gluconapin can be used for screening these compounds in the leaves and stems of this species. In addition, the progoitrin and glucobrassicanapin equations obtained can be used to identify those samples with high, medium and low contents. The calibration equations obtained were accurate enough for a fast, non-destructive and reliable analysis of the content in GNA and tGSL directly from NIR spectra. The equations for PRO and GBN can be employed to identify samples with high, medium and low contents.

Keywords: brassica rapa, glucosinolates, gluconapin, NIRS, turnip greens

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Authors: Mezghiche Kamel

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We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

Procedia PDF Downloads 769

Authors: Apurva Patil, Maithilee Kulkarni, Ashay Aswale

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This paper proposes an algorithm to develop the kinematic model of a 5 DOF robot arm. The formulation of the problem is based on finding the D-H parameters of the arm. Brute Force iterative method is employed to solve the system of non linear equations. The focus of the paper is to obtain the accurate solutions by reducing the root mean square error. The result obtained will be implemented to grip the objects. The trajectories followed by the end effector for the required workspace coordinates are plotted. The methodology used here can be used in solving the problem for any other kinematic chain of up to six DOF.

Keywords: 5 DOF robot arm, D-H parameters, inverse kinematics, iterative method, trajectories

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Authors: Lavinia B. Dulla

Abstract:

The exploration study of the fuzzy regression approach attempts to present that fuzzy regression can be used as a possible alternative to classical regression. It likewise seeks to assess the differences and characteristics of simple linear regression and fuzzy regression using the width of prediction interval, mean absolute deviation, and variance of residuals. Based on the simple linear regression model, the fuzzy regression approach is worth considering as an alternative to simple linear regression when the sample size is between 10 and 20. As the sample size increases, the fuzzy regression approach is not applicable to use since the assumption regarding large sample size is already operating within the framework of simple linear regression. Nonetheless, it can be suggested for a practical alternative when decisions often have to be made on the basis of small data.

Keywords: fuzzy regression approach, minimum fuzziness criterion, interval regression, prediction interval

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Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

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The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: bonded rubber, quasi-static test, shape factor, apparent Young’s modulus

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: Yang Yi-Fei, Luo Min-Zhou, Zhang Fu-Chun, He Nai-Bao, Xing Shao-Bang

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This paper presents an electromagnetic finite element model of permanent magnet synchronous linear motor and distortion rate of the air gap flux density waveform is analyzed in detail. By designing the sample space of the parameters, nonlinear regression modeling of the orthogonal experimental design is introduced. We put forward for possible air gap flux density waveform sine electromagnetic scheme. Parameters optimization of the permanent magnet synchronous linear motor is also introduced which is based on chaotic search and adaptation function. Simulation results prove that the pole shifting does not affect the motor back electromotive symmetry based on the structural parameters, it provides a novel way for the optimum design of permanent magnet synchronous linear motor and other engineering.

Keywords: permanent magnet synchronous linear motor, finite element analysis, chaotic search, optimization design

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Authors: Farhad Ghasemi

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Along with transforming the international system into a complex and chaotic system, the fundamental question arises: how can deterrence be reconstructed conceptually and theoretically in this system model? The deterrence system is much more complex today than it was seven decades ago. This article suggests that the perception of deterrence as a linear system is a fundamental mistake because it does not consider the new dynamics of the international system, including network power dynamics. The author aims to improve this point by focusing on complexity and chaos theories, especially their nonlinearity and cascading failure principles. This article proposes that the perception of deterrence as a linear system is a fundamental mistake, as the new dynamics of the surrounding international system do not take into account. The author recognizes deterrence as a nonlinear system and introduces it as a concept in strategic studies.

Keywords: complexity, international system, deterrence, linear deterrence, nonlinear deterrence

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Authors: Farid Khosravikia, Patricia Clayton

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The main objective of this study is to evaluate the advantages and disadvantages of various machine learning techniques in forecasting ground-motion intensity measures given source characteristics, source-to-site distance, and local site condition. Intensity measures such as peak ground acceleration and velocity (PGA and PGV, respectively) as well as 5% damped elastic pseudospectral accelerations at different periods (PSA), are indicators of the strength of shaking at the ground surface. Estimating these variables for future earthquake events is a key step in seismic hazard assessment and potentially subsequent risk assessment of different types of structures. Typically, linear regression-based models, with pre-defined equations and coefficients, are used in ground motion prediction. However, due to the restrictions of the linear regression methods, such models may not capture more complex nonlinear behaviors that exist in the data. Thus, this study comparatively investigates potential benefits from employing other machine learning techniques as a statistical method in ground motion prediction such as Artificial Neural Network, Random Forest, and Support Vector Machine. The algorithms are adjusted to quantify event-to-event and site-to-site variability of the ground motions by implementing them as random effects in the proposed models to reduce the aleatory uncertainty. All the algorithms are trained using a selected database of 4,528 ground-motions, including 376 seismic events with magnitude 3 to 5.8, recorded over the hypocentral distance range of 4 to 500 km in Oklahoma, Kansas, and Texas since 2005. The main reason of the considered database stems from the recent increase in the seismicity rate of these states attributed to petroleum production and wastewater disposal activities, which necessities further investigation in the ground motion models developed for these states. Accuracy of the models in predicting intensity measures, generalization capability of the models for future data, as well as usability of the models are discussed in the evaluation process. The results indicate the algorithms satisfy some physically sound characteristics such as magnitude scaling distance dependency without requiring pre-defined equations or coefficients. Moreover, it is shown that, when sufficient data is available, all the alternative algorithms tend to provide more accurate estimates compared to the conventional linear regression-based method, and particularly, Random Forest outperforms the other algorithms. However, the conventional method is a better tool when limited data is available.

Keywords: artificial neural network, ground-motion models, machine learning, random forest, support vector machine

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Authors: Adam L. Yanagihara, Yong Seok Park

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The goal of this paper is to converge upon a design of a brake system that could be used for a roller coaster found at an amusement park. It was necessary to find what could be deemed as a “comfortable” deceleration so that passengers do not feel as if they are suddenly jerked and pressed against the restraining harnesses. A human factors engineering approach was taken in order to determine this deceleration. Using a previous study that tested the deceleration of transit vehicles, it was found that a -0.45 G deceleration would be used as a design requirement to build this system around. An adjustable linear eddy current brake using permanent magnets would be the ideal system to use in order to meet this design requirement. Anthropometric data were then used to determine a realistic weight and length of the roller coaster that the brake was being designed for. The weight and length data were then factored into magnetic brake force equations. These equations were used to determine how the brake system and the brake run layout would be designed. A final design for the brake was determined and it was found that a total of 12 brakes would be needed with a maximum braking distance of 53.6 m in order to stop a roller coaster travelling at its top speed and loaded to maximum capacity. This design is derived from theoretical calculations, but is within the realm of feasibility.

Keywords: eddy current brake, engineering design, design synthesis, human factors engineering

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Authors: Behrang Tavousi Tehrani, Mohammad-Zaman Kabir

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Shape memory alloys (SMA) are often implemented in smart structures as the active components. Their ability to recover large displacements has been used in many applications, including structural stability/response enhancement and active structural acoustic control. SMA wires or fibers can be embedded with composite cylinders to increase their critical buckling load, improve their load-deflection behavior, and reduce the radial deflections under various thermo-mechanical loadings. This paper presents a semi-analytical investigation on the non-linear load-deflection response of SMA-reinforced composite circular cylindrical shells. The cylinder shells are under uniform external pressure load. Based on first-order shear deformation shell theory (FSDT), the equilibrium equations of the structure are derived. One-dimensional simplified Brinson’s model is used for determining the SMA recovery force due to its simplicity and accuracy. Airy stress function and Galerkin technique are used to obtain non-linear load-deflection curves. The results are verified by comparing them with those in the literature. Several parametric studies are conducted in order to investigate the effect of SMA volume fraction, SMA pre-strain value, and SMA activation temperature on the response of the structure. It is shown that suitable usage of SMA wires results in a considerable enhancement in the load-deflection response of the shell due to the generation of the SMA tensile recovery force.

Keywords: airy stress function, cylindrical shell, Galerkin technique, load-deflection curve, recovery stress, shape memory alloy

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Rangoli Goyal, Rama Bhargava

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The triple diffusive boundary layer flow of nanofluid under the action of constant magnetic field over a non-linear stretching sheet has been investigated numerically. The model includes the effect of Brownian motion, thermophoresis, and cross-diffusion; slip mechanisms which are primarily responsible for the enhancement of the convective features of nanofluid. The governing partial differential equations are transformed into a system of ordinary differential equations (by using group theory transformations) and solved numerically by using variational finite element method. The effects of various controlling parameters, such as the magnetic influence number, thermophoresis parameter, Brownian motion parameter, modified Dufour parameter, and Dufour solutal Lewis number, on the fluid flow as well as on heat and mass transfer coefficients (both of solute and nanofluid) are presented graphically and discussed quantitatively. The present study has industrial applications in aerodynamic extrusion of plastic sheets, coating and suspensions, melt spinning, hot rolling, wire drawing, glass-fibre production, and manufacture of polymer and rubber sheets, where the quality of the desired product depends on the stretching rate as well as external field including magnetic effects.

Keywords: FEM, thermophoresis, diffusiophoresis, Brownian motion

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Authors: Jaan Lellep, Shahid Mubasshar

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A numerical solution is developed for simply supported nanoarches based on the non-local theory of elasticity. The nanoarch under consideration has a step-wise variable cross-section and is weakened by crack-like defects. It is assumed that the cracks are stationary and the mechanical behaviour of the nanoarch can be modeled by Eringen’s non-local theory of elasticity. The physical and thermal properties are sensitive with respect to changes of dimensions in the nano level. The classical theory of elasticity is unable to describe such changes in material properties. This is because, during the development of the classical theory of elasticity, the speculation of molecular objects was avoided. Therefore, the non-local theory of elasticity is applied to study the vibration of nanostructures and it has been accepted by many researchers. In the non-local theory of elasticity, it is assumed that the stress state of the body at a given point depends on the stress state of each point of the structure. However, within the classical theory of elasticity, the stress state of the body depends only on the given point. The system of main equations consists of equilibrium equations, geometrical relations and constitutive equations with boundary and intermediate conditions. The system of equations is solved by using the method of separation of variables. Consequently, the governing differential equations are converted into a system of algebraic equations whose solution exists if the determinant of the coefficients of the matrix vanishes. The influence of cracks and steps on the natural vibration of the nanoarches is prescribed with the aid of additional local compliance at the weakened cross-section. An algorithm to determine the eigenfrequencies of the nanoarches is developed with the help of computer software. The effects of various physical and geometrical parameters are recorded and drawn graphically.

Keywords: crack, nanoarches, natural frequency, step

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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: M. Salih Taci, N. Tayebi, I. Bozkır

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This paper investigates the operation of a sinusoidal supplied autotransformer on the different states of magnetic polarity of primary and secondary terminals for four different step-up and step-down analytical conditions. In this paper, a new analytical modeling and equations for dot-marked and polarity-based step-up and step-down autotransformer are presented. These models are validated by the simulation of current and voltage waveforms for each state. PSpice environment was used for simulation.

Keywords: autotransformer modeling, autotransformer simulation, step-up autotransformer, step-down autotransformer, polarity

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Authors: Jorge Gonzalez-Camus

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In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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Authors: Arcady Ponosov

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Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Haowen Xi

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We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function.

Keywords: bubble, crash, finite-time-singular, numerical simulation, price dynamics, stochastic differential equations

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Authors: Sufyan Muhammad

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Recently, in achieving highly efficient but at the same time highly accurate solutions has become the major target of numerical analyst community. The concept is termed as compact schemes and has gained great popularity and consequently, we construct compact schemes for fourth order parabolic differential equations used to study vibrations in structures. For the superiority of newly constructed schemes, we consider range of examples. We have achieved followings i.e. (a) numerical scheme utilizes minimum number of stencil points (which means new scheme is compact); (b) numerical scheme is highly accurate (which means new scheme is reliable) and (c) numerical scheme is highly efficient (which means new scheme is fast).

Keywords: central finite differences, compact schemes, Bernoulli's equations, finite differences

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Authors: Qiuxiao Chen, Yan Hou, Ning Wu

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As there are deficiencies of the classic Douglas-Peucker Algorithm (DPA), such as high risks of deleting key nodes by mistake, high complexity, time consumption and relatively slow execution speed, a new Deletion-Cost Based Compression Algorithm (DCA) for linear vector data was proposed. For each curve — the basic element of linear vector data, all the deletion costs of its middle nodes were calculated, and the minimum deletion cost was compared with the pre-defined threshold. If the former was greater than or equal to the latter, all remaining nodes were reserved and the curve’s compression process was finished. Otherwise, the node with the minimal deletion cost was deleted, its two neighbors' deletion costs were updated, and the same loop on the compressed curve was repeated till the termination. By several comparative experiments using different types of linear vector data, the comparison between DPA and DCA was performed from the aspects of compression quality and computing efficiency. Experiment results showed that DCA outperformed DPA in compression accuracy and execution efficiency as well.

Keywords: Douglas-Peucker algorithm, linear vector data, compression, deletion cost

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Authors: R. A. Petre, S. E. Nichifor, A. Craifaleanu, I. Stroe

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The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a MATLAB program.

Keywords: Lagrange equations, relative motion, inertial reference frame, non-inertial reference frame

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Authors: Syed M. Jawwad Riaz

Abstract:

There has been a lot of interest in exploring the thermodynamic properties at the horizon of a black hole geometry. Earlier, it has been shown, for different spacetimes, that the Einstein field equations at the horizon can be expressed as a first law of black hole thermodynamics. In this paper, considering r = constant slices, for the Kerr-Newman black hole, shown that the Einstein field equations for the induced 3-metric of the hypersurface is expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces. As expected, it is found that the field equations of the induced metric corresponding to the horizon can only be written as a first law of black hole thermodynamics. It is to be mentioned here that the procedure adopted is much easier, to obtain such results, as here one has to essentially deal with (n - 1)-dimensional induced metric for an n-dimensional spacetime.

Keywords: black hole space-times, Einstein's field equation, foliation, hyper-surfaces

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Authors: Seong-Jin Cho, Jin Ho Kim

Abstract:

Energy harvesting is the technology which gathers and converts external energies such as light, vibration and heat which are disposed into reusable electrical energy and uses such electrical energy. The vibration energy harvesting is very interesting technology because it produces very high density of energy and unaffected by the climate. Vibration energy can be harvested by the electrostatic, electromagnetic and piezoelectric systems. The electrostatic system has low energy conversion efficiency, and the piezoelectric system is expensive and needs the frequent maintenance because it is made of piezoelectric ceramic. On the other hand, the electromagnetic system has a long life time and high harvesting efficiency, and it is relatively cheap. The electromagnetic harvesting system includes the linear generator and the rotary-type generator. The rotary-type generators require the additional mechanical conversion device if it uses linear motion of vibration. But, the linear generator uses directly linear motion of vibration without a mechanical conversion device, and it has uncomplicated structure and light weight compared with the rotary-type generator. Therefore, the linear electromagnetic generator can be useful in using vibration energy harvesting. The pole transformer systems need electricity sensor system for sending voltage and power information to administrator. Therefore, the battery is essential, and its regular maintenance of replacement is required. In case of the transformer of high location in mountainous areas, the person can’t easily access it resulting in high maintenance cost. To overcome these problems, we designed and developed the linear electromagnetic generator which can replace battery in electricity sensor system for sending voltage and power information of the pole transformer. And, it uses vibration energy of frequency more than 50 Hz by the pole transformer. In order to analyze the electromagnetic characteristics of small linear electric generator, a commercial electromagnetic finite element analysis program "MAXWELL" was used. Then, through the actual production and experiment of linear generator, we confirmed output power of linear generator.

Keywords: energy harvesting, frequency, linear generator, experiment

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Authors: Alia Alghosoun, Michael Herty, Mohammed Seaid

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We present a new class of numerical techniques to solve shallow water flows over dry areas including run-up. Many recent investigations on wave run-up in coastal areas are based on the well-known shallow water equations. Numerical simulations have also performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of coastal areas. In all these simulations the shallow water equations are solved in entire domain including dry areas and special treatments are used for numerical solution of singularities at these dry regions. In the present study we propose a new method to deal with these difficulties by reformulating the shallow water equations into a new system to be solved only in the wetted domain. The system is obtained by a change in the coordinates leading to a set of equations in a moving domain for which the wet/dry interface is the reconstructed using the wave speed. To solve the new system we present a finite volume method of Lax-Friedrich type along with a modified method of characteristics. The method is well-balanced and accurately resolves dam-break problems over dry areas.

Keywords: dam-break problems, finite volume method, run-up waves, shallow water flows, wet/dry interfaces

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Authors: Dorota Miroslaw-Swiatek, Mateusz Grygoruk, Sylwia Szporak

Abstract:

We applied a two-dimensional surface water flow model with irregular wet boundaries. In this model, flow equations are in the form of a 2-D, non-linear diffusion equations which allows to account spatial variations in flow resistance and topography. Calculation domain to simulate the flow pattern in the floodplain is congruent with a Digital Elevation Model (DEM) grid. The rate and direction of sheet flow in wetlands is affected by vegetation type and density, therefore the developed model take into account spatial distribution vegetation resistance to the water flow. The model was tested in a part of the Biebrza Valley, of an outstanding heterogeneity in the elevation and flow resistance distributions due to various ecohydrological conditions and management measures. In our approach we used the highest-possible quality of the DEM in order to obtain hydraulic slopes and vegetation distribution parameters for the modelling. The DEM was created from the cloud of points measured in the LiDAR technology. The LiDAR reflects both the land surface as well as all objects on top of it such as vegetation. Depending on the density of vegetation cover the ability of laser penetration is variable. Therefore to obtain accurate land surface model the “vegetation effect” was corrected using data collected in the field (mostly the vegetation height) and satellite imagery such as Ikonos (to distinguish different vegetation types of the floodplain and represent them spatially). Model simulation was performed for the spring thaw flood in 2009.

Keywords: floodplain flow, Biebrza valley, model simulation, 2D surface flow model

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

Abstract:

Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformations. Numerical solutions for the governing momentum and energy equations are obtained by efficient numerical techniques based on the common finite difference method with central differencing, on a tridiagonal matrix manipulation and on an iterative procedure. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.

Keywords: biomagnetic fluid, FHD, MHD, nonlinear stretching sheet

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Authors: Edamana Krishnan, Khalil Al-Ghafri

Abstract:

In this paper, modified K(n,n) and K(n+1,n+1) equations have been solved using mapping methods which give a variety of solutions in terms of Jacobi elliptic functions. The solutions when m approaches 0 and 1, with m as the modulus of the JEFs have also been deduced. The role of constraint conditions has been discussed.

Keywords: travelling wave solutions, solitary wave solutions, compactons, Jacobi elliptic functions, mapping methods

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Authors: Ramazan I. Kadiev, Arcady Ponosov

Abstract:

Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models.

Keywords: ill-posed problems, singular perturbation analysis, stochastic differential equations, switching nonlinearities

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