Search results for: Riccati algebra matrix equation.

Authors: Nisha Goyal, R.K. Gupta

Abstract:

Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to reduce nonlinear PDE to nonlinear ordinary differential equation (ODE). Some exact solutions of Einstein vacuum equations in general relativity are also obtained.

Keywords: Gravitational fields, Lie Classical method, Exact solutions.

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Authors: Noor Atinah Ahmad, Shazia Javed

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We present a discussion of three adaptive filtering algorithms well known for their one-step termination property, in terms of their relationship with the minimal residual method. These algorithms are the normalized least mean square (NLMS), Affine Projection algorithm (APA) and the recursive least squares algorithm (RLS). The NLMS is shown to be a result of the orthogonality condition imposed on the instantaneous approximation of the Wiener equation, while APA and RLS algorithm result from orthogonality condition in multi-dimensional minimal residual formulation. Further analysis of the minimal residual formulation for the RLS leads to a triangular system which also possesses the one-step termination property (in exact arithmetic)

Keywords: Adaptive filtering, minimal residual method, projection method.

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Authors: Saeed Sarabadan, Kamal Rashedi

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This article presents a numerical method to find the heat flux in an inhomogeneous inverse heat conduction problem with linear boundary conditions and an extra specification at the terminal. The method is based upon applying the satisfier function along with the Ritz-Galerkin technique to reduce the approximate solution of the inverse problem to the solution of a system of algebraic equations. The instability of the problem is resolved by taking advantage of the Landweber’s iterations as an admissible regularization strategy. In computations, we find the stable and low-cost results which demonstrate the efficiency of the technique.

Keywords: Inverse problem, parabolic equations, heat equation, Ritz-Galerkin method, Landweber iterations.

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Authors: Ibrahim El rube'

Abstract:

In this paper, a method for matching image segments using triangle-based (geometrical) regions is proposed. Triangular regions are formed from triples of vertex points obtained from a keypoint detector (SIFT). However, triangle regions are subject to noise and distortion around the edges and vertices (especially acute angles). Therefore, these triangles are expanded into parallelogramshaped regions. The extracted image segments inherit an important triangle property; the invariance to affine distortion. Given two images, matching corresponding regions is conducted by computing the relative affine matrix, rectifying one of the regions w.r.t. the other one, then calculating the similarity between the reference and rectified region. The experimental tests show the efficiency and robustness of the proposed algorithm against geometrical distortion.

Keywords: Image matching, key point detection, affine invariant, triangle-shaped segments.

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Authors: S. Nagheli, N. Samani, D. A. Barry

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In this paper, the velocity potential and stream function of capture zone for a well field in an aquifer bounded by two parallel streams with or without a uniform regional flow of any directions are presented. The well field includes any number of extraction or injection wells or a combination of both types with any pumping rates. To delineate the capture envelope, the potential and streamlines equations are derived by conformal mapping method. This method can help us to release constrains of other methods. The equations can be applied as useful tools to design in-situ groundwater remediation systems, to evaluate the surface–subsurface water interaction and to manage the water resources.

Keywords: Complex potential, conformal mapping, groundwater remediation, image well theory, Laplace’s equation, superposition principle.

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Authors: Moez Selmi, Mariem Kacem, Mehrez Jamei, Philippe Dubujet

Abstract:

Earth pressure balance (EPB) tunnel boring machines are designed for digging in different types of soil, especially clay soils. This operation requires the treatment of soil by lubricants to facilitate the procedure of excavation. A possible use of this soil is limited by the effect of treatment on the hydro-mechanical properties of the soil. This work aims to study the effect of a foaming agent on the hydro-mechanical properties of clay soil. The injection of the foam agent in the soil leads to create a soil matrix in which they are incorporated gas bubbles. The state of the foam in the soil is scalable thanks to the degradation of the gas bubbles in the soil.

Keywords: EPB, clay soils, foam agent, hydro-mechanical properties, degradation.

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Authors: Wudhichai Assawinchaichote, Sing Kiong Nguang

Abstract:

This paper examines the problem of designing a robust H8 state-feedback controller for a class of nonlinear two-time scale systems with Markovian Jumps described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, LMI-based sufficient conditions for the uncertain Markovian jump nonlinear two-time scale systems to have an H8 performance are derived. The proposed approach does not involve the separation of states into slow and fast ones and it can be applied not only to standard, but also to nonstandard nonlinear two-time scale systems. A numerical example is provided to illustrate the design developed in this paper.

Keywords: TS fuzzy, Markovian jumps, LMI, two-time scale systems.

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Authors: Arezoo Sadrinezhad, Kallol Sett, S. I. Hariharan

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In this paper, a probabilistic framework based on Fokker-Planck-Kolmogorov (FPK) approach has been applied to simulate triaxial cyclic constitutive behavior of uncertain soils. The framework builds upon previous work of the writers, and it has been extended for cyclic probabilistic simulation of triaxial undrained behavior of soils. von Mises elastic-perfectly plastic material model is considered. It is shown that by using probabilistic framework, some of the most important aspects of soil behavior under cyclic loading can be captured even with a simple elastic-perfectly plastic constitutive model.

Keywords: Elasto-plasticity, uncertainty, soils, Fokker-Planck equation, Fourier Spectral method, Finite Difference method.

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Authors: Qingqing Wang, Baocheng Chen, Shouming Zhong

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In this paper, utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to study the exponential stability problem for neural networks with discrete and distributed time-varying delays.By constructing new Lyapunov-Krasovskii functional and dividing the discrete delay interval into multiple segments,some new delay-dependent exponential stability criteria are established in terms of LMIs and can be easily checked.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.

Keywords: Neural networks, Exponential stability, LMI approach, Time-varying delays.

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Authors: Z. Pavlík, A. Trník, M. Pavlíková, M. Keppert, R. Černý

Abstract:

A new type of lightweight plaster with the thermal capacity enhanced by PCM (Phase Change Material) addition is analyzed. The basic physical characteristics, namely the bulk density, matrix density, total open porosity, and pore size distribution are measured at first. For description of mechanical properties, compressive strength measurements are done. The thermal properties are characterized by transient impulse techniques as well as by DSC analysis that enables determination of the specific heat capacity as a function of temperature. The resistivity against the liquid water ingress is described by water absorption coefficient measurement. The experimental results indicate a good capability of the designed plaster to moderate effectively the interior climate of buildings.

Keywords: Lime-pozzolan plaster, PCM addition, enhanced thermal capacity, DSC analysis.

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Authors: Weihua Ruan, Kuan-Chou Chen

Abstract:

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: Differential games, Hamilton-Jacobi-Bellman equations, infinite horizon, political-economy models.

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Authors: Dayananda Pai, Shrikantha S. Rao, Savitha G.Kini

Abstract:

In this study, the effects of machining parameters on specific energy during surface grinding of 6061Al-SiC35P composites are investigated. Vol% of SiC, feed and depth of cut were chosen as process variables. The power needed for the calculation of the specific energy is measured from the two watt meter method. Experiments are conducted using standard RSM design called Central composite design (CCD). A second order response surface model was developed for specific energy. The results identify the significant influence factors to minimize the specific energy. The confirmation results demonstrate the practicability and effectiveness of the proposed approach.

Keywords: ANOVA, Metal matrix composites, Response surface methodology, Specific energy, Two watt meter method.

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Authors: Nai-Chieh Wei, I-Ming Chao, Chin-Jung Liuand, Hong Long Chen

Abstract:

This paper combines the branch-and-bound method and the petri net to solve the two-sided assembly line balancing problem, thus facilitating effective branching and pruning of tasks. By integrating features of the petri net, such as reachability graph and incidence matrix, the propose method can support the branch-and-bound to effectively reduce poor branches with systematic graphs. Test results suggest that using petri net in the branching process can effectively guide the system trigger process, and thus, lead to consistent results.

 

Keywords: Branch-and-Bound Method, Petri Net, Two-Sided Assembly Line Balancing Problem.

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Authors: Shan Gao

Abstract:

In this paper, we consider a risk model involving two independent classes of insurance risks and random premium income. We assume that the premium income process is a Poisson Process, and the claim number processes are independent Poisson and generalized Erlang(n) processes, respectively. Both of the Gerber- Shiu functions with zero initial surplus and the probability generating functions (p.g.f.) of the Gerber-Shiu functions are obtained.

Keywords: Poisson process, generalized Erlang risk process, Gerber-Shiu function, generating function, generalized Lundberg equation.

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

Abstract:

Lightweight ceramic materials in the form of bricks and blocks are widely used in modern construction. They may be obtained by adding of rice husk, rye straw, etc, as porous forming materials. Rice husk is a major by-product of the rice milling industry. Its utilization as a valuable product has always been a problem. Various technologies for utilization of rice husk through biological and thermochemical conversion are being developed. The purpose of this work is to develop lightweight ceramic materials with clay matrix and filler of rice husk and examine their main physicomechanical properties. The results obtained allow to suppose that the materials synthesized on the basis of waste materials can be used as lightweight materials for construction purpose.

Keywords: lightweight ceramic materials, properties, agro-waste

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Authors: Abdelrahman Elsehsah, Hany Madkour, Khalid Farah

Abstract:

This article presents a 3-D modified non-linear elastic model in the strain space. The Helmholtz free energy function is introduced with the existence of a dissipation potential surface in the space of thermodynamic conjugate forces. The constitutive equation and the damage evolution were derived as well. The modified damage has been examined to model the nonlinear behavior of reinforced concrete (RC) slabs with an opening. A parametric study with RC was carried out to investigate the impact of different factors on the behavior of RC slabs. These factors are the opening area, the opening shape, the place of opening, and the thickness of the slabs. And the numerical results have been compared with the experimental data from literature. Finally, the model showed its ability to be applied to the structural analysis of RC slabs.

Keywords: 3-D numerical analysis, damage mechanics, RC slab with opening.

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Authors: K. Broniszewski, J. Woźniak, K. Czechowski, P. Orłowski, A. Olszyna

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Alumina matrix composites with addition of hexagonal boron nitride (hBN), acting as solid lubricant, were produced. Main purpose of solid lubricants is to dispose the necessity of using cooling lubricants in machining process. Hot pressing was used as a consolidating process for Al2O3-x%wt.hBN (x=1/ 2,5/ 5 /7,5 /10) composites. Properties of sinters such as relative density, hardness, Young-s modulus and fracture toughness were examined. Obtained samples characterize by high relative density. Hardness and fracture toughness values allow the use of alumina – hBN composites for machining steels even in hardened condition. However it was observed that high weight content of hBN can negatively influence the mechanical properties of composites.

Keywords: Alumina. Composites, Hexagonal boron nitride, Machining

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Authors: M. N. Azian, A. N. Ilia Anisa, Y. Iwai

Abstract:

The mechanism for extraction bioactive compounds from plant matrix is essential for optimizing the extraction process. As a benchmark technique, a soxhlet extraction has been utilized for discussing the mechanism and compared with an accelerated water extraction. The trends of both techniques show that the process involves extraction and degradation. The highest yields of 6-, 8-, 10-gingerols and 6-shogaol in soxhlet extraction were 13.948, 7.12, 10.312 and 2.306 mg/g, respectively. The optimum 6-, 8-, 10-gingerols and 6-shogaol extracted by the accelerated water extraction at 140oC were 68.97±3.95 mg/g at 3min, 18.98±3.04 mg/g at 5min, 5.167±2.35 mg/g at 3min and 14.57±6.27 mg/g at 3min, respectively. The effect of temperature at 3mins shows that the concentration of 6-shogaol increased rapidly as decreasing the recovery of 6-gingerol.

Keywords: Mechanism, bioactive compounds, soxhlet extraction, accelerated water extraction.

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Authors: Antonis Sideris, Elias Chlis Kalogeropoulos, Konstantia Moirogiorgou

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The present study proposes a methodology for the efficient daily management of fleet vehicles and construction machinery. The application covers the area of remote monitoring of heavy-duty vehicles operation parameters, where specific sensor data are stored and examined in order to provide information about the vehicle’s health. The vehicle diagnostics allow the user to inspect whether maintenance tasks need to be performed before a fault occurs. A properly designed machine learning model is proposed for the detection of two different types of faults through classification. Cross validation is used and the accuracy of the trained model is checked with the confusion matrix.

Keywords: Fault detection, feature selection, machine learning, predictive maintenance.

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Authors: Ibrahim Abu-Alshaikh

Abstract:

In this study, a new root-finding method for solving nonlinear equations is proposed. This method requires two starting values that do not necessarily bracketing a root. However, when the starting values are selected to be close to a root, the proposed method converges to the root quicker than the secant method. Another advantage over all iterative methods is that; the proposed method usually converges to two distinct roots when the given function has more than one root, that is, the odd iterations of this new technique converge to a root and the even iterations converge to another root. Some numerical examples, including a sine-polynomial equation, are solved by using the proposed method and compared with results obtained by the secant method; perfect agreements are found.

Keywords: Iterative method, root-finding method, sine-polynomial equations, nonlinear equations.

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Authors: Ezzah Liana Ahmad Fauzi, Syakila Ahmad, Ioan Pop

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The steady mixed convection boundary layer flow from a vertical cone in a porous medium filled with a nanofluid is numerically investigated using different types of nanoparticles as Cu (copper), Al2O3 (alumina) and TiO2 (titania). The boundary value problem is solved by using the shooting technique by reducing it into an ordinary differential equation. Results of interest for the local Nusselt number with various values of the constant mixed convection parameter and nanoparticle volume fraction parameter are evaluated. It is found that dual solutions exist for a certain range of mixed convection parameter.

Keywords: boundary layer, mixed convection, nanofluid, porous medium, vertical cone.

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Authors: Chinwendu. B. Eleje, Udechukwu P. Egbuhuzor

Abstract:

One of the difficulties encountered in solving nonlinear Boundary Value Problems (BVP) by many researchers is finding approximated solutions with minimum deviations from the exact solutions without so much rigor and complications. In this paper, we propose an approach to solve a two point BVP which involves a combination of Taylor series expansion method and Newton Raphson method. Furthermore, the fourth and sixth order approximated solutions are obtained and we compare their relative error and rate of convergence to the exact solution. Finally, some numerical simulations are presented to show the behavior of the solution and its derivatives.

Keywords: Newton Raphson method, non-linear boundary value problem, Taylor series approximation, Michaelis-Menten equation.

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Authors: M.A. Kamely, S.M. Kamil, C.W. Chong

Abstract:

A mathematical model of the surface roughness has been developed by using response surface methodology (RSM) in grinding of AISI D2 cold work tool steels. Analysis of variance (ANOVA) was used to check the validity of the model. Low and high value for work speed and feed rate are decided from design of experiment. The influences of all machining parameters on surface roughness have been analyzed based on the developed mathematical model. The developed prediction equation shows that both the feed rate and work speed are the most important factor that influences the surface roughness. The surface roughness was found to be the lowers with the used of low feed rate and low work speed. Accuracy of the best model was proved with the testing data.

Keywords: Mathematical Modeling, Response surfacemethodology, Surface roughness, Cylindrical Grinding.

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Authors: M. K. Moazzam, A. Salmanpour, M. Nirouei

Abstract:

In this paper we have numerically analyzed terahertzrange wavelength conversion using nondegenerate four wave mixing (NDFWM) in a SOA integrated DFB laser (experiments reported both in MIT electronics and Fujitsu research laboratories). For analyzing semiconductor optical amplifier (SOA), we use finitedifference beam propagation method (FDBPM) based on modified nonlinear SchrÖdinger equation and for distributed feedback (DFB) laser we use coupled wave approach. We investigated wavelength conversion up to 4THz probe-pump detuning with conversion efficiency -5dB in 1THz probe-pump detuning for a SOA integrated quantum-well

Keywords: distributed feedback laser, nondegenerate fourwave mixing, semiconductor optical amplifier, wavelengthconversion

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Authors: Shu Lü, Shouming Zhong, Zixin Liu

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In this paper, the robust exponential stability problem of discrete-time uncertain stochastic neural networks with timevarying delays is investigated. By introducing a new augmented Lyapunov function, some delay-dependent stable results are obtained in terms of linear matrix inequality (LMI) technique. Compared with some existing results in the literature, the conservatism of the new criteria is reduced notably. Three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed method.

Keywords: Robust exponential stability, delay-dependent stability, discrete-time neural networks, stochastic, time-varying delays.

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Authors: A. Keshavarz, Z. Roosta

Abstract:

In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: Paraxial group transformation, nonlocal nonlinear media, Cos-Gaussian beam, ABCD law.

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Authors: Sanjeeb Kumar Kar

Abstract:

The optimal control problem of a linear distributed parameter system is studied via shifted Legendre polynomials (SLPs) in this paper. The partial differential equation, representing the linear distributed parameter system, is decomposed into an n - set of ordinary differential equations, the optimal control problem is transformed into a two-point boundary value problem, and the twopoint boundary value problem is reduced to an initial value problem by using SLPs. A recursive algorithm for evaluating optimal control input and output trajectory is developed. The proposed algorithm is computationally simple. An illustrative example is given to show the simplicity of the proposed approach.

Keywords: Optimal control, linear systems, distributed parametersystems, Legendre polynomials.

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Authors: Yusuke Uchiyama, Hidetoshi Konno

Abstract:

We have investigated statistical properties of the defect turbulence in 1D CGLE wherein many body interaction is involved between local depressing wave (LDW) and local standing wave (LSW). It is shown that the counting number fluctuation of LDW is subject to the sub-Poisson statistics (SUBP). The physical origin of the SUBP can be ascribed to pair extinction of LDWs based on the master equation approach. It is also shown that the probability density function (pdf) of inter-LDW distance can be identified by the hyper gamma distribution. Assuming a superstatistics of the exponential distribution (Poisson configuration), a plausible explanation is given. It is shown further that the pdf of amplitude of LDW has a fattail. The underlying mechanism of its fluctuation is examined by introducing a generalized fractional Poisson configuration.

Keywords: sub-Poisson statistics, hyper gamma distribution, fractional Poisson configuration.

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Authors: Saman M. Siddiqui, Fang Jiancheng

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Robust nonlinear integrated navigation of GPS and low cost MEMS is a hot topic of research these days. A robust filter is required to cope up with the problem of unpredictable discontinuities and colored noises associated with low cost sensors. H∞ filter is previously used in Extended Kalman filter and Unscented Kalman filter frame. Unscented Kalman filter has a problem of Cholesky matrix factorization at each step which is a very unstable operation. To avoid this problem in this research H∞ filter is designed in Square root Unscented filter framework and found 50% more robust towards increased level of colored noises.

Keywords: H∞ filter, MEMS, GPS, Nonlinear system, robust system, Square root unscented filter.

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Authors: Chun-Ta Chen, Te-Tan Liao, Hoang-Vuong Pham

Abstract:

In this paper motion analysis on a winding stair-climbing is investigated using our proposed rotational arm type of robotic wheelchair. For now, the robotic wheelchair is operated in an open mode to climb winding stairs by a dynamic turning, therefore, the dynamics model is required to ensure a passenger-s safety. Equations of motion based on the skid-steering analysis are developed for the trajectory planning and motion analysis on climbing winding stairs. Since the robotic wheelchair must climb a winding staircase stably, the winding trajectory becomes a constraint equation to be followed, and the Baumgarte-s method is used to solve for the constrained dynamics equations. Experimental results validate the behavior of the prototype as it climbs a winding stair.

Keywords: Climb, robotic wheelchair, skid-steering, windingstair .

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