Search results for: delay differential equation

Authors: Alireza Lohrasbi, Alireza Lavaei, Mohammadali M. Shahlaei

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The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The method involves a two dimensional finite element (2D), in a vertical plan. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation were used as the governing equations. The mapping developed to solve highly deformed free surface problems common in waves formed during wave propagation, transforms the run up model from the physical domain to a computational domain with Arbitrary Lagrangian Eulerian (ALE) finite element modeling technique.

Keywords: dam break, Naiver-Stokes equations, free-surface flows, Arbitrary Lagrangian-Eulerian

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Authors: Phuoc Si Nguyen

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Infinite impulse response (IIR) filters can be designed from an analogue low pass prototype by using frequency transformation in the s-domain and bilinear z-transformation with pre-warping frequency; this method is known as frequency transformation from the s-domain to the z-domain. This paper will introduce a new method to transform an IIR digital filter to another type of IIR digital filter (low pass, high pass, band pass, band stop or narrow band) using a technique based on inverse bilinear z-transformation and inverse matrices. First, a matrix equation is derived from inverse bilinear z-transformation and Pascal’s triangle. This Low Pass Digital to Digital Filter Pascal Matrix Equation is used to transform a low pass digital filter to other digital filter types. From this equation and the inverse matrix, a Digital to Digital Filter Pascal Matrix Equation can be derived that is able to transform any IIR digital filter. This paper will also introduce some specific matrices to replace the inverse matrix, which is difficult to determine due to the larger size of the matrix in the current method. This will make computing and hand calculation easier when transforming from one IIR digital filter to another in the digital domain.

Keywords: bilinear z-transformation, frequency transformation, inverse bilinear z-transformation, IIR digital filters

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Authors: Balgaisha G. Mukanova, Yelbek B. Utepov, Aida G. Nazarova, Alisher Z. Imanov

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The problem of identifying local noise sources on a construction site using a sensor system is considered. Mathematical modeling of detected signals on sensors was carried out, considering signal decay and signal delay time between the source and detector. Recordings of noises produced by construction tools were used as a dependence of noise on time. Synthetic sensor data was constructed based on these data, and a model of the propagation of acoustic waves from a point source in the three-dimensional space was applied. All sensors and sources are assumed to be located in the same plane. A source localization method is checked based on the signal time delay between two adjacent detectors and plotting the direction of the source. Based on the two direct lines' crossline, the noise source's position is determined. Cases of one dominant source and the case of two sources in the presence of several other sources of lower intensity are considered. The number of detectors varies from three to eight detectors. The intensity of the noise field in the assessed area is plotted. The signal of a two-second duration is considered. The source is located for subsequent parts of the signal with a duration above 0.04 sec; the final result is obtained by computing the average value.

Keywords: acoustic model, direction of arrival, inverse source problem, sound localization, urban noises

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Authors: M. Karami Khorramabadi, A. R. Nezamabadi

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This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: functionally graded beam, free vibration, elastic foundation, Engesser-Timoshenko beam theory

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Authors: Puneet Kumar, Jonnalagadda Srinivas

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The authors report here vibration and buckling analysis of functionally graded carbon nanotube-polymer composite (FG-CNTPC) beams under hygro-thermo-mechanical environments using higher order shear deformation theory. The material properties of CNT and polymer matrix are often affected by temperature and moisture content. A micromechanical model with agglomeration effect is employed to compute the elastic, thermal and moisture properties of the composite beam. The governing differential equation of FG-CNTRPC beam is developed using higher-order shear deformation theory to account shear deformation effects. The elastic, thermal and hygroscopic strain terms are derived from variational principles. Moreover, thermal and hygroscopic loads are determined by considering uniform, linear and sinusoidal variation of temperature and moisture content through the thickness. Differential equations of motion are formulated as an eigenvalue problem using appropriate displacement fields and solved by using finite element modeling. The obtained results of natural frequencies and critical buckling loads show a good agreement with published data. The numerical illustrations elaborate the dynamic as well as buckling behavior under uniaxial load for different environmental conditions, boundary conditions and volume fraction distribution profile, beam slenderness ratio. Further, comparisons are shown at different boundary conditions, temperatures, degree of moisture content, volume fraction as well as agglomeration of CNTs, slenderness ratio of beam for different shear deformation theories.

Keywords: hygrothermal effect, free vibration, buckling load, agglomeration

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Authors: Anuar Ishak

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The characteristics of fluid flow and heat transfer over a permeable shrinking sheet is studied. The governing partial differential equations are transformed into a set of ordinary differential equations, which are then solved numerically using MATLAB routine boundary value problem solver bvp4c. Numerical results show that dual solutions are possible for a certain range of the suction parameter. A stability analysis is performed to determine which solution is linearly stable and physically realizable.

Keywords: dual solutions, heat transfer, shrinking sheet, stability analysis

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Authors: Cagri Mollamahmutoglu, Aykut Levent, Ali Mercan

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Micro-beams are one of the most common components of Nano-Electromechanical Systems (NEMS) and Micro Electromechanical Systems (MEMS). For this reason, static bending, buckling, and free vibration analysis of micro-beams have been the subject of many studies. In addition, micro-beams restrained with elastic type foundations have been of particular interest. In the analysis of microstructures, closed-form solutions are proposed when available, but most of the time solutions are based on numerical methods due to the complex nature of the resulting differential equations. Thus, a robust and efficient solution method has great importance. In this study, a mixed finite element formulation is obtained for a functionally graded Timoshenko micro-beam resting on two-parameter elastic foundation. In the formulation modified couple stress theory is utilized for the micro-scale effects. The equation of motion and boundary conditions are derived according to Hamilton’s principle. A functional, derived through a scientific procedure based on Gateaux Differential, is proposed for the bending and buckling analysis which is equivalent to the governing equations and boundary conditions. Most important advantage of the formulation is that the mixed finite element formulation allows usage of C₀ type continuous shape functions. Thus shear-locking is avoided in a built-in manner. Also, element matrices are sparsely populated and can be easily calculated with closed-form integration. In this framework results concerning the effects of micro-scale length parameter, power-law parameter, aspect ratio and coefficients of partially or fully continuous elastic foundation over the static bending, buckling, and free vibration response of FG-micro-beam under various boundary conditions are presented and compared with existing literature. Performance characteristics of the presented formulation were evaluated concerning other numerical methods such as generalized differential quadrature method (GDQM). It is found that with less computational burden similar convergence characteristics were obtained. Moreover, formulation also includes a direct calculation of the micro-scale related contributions to the structural response as well.

Keywords: micro-beam, functionally graded materials, two-paramater elastic foundation, mixed finite element method

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Authors: Hideki Yoshikawa, Masahiro Kaminaga, Arimitsu Shikoda, Toshinori Suzuki

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Round addition differential fault analysis (DFA) using operation bypassing for lightweight block ciphers with on-the-fly key schedule is presented. For 64-bit KLEIN and 64-bit LED, it is shown that only a pair of correct ciphertext and faulty ciphertext can derive the secret master key. For PRESENT, one correct ciphertext and two faulty ciphertexts are required to reconstruct the secret key.

Keywords: differential fault analysis (DFA), round addition, block cipher, on-the-fly key schedule

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Authors: José Alberto García Fernández, Zhimin Du, Xinqiao Jin

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Nowadays, data center industry faces strong challenges for increasing the speed and data processing capacities while at the same time is trying to keep their devices a suitable working temperature without penalizing that capacity. Consequently, the cooling systems of this kind of facilities use a large amount of energy to dissipate the heat generated inside the servers, and developing new cooling techniques or perfecting those already existing would be a great advance in this type of industry. The installation of a temperature sensor matrix distributed in the structure of each server would provide the necessary information for collecting the required data for obtaining a temperature profile instantly inside them. However, the number of temperature probes required to obtain the temperature profiles with sufficient accuracy is very high and expensive. Therefore, other less intrusive techniques are employed where each point that characterizes the server temperature profile is obtained by solving differential equations through simulation methods, simplifying data collection techniques but increasing the time to obtain results. In order to reduce these calculation times, complicated and slow computational fluid dynamics simulations are replaced by simpler and faster finite element method simulations which solve the Burgers‘ equations by backward, forward and central discretization techniques after simplifying the energy and enthalpy conservation differential equations. The discretization methods employed for solving the first and second order derivatives of the obtained Burgers‘ equation after these simplifications are the key for obtaining results with greater or lesser accuracy regardless of the characteristic truncation error.

Keywords: Burgers' equations, CFD simulation, data center, discretization methods, FEM simulation, temperature profile

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Authors: M. Naveed Akhter, Jawad Aslam, Omer Gillani

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To aid and rehabilitate increasing number of patients suffering from spinal cord injury (SCI) and stroke, a lightweight, wearable, and 3D printable exoskeletal glove has been developed. Unlike previously developed metal or fabric-based exoskeletons, this research presents the development of soft exoskeletal glove made of thermoplastic polyurethane (TPU). The drive mechanism consists of a single motor-driven antagonistic tendon to perform extension or flexion of middle and index finger. The tendon-based differential drive has been incorporated to allow for grasping of irregularly shaped objects. The design features easy 3D-printability with TPU without a need for supports. The overall weight of the glove and the actuation unit is approximately 500g. Performance of the glove was tested on a custom test-bench with integrated load cells, and the grip strength was tested to be around 30N per finger while grasping objects of irregular shape.

Keywords: 3D printable, differential drive, exoskeletal glove, rehabilitation, single motor driven

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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Authors: Hamdi Belgacem, Fradi Aymen

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In this paper we present a low power, low cost differential logic unit (LU). The proposed LU receives dual-rail inputs and generates dual-rail outputs. The proposed circuit can be used in Arithmetic and Logic Units (ALU) of processor. It can be also dedicated for self-checking applications based on dual duplication code. Four logic functions as well as their inverses are implemented within a single Logic Unit. The hardware overhead for the implementation of the proposed LU is lower than the hardware overhead required for standard LU implemented with standard CMOS logic style. This new implementation is attractive as fewer transistors are required to implement important logic functions. The proposed differential logic unit can perform 8 Boolean logical operations by using only 16 transistors. Spice simulations using a 32 nm technology was utilized to evaluate the performance of the proposed circuit and to prove its acceptable electrical behaviour.

Keywords: differential logic unit, double pass transistor logic, low power CMOS design, low cost CMOS design

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Authors: Sergio Haram Sarmiento, Arcady Ponosov

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Based on appropriate multivariate statistical methodology, we suggest a generic framework for efficient parameter estimation for ordinary differential equations and the corresponding nonlinear models. In this framework classical linear regression strategies is refined into a nonlinear regression by a locally linear modelling technique (known as metamodelling). The approach identifies those latent variables of the given model that accumulate most information about it among all approximations of the same dimension. The method is applied to several benchmark problems, in particular, to the so-called ”power-law systems”, being non-linear differential equations typically used in Biochemical System Theory.

Keywords: principal component analysis, generalized law of mass action, parameter estimation, metamodels

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Authors: Shih-Hao Chen, Chi-Wai Chow

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Visible light communication combined with spread spectrum modulation is demonstrated in this study. Differential signaling method also ensures the proposed system that can support high immunity to ambient light interference. Experiment result shows the proposed system has 6 dB gain comparing with the original On-Off Keying modulation scheme.

Keywords: Visible Light Communication (VLC), Spread Spectrum Modulation (SSM), On-Off Keying, visible light communication

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

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Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation

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Authors: Manoj Kumar Dutta

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Wavelength division multiplexing (WDM) technology is the most promising technology for the proper utilization of huge raw bandwidth provided by an optical fiber. One of the key problems in implementing the all-optical WDM network is the packet contention. This problem can be solved by several different techniques. In time domain approach the packet contention can be reduced by incorporating fiber delay lines (FDLs) as optical buffer in the switch architecture. Different types of buffering architectures are reported in literatures. In the present paper a comparative performance analysis of three most popular FDL architectures are presented in order to obtain the best contention resolution performance. The analysis is further extended to consider the effect of different fiber non-linearities on the network performance.

Keywords: WDM network, contention resolution, optical buffering, non-linearity, throughput

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Authors: Avelino Marques, Diamantino Freitas

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Some important electroacoustic systems, like loudspeaker systems, exhibit a nonminimum phase behavior that poses considerable effort when applying advanced digital signal processing techniques, such as linear equalization. In this paper, the position and the number of zeros and poles of the inverse filter, FIR type or IIR type, designed using time domain techniques, are studied, compared and related to the nonminimum phase zeros of system to be equalized. Conclusions about the impact of the position of the system non-minimum phase zeros, on the length/order of the inverse filter and on the delay of the equalized system are outlined as a guide to previously decide which type of filter will be more adequate.

Keywords: loudspeaker systems, nonminimum phase system, FIR and IIR filter, delay

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Authors: Avinash Nayak, Debopam Das

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The current work implements the variational principle to find the optimum initial perturbation that provides maximum growth in an impulsively blocked channel flow. The conventional method for studying temporal stability has always been through modal analysis. In most of the transient flows, this modal analysis is still followed with the quasi-steady assumption, i.e. change in base flow is much slower compared to perturbation growth rate. There are other studies where transient analysis on time dependent flows is done by formulating the growth of perturbation as an initial value problem. But the perturbation growth is sensitive to the initial condition. This study intends to find the initial perturbation that provides the maximum growth at a later time. Here, the expression of base flow for blocked channel is derived and the formulation is based on the two dimensional perturbation with stream function representing the perturbation quantity. Hence, the governing equation becomes the Orr-Sommerfeld equation. In the current context, the cost functional is defined as the ratio of disturbance energy at a terminal time 'T' to the initial energy, i.e. G(T) = ||q(T)||2/||q(0)||2 where q is the perturbation and ||.|| defines the norm chosen. The above cost functional needs to be maximized against the initial perturbation distribution. It is achieved with the constraint that perturbation follows the basic governing equation, i.e. Orr-Sommerfeld equation. The corresponding adjoint equation is derived and is solved along with the basic governing equation in an iterative manner to provide the initial spatial shape of the perturbation that provides the maximum growth G (T). The growth rate is plotted against time showing the development of perturbation which achieves an asymptotic shape. The effects of various parameters, e.g. Reynolds number, are studied in the process. Thus, the study emphasizes on the usage of optimal perturbation and its growth to understand the stability characteristics of time dependent flows. The assumption of quasi-steady analysis can be verified against these results for the transient flows like impulsive blocked channel flow.

Keywords: blocked channel flow, calculus of variation, hydrodynamic stability, optimal perturbation

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Authors: S. Gherbi, F. Bouchareb

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This paper deals with the novel intelligent bio-inspired control strategies, it presents a novel approach based on an optimal fuzzy immune PID parameters tuning, it is a combination of a PID controller, inspired by the human immune mechanism with fuzzy logic. Such controller offers more possibilities to deal with the delayed systems control difficulties due to the delay term. Indeed, we use an optimization approach to tune the four parameters of the controller in addition to the fuzzy function; the obtained controller is implemented in a modified Smith predictor structure, which is well known that it is the most efficient to the control of delayed systems. The application of the presented approach to control a three tank delay system shows good performances and proves the efficiency of the method.

Keywords: delayed systems, fuzzy immune PID, optimization, Smith predictor

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Authors: Mokhtar Labiod, Nabil Ikhlef, Keltoum Bouherine, Olivier Leroy

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A numerical model for the radio-frequency (RF) Argon discharge chamber is developed to simulate the low pressure low temperature inductively coupled plasma. This model will be of fundamental importance in the design of the plasma magnetic control system. Electric and magnetic fields inside the discharge chamber are evaluated by solving a magnetic vector potential equation. To start with, the equations of the ideal magnetohydrodynamics theory will be presented describing the basic behaviour of magnetically confined plasma and equations are discretized with finite element method in cylindrical coordinates. The discharge chamber is assumed to be axially symmetric and the plasma is treated as a compressible gas. Plasma generation due to ionization is added to the continuity equation. Magnetic vector potential equation is solved for the electromagnetic fields. A strong dependence of the plasma properties on the discharge conditions and the gas temperature is obtained.

Keywords: direct-coupled model, magnetohydrodynamic, modelling, plasma torch simulation

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Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

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In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation

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Authors: Aisha Iddrisu

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The proliferation of cyberviolence in the wave of increased social media consumption calls for immediate attention both at the local and global levels. With over 4.70 billion social media users worldwide and 8.8 social media users in Ghana, various forms of violence have become the order of the day in most countries and communities. Cyber violence is defined as producing, retrieving, and sharing of hurtful or dangerous online content to cause emotional, psychological, or physical harm. The urgency and severity of cyber violence have led to the enactment of laws in various countries though lots still need to be done, especially in Ghana. In Ghana, studies on cyber violence have not been extensively dealt with. Existing studies concentrate only on one form or the other form of cyber violence, thus cybercrime and cyber bullying. Also, most studies in Africa have not explored cyber violence forms using empirical theories and the few that existed were qualitatively researched, whereas others examine the effect of cyber violence rather than examining why those who involve in it behave the way they behave. It is against this backdrop that this study aims to examine various cyber violence behaviour among social media users in Ghana by applying the theory of Self-control and Social control theory. This study is important for the following reasons. The outcome of this research will help at both national and international level of policymaking by adding to the knowledge of understanding cyberviolence and why people engage in various forms of cyberviolence. It will also help expose other ways by which such behaviours are enforced thereby serving as a guide in the enactment of the rightful rules and laws to curb such behaviours. It will add to literature on consequences of new media. This study seeks to confirm or reject to the following research hypotheses. H1 Social media usage has direct significant effect of cyberviolence behaviours. H2 Ineffective parental management has direct significant positive relation to Low self-control. H3 Low self-control has direct significant positive effect on cyber violence behaviours among social, H4 Differential association has significant positive effect on cyberviolence behaviour among social media users in Ghana. H5 Definitions have a significant positive effect on cyberviolence behaviour among social media users in Ghana. H6 Imitation has a significant positive effect on cyberviolence behaviour among social media users in Ghana. H7 Differential reinforcement has a significant positive effect on cyberviolence behaviour among social media users in Ghana. H8 Differential association has a significant positive effect on definitions. H9 Differential association has a significant positive effect on imitation. H10 Differential association has a significant positive effect on differential reinforcement. H11 Differential association has significant indirect positive effects on cyberviolence through the learning process.

Keywords: cyberviolence, social media users, self-control theory, social learning theory

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Authors: Ahmed Machmoum, Malika El Kyal

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We consider 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 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 tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems

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Authors: Saidu Ibrahim, Winston M. W. Shakantu

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The problem of construction material waste remains unresolved, as a significant percentage of the materials delivered to some project sites end up as waste which might result in additional project cost. Cost overrun is a problem which affects 90% of the completed projects in the world. The argument on how to eliminate it has been on-going for the past 70 years, but there is neither substantial improvement nor significant solution for mitigating its detrimental effects. Research evidence has proposed various construction cost overruns and material-waste management approaches; nonetheless, these studies failed to give a clear indication on the framework and the equation for managing construction material waste and cost overruns. Hence, this research aims to develop a conceptual framework and a mathematical equation for managing material waste and cost overrun in the construction industry. The paper adopts the desktop methodological approach. This involves comparing the causes of material waste and those of cost overruns from the literature to determine the possible relationship. The review revealed a relationship between material waste and cost overrun that; increase in material waste would result to a corresponding increase in the amount of cost overrun at both the pre-contract and the post contract stages of a project. It was found from the equation that achieving an effective construction material waste management must ensure a “Good Quality-of-Planning, Estimating, and Design Management” and a “Good Quality- of-Construction, Procurement and Site Management”; a decrease in “Design Complexity” which would reduce “Material Waste” and subsequently reduce the amount of cost overrun by 86.74%. The conceptual framework and the mathematical equation developed in this study are recommended to the professionals of the construction industry.

Keywords: conceptual framework, cost overrun, material waste, project stags

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Authors: Kyoungjin Kim

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Nanoscale thermites such as the composite mixture of nano-sized aluminum and molybdenum trioxide powders possess several technical advantages such as much higher reaction rate and shorter ignition delay, when compared to the conventional energetic formulations made of micron-sized metal and oxidizer particles. In this study, the self-propagation of combustion wave in compacted pellets of nanoscale thermite composites is modeled and computationally investigated by utilizing the activation energy reduction of aluminum particles due to nanoscale particle sizes. The present computational model predicts the speed of combustion wave propagation which is good agreement with the corresponding experiments of thermite reaction. Also, several characteristics of thermite reaction in nanoscale composites are discussed including the ignition delay and combustion wave structures.

Keywords: nanoparticles, thermite reaction, combustion wave, numerical modeling

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Authors: Luke Ukpebor, C. E. Abhulimen

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Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy.

Keywords: A-stable, exponentially fitted, four step, predator-corrector, second derivative, stiff initial value problems

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Authors: Adriano Valdes-Gomez, Francisco Javier Sevilla

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We devise a numerical algorithm to simulate the diffusion of a Brownian particle restricted to the surface of a three-dimensional sphere when the particle is under the effects of an external potential that is coupled linearly. It is obtained using elementary geometry, yet, it converges, in the weak sense, to the solutions to the Smoluchowski equation. Rotations on the sphere, which are the analogs of linear displacements in euclidean spaces, are calculated using algebraic operations and then by a proper scaling, which makes the algorithm efficient and quite simple, especially to what may be the short-time propagator approach. Our findings prove that the global effects of curvature are taken into account in both dynamic and stationary processes, and it is not restricted to work in configuration space, neither restricted to the overdamped limit. We have generalized it successfully to simulate the Kramers or the Ornstein-Uhlenbeck process, where it is necessary to work directly in phase space, and it may be adapted to other two dimensional surfaces with non-constant curvature.

Keywords: diffusion on the sphere, Fokker-Planck equation on the sphere, non equilibrium processes on the sphere, numerical methods for diffusion on the sphere

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Authors: Ibrahim M. Mehedi, Uzair Ansari, Ubaid M. Al-Saggaf, Abdulrahman H. Bajodah

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This paper presents a methodology for balancing a rotary inverted pendulum system using Robust Generalized Dynamic Inversion (RGDI) under influence of parametric variations and external disturbances. In GDI control, dynamic constraints are formulated in the form of asymptotically stable differential equation which encapsulates the control objectives. The constraint differential equations are based on the deviation function of the angular position and its rates from their reference values. The constraint dynamics are inverted using Moore-Penrose Generalized Inverse (MPGI) to realize the control expression. The GDI singularity problem is addressed by augmenting a dynamic scale factor in the interpretation of MPGI which guarantee asymptotically stable position tracking. An additional term based on Sliding Mode Control is appended within GDI control to make it robust against parametric variations, disturbances and tracking performance deterioration due to generalized inversion scaling. The stability of the closed loop system is ensured by using positive definite Lyapunov energy function that guarantees semi-global practically stable position tracking. Numerical simulations are conducted on the dynamic model of rotary inverted pendulum system to analyze the efficiency of proposed RGDI control law. The comparative study is also presented, in which the performance of RGDI control is compared with Linear Quadratic Regulator (LQR) and is verified through experiments. Numerical simulations and real-time experiments demonstrate better tracking performance abilities and robustness features of RGDI control in the presence of parametric uncertainties and disturbances.

Keywords: generalized dynamic inversion, lyapunov stability, rotary inverted pendulum system, sliding mode control

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Authors: Kankrong Suangka

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This research explored behaviors of toll way users that impact their decision to use the Electronic Toll Collection System (ETC). It also went on to explore and evaluated the efficiency of toll plaza in terms of number of ETC booths in toll plaza and its lane location. The two main parameters selected for the scenarios analyzed were (1) the varying ration of ETC enabled users (2) the varying locations of the dedicated ETC lane. There were a total of 42 scenarios analyzed. Researched data indicated that in A.D.2013, the percentage of ETC user from the total toll user is 22%. It was found that the delay at the payment booth was reduced by increasing the ETC booth by 1 more lane under the condition that the volume of ETC users passing through the plaza less than 1,200 vehicles/hour. Meanwhile, increasing the ETC lanes by 2 lanes can accommodate an increased traffic volume to around 1,200 to 1,800 vehicles/hour. Other than that, in terms of the location of ETC lane, it was found that if for one ETC lane-plazas, installing the ETC lane at the far right are the best alternative. For toll plazas with 2 ETC lanes, the best layout is to have 1 lane in the middle and 1 lane at the far right. This layout shows the least delay when compared to other layouts. Furthermore, the results from this research showed that micro-simulator traffic models have potential for further applications and use in designing toll plaza lanes. Other than that, the results can also be used to analyze the system of the nearby area with similar traffic volume and can be used for further design improvements.

Keywords: the electronic toll collection system, average queuing delay, toll plaza configuration, bioinformatics, biomedicine

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Authors: M. Kumpugdee-Vollrath, M. Tabatabaeifar, M. Helmis

Abstract:

Shellac is a natural polyester resin secreted by insects. Pectins are natural, non-toxic and water-soluble polysaccharides extracted from the peels of citrus fruits or the leftovers of apples. Both polymers are allowed for the use in the pharmaceutical industry and as a food additive. SSB Aquagold® is the aqueous solution of shellac and can be used for a coating process as an enteric or controlled drug release polymer. In this study, tablets containing 10 mg methylene blue as a model drug were prepared with a rotary press. Those tablets were coated with mixtures of shellac and one of the pectin different types (i.e. CU 201, CU 501, CU 701 and CU 020) mostly in a 2:1 ratio or with pure shellac in a small scale fluidized bed apparatus. A stable, simple and reproducible three-stage coating process was successfully developed. The drug contents of the coated tablets were determined using UV-VIS spectrophotometer. The characterization of the surface and the film thickness were performed with the scanning electron microscopy (SEM) and the light microscopy. Release studies were performed in a dissolution apparatus with a basket. Most of the formulations were enteric coated. The dissolution profiles showed a delayed or sustained release with a lagtime of at least 4 h. Dissolution profiles of coated tablets with pure shellac had a very long lagtime ranging from 13 to 17.5 h and the slopes were quite high. The duration of the lagtime and the slope of the dissolution profiles could be adjusted by adding the proper type of pectin to the shellac formulation and by variation of the coating amount. In order to apply a coating formulation as a colon delivery system, the prepared film should be resistant against gastric fluid for at least 2 h and against intestinal fluid for 4-6 h. The required delay time was gained with most of the shellac-pectin polymer mixtures. The release profiles were fitted with the modified model of the Korsmeyer-Peppas equation and the Hixson-Crowell model. A correlation coefficient (R²) > 0.99 was obtained by Korsmeyer-Peppas equation.

Keywords: shellac, pectin, coating, fluidized bed, release, colon delivery system, kinetic, SEM, methylene blue

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