Search results for: mathematical method

Authors: Maryam Khazaei Pool, Lori Lewis

Abstract:

This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions including Burgers equation, spline functions, and B-spline functions are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ Equation, Septic B-spline, Modified Cubic B-Spline Differential Quadrature Method, Exponential Cubic B-Spline Technique, B-Spline Galerkin Method, and Quintic B-Spline Galerkin Method.

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Authors: Mohsen Keyvanfard

Abstract:

A new, simple and highly sensitive kinetic spectrophotometric method was developed for the determination of trace amounts of Ru(III) in the range of 0.06-20 ng/ml .The method is based on the inhibitory effect of ruthenium(III) on the oxidation of Rhodamine B by bromate in acidic and micellar medium. The reaction was monitored spectrophotometrically by measuring the decreasing in absorbance of Rhodamine B at 554 nm with a fixedtime method..The limit of detection is 0.04 ng/ml Ru(III).The relative standard deviation of 5 and 10 ng/ml Ru(III) was 2.3 and 2.7 %, respectively. The method was applied to the determination of ruthenium in real water samples

Keywords: Ruthenium ;Inhibitory; Rhodamine B; bromate

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Authors: Taiyo Matsumura, Kuninori Takahashi, Takashi Ono

Abstract:

The purpose of this research is to improve the convenience of waiting for trains at level crossings and stations and to prevent accidents resulting from forcible entry into level crossings, by providing level crossing users and passengers with information that tells them when the next train will pass through or arrive. For this paper, we proposed methods for estimating operation by means of an average value method, variable response smoothing method, and exponential smoothing method, on the basis of open data, which has low accuracy, but for which performance schedules are distributed in real time. We then examined the accuracy of the estimations. The results showed that the application of an exponential smoothing method is valid.

Keywords: Exponential smoothing method, open data, operation estimation, train schedule.

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Authors: J. A. Michline Rupa, S. Ganesh

Abstract:

This paper proposes a backward/forward sweep method to analyze the power flow in radial distribution systems. The distribution system has radial structure and high R/X ratios. So the newton-raphson and fast decoupled methods are failed with distribution system. The proposed method presents a load flow study using backward/forward sweep method, which is one of the most effective methods for the load-flow analysis of the radial distribution system. By using this method, power losses for each bus branch and voltage magnitudes for each bus node are determined. This method has been tested on IEEE 33-bus radial distribution system and effective results are obtained using MATLAB.

Keywords: Backward/Forward sweep method, Distribution system, Load flow analysis.

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Authors: Hans H. Diel

Abstract:

A computer model of Quantum Theory (QT) has been developed by the author. Major goal of the computer model was support and demonstration of an as large as possible scope of QT. This includes simulations for the major QT (Gedanken-) experiments such as, for example, the famous double-slit experiment. Besides the anticipated difficulties with (1) transforming exacting mathematics into a computer program, two further types of problems showed up, namely (2) areas where QT provides a complete mathematical formalism, but when it comes to concrete applications the equations are not solvable at all, or only with extremely high effort; (3) QT rules which are formulated in natural language and which do not seem to be translatable to precise mathematical expressions, nor to a computer program. The paper lists problems in all three categories and describes also the possible solutions or circumventions developed for the computer model.

Keywords: Computability, Foundation of Quantum Mechanics, Measurement Process, Modeling.

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Authors: Young Kuen Cho, Dae Won Lee, Young-Jin Jung, Sung Kuk Kim, Dong-Hyun Seo, Chang-Yong Ko, Han Sung Kim

Abstract:

Many medical devices are driven by motor pumps. Some researchers reported that the vibration mainly affected medical devices using a motor pump. The purpose of this study was to examine the effect of stiffness and damping coefficient in a 3-dimensional (3D) model of a motor pump and spring. In the present paper, experimental and mathematical tests for the moments of inertia of the 3D model and the material properties were investigated by an INSTRON machine. The response surfaces could be generated by using 3D multi-body analysis and the design of experiment method. It showed that differences in contours of the response surface were clearly found for the particular area. Displacement of the center of the motor pump was decreased at K≈2000 N/M, C≈12.5 N-sec/M. However, the frequency was increased at K≈2000 N/M, C≈15 N-sec/M. In this study, this study suggested experimental technique for vibration reduction for a motor pump in medical device. The combined method suggested in this study will greatly contribute to design of medical devices concerning vibration and noise intervention.

Keywords: Motor pump, Spring, Vibration reduction, Medicaldevices, Moment of Inertia

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Authors: Ruiheng Li, Amir Parsa Anvar, Amir M. Anvar, Tien-Fu Lu

Abstract:

High redundancy and strong uncertainty are two main characteristics for underwater robotic manipulators with unlimited workspace and mobility, but they also make the motion planning and control difficult and complex. In order to setup the groundwork for the research on control schemes, the mathematical representation is built by using the Denavit-Hartenberg (D-H) method [9]&[12]; in addition to the geometry of the manipulator which was studied for establishing the direct and inverse kinematics. Then, the dynamic model is developed and used by employing the Lagrange theorem. Furthermore, derivation and computer simulation is accomplished using the MATLAB environment. The result obtained is compared with mechanical system dynamics analysis software, ADAMS. In addition, the creation of intelligent artificial skin using Interlink Force Sensing ResistorTM technology is presented as groundwork for future work

Keywords: Manipulator System, Robot, AUV, Denavit- Hartenberg method Lagrange theorem, MALTAB, ADAMS, Direct and Inverse Kinematics, Dynamics, PD Control-law, Interlink Force Sensing ResistorTM, intelligent artificial skin system.

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Authors: İnci M. Erhan

Abstract:

A numerical method for solving the time-independent Schrödinger equation of a particle moving freely in a three-dimensional axisymmetric region is developed. The boundary of the region is defined by an arbitrary analytic function. The method uses a coordinate transformation and an expansion in eigenfunctions. The effectiveness is checked and confirmed by applying the method to a particular example, which is a prolate spheroid.

Keywords: Bessel functions, Eigenfunction expansion, Quantum billiard, Schrödinger equation, Spherical harmonics

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Authors: A. Nikkar, M. Mighani

Abstract:

In this study, a new reliable technique use to handle the foam drainage equation. This new method is resulted from VIM by a simple modification that is Reconstruction of Variational Iteration Method (RVIM). The drainage of liquid foams involves the interplay of gravity, surface tension, and viscous forces. Foaming occurs in many distillation and absorption processes. Results are compared with those of Adomian’s decomposition method (ADM).The comparisons show that the Reconstruction of Variational Iteration Method is very effective and overcome the difficulty of traditional methods and quite accurate to systems of non-linear partial differential equations.

Keywords: Reconstruction of Variational Iteration Method (RVIM), Foam drainage, nonlinear partial differential equation.

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Authors: Li Jiang, Baoguang Tian

Abstract:

In this paper, we present the preconditioned mixed-type splitting iterative method for solving the linear systems, Ax = b, where A is a Z-matrix. And we give some comparison theorems to show that the convergence rate of the preconditioned mixed-type splitting iterative method is faster than that of the mixed-type splitting iterative method. Finally, we give a numerical example to illustrate our results.

Keywords: Z-matrix, mixed-type splitting iterative method, precondition, comparison theorem, linear system.

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Authors: N. M. Nusi, M. Othman, M. Suleiman, F. Ismail, N. Alias

Abstract:

In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximum time step size and more accurate than the conventional finite difference time domain (FDTD) method and other existing method of natural ordering.

Keywords: FDTD, Scalar wave equation, alternating direction implicit (ADI), alternating group explicit (AGE), asymmetric approximation.

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Authors: H. Alaleh, N. Hedayat, A. Alaleh, H. Ayazi, A. Ruhani

Abstract:

Run-offs are considered as important hydrological factors in feasibility studies of river engineering and irrigation-related projects under arid and semi-arid condition. Flood control is one of the crucial factor, the management of which while mitigates its destructive consequences, abstracts considerable volume of renewable water resources. The methodology applied here was based on Mizumura, which applied a mathematical model for simple tank to simulate the rainfall-run-off process in a particular water basin using the data from the observational hydrograph. The model was applied in the Dez River water basin adjacent to Greater Dezful region, Iran in order to simulate and estimate the floods. Results indicated that the calculated hydrographs using the simple tank method, SCS-CN model and the observation hydrographs had a close proximity. It was also found that on average the flood time and discharge peaks in the simple tank were closer to the observational data than the CN method. On the other hand, the calculated flood volume in the CN model was significantly closer to the observational data than the simple tank model.

Keywords: Simple tank, Dez River, run-off, lag time, excess rainfall.

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Authors: Fahad Alsharari, Mohd Salmi Md Noorani

Abstract:

A Motzkin shift is a mathematical model for constraints on genetic sequences. In terms of the theory of symbolic dynamics, the Motzkin shift is nonsofic, and therefore, we cannot use the Perron- Frobenius theory to calculate its topological entropy. The Motzkin shift M(M,N) which comes from language theory, is defined to be the shift system over an alphabet A that consists of N negative symbols, N positive symbols and M neutral symbols. For an x in the full shift, x will be in the Motzkin subshift M(M,N) if and only if every finite block appearing in x has a non-zero reduced form. Therefore, the constraint for x cannot be bounded in length. K. Inoue has shown that the entropy of the Motzkin shift M(M,N) is log(M + N + 1). In this paper, a new direct method of calculating the topological entropy of the Motzkin shift is given without any measure theoretical discussion.

Keywords: Motzkin shift, topological entropy.

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Authors: Nicolay Zarutskiy, Roman Bulkin

Abstract:

The paper deals with the existing methods of force-torque sensor calibration with a number of components from one to six, analyzed their advantages and disadvantages, the necessity of introduction of a calibration method. Calibration method and its constructive realization are also described here. A calibration method allows performing automated force-torque sensor calibration both with selected components of the main vector of forces and moments and with complex loading. Thus, two main advantages of the proposed calibration method are achieved: the automation of the calibration process and universality.

Keywords: Automation, calibration, calibration device, calibration method, force-torque sensors.

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Authors: Danni Cong, Meiping Wu, Hua Mu, Xiaofeng He, Junxiang Lian, Juliang Cao, Shaokun Cai, Hao Qin

Abstract:

Gravity field is of great significance in geoscience, national economy and national security, and gravitational gradient measurement has been extensively studied due to its higher accuracy than gravity measurement. Gravity gradient sensor, being one of core devices of the gravity gradient instrument, plays a key role in measuring accuracy. Therefore, this paper starts from analyzing the working principle of the gravity gradient sensor by Newton’s law, and then considers the relative motion between inertial and non-inertial systems to build a relatively adequate mathematical model, laying a foundation for the measurement error calibration, measurement accuracy improvement.

Keywords: Gravity gradient, accelerometer, gravity gradient sensor, single-axis rotation modulation.

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Authors: S. A. Eftekhari

Abstract:

In this paper, a numerical algorithm using a coupled Galerkin-Differential Quadrature (DQ) method is proposed for the solution of dam-reservoir interaction problem. The governing differential equation of motion of the dam structure is discretized by the Galerkin method and the DQM is used to discretize the fluid domain. The resulting systems of ordinary differential equations are then solved by the Newmark time integration scheme. The mixed scheme combines the simplicity of the Galerkin method and high accuracy and efficiency of the DQ method. Its accuracy and efficiency are demonstrated by comparing the calculated results with those of the existing literature. It is shown that highly accurate results can be obtained using a small number of Galerkin terms and DQM sampling points. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.

Keywords: Dam-reservoir system, Differential quadrature method, Fluid-structure interaction, Galerkin method, Integral quadrature method.

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Authors: Rujira Kongnuy, Puntani Pongsumpun, I-Ming Tang

Abstract:

Mathematical models can be used to describe the dynamics of the spread of infectious disease between susceptibles and infectious populations. Dengue fever is a re-emerging disease in the tropical and subtropical regions of the world. Its incidence has increased fourfold since 1970 and outbreaks are now reported quite frequently from many parts of the world. In dengue endemic regions, more cases of dengue infection in pregnancy and infancy are being found due to the increasing incidence. It has been reported that dengue infection was vertically transmitted to the infants. Primary dengue infection is associated with mild to high fever, headache, muscle pain and skin rash. Immune response includes IgM antibodies produced by the 5th day of symptoms and persist for 30-60 days. IgG antibodies appear on the 14th day and persist for life. Secondary infections often result in high fever and in many cases with hemorrhagic events and circulatory failure. In the present paper, a mathematical model is proposed to simulate the succession of dengue disease transmission in pregnancy and infancy. Stability analysis of the equilibrium points is carried out and a simulation is given for the different sets of parameter. Moreover, the bifurcation diagrams of our model are discussed. The controlling of this disease in infant cases is introduced in the term of the threshold condition.

Keywords: Dengue infection, equilibrium states, maternalantibodies, pregnancy and infancy.

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Authors: Xijian Wang

Abstract:

This paper is concerned with the numerical minimization of energy functionals in BV ( ) (the space of bounded variation functions) involving total variation for gray-scale 1-dimensional inpainting problem. Applications are shown by finite element method and discontinuous Galerkin method for total variation minimization. We include the numerical examples which show the different recovery image by these two methods.

Keywords: finite element method, discontinuous Galerkin method, total variation minimization, inpainting

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Authors: M. Ziółkowska, J. T. Duda, J. Milewska-Duda

Abstract:

This paper describes an approach to the adsorption phenomena modeling aimed at specifying the adsorption mechanisms on localized or nonlocalized adsorbent sites, when applied to the nanocarbons. The concept comes from the fundamental thermodynamic description of adsorption equilibrium and is based on numerical calculations of the hydrogen adsorbed particles volume on the surface of selected nanocarbons: single-walled nanotube and nanocone. This approach enables to obtain information on adsorption mechanism and then as a consequence to take appropriate mathematical adsorption model, thus allowing for a more reliable identification of the material porous structure. Theoretical basis of the approach is discussed and newly derived results of the numerical calculations are presented for the selected nanocarbons.

Keywords: Adsorption, mathematical modeling, nanocarbons, numerical analysis.

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Authors: Faranak Rabiei, Fudziah Ismail, S. Norazak, Saeid Emadi

Abstract:

In this paper we developed the Improved Runge-Kutta Nystrom (IRKN) method for solving second order ordinary differential equations. The methods are two step in nature and require lower number of function evaluations per step compared with the existing Runge-Kutta Nystrom (RKN) methods. Therefore, the methods are computationally more efficient at achieving the higher order of local accuracy. Algebraic order conditions of the method are obtained and the third and fourth order method are derived with two and three stages respectively. The numerical results are given to illustrate the efficiency of the proposed method compared to the existing RKN methods.

Keywords: Improved Runge-Kutta Nystrom method, Two step method, Second-order ordinary differential equations, Order conditions

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Authors: Montri Maleewong, Sirod Sirisup

Abstract:

The POD-assisted projective integration method based on the equation-free framework is presented in this paper. The method is essentially based on the slow manifold governing of given system. We have applied two variants which are the “on-line" and “off-line" methods for solving the one-dimensional viscous Bergers- equation. For the on-line method, we have computed the slow manifold by extracting the POD modes and used them on-the-fly along the projective integration process without assuming knowledge of the underlying slow manifold. In contrast, the underlying slow manifold must be computed prior to the projective integration process for the off-line method. The projective step is performed by the forward Euler method. Numerical experiments show that for the case of nonperiodic system, the on-line method is more efficient than the off-line method. Besides, the online approach is more realistic when apply the POD-assisted projective integration method to solve any systems. The critical value of the projective time step which directly limits the efficiency of both methods is also shown.

Keywords: Projective integration, POD method, equation-free.

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Authors: Océane Grosset, Charles Pézerat, Jean-Hugh Thomas, Frédéric Ablitzer

Abstract:

This paper presents a method to take into account the fluid-structure coupling into an inverse method, the Force Analysis Technique (FAT). The FAT method, also called RIFF method (Filtered Windowed Inverse Resolution), allows to identify the force distribution from local vibration field. In order to only identify the external force applied on a structure, it is necessary to quantify the fluid-structure coupling, especially in naval application, where the fluid is heavy. This method can be decomposed in two parts, the first one consists in identifying the fluid-structure coupling and the second one to introduced it in the FAT method to reconstruct the external force. Results of simulations on a plate coupled with a cavity filled with water are presented.

Keywords: Fluid-structure coupling, inverse methods, naval, vibrations.

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Authors: Beata Jackowska-Zduniak

Abstract:

We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism).

Keywords: Mathematical modeling, ordinary differential equations, endocrine system, stability analysis.

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Authors: I. López , J. Garay, R. Carreño, Z. Varga

Abstract:

Monitoring of ecological systems is one of the major issues in ecosystem research. The concepts and methodology of mathematical systems theory provide useful tools to face this problem. In many cases, state monitoring of a complex ecological system consists in observation (measurement) of certain state variables, and the whole state process has to be determined from the observed data. The solution proposed in the paper is the design of an observer system, which makes it possible to approximately recover the state process from its partial observation. The method is illustrated with a trophic chain of resource – producer – primary consumer type and a numerical example is also presented.

Keywords: Monitoring, observer system, trophic chain

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Authors: Anton A. Larenkov, Alesya Ya Maruk

Abstract:

In the present study, highly effective iTLC single strip method for the determination of radiochemical purity (RCP) of ⁶⁸Ga-BCA-peptides was developed (with no double-developing, changing of eluents or other additional manipulation). In this method iTLC-SG strips and commonly used eluent TFA_aq. (3-5 % (v/v)) are used. The method allows determining each of the key radiochemical forms of ⁶⁸Ga (colloidal, bound, ionic) separately with the peaks separation being no less than 4 σ. Rf = 0.0-0.1 for ⁶⁸Ga-colloid; Rf = 0.5-0.6 for ⁶⁸Ga-BCA-peptides; Rf = 0.9-1.0 for ionic ⁶⁸Ga. The method is simple and fast: For developing length of 75 mm only 4-6 min is required (versus 18-20 min for pharmacopoeial method). The method has been tested on various compounds (including ⁶⁸Ga-DOTA-TOC, ⁶⁸Ga-DOTA-TATE, ⁶⁸Ga-NODAGA-RGD₂ etc.). The cross-validation work for every specific form of ⁶⁸Ga showed good correlation between method developed and control (pharmacopoeial) methods. The method can become convenient and much more informative replacement for pharmacopoeial methods, including HPLC.

Keywords: DOTA-TATE, 68Ga, quality control, radiochemical purity, radiopharmaceuticals, iTLC.

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Authors: Naren Bag, S. Bhattacharyya, Partha P. Gopmandal

Abstract:

In this study, we have analyzed the transport of analytes under a two dimensional steady incompressible flow of power-law fluids through rectangular nanochannel. A mathematical model based on the Cauchy momentum-Nernst-Planck-Poisson equations is considered to study the combined effect of mixed electroosmotic (EO) and pressure driven (PD) flow. The coupled governing equations are solved numerically by finite volume method. We have studied extensively the effect of key parameters, e.g., flow behavior index, concentration of the electrolyte, surface potential, imposed pressure gradient and imposed electric field strength on the net average flow across the channel. In addition to study the effect of mixed EOF and PD on the analyte distribution across the channel, we consider a nonlinear model based on general convective-diffusion-electromigration equation. We have also presented the retention factor for various values of electrolyte concentration and flow behavior index.

Keywords: Electric double layer, finite volume method, flow behavior index, mixed electroosmotic/pressure driven flow, Non-Newtonian power-law fluids, numerical simulation.

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Authors: M. Faraji, F. Berroug

Abstract:

A one-dimensional mathematical model was developed in order to analyze and optimize the latent heat storage wall. The governing equations for energy transport were developed by using the enthalpy method and discretized with volume control scheme. The resulting algebraic equations were next solved iteratively by using TDMA algorithm. A series of numerical investigations were conducted in order to examine the effects of the thickness of the PCM layer on the thermal behavior of the proposed heating system. Results are obtained for thermal gain and temperature fluctuation. The charging discharging process was also presented and analyzed.

Keywords: Phase change material, Building, Concrete, Latent heat, Thermal control.

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Authors: Xiaohui Han, Yuhan Wang, Jing Shi

Abstract:

This paper proposed a stiffness analysis method for a 3-PRS mechanism for welding thick aluminum plate using FSW technology. In the molding process, elastic deformation of lead-screws and links are taken into account. This method is based on the virtual work principle. Through a survey of the commonly used stiffness performance indices, the minimum and maximum eigenvalues of the stiffness matrix are used to evaluate the stiffness of the 3-PRS mechanism. Furthermore, A FEA model has been constructed to verify the method. Finally, we redefined the workspace using the stiffness analysis method.

Keywords: 3-PRS, parallel mechanism, stiffness analysis, workspace.

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Authors: Abdolali Basiri

Abstract:

In this paper we present an efficient method for inverting an ideal in the ideal class group of a Cab curve by extending the method which is presented in [3]. More precisely we introduce a useful generator for the inverse ideal as a K[X]-module.

Keywords: Cab Curves, Ideal Class Group

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Authors: Richard L. Summers

Abstract:

The advanced computational analysis of biological systems is becoming increasingly dependent upon an understanding of the information-theoretic structure of the materials, energy and interactive processes that comprise those systems. The stability and survival of these living systems is fundamentally contingent upon their ability to acquire and process the meaning of information concerning the physical state of its biological continuum (biocontinuum). The drive for adaptive system reconciliation of a divergence from steady state within this biocontinuum can be described by an information metric-based formulation of the process for actionable knowledge acquisition that incorporates the axiomatic inference of Kullback-Leibler information minimization driven by survival replicator dynamics. If the mathematical expression of this process is the Lagrangian integrand for any change within the biocontinuum then it can also be considered as an action functional for the living system. In the direct method of Lyapunov, such a summarizing mathematical formulation of global system behavior based on the driving forces of energy currents and constraints within the system can serve as a platform for the analysis of stability. As the system evolves in time in response to biocontinuum perturbations, the summarizing function then conveys information about its overall stability. This stability information portends survival and therefore has absolute existential meaning for the living system. The first derivative of the Lyapunov energy information function will have a negative trajectory toward a system steady state if the driving force is dissipating. By contrast, system instability leading to system dissolution will have a positive trajectory. The direction and magnitude of the vector for the trajectory then serves as a quantifiable signature of the meaning associated with the living system’s stability information, homeostasis and survival potential.

Keywords: Semiotic meaning, Shannon information, Lyapunov, living systems.

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